The Fallacy of Endless Growth: Exposing Capitalism's Insustainability

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Winter 2008

The fallacy of endless growth: Exposing capitalism's insustainability

William S. Strauss University of New Hampshire, Durham

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THE FALLACY OF ENDLESS GROWTH

EXPOSING CAPITALISM’S INSUSTAINABILITY

WILLIAM S. STRAUSS BS, BUSINESS ADMINISTRATION, UNIVERSITY OF NEW HAMPSHIRE, 1992 MBA, UNIVERSITY OF NEW HAMPSHIRE, 1994

DISSERTATION

Submitted to the University of New Hampshire

in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

Earth and Environmental Sciences and

Economics

December, 2008

UMI Number: 3348319

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iii

TABLE OF CONTENTS

TABLE OF CONTENTS ...... iv LIST OF FIGURES ...... vi ABSTRACT ...... xi INTRODUCTION ...... 1 A Vision of a Zero-growth World ...... 1 The End of Economic Growth ...... 3 A More Rigorous Discussion of the Topics of this Project ...... 6 What is the Value of this Research? ...... 9 The Search for Ideas and Tests of Truth...... 13 Summary of Chapter One: Economic Growth and the Rise of Capitalism ...... 15 Summary of Chapter Two: The Ubiquitous (and Dangerous!) Growth Assumption Lurking in the Shadows ...... 16 Summary of Chapter Three: Complex Dynamics, Complex Systems: Where are We Going? ...... 18 Conclusion to the Introduction...... 20 CHAPTER ONE ...... 22 ECONOMIC GROWTH AND THE RISE OF CAPITALISM ...... 22 Part One: From Subsistence to Plenty ...... 22 A Story of Demographic Transition ...... 29 A Discussion of the Transition from the Malthusian Era into the Current Regime .. 35 Natural Selection, Environmental Pressures, and Lifestyle Preferences ...... 36 The Trade-off between Current Generation and Future Generation Consumption ...... 37 Natural Selection and Productivity Growth...... 46 Part Two: Natural Selection and the Transition to Sustained Economic Growth ...... 51 The Decisions Facing each Generation ...... 51 The Optimization of Intertemporal Utility ...... 55 A Dynamic Story of Evolution ...... 60

iv The Effects of Trade on the Process of Transition from the Malthusian Regime .... 70 Conclusion to Part Two ...... 71 Part Three: The Hurdle: Getting Past the Distributional Problems of the Current Economic Regime ...... 72 The Foundation for an Unequal Society ...... 79 A Basic Model of Inequality and Revolution ...... 83 Autocracy and Democracy ...... 94 Trade and the Patterns of Growth ...... 102 Conclusion ...... 108 CHAPTER TWO ...... 110 MODERN GROWTH THEORY: A CLOSE LOOK AT THE THE DETAILS AND THE LONG-RUN PREDICTIONS – CLASSIC VIEWS EXPLORED AND MODIFIED WITH NON-TRADITIONAL TWISTS ...... 110 Introduction ...... 110 A Closer Look at Accumulation, Production, and Innovation ...... 115 The Solow-Swan Model and Extensions ...... 119 Solow-Swan and a Thermodynamic View of Economic Activity ...... 131 Growth with Consumer Optimization – Ramsey and Beyond ...... 155 Current Endogenous Growth Models: Knowledge, Education, Diffusion, Innovation, and the Proliferation of Goods ...... 194 Uzawa-Lucas-Rebelo: Human Capital in Production ...... 196 Endogenous Growth through Innovation and Diffusion ...... 204 Conclusion ...... 218 CHAPTER THREE ...... 220 WHERE WE HAVE BEEN, HOW WE GOT HERE, AND WHERE WE MIGHT GO ...... 220 Introduction ...... 221 The Background for the Model ...... 223 The Model’s Underpinning ...... 230 The Simulation Model ...... 234 Capital ...... 236 Labor ...... 237 Energy Services ...... 239 The Production Function ...... 247

v Simulating the Future ...... 249 Inequality and Social Unrest ...... 263 Finding a Path to a Stable Future ...... 269 CONCLUSION ...... 278 REFERENCES ...... 282 Appendix A - The CC Locus ...... 297 Appendix B - The Math behind the Ramsey Simulations ...... 300 Appendix C - Vensim Code and Economic Data ...... 303

LIST OF FIGURES

Figure 1. Real wage and population 1250-1800 (Hanson and Prescott, 1999)...... 25 Figure 2. Golden rule...... 40 Figure 3. Golden rule with population change...... 41 Figure 4. Carrying capacity...... 42 Figure 5. Consumption and child-rearing...... 57 Figure 6. Technological growth and education choice...... 59 Figure 7. Wealth and fertility...... 63 Figure 8. Steady State A...... 65 Figure 9. Steady State B ...... 65 Figure 10. Steady State C...... 66 Figure 11. Dynamics A...... 67 Figure 12. Dynamics B...... 68 Figure 13. Dynamics C...... 68 Figure 14. Income distribution (Organization for Economic Cooperation and Development [OECD], 2007)...... 76 Figure 15. Growth versus inequality (Rodrik, 1999)...... 81 Figure 16. Per capita growth versus diversity (Easterly, 2000)...... 83 Figure 17. Accumulation over time of the rich...... 97 Figure 18. Capital to return on capital based on capital mobility...... 104 Figure 19. Real income per capita 1200-2100 (Clark, 2007)...... 112 Figure 20. Population of Japan (National Institute of Population and Social Security Research, 2006)...... 113 Figure 21. Long view of per capita income (from data in Clark, 2007)...... 119 Figure 22. The golden rule of Solow-Swan...... 122 Figure 23. Savings rates (International Monetary Fund, 2007)...... 123 Figure 24. Solow-Swan steady state...... 124

vi Figure 25. Numerical example of growth in output and consumption...... 126 Figure 26. Numerical example of growth in output and consumption (zero population growth)...... 127 Figure 27. Numerical example of growth in output and consumption (convergence to zero growth)...... 128 Figure 28. Numerical example of growth in output and consumption (net change in capital investment)...... 129 Figure 29. Numerical example of growth in output and consumption (ROI)...... 130 Figure 30. Plot of production versus production factor x...... 133 Figure 31. Plot of production versus production factor x beyond the optimal x...... 134 Figure 32. The economic cycle in thermodynamic terms...... 136 Figure 33. Growth of rich and poor with 65% to the rich...... 140 Figure 34. Growth of rich and poor with 95% to the rich...... 141 Figure 35. Growth of rich and poor with 125% to the rich...... 142 Figure 36. Actual GDP per capita – US, Europe, China, Africa (from Maddison, 2007)...... 143 Figure 37. Actual GDP per capita – poorest nations (from IMF, 2007)...... 143 Figure 38. Growth of rich and poor with 35% to the rich...... 145 Figure 39. Real return on investment – rich get 65%...... 147 Figure 40. Real return on investment – rich get 95%...... 148 Figure 41. Real return on investment – changes in the initial standard of living...... 150 Figure 42. Return on investment – rich get 35%...... 151 Figure 43. GDP of 140 countries – mean and median (from IMF data, 2007)...... 153 Figure 44. GDP per capita – poor 20th percentile versus rich 20th percentile (from IMF data, 2007) ...... 154 Figure 45. Ramsey golden rule...... 162 Figure 46. US Savings Rate (Bureau of Economic Analysis, 2008)...... 163 Figure 47. Ramsey ponzi violation (Bureau of Economic Analysis, 2008, & Dept. of Health and Human Services, 2008)...... 164 Figure 48. US net worth and savings relative to disposable income (BEA, 2008)...... 165 Figure 49. Scatter plot of Figure 48 data...... 165 Figure 50. The Ramsey model benchmark with zero population growth and zero technology improvement...... 170 Figure 51. Ramsey model with technology growth at 2% per year...... 171 Figure 52. Ramsey model with technology growth at 8% per year...... 172 Figure 53. Ramsey model response to a technology shock...... 175 Figure 54. Ramsey model time paths for rich and poor economies...... 176 Figure 55. Capital intensity change for rich and poor...... 177 Figure 56. Capital intensity change effect on savings for rich and poor...... 178 Figure 57. Beverton-Holt model of population growth...... 179 Figure 58. Ramsey model – long-run stability under traditional assumptions...... 184 Figure 59. Ramsey model – long-run instability with a high level of guard labor...... 185

vii Figure 60. Ramsay Model – attractor of the guard labor externality model with ࣁ set to 4.8...... 186 Figure 61. Ramsey model – bifurcation diagram on the guard labor parameter...... 187 Figure 62. Ramsey model – bifurcation diagram on alpha...... 188 Figure 63. Ramsey model – bifurcation diagram in alpha and eta space...... 189 Figure 64. Ramsey model – labor’s share with a low guard labor...... 190 Figure 65. Ramsey Model – labor’s share versus capital intensity with guard labor at 1.2...... 191 Figure 66. Ramsey model – guard labor versus capital intensity with labor’s share high (0.8)...... 192 Figure 67. Ramsey model – guard labor versus leisure choice with labor’s share at 0.6...... 193 Figure 68. The stock of trademarks 1871-2000. (See Footnote 44 for sources.) ...... 196 Figure 69. Real total R&D expenditures in the US (National Science Foundation, 2007)...... 206 Figure 70. Change in R&D spending and net total multifactor productivity (NSF, 2007, and BLS, 2008)...... 207 Figure 71. Ratio of R&D to output. (See Footnote 48 for sources.) ...... 210 Figure 72. R&D and output for three specific sectors. (See Footnote 48 for sources.) ...... 212 Figure 73. Probability distribution of R&D to output data – 1987 to 1996. (See Footnote 48 for sources.) ...... 213 Figure 74. Probability distribution of R&D to output data – 1997 to 2004. (See Footnote 48 for sources.) ...... 214 Figure 75. CC and QQ locus for endogenous growth with innovation...... 217 Figure 76. Technological efficiency of energy conversion to work...... 229 Figure 77. Energy Intensity of output...... 230 Figure 78. ICT as a fraction of total capital (using data from Jorgenson and Stiroh, 2000)...... 233 Figure 79. Schematic of simulation model structure...... 235 Figure 80. Capital module...... 236 Figure 81. Simulation versus empirical data for capital...... 237 Figure 82. Labor module...... 238 Figure 83. Simulation versus empirical data for labor...... 239 Figure 84. Energy intensity of capital...... 239 Figure 85. Primary energy intensity of output...... 240 Figure 86. Schematic of energy module...... 241 Figure 87. Simulation versus empirical data for energy intensity of output...... 242 Figure 88. Production section of energy service module...... 242 Figure 89. Simulation versus empirical data for efficiency of energy conversion...... 244 Figure 90. Innovation section of the energy service module...... 244 Figure 91. Simulation versus empirical data for energy services...... 245

viii Figure 92. Simulation versus empirical data for energy service intensity of output. . 246 Figure 93. Energy services module...... 247 Figure 94. The production function module...... 248 Figure 95. Simulation versus empirical data for GDP...... 248 Figure 96. Monetary value of output...... 249 Figure 97. Doing what we did until 2050 – GDP...... 250 Figure 98. Doing what you did to 2050 – labor intensity of output...... 251 Figure 99. Net labor growth rates...... 252 Figure 100. Labor intensity with uncertainty...... 252 Figure 101. Doing what you did until 2080 – energy services intensity of output...... 254 Figure 102. Doing what you did to 2080 – primary energy demand...... 255 Figure 103. Future with lower technology growth but labor growing – conversion efficiency...... 256 Figure 104. Future with lower technology growth but labor growing – GDP...... 256 Figure 105. Future with lower technology but labor growing – labor intensity of output...... 257 Figure 106. Future with lower technology but labor growing – energy services per unit of labor...... 258 Figure 107. Future with lower technology and capital and labor stable – output per unit of labor...... 259 Figure 108. Future with lower technology and capital and labor stable – comparing output per unit of labor and capital intensity...... 259 Figure 109. Future with lower technology and labor and capital stable –primary energy...... 260 Figure 110. Future with lower technology and labor and capital stable – GDP...... 261 Figure 111. Future with lower technology and labor and capital stable – GDP per capita...... 262 Figure 112. When guard labor/capital goes too far...... 264 Figure 113. Capital formation with simplified production function – “normal” guard to physical capital ratio...... 266 Figure 114. Capital formation with simplified production function – higher guard to physical capital ratio...... 267 Figure 115. Capital formation with simplified production function – chaos...... 267 Figure 116. When guard labor/capital goes too far – time series of GDP...... 268 Figure 117. Looking for a future – ideal GDP path...... 269 Figure 118. Looking for a future – the limits of the production function...... 270 Figure 119. Looking for a future – the limits of the production function again...... 271 Figure 120. Looking for a future – the limits of the model...... 272 Figure 121. Looking for a future – innovation continues...... 273 Figure 122. Looking for a future – the limits to efficiency...... 274 Figure 123. Looking for a Future – the decline in the marginal productivity of energy services...... 274

ix Figure 124. Looking for a future – stable long-run growth – GDP...... 275 Figure 125. Looking for a future – stable long-run growth – marginal productivity of energy services...... 276 Figure 126. Looking for a future – stable long-run growth – sustained per unit of labor output...... 276 Figure 127. Looking for a future – stable long-run growth – energy services intensity of output...... 277 Figure 128. Current events – oil shock – recession...... 279 Figure 129. Current events – oil shock – price shock...... 279

ABSTRACT

THE FALLACY OF ENDLESS GROWTH

EXPOSING CAPITALISM’S INSUSTAINABILITY

William Strauss

University of New Hampshire, December, 2008

What if we were to have 100 years of no growth? What if conditions were such that there is no future scenario under which growth will ever occur again? We might characterize this as impossible, as a vision that violates the outcome that we as innovative people must realize.

In the document that follows I will show you our world as it must be sometime in the future. I will describe a world in which the real growth of the world economy is zero and remains zero. I will tell a story of a world that is so different from what we take for granted that today’s economic systems, political systems, and social systems will no longer work.

Importantly (and unique to this research), this story will be told from within the boundaries of modern economic growth theory. That is, rather than follow an ecological and/or geographical path to explore limits to growth, this research is an “inside job” that suggests that when modern growth theories are decoupled from assumptions that have no basis in how the real world is developing but are, for the most part, mathematical conveniences applied for the sake of “stability,” then the long-run economic outcome is no longer capitalism.

In the shadows beneath the foundations of capitalism lurk assumptions that are so ubiquitous as to be almost invisible. This research works back to the source of the myth of endless growth and suggests that the source is simply something we have made up.

xi Furthermore, with increasing rigor, it exposes the fallacies that allow our world-view to

take endless growth as a given and natural state upon which we can make choices; upon which,

in the aggregate, are taking humankind on a very bad trip. Unaware, we are blinded from

knowledge because we do not question the assumption of more forever. The regime of endless

growth is a sort of fission-like chain reaction in which, depending upon one’s perspective, the by-products are desirable or toxic. This research shows that some of the by-products are social

and ecological anti-matter.

xii

INTRODUCTION

“Capitalism - An economic system in which the means of production and distribution are privately or corporately owned and development is proportionate to the accumulation and reinvestment of profits gained in a free market” (American Heritage Dictionary, 2006).

“Inside job - A crime perpetrated by, or with the help of, a person working for or trusted by the victim“ (American Heritage Dictionary, 2006).

“If it was straightforward, then simple laws operating in simple circumstances would always lead to simple patterns, while complex laws operating in complex circumstances would always lead to complex patterns. . . . This no longer looks correct, but it’s taken time to find out because we seem to be predisposed to such a principal” (Stewart, 2001, p. 171).

A Vision of a Zero-growth World

Imagine a year in which the national economy does not grow. This is not hard to do.

We have all experienced and read stories about recessions of various lengths and depths. But of

course these recessions always end, and the economy resumes its “normal” rate of growth.

Opinions vary as to what this long-run normal growth rate is, but opinions unanimously assign a positive value to it: there is no doubt that we will come out of it and get on with the business of growing our economy.

Now imagine 10 years of no growth. No one will argue against characterizing this situation as “bad.” But again, we fully expect that the cycle will follow a pattern that returns us to our rightful condition: the growth of the aggregate output and aggregate income of the nation.

What if we were to have 100 years of no growth? What if conditions were such that there were no future scenario under which growth would ever occur again? We might

1 characterize this as impossible, as a vision that violates the outcome that we must realize as innovating people. The good news is that this situation is unlikely–soon. The bad news is that this situation will occur and will persist indefinitely–someday. In the pages that follow I will show you our world as it must be sometime in the future. I will describe a world in which the real growth of the world economy is zero and remains zero. I will tell a story of a world that is so different from what we take for granted that today’s economic systems, political systems, and social systems will no longer work.

Perhaps most importantly (and unique to this research), this story will be told from within the boundaries of modern economic growth theory. That is, rather than follow an ecological and/or geographical path to explore limits to growth, this research is an “inside job” that suggest that when modern growth theories are decoupled from assumptions that have no basis in how the real world is developing but are, for the most part, mathematical conveniences applied for the sake of “stability,” then the long-run economic outcome is no longer capitalism.

There are times in the following chapters when the economic stories create political by- products, but the path is neither via resource depletion or waste-sink constraints, nor by the complex outcomes that migration and agglomeration create, nor by any pathway other than that predicted from within modern economic growth theory.

There are many opinions about how social, economic, and political forces create change, and there are many viewpoints about how those forces have brought us to where we are today and will take us into the future. In a sense, however, this investigation will be released from the traditional constraints associated with understanding the world as we know it: it will describe a future in which growth by any measure is zero and, as you will see, much of the diversity of opinion will dissolve into irrelevancy.

The End of Economic Growth

We believe in the inevitability of economic growth with something that approaches a religion. It is unquestioned, fully expected, and inevitable. Policymakers may botch economic development with various degrees of severity, but, given time, the natural processes of social, political, and economic activity will correct these mistakes. Even if the basis for decision-making is flawed in our globalized interconnected transnational world economy, persistent bad spots will be cured by osmosis as the influences of successfully growing systems permeate the underperforming areas. Economic thought in general holds that someday there will no longer be a developing world but only a developed world growing together harmoniously.

One might immediately disagree with that last statement. One might say there will always be conflict, always be a significant segment of the world population that is poor and marginalized, always be areas of the world that will not fully participate or even move towards the standards of living that the many enjoy. It is possible that repeated cycles of conflict at the global level will delay the inevitable (perhaps even for a very long time if we play out the full potential for destruction that we hold in our arsenals). However, assuming that humankind survives and maintains not only today’s infrastructure but continues to innovate and develop better ways to undertake economic activity, common orthodoxy suggests that it is inevitable that all of the world will converge towards a common level of prosperity.

The foundation of this belief is the foundation of our understanding of our motives as humans: we seek to maximize our wellbeing and minimize our suffering. The aggregation of these motives combined with the rule of law results in people working in systems that ultimately increase the aggregate wellbeing of the nation. History has demonstrated that systems that fail to do this are replaced by systems that do. Since the industrial revolution

3 humankind has had a long and somewhat consistent history of growing the world’s output and the world’s income, not only in absolute terms but in per capita terms as well.

What about those marginalized sectors? Although the story of development continues to weave tales of income inequality and growing disparities between wealth and poverty, it is impossible for some of the world to grow faster than the rest of the world forever. The ability of the disadvantaged masses to threaten the stability of the wealthy minority is continuously gaining strength as communications and information infrastructure open channels of strategic coordination that did not exist a decade ago. The poor majority, both within and among nations, will vote with violence when necessary until the disparities begin to shrink consistently and continuously. Furthermore, ideologically the developed world espouses a world of opportunity, and, in spite of disjointed rhetoric that often divides rather than joins, underlying the warring words are real dreams for a future in which everyone can share in the rewards of world growth.

This work does not pretend to ignore or minimize the challenges facing the world today with respect to the integration of diverse social and religious systems. It is true that the foundation of this work is the belief that just as the past has produced a somewhat consistent pattern of aggregate world growth, the future will do the same; that social, economic, and political agendas will emerge that will allow not only consistent growth but also convergence.

Underlying this work is a belief that everything will mutate, that the world’s social, political, and economic landscape centuries from now will be different in ways so profound that our best ideas today will appear naïve or foolish.

But at the heart of this work’s thesis is the profound need to overcome a deep pessimism regarding the ability of our world civilization to overcome the challenges of moving past an era in which differences trigger destruction. The reader needs to know that the author

4 struggles with that challenge. Unless there is a deeply fundamental shift in how the rhetoric of freedom and free-market economics translates into policy and action, it will be a long, dark, and bloody period. We can only hope that solutions are found and that great leaders emerge that can work toward implementing those solutions. However, the final chapter of this work offers some suggestions for change now that will improve the probability of having a long-run outcome in which harmony and balance are achieved.

Let us suppose that humankind manages to overcome the challenges outlined above and that a Darwinian evolution brings us forward to a future vantage point.

The chapters that follow are a vehicle to that vantage point: a world in which population growth has stabilized and productivity growth has reached some limit such that it too becomes stable. The journey to that conclusion will be carefully taken in many steps.

First the paper will tell a story of how we have arrived at today’s vantage point. It is a story of a long history in which most of humanity lived in a persistent Malthusian trap. It is the story of how, only in the past few hundred years, certain economies have broken free from that trap, embarking on a regime of permanent increases in the standard of living. This is an important story because it creates the foundation for the “econocentric” ideas that growth is naturally and forever part of our civilization. Part of that story, however, also identifies how some economies have been left behind in the transition. The last section of the first chapter tells the story of how we might transition the violent by-products of growth and continue the history of humankind into a stable future.

Then the paper looks at economic growth theory. It will investigate how the assumption of growth forever has become an invisible assumption in all of our ideas about what is good and bad for nations. At each step the work shows what happens to the model’s predictions if the assumptions that drive growth in the model are revised to have a zero growth outcome.

5 Next, using simulation, a search is undertaken of the future for sets of potential paths for our society. The model’s components are based on the theoretical models developed in earlier sections. The search is for a path to a stable and sustainable socio-economic system.

Insight will be found in understanding how today’s parameters must be adjusted to reach that future.

Although we are temporally far from the zero-growth world, we are inexorably connected to it: our decisions today determine how (and if) we find the stable future at the end of everyone’s rainbow.

A More Rigorous Discussion of the Topics of this Project

The socio-economic system that dominates decision making depends upon an assumption of endless growth. This assumption is fallacious. Furthermore, the imperative for continued growth is the foundation for current and continued deteriorating indicators of social and ecological well-being.

This project has three primary objectives: 1) to unmask how the assumption of endless growth has become an invisible but vital bridge to a systemic denial of the ability of current dominant economic systems to provide a basis for an equitable and sustainable world system; 2) to identify and codify the necessary elements of an ideal world system in which decisions are considerate of the current and future needs of the entire ecosphere and in which all living things live with a decent happiness; and 3) to create a realistic plan that can actualize the necessary interventions and transform the dominant decision-making algorithms.

One would like to be optimistic about the future, yet in every dimension there are troubling trends. This research project is an attempt to find a way to understand the elemental source of the path-defining mechanisms that seem to be leading civilization into deeper trouble.

6 To understand the underlying motivators, one must explore the context of our perceptions. At the foundation is a system that has become both massively connected and massively disconnected. We (herein, “we” is a characterization of the aggregated choices and actions that lead to aggregated outcomes) rely on ever more complexly integrated systems of supply. These systems for supply generate ever more complex relationships among the inherently complex symbiosis of the planet’s inanimate and animate components. At the human level the dynamics of culture, religion, and politics, mixing with the economic realities of

transnational dependencies, offer forces and pressures that add to the discordance in relations

rather than moving us toward harmony. At lower levels of the animate space, the dominance of

human-derived outcomes is causing changes that are becoming more easily observable as the

pace of change switches from the long-wave ecologically balanced evolution of species and

habitats to a new regime of rapid alteration and extinction. Supporting the animate space, the

complex systems of earth, air, and water are being stressed by this regime of rapid alteration.

The source and sink functions that have allowed the animate space to exist are being distorted

and disconnected.

The title page of Marshall’s Principles of Economics (eight volumes from 1890 to 1920) states, “Natura non facit saltum” – nature does not take a leap. In other words, the orthodoxy

upon which decisions affecting the systems of earth, air, water, and life are made assumes

continuous connections over time. In a world in which reality moves gradually and steadily

through a Darwinian evolutionary process, this assumption does not seem inappropriate;

Marshall should not be faulted for his axiomatic proclamation. But over the last century, the

pace of change and the magnitude of human-dominated outcomes have altered, and our

confidence of stability from within a Newtonion world-view has come under great pressure.

7 Although mathematics, the hard sciences (physics, biology, and earth sciences) and many academic economists have accepted the significance of the reality of dynamic discontinuity, dominant decision makers are connected to the politics of a system that relies on an ever more complex supply chain to maintain the orthodox expectation of an endlessly growing standard of living. As a result, they continue to assume that changes today will lead to predictable and/or reversible outcomes.

This is a myth. There are fallacies inherent in the assumptions of predictability, reversibility, and endless growth.

And that is part of the purpose of this project: to expose and elucidate upon these fallacies that live at the lowest levels of our decision models. Connecting the reality of how the world is changing to the way in which decisions are made is an interdisciplinary undertaking wherein economics, ecology, social systems, politics, psychology, and science overlap.

But if this undertaking were only to expose the flawed epistemology 1 that guides our choices, the project would be unfinished. This project must also find a way to get from now to a future in which balance is restored. Excluding the potential for interplanetary travel as a safety valve for the planet, this means identifying a future system in which the actions of humans and the responses of the rest of the ecosystem result in a sustainable outcome.

An important aspect of this project is charting the path of transition from now to that future system. It is not as simple as identifying a rational set of requirements and milestones.

When reasons are based upon a flawed foundation, bad choices can appear reasonable.

Perceptions, the conduit for knowledge, can be denied or altered by dependence. Since the

1 Epistemology is the study of theories of knowledge. Its subject matter includes the role of sense perception in the acquisition of knowledge, the possibility of attaining objective knowledge, the psychological aspects of knowledge, and – on some accounts – the sociological aspects of knowledge

8 system depends upon growth, this research suggests that this leads to a form of addiction 2.

One of the undisputed facts about addiction is that it is a source of perceptual distortion. So the

system’s growth imperative is complicated by a feed-back loop that not only compounds the

problem but also provides all of us with an invisible veil of denial that allows us to delink action

and consequence. In the terms of addiction, recovery is necessary.

What is the Value of this Research?

This project has both theoretical and practical value. The theoretical value will be realized through the deconstruction of mainstream economic growth theory. In this deconstruction it will be shown that the foundation of capitalism, a positive rate of return on capital investment, requires growth. The work shows how the current system is, in essence, an epic Ponzi scheme. As in all Ponzi schemes, there are those at the top of the pyramid and those at the bottom; that necessary structure is replicated and is magnified over time. Furthermore, the growth imperative that spins off from the quest for endless positive returns (a bigger and taller pyramid) generates forces that are realized in the ongoing alterations to the urban/rural relationships and more generally to developed/less-developed/undeveloped societal relationships.

There is a vast literature on growth theory and a large literature on specialization and agglomeration. However, in general, the literature says little about capitalism’s growth imperative (Gordon and Rosenthal, 2003, are a rare exception) and how this addiction to growth, with its ever larger pyramid scheme and the systemic denial of the inevitable outcomes,

2 “Addictive behaviors may be considered as those that meet two criteria. . . . First, they are motivated by short-term gain. . . . Second, they involve a degree of diminished control over behavior” (McMurran, 1994, p.49).

9 links to the inevitable broken promises for wellbeing for all, be it at the micro level, among nations, or among regions. Although writers have documented how cultural identities are subsumed by the transnational supply chain and how environmental deterioration accompanies this loss of history, none have reached down to the first principles upon which the rationale for these changes is based and looked deeply into the economics of a future that will not be what it was supposed to be.

This work follows a few small branches in the economics literature that recognize the fundamental fallacy of endless growth. The research also bridges from the new literature that builds upon the roots of complex systems, chaos theory, economic discontinuities, and nonlinear systems to the dreadfully real malsymptoms that are being observed in the rapidly altering interfaces between those that have much and those that have little. The malsymptoms extend even to those that are full participants in the richest places as a psychological malaise manifested as a persistent sense of unfulfillment. This research suggests that the actions of impaired decision makers and the reactions of the affected masses are feeding back into the dynamic complex life-supporting systems that we are supposedly trying to make better, but are in fact making worse.

There is a scarcity of work that challenges the exemplar of endless growth. A quick

Google search shows in excess of 7,630,000 hits for the phrase “economic growth.” A search for

the phrase “sustainable economic growth” yields 719,000 hits (thus showing the relative

popularity of this oxymoronic tool of denial for many). Just two years ago, “zero-growth

economy” and “steady-state economy” yielded far fewer results (2,400 and 41,300

respectively). As of this writing in June, 2008, they yield 66,900 and 939,000 results

respectively, suggesting a growing awareness of the importance of investigating a future that is

unlike anything we can image now. But a look at the Google links reveals that all of the

10 websites envision the general ecological story and none, as this works does, pulls the rug out from under the rubric that drives policy and decision making in our capitalistic system. In contrast, the phrase “growth addiction” in conjunction with the word “economic” yields 611 results.

The theoretical contribution of this work will begin to remedy that shortcoming in the literature. However, this work also has valuable practical uses. The simulation that is the centerpiece of Chapter Three will identify changes now that will lead to a future that works.

Although beyond the boundaries of economic growth theory, we can infer that the changes will connect to the ecological story and promote a balance between economic/ecological sources

(production/depletion) and sinks (depreciation/pollution). But we will demonstrate rigorously that the changes could dismantle capitalism’s pyramid scheme and ameliorate the symptoms of the exploitation of natural and human capital.

This project broadens the literature that unifies growth, capitalism, complex systems, geography, and social relationships. It identifies a set of practical, fundamental, and realistic

(within the current paradigm) changes for a process of evolution away from the current system.

The research identifies behavioral choices that can provide for safe passage into a balanced and harmonious future in which zero-growth is okay. And, by the way, we have to suspend concern about the current and real challenges that face our civilization since the path to a balanced future in economic terms will occur over the long-run. As already noted, this research will rarely stray outside of economic theory for defining the pathways and thus will in many cases ignore the current real problems, not the least of which are competition for finite energy resources and the “clash of civilizations” that face our world now. This does not mean that these problems should not be considered critical. But the purpose of this “inside job” is to expose something fundamental about how we think about the future—that “Capitalism - An economic system in

11 which … development is proportionate to the accumulation and reinvestment of profits gained in a free market (American Heritage Dictionary, 2001)” cannot go on forever.

As a scholarly work, this project does not just broaden a subset of the literature but also breaks new ground. Not one author, including those for whom the assumption of endless growth is observed to be a false god–for example, Ayres (1998); Daly (1991, 1996 1999a,

1999b); Meadows (1992)–provides us with a rigorous deconstruction of the foundations of the economic theory (and thus the consumption and production choices) that underlies the world system. A deconstruction of the received wisdom from the mainstream and almost universally accepted economic models of progress will be at the heart of the exposé.

We observe significant increases in the ability of our civilization to produce goods and services that make many of our lives more comfortable, generally healthier, and longer. Yet we also observe changes in relationships among nations, regions, cultures, and classes that one finds hard to classify as a progression toward a better world (Gilbert & Gugler, 1992; Sassen,

2000; Kaldor, 2003). There are also many warnings of threatening changes to the planetary systems that support life (Clark & Munn, 1986; van den Bergh & Gowdy, 1998; Daly, 1991, 1996,

1999a, 1999b). Progress3 as defined within the regime of endless growth is a sort of fission-like chain reaction in which, depending upon one’s perspective, the by-products are desirable or toxic. This research suggests that some of the by-products are a social and ecological anti- matter.

In the shadows beneath the foundations of capitalism lurk assumptions that are so

ubiquitous as to be almost invisible. What follows works back to the source of the myth of

3 The word is italicized because the definition is an “advance toward a higher or better stage” ( The American Heritage Dictionary of the English Language, 2001). However, this work suggests that progress as it is currently created also causes changes that are not part of an advance toward a higher or better stage.

12 endless growth and shows that the source is simply something we have made up. When that myth is removed, the entire set of choice templates is radically altered.

The Search for Ideas and Tests of Truth

This research project is about the accumulation of man-made capital (the basic source

of economic growth). The work will certainly acknowledge how natural and social constraints

affect the future of growth and what that will do to alter the future world system (both

manmade social and political systems as well as the complex ecological systems upon which life

is based). In fact one of the deconstructions in Chapter Two shows the inevitability of chaos

(both social and mathematical). Thus this project follows paths that identify how, from an

economic perspective, the returns to capital are connected to changes in the relationship

between man-made capital and exhaustible resources. If, for example, investment falls

continuously, future generations’ welfare levels will fall behind those of current generations. If

sustainability is defined as the maintenance of welfare levels over time, then long-term

development will not satisfy the sustainability criterion. That is not to say that the future needs

to be grim, just different. After all (and this will be explored more rigorously later), how much

“stuff” do we really need?

The investigation, particularly in the early growth models looked at in Chapter Two,

challenges several conventional assumptions: the standard received wisdom of mainstream

economic thought assumes that either there is never-ending resource-augmenting technological

progress or that the elasticity of substitution between natural resources and man-made capital

is equal to or greater than one (Stiglitz, 1974; Dasgupta & Heal, 1974; Meadow, 19724). Also,

the assumption of no limits to the accumulation of man-made capital is necessary to justify a

4 Meadow assumes an elasticity of substitution of zero! and derives a catastrophic outcome in the near term.

13 sustainable future. (See Cleveland & Ruth, 1997, for a critique of this assumption.) These assumptions will be looked at carefully in Chapter Two.

The more recent view of man-made capital (endogenous or new growth theory) allows for a shift from goods to services as knowledge or human capital supplements the accumulation of physical capital as the foundation for continued growth. These models (see, for example,

Grimaud & Rougé, 2003) do yield sustained growth in the presence of non-renewable resources.

For a rebuttal to this assumption, which returns the argument for long-run growth to that shown in Stiglitz (1974), see Agnani, Gutierrez, & Ize (2003). But, as will be argued, the underlying assumptions about the marginal cost of innovation are flawed. In fact, in all of the growth theory models from Solow to the present, foundational assumptions are shown to be flawed. Chapter Two, with increasing rigor, identifies the fallacies that allow our world-view to take endless growth as a given and natural state upon which we can make choices; upon which, in the aggregate, are taking humankind on a very bad trip.

The search for understanding cannot stop at the end of the last equation that proves it is possible to have an economically hard landing (very hard, like from 10,000 feet without a parachute). Coupled with the mathematics must also be an investigation of the broad implications of the futures identified in this paper. Throughout the next chapters these implications will be highlighted. A comprehensive investigation necessitates a multidisciplinary approach and a multi-methodology approach that shows how these predictions will affect the complex systems that make history. That comprehensive discussion will be presented in a future extension of this work beyond the boundaries of this paper.

This paper is organized as follows:

14 Summary of Chapter One: Economic Growth and the Rise of Capitalism

At the heart of this entire project is the life source of the current world system: growth.

In our system today growth is good; zero or negative growth is bad. It is uncontroversial to

expect that if one is poor relative to many, then one desires to grow richer. It is uncontroversial to expect that if one is growing poorer, one is unhappy with one’s fate. We also take for granted the expectation that over time there will be economic growth and thus that societies will become better. What then is this wonderful growth-stuff coveted by so many, and why is it

so ingrained into our perceptions of what is best for the world?

Rather than attempt to deconstruct that question into an investigation of the genesis of

how living organisms make choices, this research tells the story of how the majority of the

human race moved from a long history of living at or near subsistence levels to the relatively

recent regime of sustained growth in per capita consumption. That journey through recent

history chronicles the evolution of capitalism (Golor, 2005; Galor & Mountford, 2002; Kalemli-

Ozcan, 2002; Cervellati & Sunde, 2002; Bourguignon & Verdier, 1999; O’Rourke, 1999; Hannson

& Stuart, 1990).

The story is basically one in which the idea of investment transmutes from simply putting up food for the winter and having lots of offspring to transferring surplus wealth into the development of more productive systems (by improving both material and human means of production). The fundamental separation between the operators of productive systems and the owners of productive systems not only brought industrialization and a growing array of goods and services but also created the imperative for continuous growth (Gordon & Rosenthal, 2003) because without growth, the return on investment evaporates (Foster, 2002).

Since growth is necessary for the financial well-being of investors, the growth imperative permeates all of the cultural and political folkways and mores of the capitalism-

15 dominated world via decisions influenced by those with surplus wealth (Angeletos & Kollintznas,

2000). Studies of the mechanisms underpinning decision-making cross many disciplines, but they all hinge on how individuals choose to make themselves happiest, which is fundamentally an economic choice. From that simple root, a vast literature has grown. (See Long and Wong,

1997, for a comprehensive survey of economic growth theory.) Lurking in the vast literature about utility maximization, profit maximization, and well-being is an unsettling circular dependency. The definition of well-being is culturally derived; culture is a response to history; history is the chronicle of decisions; decisions are the result of choices; choices are culturally defined; and well-being is sought through choices that are meant to increase one’s stock of goods and wealth (Crimmins et al., 1991; Scitovsky & Frank, 1992; Schor, 1998, Ng, 2000; Argyle,

2002). That system of logic generates the requirement for continuous growth, and the feedback loop is endless and forever amplifying.

However, endless and forever amplifying growth is impossible. The first chapter’s models show that the logical outcome of a continuation of this system into the future is compounding and amplified social unrest. Given the story told in Chapter One, it is no surprise that terrorism is on the rise and that an increasing proportion of the wealth of those at the top of the pyramid must be dedicated to countering this force.

Summary of Chapter Two: The Ubiquitous (and Dangerous!) Growth Assumption Lurking in

the Shadows

Chapter Two of this research demonstrates that endless growth is impossible and then investigates the theoretical outcomes of removing the assumptions that lead to positive growth from those models that are most widely used by mainstream decision-makers. By viewing the altered outcomes, the research will have a perspective from which to critically assess the real effects on our current world systems of perusing policies that are slaves to growth addition.

16 Chapter Two details the history of modern economic growth theory. But the narrative and the mathematics are not the usual textbook review. At each stop along the historical path from Solow to the present, an investigation into the sources of the growth predictions yields a troubling pattern: ingrained in the thought are assumptions that, if removed, lead to

uncomfortable outcomes.

This chapter also connects these insights regarding the economic thought that underpins policy choices to the policies that are necessary to maintain the cycle of endless growth. Many of the politico-social by-products of “progress” are observable through the reactions of people. (As shown in Chapter One, they are manifested in terrorism, crime, war, hunger, and premature mortality). However, many are also manifested through the reactions of the ecosphere to the actions of people. Critical changes to the earth’s life-supporting systems and the connections to policy choice would appear to be easily correlated (Robinson &

Srinivasan, 1997; Rao, 2000; Hardoy et. al., 2001). However, a majority of policy-makers deny

(or ignore) rigorously proven connections and make policy accordingly (Congressional Vote

Watch5).

Obviously political choice and socio-economic effects are connected. This chapter’s contribution to the body of knowledge regarding the social and ecological consequences of

“progress” is to reveal the economic axiomatic fallacy that allows the denial of certain consequences to exist. Choices, from policy-makers guiding the outcomes for many, to individuals whose sphere of influence and accountability is small, are made from within an expectation of a regime of endless growth and thus an exponentially larger set of goods and services for all forever. Chapter One shows that the spin-offs of this continuously accelerating chase for more has created many of the malsymptoms of modern society. The research and

5 Retrieved from http://whistler.sierraclub.org/votewatch/.

17 particularly this chapter suggest that persistent inequality and marginalization, environmental abuse and ecological short-sightedness, and an increasing willingness to exploit labor in the name of productivity are not the result of bad people being overtly selfish and greedy but are the result of people’s inability to perceive the full array of choices and thus to understand that their choices are suboptimal. As Chapter Two demonstrates, in some cases, using insights

gained in Chapter One, the growth theory we depend on for policy making results in chaotic

outcomes (both in mathematical and social terms). Unaware, we are blinded from knowledge

because we do not question the assumption of more forever.

Summary of Chapter Three: Complex Dynamics, Complex Systems: Where are We Going?

We are on a treadmill that is running faster and faster. We have more of everything,

but we are less able to feel comfortable about our lives (Scitovsky, 1992; Argyle, 2001;

Easterbrook, 2003). Chapter Three investigates how the growth imperative has entered the

dynamics of humankind’s artifice of economic systems and what that could mean for the future

by building a simulation. But the research also finds a way off the treadmill. The outcomes of

the simulation are used to find behavioral characteristics that might be altered to chart a path

that is rational.

The chapter centers on the construction of a simulation. A technique developed for this research uses a systems dynamics software; this chapter integrates the lessons learned in

Chapters One and Two into a simulation. The outcome is an investigation into the expected paths going forward and what growth outcomes can occur in the long run.

Guidance is derived by following the literature on complex systems and chaos. For example, microeconomic foundations altered to accept discontinuities in imperfectly competitive markets and the connection into complex macroeconomic dynamics (based on

Rosser, 2000, 2001) provides insight into how to build the feedback loop structure of the model.

18 The simulation is informed by the work in Chapters One and Two. The simulation shows how choices within a growth-addicted world lead to outcomes that concatenate into unpredictable and potentially catastrophic outcomes. Furthermore from chaos theory we also see that even in deterministic systems, unexpected changes, large jumps, and seemingly random behavior are possible. The simulation will find these even without the need for random seeding.

The academic, quasi-academic, and popular literature are robust with predictions about what an ideal sustainable future would be (see among others Hawken et. al. 1994, 1999; Wilson,

2002; Copeland & Taylor, 2003) and with ideas for how a sustainable future should be organized

(see among others Ostrom, 1990; Daly, 1991, 1996; Cognoy, 1999; Korten, 1999; Rao, 2000).

What is universally missing, however, is a strategic plan for transitioning from now to that future that is founded from within mainstream capitalism-centric economic theory. In finding ways to change the outcomes of the simulation so that a sustainable non-chaotic future is possible, this research identifies behavioral choices that lead to that outcome. That is not to say that the prescriptions may be any different than those offered in the diverse ”limits-to-growth” literature in terms of consumption choices and how wealth is distributed; what differs is that the rationale is shown to be driven by deeply ingrained economic assumptions that lurk in the logic of policy making.

Yet identifying the fallacy at the root is insufficient if real action for change is to occur.

The psychology of the growth addiction (McMurran, 1994), which distorts personal and public choice, suggests that axiomatic changes are necessary for beginning that transition. That research suggests that it is (and has been) useless to use predictions of dire outcomes as a motivator for change. This is particularly true when linear thinking based on an apparently endless growth curve dominates the forecast models used by policy makers (i.e., the world in which we live now). However, by showing clearly and unambiguously that the assumptions

19 underlying these models are flawed and that the problems that are being generated by the growth quest are only going to magnify in ways that increasingly challenge capitalism’s basic promise (a positive return on investment), this work indentifies a starting point for change. For example, in Chapter Two, using a favorite tool of capitalism, a discounted present value model, the real current-value cost to capital of chasing positive returns is shown to be overbearing not in the long-term but in the medium-term. Perhaps that finding will get some attention.

The model also integrates the insights from Chapter One on revolution and social unrest to identify those behavioral changes that can begin to interfere with the positive feedback loops that are amplifying zealotry. Although the “clash of civilizations” is not within the purview of this research, the socio-economic story told in Chapter One provides an entry point into understanding some of the motives for violent choices.

Addiction (to growth) is powerful, and change, even in the face of rational current-event reasons, is likely to be resisted. Short-term gains and continued growth will be fought for from intra- and internationalistic perspectives with policy choices and military forces. This work will end before a strategic plan for change is written. That will be the basis of future work. But we can envision that the plan will include interventions that can be accomplished by a rational, democratically placed majority who have heard and will understand the message of the fallacy of endless growth. One needs great optimism to hold onto that hope, but that is another story.

Conclusion to the Introduction

This project demonstrates that the expectation for endless growth is fallacious. In

Chapter One we follow the pathway from zero growth to sustained growth. In Chapter Two we come to understand why endless growth is not questioned but in fact is supported with subtle

(and not so subtle) parameter and specification choices. Then in Chapter Three the work, through a simulation, shows potential outcomes. This will leave a strong foundation for carrying

20 this project forward in future work (Chapter Four and beyond) into perhaps the most important phase: creating a strategic plan for transitioning from now to then.

CHAPTER ONE

ECONOMIC GROWTH AND THE RISE OF CAPITALISM

Part One: From Subsistence to Plenty

“It is not the strongest of the species that survive, nor the most intelligent, but the one

most responsive to change”6

Economic growth is the bottom line. It is what is expected and what is desired. It is the

foundation of all of our expectations about the future and of our evaluations of the present. We

expect sustained and continuous growth. If an economy is not growing, there is something

wrong with it.

The definitions of growth are oddly inconsistent. Economics texts generally define

growth as an increase in output per person (gross domestic product or GDP per capita). Growth

in GDP per capita also implies in increase in the average standard of living since each person, on

average, gets a bigger slice of the economic pie. This is true because the national output

approximately equals the national income.

Yet when reference is made to whether we have a “normal” economy or an economy in

recession, the metric of choice is just the aggregate output of the economy or GDP, not GDP per

capita. They are not at all the same. It is possible for aggregate growth to increase at exactly

the same rate as population growth. If that were so, then GDP would be growing, but GDP per capita would not. Thus, although there may be absolute growth in the value of economic

6 This quote has become attributed to Darwin and is cited frequently; but it does not appear in his published works.

22 activity during a year, an increase in the standard of living will not occur unless output increases faster than the growth in the population. Both definitions of “growth” are important. However, as we will see, it is the growth in output per capita that is the key to a regime of sustained welfare-enhancing social evolution.

History has not always provided humankind the luxury of sustained growth in our

standard of living. For most of our past we have experienced absolute growth as the population

has expanded but not growth in output per capita. Drawing upon recent work that synthesizes

evolution and economic growth, we can tell a story that takes us from the long history of

agrarian/peasant society into the world we currently inhabit.

In summary, this chapter will show how a simultaneous relationship between the

evolution of humankind and economic growth during the long history of economic stagnation

prior to the transition to sustained growth promoted a process of natural selection that shaped

the evolution of humans; the evolution of the human species led to changes that eventually

allowed humankind to evolve from the long period of stagnation to the current regime of

sustained growth. The framework that we will build allows us to tell a unified story of the

evolution of productivity enhancing technology, of population growth, and thus economic

output per capita. We will span the transition from a Malthusian epoch of stagnation, which

lasted for most of our recorded history, to the regimes of sustained economic growth that

developed nations experience in today’s world.

We also note that even in today’s modern era many economies have failed to make this

transition. The framework we will build in this chapter will tell a story in which the patterns of

international trade have delayed or excluded some economies from following the path we map

out.

23 During the Malthusian era7 technology evolved slowly, and the growth of population prevented a sustained increase in the standard of living (output per capita). A Darwinian decision-making schema created a tension between the quality and quantity of children. The tension is as follows: a quantity preference had a positive direct effect on fertility rates, but it negatively affected the quality of offspring, their health, and therefore their fertility rates. In the

Malthusian era, the evolutionary pressure created an evolutionary advantage to quality preferences.8 Eventually this process of natural selection increased the quality of the

population, which in turn caused faster technological progress and which ultimately launched

the transition from the long dark era of stagnation. The developed world that we live in now

and our fundamental expectations for sustained growth are derived from a demographic

evolution that had breached a critical mass.

But for the most of human existence economies have been in a Malthusian stagnation.

Missing the basic addition of productivity growth that we take for granted today, the

diminishing returns to labor had a self-equilibrating effect on the size of the population.

Gradual improvements in technology or increases in the availability of land lead to a larger but

not a richer population. The growth rate of output per capita had been negligible for most of

recorded history. In Europe between 500 and 1500 the average growth rate of GDP per capita

was about zero. This is particularly striking considering that the average annual rate of

population growth in Europe between 500 and 1500 was 0.1 percent. World population also

grew at an average rate of less than 0.1 percent per year from the year 1 to 1750, suggesting

that the pattern of population growth over this era follows the Malthusian pattern. Changes in

7 According to Thomas R. Malthus (1798), if the standard of living is above the subsistence level, population grows, whereas if the standard of living is lower than subsistence, population declines by either a purposeful drop in fertility (“preventative check”) or by malnutrition, famine, and disease (“positive check”). 8 In this era “the perpetual struggle for room and food” (Malthus,1798, p. 48) left limited resources for child rearing.

24 the growth rates of population and wages are also congruent with the Malthusian regime. After the Black Death there was a period of higher real wages followed by faster population growth associated with a strong positive correlation between rising real wages and marriage rates.

Figure 1 plots the real farm wage for the period 1265-1800.9 The figure illustrates a key

characteristic of the Malthusian era. When population falls, there is an increase in real wages.

The increase in real wages causes fertility rates to increase and population growth increases; as

the population begins to recover, the real wage falls.

Figure 1. Real wage and population 1250-1800 (Hanson and Prescott, 1999).

There was a gradual shift from the long era of Malthusian stagnation into the current

regime of sustained growth. In Europe between 1500 and 1700 the average growth rate of

income per capita was 0.1 percent per year. This rose slightly to 0.2 percent between the years

9 Hansen and Prescott (1999 note that the English population series is from Clark (1998a) for 1265-1535 and from Wrigley et al. (1997) for 1545-1800. The nominal farm wage series is from Clark (1998b), and the price index used to construct the real wage series is from Phelps-Brown and Hopkins (1956). The data have been normalized to be 100 in 1265 and have been smoothed using the Hodrick-Prescott filter with a smoothing parameter of 100.

25 1700 and 1820. As income per capita grew, population growth increased. From 1500 to 1700 population grew at a rate of 0.2 percent and from 1700 to 1820 at 0.4 percent rate. The linkage of higher income to higher population growth was the same in this period as it had been throughout the era of Malthusian stagnation, but there was a counteracting effect. Whereas traditionally a higher population had diluted resources per capita and lowered income per capita (often to below the sustenance level thus triggering Malthus’s positive check) , technological progress was increasing at a rate rapid enough to allow income to keep rising. This is a remarkable shift, all the more remarkable because it took place during a concurrent fall in mortality. The growth of the population increased at an increasing rate because more children lived to be old enough to have children and, of course, because each person lived longer.

Between the 1740s and the 1840s, life expectancy at birth rose from 33 to 40 in England and

from 25 to 40 in France. Remarkably the growth in output per capita still remained not only

positive but increasing. Over the period 1820-1870 the average growth of output per capita in

Europe rose to an annual rate of 1.0 percent.

Key to the shift from the Malthusian trap to sustained growth was a dramatic change in

fertility rates.10 Fertility rates had been increasing in Western Europe until the second half of

the nineteenth century, peaking in England and Germany in 1870s. The reduction in fertility became most rapid in Europe at the beginning of the 20th century. In England, for example, live

births per 1000 women age 15-44 fell from 153.6 in 1871-80 to 109.0 in 1901-10. This drop was

clearly a demographic shift and not the cause of increased infant mortality. In fact, infant

mortality was declining during this period.

10 Malthus (1798) predicted that fertility would fluctuate rationally with income expectations. “But as from the laws of our nature some check to population must exist, it is better that it should be checked from a foresight of the difficulties attending a family and the fear of dependent poverty than that it should be encouraged, only to be repressed afterwards by want and sickness” (p. 29).

26 There was a concurrent shift in how children were treated. The average number of years of schooling in England rose from 2.3 for the group that was born between 1801 and 1805 to 5.2 for the group born in the years 1852-56, and 9.1 for the group born from 1897-1906.

Parents were choosing quality over quantity.

The population growth decline and the improvement in the quality of the labor force resulted in a sustained average annual increase in income per capita of 2.2 percent over the period 1929-1990. Something happened that allowed many of today’s economies to shift gears, leave the era of subsistence living behind, and embark on a path of sustained growth in the standard of living.

What happened, however, did not happen universally. Clearly much of the world population does not have a rising standard of living. Much of the world’s population continues to live (and die) at the subsistence level. As we will see, the Malthusian pressures not only influenced what parts of the world first experienced technological development but also how that progress was enhanced or impeded. We will show that harsh and cyclical environmental conditions along with limited land promoted a natural selection process that increased the proportion of the population with preferences to spend more time working, to save and accumulate permanent structures, to be less likely to overuse the land, and to devote higher and more focused resources to the education and upbringing of fewer but more fit offspring. In a climatological setting in which there were winter/summer cycles, people making choices that resulted in a more certain and higher per person consumption were favored. In a demographic setting in which there were few choices to expand into new lands, people with the ability to innovate given resources into greater output were favored. In the north, the demographic transition from Malthusian stagnation was enhanced by the climate.

27 Once the transition began in the north, the south was at a disadvantage. If there is no demand for skilled labor, parents will raise unskilled children. In a world of open trade, those economies that were first starters in the transition progressed to specialize in the production of industrial goods,11 whereas those economies that did not reach the transition point first progressed to specialize in agricultural (or raw material) production. International trade not only widened the technological gap between advanced and less advanced economies; it also reinforced the initial patterns of comparative advantage. With world trade, the demographic transition of the advanced countries were (are) accelerated and the transition for the less advanced countries was (is) retarded. If the less advanced economy’s share of world income continues to fall over time, the country will never experience the demographic transition that lowers fertility rates, increases the number of skilled offspring, and allows the economy to eventually experience a rising standard of living.

This inequality is unsustainable in the long-run. We discuss this and propose several scenarios for how this imbalance will be corrected in Chapter Three.

11 The industrial revolution began in northern Europe. Industrialized nations continue to be overrepresented in regions with harsh winters.

A Story of Demographic Transition

For the most part modern economic theory has concentrated on the current regime,

and the models are often inconsistent with the long period in which per capita income was

stagnant. A common flaw is the assumption that population growth is exogenous. These

economic models, which do not incorporate Malthusian elements, imply that a market economy

will result in strictly positive growth. This is not what most of recorded history has documented.

Models that do not account for the relationship of the economy to population growth are

unable to explain the long epoch of Malthusian stagnation in which the output per capita varied

around the subsistence level.

Since this work is looking at a broad span of time, we must search for a more unified approach to understanding how growth has been determined. The models that we use for understanding growth are based on endogenous population growth: that is, population growth that is determined by other factors in the social system. A unified evolutionary theory must recognize the integral relationship between the evolution of the human species and the transition from a Malthusian era to the current regime of sustained growth. At the heart of this approach is the premise that due to a Darwinian process of natural selection, the characteristics and the weights that these characteristics have in determining choices are highly relevant for the understanding of the evolution of economic growth. We focus on the evolution of preferences in humankind in recent history and the simultaneous relationship between choices regarding offspring and changes in the aggregate productivity of social systems.

Darwinian models generally relate population growth to the ability of members of the

species to survive. The models develop an evolutionary theory in which decisions regarding

offspring (how many and the tradeoff between the number of children and the level of

29 resources that are placed into their education) are based on household decisions that are natural outcomes of environmental pressures. This framework allows an indirect relationship between population growth and income. This is an important component to the model since this framework enables the model to capture both the direct relationship between population growth and income per capita that persisted until well into the 19th century as well as the reversal in this relationship that occurred during the demographic shift that lead the way to the current regime of sustained economic growth. We will see that the connections between economic growth and actual evolutionary changes in humankind shifted history from

Malthusian stagnation into what we see today as the model for the world economy. In later chapters we will extend this model well into the future and see where our evolutionary path will lead us.

The story of the evolution of economic growth from pre-history to the present takes us through four stages.

The first stage mirrors the majority of the history of humankind. It is the Malthusian

world. The economy relied only on the land as a source of output. The majority of the

population existed near a subsistence consumption level. Spurts of technological improvement

in hunting or farming permitted the per capita output to rise above the subsistence level of

consumption. As a consequence of these improvements, the population grew. The greater the

difference between the level of subsistence income and the increase in income resulting from

these improvements, the more rapid was population growth. But as the population increased,

the rise in output that was realized from the incorporation of the better hunting or farming

techniques was spread among the larger population. If there were no further technological

progress, within a few generations, people’s share of the output returned to the subsistence

level. This return to subsistence could happen much more rapidly given unfavorable

30 environmental shocks such as drought or disease. Over time the average per capita share of output was self-equilibrating and fluctuated around the subsidence level. The economy was trapped in a Malthusian stagnation. During the long Malthusian era that stretched back into prehistory, people toiled for survival.

In that early era in the history of mankind, the population of the world placed little value on the quality of their offspring versus the quantity of the children. The world in those times evolved exceedingly slowly. There was an imperceptible change in how one generation to the next carried on with the task of surviving. Output per capita and the population were essentially unchanging.

Events that reduced population or increased the food supply induced changes in the share of output per person and caused changes in fertility. If the population was reduced due to an epidemic, the remaining people could live above the subsistence level and would have both more children and longer living children. Within a few generations, the population would return to a level at which the share of output per person returned to the subsistence level. If food supply was increased due to finding more land or an improvement in how food was grown and hunted, the population would again grow until the share of output per person was at the subsistence level.

Although there was little incentive to choose to raise “quality” children, quality children did occasionally arise. Certain members of the population, often by rights of power, received a larger share of the output and lived more comfortably. History records a long record of family- based ruling regimes. These regimes, due to increased income and wealth, were able to have consistently high fertility rates without being exposed to the self-equilibrating forces of

Malthusian stagnation. Somewhat insulated from the struggle for survival, these groups were differentiated from the general population. Given a choice between physical or intellectual

31 ability, offspring that displayed intellectual ability inherited the positions of power. As civilization progressed, other family groups (some members of the merchant class, for example) shifted toward a propensity for selecting intellectually superior offspring as their income and wealth increased.

The effects of Malthusian pressure on fertility rates combined with a Darwinian process of selection affected the genetic composition of the population.12 These gradual changes in the population are at the heart of how our model for the history of economic growth evolves.

The second stage of our stylized history focuses on the Darwinian process. In the

Malthusian economic environment (as, in fact, at any point in time in history), variety and natural selection continued the evolution of the human species. People’s preferences were formed by a Darwinian survival strategy. As in the survival and evolution of all species, the evolution of humankind selected those who fit the changing economic environment naturally,

increasing the likelihood of the survival of the human species.

Individuals’ preferences were naturally influenced by a desire for consumption to be

above the subsistence level. This choice was integrated into a fundamental choice over the

quality versus the quantity of their children. These choices go right to the core of Darwinian

survival representing the seminal trade-off that exists in nature: the trade-off between

resources allocated to the parent versus the offspring and the trade-off between the number of

offspring and the resources allocated to each offspring.

12 The evolution of preferences through a Darwinian economic process is nicely developed in “Endogenous Preferences: The Cultural Consequences of Markets and other Economic Institutions” by Samuel Bowles, 1998, and in “Malthusian Selection of Preferences” by Ingemar Hansson and Charles Stuart, 1990.

32 The primary desire for consumption to remain above subsistence is the basic insurance for physical survival of the parents. This also increased the likelihood of the survival of the family since resources allocated toward parental consumption beyond the subsistence level raised the parents’ labor productivity. This increase in output helped to provide a buffer against famine. The positive effect on the fitness of the parent also helped to resist disease, but these positive effects had countervailing effects on the survival of the family line. The allocation of resources to the parents implied a reduction in the resources allocated to the offspring.

The other dimension of the fundamental choice that human beings confront, like all species, is the trade-off between an offspring’s quality and quantity. An evolutionary advantage may be derived by choosing quantity. This has a positive effect on fertility rates. However, the choice for more offspring adversely affects the quality of the offspring. Regardless of whether the measure of quality is physical or intellectual, on average, their ability to produce will be lower. Thus the choice for more quantity may generate an evolutionary disadvantage.

In any era the household must make choices regarding the number of children to have

(and thus the quality of those children). This choice is influenced by the total amount of resources that can be devoted to child-raising and labor market activities.13 In the era that marks the transition from the Malthusian world toward the modern era of constant growth per capita, the Malthusian pressures generated an evolutionary advantage for individuals whose preferences were biased toward child quality. This evolutionary advantage increased their numbers, and, since preferences are hereditary, more and more of the population chose quality over quantity.

The third stage of our history connects the process of economic growth and the natural selection process. The link between the levels of education received and the resulting effects on

13 This concept is developed by Becker(1991) in A Treatise on the Family.

33 technological growth is well documented. Thus it follows that since the process of natural selection resulted in an increase in the number of individuals whose preferences were for child quality and this increase had a positive effect on the average quality of the population, the rate of technological progress increased.

The fourth stage in our history brings us to the present, linking the increase in the rate of technological progress to the transition into sustained economic growth. The increase in the rate of technological progress increased the expected benefits of having workers with broader and deeper knowledge and thus parents were more motivated to substitute child quality for child quantity. We can envision how this motivation was reinforced if we simply note that technological progress reduces the adaptability of the current workforce in the more rapidly changing work environment. Education, however, helps both children and workers to mitigate the effects of increasingly more rapid technological progress. In a nutshell, skilled individuals possessed a comparative advantage over unskilled individual in adapting to the changing technological environment.

Based on our ideas about the evolution of preferences, we see that technological progress caused two effects that are both complimentary and opposed. The first effect caused an increase in the expected value of having skills versus being unskilled and induced parents to reduce the number of children and simultaneously raise the quality of each child. Parents substitute quality for quantity. The second effect was a result of the general benefits of the increased output that technological progress generated. As the income of households rose above the subsistence level, the families had more resources for both providing education

(quality) as well as having more children (quantity). Since both effects increased the average quality of the population, technological progress was further accelerated as the relative number of skilled individuals increased. Once technological progress became sufficiently rapid, the

34 substitution effect (quality over quantity) dominated the income effect, and technological progress, operating through a Darwinian process that changed preferences, caused a reduction

in fertility rates. An historical demographic transition occurred that changed how developed

nations grow.

What follows is a detailed expansion of this summary. The text will carry us from the

early days to the present.

A Discussion of the Transition from the Malthusian Era into the Current Regime

In the text that follows we will first model how people came to possess the preferences that allowed the demographic transition from the Malthusian era in which per-capita consumption determined population growth. We will then create a model for how the transition takes place that allows a disconnection between per-capita consumption and population growth and thus a sustainable rise in the standard of living. Finally, based on the insights from the first model, we will show that if some nations begin the transition before others, they will have a persistent advantage over the late starters.

This final insight will provide us with a starting point for discussing how to transition

from the world we now live in into the future.

35 Natural Selection, Environmental Pressures, and Lifestyle Preferences

"Then a policy-maker was heard to say, ‘Forget grand optimality. Solovians are a simple

people. We need a simple policy...If we make investment a constant proportion of

output, our search for the ideal investment policy reduces to finding the best value of s,

the fixed investment ratio.’ ‘It's fair,’ Solovians all said. The King agreed. So he

established a prize for discovery of the optimum investment ratio" (Phelps, 1961, p. 638)

Suppose that long ago in pre-industrial times there were two groups of people.

Members of the one group had a heritage of being prone to idleness and immediate

consumption. The other group’s heritage was to work and accumulate an excess stock of food.

The second group would be more likely to survive unexpected production shocks. The second

group would also be more likely to have better fitness due to more consistent consumption

patterns. Since per-capita consumption determined population growth, this group would also

have more consistent growth in its numbers. Over time, members of the group that was prone

to work and save would be become the majority group. As we will see, Edmund Phelps’s golden

rule will play an important role in the selection process.

The model that follows is based on the work of Hansson and Stuart (1990). The key

component of the model is that the forces that promote the selection of preferences for work

and saving versus indolence and immediate consumption are based on optimizing the number

of sustainable offspring though intergenerational savings.14 The “savings” in this case is the sacrifice of consumption in the current generation that benefits the next generation. This would include the degree to which the parent takes time from their labor or leisure to support, raise,

14 Laurence Kotlikoff and Laurence Summers (1981) estimate that intergenerational savings (versus intragenerational savings such as wealth accumulated early in life and decumulated later) is as high as 80 percent of total savings.

36 and educate the offspring as well as transfers of accumulated assets such as a dwelling or other physical objects that represent wealth.

The Trade-off between Current Generation and Future Generation Consumption

The model abstracts the world into unique groups of people with unique preferences.

These preferences are developed from a process of natural selection that favors those choices that yield optimal survivability. Preferences are then passed on to the next generation. The total population of this world is constrained by the carrying capacity of the environment. Thus the land and fisheries are a public good that are part of the production of output. For simplicity, the growth rate of the carrying capacity is exogenous. (This assumption is removed in later sections.)

If the total population of all of the groups in time period t is denoted by Nt then the quantity of input available of the public good in each of the group’s production functions is 1/ Nt

(the total of the public good is normalized to one for simplicity). The production function is assumed to have characteristics that are consistent with pre-industrial output; thus the function is amiable to being manipulated as a concave continuous twice-differentiable function around changes in both 1/ Nt and per-capita capital kt.

The model is focused on the connection between the size of the population and the

choices made by the clans, so the production function used will be fNk(,)tt. The inversion of

1/ Nt to Nt implies that an increase in the total population of the world will increase the

crowding of the commons and will lower per-capita output; i.e., fN 0 . Augmenting the specification slightly can allow the carrying capacity of the environment to grow by discounting

t the population effect with the growth rate; NgMtt/(1 ) .

37 Both for mathematical purposes and in terms of common sense, if either input equals zero, output equals zero. It is assumed that the Inada conditions hold for the marginal product

of capital, fk .

Consumption above the subsistence level results in a higher resistance to environmental shocks and malnutrition. Thus, given higher consumption, the average number of children that survive to have their own offspring will be greater, and adults will also live longer and have more children. Therefore, the population growth rate, p, from time t to t+1 will be a function of

consumption: pc()t ! 0 with d1p (0) 0 , pc ! 0 , and pcc d 0 .

Specifying the basic model of production to show how the total output for an active generation of a given clan is split between consumption and savings (savings is assumed equal to investment in capital, k) yields the following:

fM(,) k c [(1())] k pc k (1.1) tt t t1 t t

The split is between current consumption and increasing the stock of capital by forgoing current

consumption.

In the very-long-run,15 population will be constant (given a fixed level of the public good and no technological growth). At that equilibrium point equation (1.1) becomes

fMk(,) c kpc () (1.2)

In other words, to maintain constant capital per capita, an investment of kp() c is required to

offset population growth. Also, in the steady state where the carrying capacity of the

environment grows are rate g , the rate of population growth must be pc() g. That is, per-

15 In this case we distinguish the very-long-run from the long-run in as much as in the long-run there is a complete adjustment of inputs and outputs to a given set of tastes and preferences. In the very-long-run tastes and preferences are also stable.

38 capita consumption will be at the level that holds population growth equal to the growth rate of the carrying capacity of the environment.

By requiring that the selected behavior in the steady state be the result of a choice that maximizes the well-being of the clan, the model relates optimum well-being with the choice for capital formation and thus optimal consumption. By differentiating (1.2) with respect to capital and choosing the maximum for dc/ dk , i.e., dc/0 dk , we see that

fMkk (,) pc () (1.3)

This outcome is the “golden rule for capital accumulation.”16 In a Malthusian environment the tendency for surviving groups will be to converge towards the golden rule savings rate by selecting the best split between consumption and investment.

The mechanics by which this tendency is enforced are illustrated by the following numerical example. Specify that pc() c.5 1 and fMk( , ) ( k / M ).5 .5 k .5. For simplicity, set the maximum population to one and growth, g, at zero. It follows that the very- long-run equilibrium rate of population growth must be zero; pc()* 0. If the population

growth is zero, then c* 1. Therefore output must be (/kM* * ) .5 .5.51 k * . The golden

**.5 rule requires that the marginal product of capital be fkMk .5( / ) .5 0 . Figure 2 illustrates this relationship:

16 The level of savings and investment that an economy enjoying balanced growth would need to support in order to maximize the long-term value of consumption per head.

39 Population Growth, p(c)

Per-Capita Capital, k

0.0 0.5 1 1.5 2

Figure 2. Golden rule.

In the example, in the steady-state the optimal level of capital per-capita is 1.0. If

* certain groups made choices that were at variance with k , it would cause the population to decrease. Choices other than k* would be bad choices, and natural selection would disfavor

groups that passed on preferences that carried forth these choices. Groups that made good

choices would replenish the population until it returned to the steady-state quantity. To see

this, suppose population decreased from 1.0 to 0.95. Figure 3 shows this situation:

40 Population Growth, p(c)

Per-Capita Capital, k

0.0 0.5 1 1.5 2

Figure 3. Golden rule with population change.

Groups that choose k at the golden rule would experience positive population growth and the

total population would rise. The converse is also true so that any level of population other than

1.0 will evoke Malthusian pressures that will favor groups that get the investment/consumption

choice right and drive the population back to the carrying capacity of the environment.

If the growth rate of the commons is allowed to be above zero, then all surviving groups will

grow at the growth rate of the carrying capacity of the environment. Thus pc() g. This is illustrated in Figure 4, where the total population is again set to 1.0:

41 Population Growth, p(c)

p(c*)=g k*

Per-Capita Capital, k

0.0 0.5 1 1.5 2

Figure 4. Carrying capacity.

How the groups determine the optimal consumption / investment split In the spirit of this analysis, in which natural selection is relied upon to continuously

improve the survivability of the species, the expectation is that that the aggregate of choices will

result in the best possible outcome. This is modeled using the standard utility maximization

approach in which each generation makes choices that are based on seeking the best approach

to the long-term fitness of their members.

As has been demonstrated, the criterion for this selection is to maximize the population

(and thus consumption), given the carrying capacity of the environment. Each generation will choose the current period’s consumption (and the implied investment level that is the residual of that choice). They will also consider the future generation’s consumption in terms of optimal survivability (in terms of optimal population growth rates which are a function of the consumption choice). The utility of future generations will be discounted by G such that a larger discount rate means that the current generation is more selfish (or shows less concern for the well-being of their offspring and future generations).

42 Thus for generation x the utility they gain from consumption in a future period t is discounted by the compounded discount rate. But the utility they gain is also a function of the compounded growth rate of the population. A higher future growth rate will increase current utility. Generation x’s utlity from consumption in period t can be written as

tz uc(tx )[1 pc ( )][1 pc ( x11 )]...[1 pc ( t )] / (1 G ) (1.4)

Assuming that the planning horizon is finite to time T the utility maximizing problem for generation x is

xT T 1 §·1()pcxv §·1()pc Uucucx ()()xx1 ¨¸... ¦uc ( t ) ¨¸ (1.5) ©¹11GGtx vx ©¹

subject to the constraint described in (1.1).

The first-order conditions for utility maximization are

xT v1 °°½wwupªº§·1() pcw ®¾«»¦ uc()v ¨¸/(1)G u ¯¿°°wwcctt¬¼vt 1 wt 1©¹1G (1.6) t1 ªº§·1() pcv §·wp «»¨¸O ¨¸10kt1 ¬¼vx ©¹1wG ©¹ct

OOtk(1)(1())0fp t11 c t (1.7) where xtxTdd1 .

The investigation is concerned with the very-long-run solution and the determination of whether or not there is a unique discount rate that will satisfy the maximization problem when consideringT of.

To this end, on the path to the very-long-run, sequential generations will act the same.

That is, natural selection will insure that these generations will have discovered the correct

43 (equilibrium) rates for k*, c*, and M*. Thus plugging in the equilibrium conditions and combining the first order conditions yields equation (1.8):

vt1 wwuuªºxT §·1(*) pc uc(*) «»¦ ¨¸(1 G wwcp¬¼«»vt 1 ©¹1G (1.8) vt2 ªº1 f °°½wwupªºxT §·1(*)pc k u uc(*) «»®¾«»¦ ¨¸1 G ¬¼11wwGG¯¿°°cc¬¼«»vt 2 ©¹

By allowing T of there are two potential outcomes that maintain the equality. First setting pc(*)! G and letting T of would require that f of which would further k ,

require that k o 0 . Zero capital would extinct the population and thus is not an allowable choice. Setting pc(*)d G and let T of then (1.8) reduces to

G fk (1.9)

This is an important conclusion. The intergenerational discount rate is exactly equal to the marginal product of capital (evaluated at the equilibrium values for per-capita capital, k * and the growth discounted equilibrium population, M *). Recalling the golden rule and

combining that with (1.9) yields

G*(*) pc (1.10)

Because the discount rate that is selected from the process of natural selection (the assumption is that the survivors get it right) is the same as the population growth rate and,

1(*) pc using the ratio of the two, , which is one, current utility is just the un-weighted sum of 1*G all future utility derived from the consumption levels of future generations.

44 To reach this conclusion (that is, to require that the current generation maximize their utility based on current and all future generations) requires that all future generations receive exactly the same weight in the summation as the current generation. For utility maximization, the current generation must have great care for future generations’ consumption. This implies great care in the selection of savings (investment) versus consumption.

An interesting conclusion that will be referred to in later chapters is based on

fMk (*,*)(*) k pc. That is, the marginal product of capital or the real interest rate equals

the growth rate of the population given some Ng*/1 . In other words, the real interest rate is based only on g ; productivity is the sole determinant of the real interest rate since the

growth to the steady-state population is already discounted (assuming, of course, that the

investment/consumption choice for current and all future generations is optimal for the survival

of the species).

The expectation that current and future generations make optimal choices may sound

fanciful. However, recall that this exercise looks to a very-long-run equilibrium; thus the

expectation is that consistently poor choices will result in the ultimate demise of a regime and

the replacement of that regime with one that does make consistently optimal choices. In a later

section of this chapter there is discussion about how social unrest and war are mechanisms for

affecting the resolution of imbalances that arise from consistent suboptimal choices.

Notice also that the requirement for the model is that the rate of population growth is

the same as the growth rate of the carrying capacity of the environment. This is not the

observed fact in the post-industrialized era in areas that are “developed” wherein population

growth rates have been lower than the growth rate of output. In Part II of this discussion this

disparity is reconciled, showing how, at a certain point, preferences for the quantity versus

quality of offspring shift. The analysis will use the conclusions developed in this part as a

45 foundation for the model. However, as will be shown in the next section, some groups will move forward toward the transition more rapidly than others. Furthermore, as will be demonstrated in Part III of this discussion, once different rates of growth are established, then

they tend to persist. Later chapters will discuss how these differences might be undone in the

long-run. However, first the discussion of how natural selection drives the determination of

which of the groups progress and which do not needs to be completed.

Natural Selection and Productivity Growth

In A Study of History Arnold Toynbee (1934) suggests that economic evolution has been guided by responses to environmental challenges. He suggests that “hard countries,” for example, have elicited a response from the inhabitants that selected traits that raise the probability of surviving the difficult conditions. In an agrarian pre-industrial world harsh winters would favor groups that were better at accumulating (saving) and building shelter (investing).

This concept is incorporated into the model by adding an environmental harshness parameter to the population growth function. An increase in the parameter E indicates a

harsher environment and lowers the population growth rate; i.e., pE 0 .

It is also sensible to expect that there will be different preferences for labor versus leisure given harsh versus moderate climates. If we call labor per-capita h , then leisure per- capita is lh{1 . Furthermore, more leisure will result in higher population growth. The

intuition for that statement is that greater leisure time versus labor time will promote better

health, more sexual activity, and higher level social institutions. However, more leisure, by

reducing labor, also lowers the group’s output for consumption and capital formation. Thus l is added to the population growth function and h is added to the group’s production function.

46 The partial second derivatives for population growth are as follows: pcE ! 0 , pcl d 0 .

These derivatives show that if the environment is harsher, then the marginal benefit of consumption increases relative to leisure.

For the production function, both fk and fh are greater than zero. It is assumed that

fMk 0 and fMh 0 . These signs are based on the fact that as population is larger, given the

fixed size of the commons, per capita output falls ( fM 0 ). Thus, if M is increasing, both fk

and fh are reduced.

Environmental conditions will influence behavior, so both the leisure and harshness parameters are now included in the utility function. Thus, as before, to investigate the behavior that maximizes well-being (population growth which is now a function of consumption, leisure, and harshness) a constrained optimization relationship is formed. This is described as a

Lagrangian on Upcl((,,))E subject to

cfmkhkpcl (,,) (,,)E (1.11)

The total population, M , for simplicity is calibrated to one.

The first order conditions for population growth maximizing choices are

fpclk (,,E ) (1.12)

1 kpcc p 1 . (1.13) fkpphllh f

Equation (1.12) is the golden rule for capital accumulation. Equation (1.13) describes the well- being maximizing mix of consumption and leisure.

In order to investigate how different degrees of environment harshness influence natural selection, comparative statistics are performed on the equilibrium conditions (1.11)-

47 (1.13). Recall also that pcl(,,E ) g; that is, the total population growth rate is equal to the

growth rate of the productive capacity of the environment. The analysis is also simplified by

specifying a linear form for p()x is the form of

K()EPEWEcl () () (1.14)

Also stipulated is that an increase in the harshness of the environment will reduce

output for given inputs; i.e., fMkhE ( ,,) 0. The validity of the conclusions thus relies on whether or not an increase in environmental harshness lowers output across all inputs. The scope of this analysis suggests that an increase in harshness that does cause a negative impact

on production will cause groups to adopt preferences that differentiate them from groups that do not face such environmental challenges. Therefore our stipulation is does not unfairly bias the conclusions.

The cross derivatives among inputs to production are assumed to be positive.

The effect of harshness on per-capita labor is shown below.

dh ªºpf §·ff dM chE f kh Mk !0 (1.15) «»¨¸Mh C dM¬¼«» pckk©¹ f dB

2 dM pE Where Cfff [()/0kk hh kh f kk ! and 0 . dpfE cM

dM Signing 0 is straightforward and suggests that if environmental harshness dE

dh increases, then the equilibrium population density is reduced.17 The components of are in dE

17 This conclusion is well supported in both historical and current population demographics. See the following map (American Association for the Advancement of Science, 2006):

48 pf three parts. The first term, chE , is greater than zero because as the environment becomes pc

harsher, the relative value of consumption rises; that is, p ! 0 18 The terms augmented by cE .

dM 0 combine to be less than zero. dE

dh The fact that is greater than zero shows that per-capita labor increases with an increase in dE

environmental harshness. This conclusion is reinforced by

dkff dM dh Mk !kh 0 (1.16) dfdfdEEE kk kk ,

which shows that capital increases with increased harshness. Also, the comparative statistics

show that per capita consumption increases with harshness due to a fall in population density

combined with a rise in per capita labor:

dc dM dh ffMh!0 (1.17) dddEEE.

18 Higher caloric intake, more consistent caloric intake (storage and storage shelter), and conservation of caloric intake (clothing) are all considered as consumption.

49 These comparative statistics provide the basis for the next section in which the subject is the transition from the Malthusian era into the modern era of sustained increases in per capita income. In this model of the pre-industrial world, natural selection, which favors choices that return optimal rates of population growth, can explain preferences for work versus leisure.

We see that the choice between consumption and saving has been determined by the golden rule at which consumption per capita in the current and in all future periods was maximized consistent with steady-state growth. The tendency of these forces was to differentiate groups across regions in response to different levels of environmental challenges.19

This conclusion provides a foundation for the next sections. The transition from the prolonged period of economic stagnation into the current regime of sustained growth in per-capita income that the developed world has enjoyed for nearly two hundred years required an increase in the pace of technological change. As we have seen, natural selection and utility maximizing behavior differentiated certain groups from others. In the next section, a model is developed for how this differentiation not only increased the proportion of skilled labor, but also eventually changed preferences that led to a key disconnection between economic well-being and fertility rates. Without this disconnection, increases in output would be diluted by increases in population as they were in the Malthusian era.

19 Lower population density combined with a preference to devote more resources to the upbringing and education of children (spending per pupil in real US dollars) as a trait of those living in harsher climates is supported by data from the World Bank and the US Dept. of Education on average spending per pupil. Comparisons were made for northern and southern Europe and northern and southern US. (See World Bank, World Development Indicators, 2001, Table 2.11, Education Inputs; and National Center for Education Statistics, Statistics in Brief, May 2002.) This anecdotal observation’s basis is further supported in the next section. Work done by Hansson and Stuart (1988) suggests that northern European countries have a lower tax-driven elasticity of labor supply than southern European countries. By no means conclusive, this work does suggest that controlling for macroeconomic influences, northerners have a stronger work ethic.

50 In the last section of this chapter, the differentiation across regions that was shown to be a product of environment above is the basis for understanding how, in today’s world, there is such a large disparity between income per capita.

Part Two: Natural Selection and the Transition to Sustained Economic Growth

In this section a model will be developed that will allow the heterogeneity of the groups to eventually bring the proportion of individuals in those groups to a level after which utility maximizing behavior leads to a disconnection between income level and fertility.20 The first part of the analysis will outline how labor is augmented by human capital (based on the quality of upbringing) to enhance the production of goods from the land. Decisions made by each generation influence the well-being of following generations. Next the analysis works out the time paths for the key variables that drive the utility maximization problem faced by each generation. Finally, a dynamic system is analyzed, and phase diagrams are derived that show that when the proportion of certain types of individuals in the group exceeds a critical level, the economy experiences a release from the bounds of the Malthusian stagnation and “takes off.”

The Decisions Facing each Generation

This section and the next will simplify the economy to only two input factors for

production: labor and land. Physical capital is not included in the production function. The role

of this model is to explore human capital rather than the role of physical capital and asset

accumulation. Using physical capital (and thus a need for interest rates and property rights)

would make the model intractable. Their exclusion does not detract from the fundamental

qualitative inferences that will be made.

20 The analysis that follows gains its inspiration from work by Galor and Moav (2002).

51 The inputs of land and labor are augmented by an endogenously determined technology. The supply of land is considered fixed over time and is exogenous. The supply of effective labor (efficiency units) is a function of the preceding generation’s choices for the number or children and the amount of education that each child receives.

Production at time t is

1DD YHttt () AX . (1.18)

The output is from constant returns technology where Ht is the aggregate quantity of

efficiency labor, X is the land, and At is the level of technology, andD (0,1) . The product of

AXt represents the effective resources available to labor.

There are no property rights in this conception (perhaps not an unreasonable assumption for most of pre-industrial history), so that there are no rents. Wages are derived

from output per efficiency unit of labor:

AX wx t D (1.19) t H t .

Each generation represents one time period. Each individual lives for two periods. In the first period, t 1, they are children and in the second period they are parents. In the

second period the parents allocate their one unit of time between labor and child rearing. They

must choose between the quantity and the quality of children. They also must participate in the

labor market to receive wages that they consume in the second period. The amount of the

parents’ time that the child consumes in the first period determines the quality of the child.

Individuals in each generation t are differentiated by their preference for the quality

versus the quantity children. Members of each preference type, i , pass on their preferences

52 from generation to generation. The distribution of types will change with time given changes in the social and economic systems. In other words, a basic Darwinian survival mechanism will assure evolutionary change that maximizes the survival of the population. Depending on the economic regime, preferences will shift between greater fertility or greater nurturing and education of offspring.

The base level constraint is to maintain a subsistence level of consumption.

Consumption above that level has a positive effect on the wellness of individuals and thus their ability to weather adverse shocks such as disease, famine, and the seasonal variations of output.

Consumption above subsistence also improves labor productivity.

Utility is derived from a choice of the number of children and their quality, given that the parents’ time must be allocated to child-rearing and wage earning. Utility is also a function of household consumption. It is assumed that utility is derived from consumption above the subsistence level only.21 Thus the preferences of persons of type i in generation t are:

iiiii i ucnwhtttt (1JJE ) ln [ln ln11t ] where J (0,1) and E (0,1) (1.20)

i i i ct is the consumption of households, nt is the number of children, ht1 is the human capital of

i each of the offspring, wt1 is the wage per efficiency unit of labor, and E is the relative weight given to quality by the people of type i . The distribution of E i in each generation will change over time as the population reacts to changes in the economic environment. The utility function is strictly monotonically increasing and strictly quasi-concave and will yield an interior solution,

given that wages are of sufficient magnitude for consumption to be above the subsistence level.

If wages are insufficient and consumption is at the minimum c ! 0 , then a corner solution is reached.

21 This simplifies the mathematics but does not impact the analysis.

53 Two components contribute to the time necessary for raising a child. W n is the fraction

of a parent’s total time endowment that is required to raise any child. As long as WJn there will be population growth. If W n were greater than J , there would insufficient time to raise

offspring after the time necessary to provide subsistence consumption and the population

would shrink. The other component that consumes the parents’ allocation of time is the

providing of education beyond the basics. If the quality (i.e., the level of education) for a

i member of type i in generation t is et1 and the fraction of time allocated to providing that

e nei education is W then the total time cost for a parent isWW et1 .

If a type i person in generation t is endowed with a level of human capital and their entire life were spent in labor, the (potential) income is:

zwhxhii{{D iwhich implies that zx(, hi ) (1.21) ttttt tt.

This potential total earning is divided between consumption and the cost of raising children.

in ei The opportunity cost of raising a child is whtt[]WW e t1 ; therefore the parent faces the budget constraint:

ii n ei i i i whntt t()WWd{ et1 c t wh tt z t (1.22)

The final component necessary for solving the optimization problem is the process for human capital production. We already see that the level of education improves human capital.

The feedback from technological improvement into the Darwinian process is intuitively understood as a complimentary relationship between skill level and survivability in an evolving socioeconomic environment. In other words, technological progress increases the returns to education (a positive productivity effect). Technological progress also effectively lowers the

54 value of human capital for a given level of education (a negative attrition effect). If the rate of

AAtt1 progress in technology is gt1 { , then At

ii hhegttt111 (, ) (1.23)

i where h()x! 0, he ! 0 , hee 0 , hg 0, hgg ! 0 , heg ! 0 for t(,egtt11 )0 and

limgtofhg (0, 1 ) 0 and h(0,0) 1.

In Chapter Two we will investigate what happens to this model when the rate of technological growth becomes zero.

The Optimization of Intertemporal Utility

The people of a given generation must choose how many children to have and the level of quality that these children will be provided. This choice also determines their level of consumption. Combining (1.22) and (1.23) into (1.20) yields:

{neii , } arg max{(1JWWJE )lnwhi [1 n in ( ei e )] [ln ni i ln whe (i , g )]} (1.24) tt11tt t t t t1 t1 t1,

subject to

iinei whtt[1 n t (WW et1 )] t c ;

ii (,nett1 )t 0

If z is the quantity of potential income (where zc{/(1J )) below which there is no longer

i i sufficient time for child rearing, then if zct d , it follows that nt 0 ; in other words those type

i i ’s become extinct. If the potential income zzt , then a person must use a larger part of their allocation of time (larger than1J , the time spent not raising children) to attain

55 subsistence consumption. For increasing levels of human capital it takes less time in the labor force for achieve subsistence consumption; thus there is more time for raising offspring.

It is clear that higher labor efficiency will yield more time for raising offspring. However, it is not the level of income that determines the preference between the quality and quantity of offspring. What is important is the rate of technological progress and the preference for quality,

E i .

Noting that as long as potential income is greater than that necessary for subsistence

i consumption, zct t , we have

i in ei J if zzt t ; nett[]WW1 ® . (1.25) i if i ¯1(/ czt ) zzt

The parent, if faced with a potential income that is lower than z , must then allocate more than

1 O of their time for acquiring subsistence consumption. This also implies that the fraction of time left for child-rearing is less thanJ .

The trade-off between consumption and child-rearing is illustrated in the figure below.

Consumption is on the x-axis, and time spent raising children is on the y-axis. The budget constraint, z , is shown in three progressively increasing levels. Since the specification for utility is such that only consumption above the subsistence level adds to the function, the income expansion path is vertical until z is greater than that required for subsistence consumption and is horizontal thereafter.22

22 If the specification were for the consumption portion was to be (1J ) ln(cci ) then the income t , expansion path would be convex.

Figure 5. Consumption and child-rearing.

The relationship between education and technological progress is what inspires the Darwinian process of selection for quality offspring versus mere quantity. This relationship can be characterized as a function of both the cost of child-rearing and the preference for quality

children. It is intuitive to state that the quality of children is positively linked to the rate of

ii technological growth. Thus at a given preference for quality, if egtt11 HE(,) , then H g ! 0

and H E ! 0 .

The level of human capital for the i type in the period t 1 is thus:

hheghgii (, ) ((,),)HEi g { hg t ( ) (1.26) ttt111 t 1 t 1 t 1.

ii If we substitute egtt11 HE(,)into (1.26) and note that

iiiDD zxhgtt ((HE t ; ),) g t xhg t ( ( t )), then if income is greater than subsistence, we can make

the following statement about the number of offspring:

57 ne i i i °JW/[t WH (gifzztt1 ; E )] ii i i nnt ® {(,;)(,(,());)gtt11zEE ng tzx thg t (1.27) °(1 [cz /ie ] / [WH ( g ; E i ) ifz i z ¯ tt1 t .

If we note that education, et1 , responds to growth, gt1 , in such a way as to counteract the

whgi () dilution effects of growth on human capital, then it is natural to assume that t 0 . As wgt

i long as the consumption constraint, zhg/()t is not binding, a partial derivative on (1.27) is

ii i 1/D wwng(ttt1 , zx ( , h ( g ));E ) / x t 0 . If xzhgtt /() . The partial is greater than zero, and

the second partial is less than zero.

It follows then that evolution has the following influences on the choice of quality versus

quantity children (Conclusion One):

1. Growth from technological progress causes parents to choose to have fewer

i i children of higher quality. That is wwngtt/01 d and wwtegtt11/0.

2. If the subsistence constraint is binding (they are below subsistence

i consumption, zzt ) , then an increase in income raises the number of

ii ii children but not their quality. That is, ww!nztt/0and wweztt/0 .

3. If income is above z , then an increase in income has no effect on quantity or

quality of children.

Therefore what determines the quality of offspring is not income but, for some level of

technological change, it is the type of parents. Differences in human capital, particularly the size

of the quality parameter, E , between groups of parents determine the choice.

It becomes important to understand the distribution and the types of human capital in order to construct an evolutionary story. As a foundation, assume that the population is of two

58 types. Type a is the quality type and possesses a high quality parameter EEa ! and type b is the quantity type and possesses a low quality parameter. At any time t the population total is

ab LLLttt . Mutation may occur, and members may migrate from group to group. However, for our argument we keep each group homogeneous.

Based on the conclusions above, the sole determinant of how educated the offspring are is technological progress. But if we assume that the group with quality offspring makes decisions based on their attitude about child quality, we can state that they do invest in the

a human capital of the offspring even if technological change is zero: ett !0 . That is, even if

a gt1 0 , the type a’s invest in education. We can see this by noting that as long as EE! ,

aa bb i then it must be true that ggtt11()EE! (). There exists some g()0E t so that it is only

i i necessary for ggt1 ! or EE! for eg()0t1 ! . This is illustrated in the figure below by plotting the effect of technological growth on the choice for education.

Figure 6. Technological growth and education choice.

a The aggregate level of education is a function that averages the two. If qLLttt{ / (the ratio of quality people to the total population), then

59 ab eqegtt ()(1)() r{ qegegq t t (,) rt, (1.28)

which is increasing and strictly concave with respect to gt .

i Making ft the amount of time that a type i individual devotes to labor force participation, the aggregate supply of efficiency units is

HLfhLfhLqfh a aa b bb [](1)aa qfhbb (1.29) ttttttttttt ttt.

iiD From (1.25) and the fact that zxhgtt () tfor iab , ,

i ii°1tJ if zt z fftt ® {(,)gxr (1.30) ° ii ¯cz/ tt ifzd z

i i with the partials fgxxtt(,)0 , fgxgtt(,)0! for the second case.

A Dynamic Story of Evolution

We are now ready to discuss how natural selection and the choice for the level of quality is a necessary component of for the transition out of the Malthusian trap into the current era of sustained growth in income per capita. In a later chapter, we will revisit the conclusions reached in this section. However, as we will see in that chapter, the model responds differently under a zero growth assumption.

For now, suppose that technological progress is a result of the level of education in the society. The progress in technology, A , that takes place from time t to t 1is a function of the

average level of education/quality amongst the workers at time t , et . Thus

AAtt1 gett1 { \ () (1.31) At

60 with the rate of progress increasing on average education. Solving (1.31) and substituting, we have

AgAeA [1 ] [1\ ( )] (1.32) ttttr11 .

From (1.28) and the above we can say that growth in the period following is determined by

growth in the current period and the average quality of the workforce:

geqgggqtt1 \ (( ,tt )){ ( ,t ) (1.33) with the first derivatives on g and q positive. Diminishing marginal benefit assures concavity.

We must also specify the time effects on population size and fertility between the two

types of individuals. Recall that xAXHtt / t denotes the effective resources per efficiency

i unit of labor. If nt is the number of offspring (fertility rate) for type i , then the population for

iii type i is LnLttt1 . From the work above, we know that

nngxqii (,,) (1.34) tttt.

Since the total population is the sum of the populations of each type and the ratio of quality

a people to the total population is qLLttt{ / , then

nqn{ab(1 qn ) (1.35) ttt rt.

Therefore the evolution of the proportion of quality types is

na qqqgxq t {(,,) (1.36) ttttt1 n t .

61 We now have the information necessary to illustrate the relationship between the economy

(i.e., the level of effective resources or wages) and the evolution of the types of individuals.

When early man was simply surviving, the wealthier quality households had an initial advantage over the quantity households. However, at some level of effective resources, x that exists between subsistence living and z the following is true:

! nforxxb ° ttt ab° nnforxxtt® t (1.37) ° b ° !nforxxtt ¯ .

This conclusion follows logically from (1.27) and Conclusion One reached in that section. (1.37)

is true as long as xchgzhgii([ / ( )]1/DD ,[ / i ( )]1/ ) thus tt t;

ba ww!wwngxq(,;)/tt x t ngxq (,;)/ tt x t. So although the quality types have an initial advantage, as effective resources per efficiency unit of labor rise sufficiently (that is, xxgqtt! (;)), the Malthusian pressure reduces and the rate of population growth among

quantity types overtakes that of the quality types. Note that Conclusion One also suggests that

as the rate of technological progress advances, the substitution of quality for quantity will bring

about a demographic transition, and fertility rates will decline. We will investigate that farther

down. This early relationship between wealth and fertility is illustrated in Figure 7 below:

Figure 7. Wealth and fertility.

Consistent with the arguments above, we can also say that the growth rate of the

efficiency of labor is also a function of technological progress, effective resources, and the

proportion of quality individual in the population. Thus,

H qnfhaaa(1 qnf ) aaa h P {tt1111 ttttttt1 11 (1.38) t Hqfhqfhaa(1 ) aa ttttttt,

and as long as the society is above the basic replacement level of fertility, therefore

PPtttt1 (,,)gxq. So effective resources per efficiency unit of labor, xAXHtr{ / t, is a function of the rate of technological change and the growth rate of efficiency units of labor:

1 g xx t1 {(,,)gxq (1.39) tttt1 1 P t1 .

63 It is clear that the development of the economy is described by the path of output,

population, technology, education, and human capital. The path is determined by xt , qt , gt

(the time path of effective resources per efficiency unit of labor, the rate of technological progress, and the fraction of quality types in the population) so that equations (1.33), (1.36), and (1.39) are satisfied in every period t . The analysis is facilitated (and simplified to two

dimensions) if the equation of motion for growth, geqgggqtt1 \ (( ,tt )){ ( ,t ), is recognized

to be the outcome of gett1 \ () and eegqttt (,).

This relationship can be illustrated in the relationship of growth to education. The relationship of education to technology to the demographic dominance of quality types allows an endogenous shift that creates dramatic changes on the resulting steady-state outcome. As

q increases, the curve eegqttt (,) shifts upward. Below are three charts: Figures 8 , 9, 10, where the superscripts L, U and H refer to those levels at which stable steady state equilibriums are reached . The first shows the outcome in a world in which the fraction of type a individuals

(those that prefer quality) is zero. The second chart shows where the fraction is below that

required for take-off. And the third where the fraction is above qˆ .

In the first and second charts, there is a low steady state equilibrium (L) where

gqLb() g(and only individuals of type a invest in education) and a high steady state equilibrium (H) at which both types of individuals invest in human capital. In the third chart since qq! ˆ there is only the high steady state node. The unique critical boundary node between the low and high nodes is designated with a U.

Figure 8. Steady State A.

Figure 9. Steady State B

Figure 10. Steady State C.

In the final chart, both types of humans invest in human capital.

The analysis above also yields a two dimensional representation of the relationship

between the rate of technological progress, gt , and the effective resources per efficiency unit of

labor, xt , for a given ratio of the type a individuals, q . It can be shown (see Appendix A for

details) that in the plane of gt and xt there exist three loci that create a phase diagram of a

dynamical system in which for all time, gggqtt1 (,) and xxgxqttt1 (,,)are both jointly satisfied. The three loci are

x The subsistence consumption frontier (CC), which separates the region where

the subsistence constraint is binding for some individuals from the region in

which it is not binding for any individuals.

x The labor/technology equilibrium (XX) along which, given a level of q , the

effective level of efficiency units of labor, xt is in steady state. Along this locus

66 the growth rate of efficiency units of labor, ut , and the rate of technological

progress are equal.

x The technology equilibrium (GG) which is the relationship between gt , the rate

of technological progress, and xt , the effective resources per efficiency unit of

labor, so that for a given level of type a humans, the rate of technological

progress, gt is in steady state (GG).

The diagrams below (Figures 11, 12, 13) illustrate the conclusions above.

Figure 11. Dynamics A.

Figure 12. Dynamics B.

Figure 13. Dynamics C.

The first and second phase diagrams above (11, 12) show the world in an era when the

ratio of type a individuals, q is either non-existent or small. Notice that the GG locus consists

68 of three vertical lines at the steady state levels of g for three conditions that are based on the three outcomes from the relationships shown in figures 7, 8 and 9 above.23 In the first two

diagrams the world always seeks a stable steady state equilibrium at the intersection of the XX

and GG loci. In both cases the world is locked in a Malthusian trap in which the aggregate of

income per person is constant.

As development progresses and qt increases, the Malthusian trap disappears, and the system enters a stage of permanent positive growth in effective resources per unit of labor as illustrated in the third phase diagram. Note also that the system converges to a steady state level of technological progress that is high.

At the point at which type b individuals start investing in the quality of their offspring

(point g b on the charts above) the growth rate of the average level of education increases.

There follows an acceleration in the rate of technological progress such as that seen in the

Industrial Revolution. The relationship between technological progress and the level of education reinforces the growth process. Society eventually crosses the subsistence consumption frontier (the CC locus), and a demographic transition occurs. The rate of population growth declines, and the average level of education increases.

As we will see in a later chapter, a minor alteration of several of the assumptions required to derive the loci will change the outcome of the exercise and allow the system to return to a neo-Malthusian trap: a constant income per person is the normal state in the zero growth world of the future.

23 See appendix A: The GG locus is unaffected by the effective resources per efficiency unit of labor.

69 The Effects of Trade on the Process of Transition from the Malthusian Regime

This section presents a simple model that follows upon the conclusions reached above.

Suppose now that we have two economies identical in all ways except that one of the economies has developed somewhat better technology. The two economies produce both a manufactured good and an agricultural good.

The reader may recall that in an earlier section of this work we see that exogenous pressures differentiate populations. Now suppose that Economy A has responded to environmental harshness and has developed a set of technologies that improve both their production of an industrial good and an agricultural good. So

mA mB aA aB []AAtt! [] and []AAtt! []. Also, if we assume that progress is more rapid in the

AB mm ½½AAtt industrial sector than the agricultural sector, then it is also true that ®¾®¾aa! . In ¯¿¯¿AAtt

autarky, the relative price of the agricultural good in the technologically more advanced

economy A, p A , is higher than the autarkic relative price of the agricultural good in the less

AB advanced country; that is, pptt! .

* If trade is established, the open economy relative price of the agricultural good, pt , is

BA* between the autarkic prices. Thus, ppptttdd. If we remove the possibility of equality of

prices, each country will completely specialize in production. Members of the less advanced

economy perceive an increase in the price of the agricultural good and are induced to produce

more. Members of the more advanced economy perceive a reduction in the price of the agricultural good and thus produce less. Country A specializes in the skill-intensive industrial good, and Country B specializes in the agricultural good.

70 This demand for skilled or unskilled labor feeds back into the mechanism for the selection of the number of offspring that we developed above. As we noted above, population growth is affected positively by the level of aggregate resources in the economy and negatively by the return to human capital. The production of skilled offspring simply takes more time and a more concentrated effort.

International trade amplifies the process. The transition into the post-Malthusian era is expedited by trade for the advanced country and is retarded by trade for the less advanced country. As the ratio of skilled to less skilled workers rises in the advanced country and falls in the less advanced country, the gap between the two will widen and further reinforce the patterns of comparative advantage.

If the share of world income for Economy B falls over time as Economy B completely specializes in agricultural production, then the economy would never create a demand for skilled workers and would never transition from the Malthusian trap.

The solution would be for Economy B’s share of the world’s income to rise over time.

Then eventually Economy A will have insufficient productive capacity to meet world demand for the skill intensive good, and Economy B will begin demanding skilled workers.

We could also tell this story based on reliance upon a natural mineral wealth as well as the agricultural good. The lesson is the same. There is a self-reinforcing mechanism put into play by world trade that widens rather than narrows the gap between developed and undeveloped economies. This is illustrated in detail in Chapter Two in the context of growth theory.

Conclusion to Part Two

This section has set the foundation for understanding how the current regime of sustained growth in the standard of living has arisen. The conclusions we have found will be the

71 basis for advancing this exercise into the future. That is, we will test the future’s ability to maintain a sustained growth in income per capita. We will identify the conditions that occur as we reach farther into the world ahead.

We have also identified the unpleasant side effects of growth in an international environment. The next chapter will consider more closely these conditions within modern growth theory.

Part Three: The Hurdle: Getting Past the Distributional Problems of the Current Economic

Regime

"The whole system of capitalist production is based on the fact that the workman sells

his labour-power as a commodity. Division of labour specializes this labour-power, by

reducing it to skill in handling a particular tool. So soon as the handling of this tool

becomes the work of a machine, then, with the use-value, the exchange value too, of

the workman's labour-power vanishes; the workman becomes unsaleable, like paper

money thrown out of currency by legal enactment. That portion of the working-class,

thus by machinery rendered superfluous, i.e., no longer immediately necessary for the

self-expansion of capital, either goes to the wall in the unequal contest of the old

handicrafts and manufactures with machinery, or else floods all the more easily

accessible branches of industry, swamps the labour-market, and sinks the price of

labour-power below its value” (Marx, 1906 p. 470)

"We stand at the end of what may go down in history as the Century of Development. If

we tear our gaze away from the fantasies of futurology and look at the real world

72 around us, what we see are unprecedented forms of mass poverty, unprecedented

forms of mass killing, unprecedented methods of regimentation, unprecedented

pollution, destruction, and uglification of the earth, and unprecedented concentration

of wealth and power in the hands of few… we tell ourselves that all of this must have

been some kind of deception, an impostor, a false development, and that surely there

must still be a true development yet to come. Modernization and development never

meant the elimination of poverty, but rather the rationalization of the relationship

between the rich and the poor. In this sense development not only includes the

development of poverty, but the development of the technology of management and

oppression necessary to keep people in their position of relative poverty… Thus world-

scale development also includes the development of the police state. . ." (Lummis, 1991,

p. 31).

"In the early stages of rapid economic development, when inequalities in the

distributions of income among different classes, sectors, and regions are apt to increase

sharply, it can happen that society's tolerance for such disparities will be substantial.

But this tolerance is like a credit that falls due at a certain date. It is extended in the

expectation that eventually the disparities will narrow again. If this does not occur,

there is bound to be trouble and, perhaps, disaster" (Hirshman, 1973, p.545)).

In the context of our investigation into the transition from the current regime wherein the expectation is for continued growth in income per capita to a future regime in which there is no growth, we need to investigate what paths are available for passing from the current to

73 future regimes. From the feasible paths, perhaps we can gain a sense of optimism that the turmoil of today’s world system will abate.

Throughout history the paths that nations have followed have been determined by many forces. But underlying the decisions of most leaders have been considerations for gaining and preserving economic power. Quite often, these decisions, thought national in scope, have been less concerned with the distribution of wealth than with the maintenance of a dominant regime (Lindert & Williamson, 1985). The strategic choices facing the political powers often were developed, in part, by considering methods for limiting social disturbances so that the business of growth (in a very broad sense) could continue with minimal uncertainty (Acemoglu

& Robinson, 1997). There is little dispute among researchers regarding the relationship of uncertainty (i.e., increased non-diversifiable risk) and growth (Barro, 1995). Nor is there much dispute regarding the relationship between increased income inequality and political instability

(Muller & Seligson, 1987). The source of divergent analysis often resides in the way in which long-term growth in inequality results in changes within the regime and what effects those changes have on economic growth in both the short and long runs. Some research (Perrson &

Tabellini, 1994; Alesina & Rodrik, 1994; Rodrik, 1997) suggest that high inequality leads to a heightened sensitivity to external shocks and, if the regime is prudent, a strategy of redistribution of national wealth will follow. Some countries, however, have a history of following fiscal and monetary policies that, after adverse terms of trade shocks, have resulted in large distributional consequences brought about by changes in key relative prices (the real exchange rate, real wages, and the rural-urban terms of trade) (Rodrik, 1997b). Others (Saint-

Paul, 1995; Benabou, 1996) suggest that less inequality leads to more redistribution through a more efficient banking system and better access to credit and that such redistribution leads to increased capital accumulation and higher growth.

74 In either case, those in political power must make decisions based on signals received from both the social and economic forces prior to altering the regime. These signals, both economic and political in nature, can be used by the regime in power to make changes along several fronts. For example, if inequality and social unrest are growing, the regime may offer democracy (i.e., the poor majority can vote on a redistributive policy). They may choose, rather than to raise the income level of the poor, to increase the flow of resources into guard labor and guard capital (army, police, private security, secure compounds, jails). Or, a more humanitarian regime may not offer democracy but may, in the guise of a benevolent dictator, redistribute optimally. This essay suggests that there are several mathematically stable outcomes. Two of the outcomes require a degree of distribution such that the gap between the rich and poor does not increase. One of these outcomes has no redistribution so that the gap grows. The mathematics suggests that in the long-run social unrest subsides or grows; interestingly however, it is possible that even with the extension of the democratic franchise, social unrest can grow.

It is clear from a preponderance of research (see Zweimuller, 2000, for a review of recent data) that income inequality is increasing. For example, recent data shows that some gini’s have trended higher. For many developing nations, the disparities have remained high.

75 50 45 40 35 30 25 20 Gini Coefficient Gini 15 10

Gini – Mid 80s Gini – 2000 Source: OECD

Figure 14. Income distribution (Organization for Economic Cooperation and Development

[OECD], 2007).

If inequality is increasing within and between nations, then is not social unrest

increasing? And if social unrest is increasing, is the reliance on security forces and the hardware

for enforcing that security increasing? This section will make those linkages.

On an intra-country scale, we may imagine the outcome of these linkages as a buildup

of internal security forces. Such activities certainly occur in many developing nations, but less

overtly, internal securitization also takes place in developed democracies.

This section of this chapter will propose that, over time, the key determinant to the

growth in the propensity for social unrest will be the gap between the desired and actual levels

of consumption of the majority of the members of a society. More precisely, it is the change in

the gap over past history (promises of improvement will not suffice) that will determine the

level of satisfaction (dissatisfaction) that the members of the society will have.

Note that the change in the gap between an agent’s actual level of consumption and the desired level is relative; i.e., absolute income levels are not key. However, note that if the

76 "poor" are relatively well off, then a much larger change in per capita income is required to produce a given relative change. Thus, lower income countries with a high Gini coefficient are more likely to have a more extreme change in the gap and a more problematic level of dissatisfaction. The combination of the exclusion of the majority poor sector from the process of wealth accumulation that the minority elite enjoy and the misery that the poor acquire from not being able to consume desired quantities of goods will be the foundation of the central model in this section. At some point in time, the threat of social unrest (revolution, terrorism) will become so great that either the society transforms into a total police state (in which case all wealth has been transferred to the army and police, and growth falters completely), or the majority will gain power and redistribute according to a voted-upon tax, and growth will converge towards the long-run stable state. The first case may result in a restarting of civilization. The second case is the desirable path.

According to the model to be presented below, if unfavorable trends in income distributions were to persist, either continued growth in police and army (and, in general,

“guard” labor that could even include workplace supervisory personnel) would be required to maintain stability, or, at some point in time, the threat of anarchy and revolution would become real. Thus, although revolution is generally thought of as a violent conflict, the signal that unrest is growing toward a crisis threshold can be rationally interpreted by the elite and may, eventually, lead to a more stable blend between capitalism and democracy in which redistribution is seen as a necessary component in the process of growth with stability.

This potential for anarchy also is important in Chapter Two, wherein a simple change in an influential growth model shows that the long-run outcome of resisting growing inequality with force is chaos.

77 Below we will propose several interrelated models that will investigate the closed economy relationships between inequality, income and consumption, civil unrest, and policy.

The results will then be subjected to an opening to international trade. This work will build on a literature on political economy and growth. Roemer (1985) posits the possibility of revolution but does not correlate it to the level of inequality. Ades (1995) offers a model in which there is concentration of power with the elites. Neither of these models allows the elite to perceive signals of unrest and use them in the decision-making process. More closely aligned with this paper's technique is the work of Acemoglu and Robinson (1996). However, their economy does not allow for guard labor and the associated gradual depletion of the elite’s assets. And more significantly, none of the above techniques specify the way in which zealotry and enhanced communications infrastructure may enter into the dynamic process. This work does and, in doing so, extends the literature in a minor but significant way. Finally, the work of Rodrik (1997) has been useful in finding a transition from the closed to the open economy. Rodrik outlines a specification for wage dynamics versus capital mobility that I have adopted, bringing fundamental alterations into the income growth patterns and allowing me to explore how my model responds to international trade. Also the work of Diego Puga (1996) has provided inspiration for investigating how the mobility of labor and the transportation costs manufacturing faces affect income distribution.

This section proceeds as follows: the next part will set the foundations for the political response to an unequal society. In the next section, the way in which the changes in income and consumption patterns create political forces beyond the simple accounting of present values of future incomes will be modeled. The following section will perform several experiments on the model using different regimes with different decisions. The final section will show how the globalization of trade patterns combined with mobile capital and immobile labor

78 accelerate the outcomes identified for the closed societies. Finally, the last part will offer some concluding remarks.

The Foundation for an Unequal Society

In this opening section, we will simply show how inequality can be tolerated even when there is democracy. In subsequent sections we will show how this tolerance can lead to unstable (in a social sense) outcomes.

Consider a continuum of agents i [0,1]that have log normally distributed

endowments shown as xyNmii{'ln ~ ( ,2 ) . This specification for income distribution is a

good approximation of the empirical distribution (Clarke, 1992) and also allows inequality to be

defined as the size of this variance. We can see that as the variance, '2 , increases, the distances between per capita incomes and the median income also increases:

'2 2[ln(Ey [i ]) m ] . The economy has two types of agents that face two choices. The

1 agents are either the non-elite (poor), O , or the elite (rich),1 O . I will assume that O ! 2 .

The choices they face are between two stylized policies: complete non-intervention by the government whereby each agent consumes his/her endowment so that cyii for all i, or complete redistribution whereby agents pool resources and each consumes cEyii []. If the

tax rate menu is t [0,1] and, for now, sharing is restricted to either zero or one, then the proportion, p , of agents in favor of the second policy will be all those whose endowments are

below the mean:

''2 /2 p )()() ) (1.40) ' 2 ,

79 where ) is the c.d.f. of a standard normal. Since the income distribution is skewed left and the

median is less than the mean, if simple majority rule were to dictate, since the proportion in

favor will always be greater than 1/2, redistribution will always take place. The assumption is

that all agents vote. If some proportion of the poor, [ , do not vote (or if money buys influence

1 and legislation is self-serving), then the threshold for redistribution may not be )(0) 2 , but

1 may be higher: i.e., 2 [ . In Parts Two and Three, the relation between the proportion of poor

and the effects on redistribution will be more closely examined. The important point to note is

wp that ! 0 . That is, no matter the bias, as inequality increases, the likelihood of redistribution w'

increases. Note that this analysis could be realistically extended by adding a middle class. If the

middle class’s income were marginal with respect to consumption, then the threshold for

redistribution would be even higher since a proportion of the middle class would see their level

of income decline even with the transfer.

If we note that any redistribution could entail some deadweight loss, this conclusion is reinforced. Suppose that redistribution requires that available resources y are reduced to

yeB where B>0. Then

'BB2 /2 ' p )()() ) (1.41) ''2 ,

wp and is even more positive. w'

Thus one would expect that the empirical record would show that more unequal

countries distribute more. Although there is support for the notion that inequality hampers

growth (see Persson and Tabellini, 1991; Alesina and Rodick, 1994, and the chart below from

80 Rodrik, 1999; work by Benabou, 1996; Keefer and Knack, 1995, Lindert, 1996, and Perotti, 1992,

1994, 1996) all show no correlation between the share of income of the median voter and government transfers as a fraction of GDP. Several reasons for this are developed below.

Figure 15. Growth versus inequality (Rodrik, 1999).

Suppose that the model now allows for a net gain as a result of distribution and agents

achieve an increased efficiency so that they can consume yeB (for example, if incomplete financial markets which limit access to credit are repaired, or if the tax revenues are used to subsidize public education, there will be net gains). Now the fraction of people who support redistribution is higher as

BB'2 /2 ' p )()() ) (1.42) ''2 .

81 Looking at equation 1.41, we can see that the two effects reinforce each other so that at low levels of ' almost no support for redistribution exists and that this proportion will rise monotonically with an increase in ' . In equation 1.42, however, the effects are opposite. Thus

B ' at low levels of ' , p is very high. But as inequality increases, () first gets smaller as the ' 2 proportion of those who will lose from redistribution increases (the left term falls faster than the right term rises) and then, as the number of poor grows large, the right term dominates.

The pattern is non-monotonic. Thus, if a society begins with a large enough wealth disparity to be at a point below the threshold proportion, there will never be support from the voters for redistribution, and disparities will continue into the next generation. If, however, the initial condition is the same as is in the section above, then low inequality will allow political support for policies that promote efficiency (perhaps education subsidies24), and disparities may not

grow. (Of course, at low deltas the poor have very little political voice.) Eventually the

preponderant proportion of poor will cause strong support for redistribution. Note that the

addition of a middle class will raise the threshold proportion and widen the span of non-

support.

However, more recent research (Krugman, 2002) suggests that the middle class,

suffering from a form of wealth illusion, may actually believe that they are soon to join the ranks

of the wealthy and thus tend to resist redistribution schemes. The hypothesis appears

reasonable and helps to explain, in the absence of the prospect that elected officials do not vote

the voice of the electorate, why the top of the income distributions continues to gain at the

expense of all the others. A strong middle class is good for an economy (see the chart below).

However, the reality of recent history has worked against the maintenance of that outcome.

24 "A major commitment to mass education is freque ntly symptomatic of a major shift in political power and associated ideology in a direction conductive to a greater upward mobility for a wider segment of the population" (Easterlin, 1981, p. 14).

Figure 16. Per capita growth versus diversity (Easterly, 2000).

Thus we see that even in a democracy and even with obvious net gains from redistribution, there may not be support for a policy change towards income redistribution.

The next part of this section will develop a model that brings into account several methods by which the poor can affect redistribution.

A Basic Model of Inequality and Revolution

The economy is now more fully described in a non-overlapping-generations model in which generations can bequest an endowment on succeeding generations based upon accumulation during lifetime. The model is also simplified by ignoring (for now) both the case in which efficiency gains occur and the stochastic nature of income distribution. Each agent lives one period and has one offspring. As noted above, there are elite (rich) and non-elite (poor)

1 with proportions 1 O and O where O ! 2 . Superscripts r and p will be used for rich and poor.

We will have a composite good, y , with price one and an asset that embodies physical and

83 human capital, h . Prior to time zero, the economy is in steady state and at time zero we have

rp hh00!!1.

We will assume that production is linear in capital and that physical capital is fixed so that only changes in human capital will change output. Labor is fixed at one. Output is described by YAH where H is the quantity of human capital. Note that Hhdi i which tt t tt³

rp in our simple case is hhtt . We will also assume perfect competition in which the market for

human capital is undistorted so that wages per unit of human capital (before taxes) are equal to

wAt .

We will assume that agents' utility is a function of two components: consumption, ct ,

and the ability to bequeath an endowment upon the succeeding generation, et1 . That is, utility

iii for agent i=poor or rich is uce(,tt1 ). Poor agents are assumed never to be satiated by their

p consumption ct if below some level of consumption, cˆt . Thus, although poor agents may not

be at a subsistence level, if they are below the desired consumption level benchmark, they will

allocate all of their income to consumption. (In a later part of this section there will be a

derivation of another component of the poor agent's view of income and consumption. This

component, the poor agents' political utility, can create a zealotry that acts as a scaling

mechanism in the accounting used in the decision making process that is used in the concluding

part of this section.) Thus, if agents allocate 1J to consumption and J to their bequest, then

p J [0,1) for the poor will depend on the gap ()ccˆ p . The rich will always be above the tt C

consumption benchmark and will consume at least cˆt . At some level of income greater than

yˆ p , poor agents will begin to save and J will be greater than zero. This way of envisioning

consumption creates the potential for a persistence of non-endowments even as mean income

84 rises. Furthermore, as we will investigate more fully later, if cˆt1 changes, then savings in the subsequent generation may be reabsorbed (or enhanced) and dissatisfaction can be augmented.

Utility can be represented as

uceiii( , ) (1JJ ) ln ci ln e i for irp , and ei !1 (1.43) tt11t t t1 .

Note that under this specification the minimum savings (education) bequest is one. Also note

that until yˆ p is reached, the poor agent will leave nothing to the offspring. If I set the minimum human capital to unity, then the offspring will have

hZeii max{1; ( )E } where Z !1 and 01 E (1.44) tt11 .

Thus, if over time no new bequeaths are given in subsequent generations, human capital will

depreciate and converge back to the minimum of one.

If we set the agent's budget constraint as

ceiid y i (1.45) tt1 t,

i i where yt is the after-tax income of household i , we see that yt is equal to the product of the price (wage) of one unit of human capital times the level of human capital the agent has, all reduced by the tax rate on income, plus a transfer the agent receives from the state:

iii ywhTttttt (1W ) (1.46)

Thus the agent will wish to

max uc(,ii e ) S.T. equations (1.45) and (1.46). (1.47) ii tt1 cett, 1

85 We also require that

eyii J if J y i !1, and ei 0 if J y i d1 tt1 t t1 t ,

which requires that if the agent's after-tax income is below one, they will consume all of it.

The government is controlled by the elite at time zero, and they set the tax rate.

i Furthermore, the distribution of Tt is uniform and thus is Tt . The government is constrained by

TAH W (1.48) ttt.

The agents in this economy can apply their efforts to either the production process

using A or to a non-market and untaxed process B . (Among other things, this prevents a

100% tax rate as we will show in the next paragraph.) We will impose the restriction that

i J A 1 so that without subsidy, an agent with ht 1 will be unable to bequest anything to the offspring since there is no residual after consumption. We will also impose that ZA()J E ! 1.

This says that when accumulation does take place, some steady state at which hss !1 can be

reached. This allows the rich to accumulate in the absence of taxation and transfer (and later,

as we will show, in the absence of a diversion of capital into guard labor) since there is always a

residual.

If we inspect the ith agent's tax preference, we see that the agent will recognize that by taxing income he/she will be taxing him/herselves. The agent will also get a return from the aggregate transfer. The agent will want to gain the largest benefit, and this can be represented as

max (1W tt ) AT (1.49)

86 where from (1.48) we know that TAHttt W . The optimal tax rate will depend on the

r p relationship between the levels of average aggregate human capital, ht and ht , and the

relationship of the market to non-market production processes, A and B . Clearly, since

r r hHtt! the rich will always choose W t 0 since, without accounting for efficiency gains (as discussed in Part One of this section), the rich will never choose to move to a lower level of welfare. For the poor, however, the problem is not as straightforward. If some agents do not

p participate in the market production (the taxed) process, then a choice of W t 1 will yield a lower benefit than some lower level of tax. The poor agent wishes to find the inflection point on

AB the Laffer curve. In our simple case that point will be W p . Thus if no agents use B t A technology then a tax rate of 100%, i.e., a compete pooling of resources, is optimal for the poor.

Thus the rich will not wish to be taxed, and the poor will. If there is not democracy, a redistribution may or may not take place depending on the nature of the elite’s relationship with the members of society. Also, the elite’s vision regarding the effect of policy on future generations of elite will also play a role in the current decision-making process. Even if there is democracy, as was shown in section above, no redistribution or sub-optimal redistribution may take place.

The poor also possess a technology for civil unrest (revolution), 5(,GF ) where

P()! 0, G ! 0 , and F ! 0 . 5(,GF ) is a function of the level of coordination (organization)

that the poor possess, G , and a parameter the measures zealotry, F .

We will assume that coordination is a function of the level of development communications infrastructure. As agents become more able to communicate, they are able to better coordinate their efforts. Recent history has been a chronicle of rapidly enhanced

87 communications infrastructure. Both the ease and speed of transmitting information in many forms has rapidly increased the ability of the disenfranchised to work together. Witness simply the proliferation of websites operated by non-state actors with violent intents. In this model, as better communication and thus coordination is developed, then G goes from less than one to greater than one.

Zealotry is a function of the change over time of the relationship between the rich and poor agents’ incomes and consumption patterns. Intuitively, if the relationship is deteriorating

(i.e., the gap between desired and actual consumption is increasing) over time, then the poor agents will be more willing to engage in civil unrest. We will develop this parameter by considering our economy's two types of people: type R and type P (rich and poor). Now suppose that at time zero that the rich and the poor have similar endowments. Also, for the moment, assume that the future incomes of P are strongly linked to the fortunes of R but that the current incomes of R are independent of P. Furthermore, assume that the level of contentedness that the type P's have with the way in which the economy is moving is such that the political utility (shown as U P or U R ) of P is determined by their own current income,

YtP (), by the current income of the type R's, YtR (), and by their own expected future income,

f eYtdtEtUtP() P (). Thus, UUYYEPPRP (,, ). Obviously both U ! 0 and U ! 0 . The ³ 1 3 1

wwUEPP partial on the middle term is UUU . (For notational cleanliness, the time 22wwYYRR3 arguments are left off.) The left-side term reflects the P agent's pleasure (dissatisfaction) at the gain (loss) of the R agent. The right-side term reflects the P agent's concern for the R agent's income as a predictor of his/her future income.

88 wE P Both the partials U and may be positive or negative depending on history. If 2 wY R

increases for the rich have resulted in real increases in income for the poor, then the overall P

political utility will improve as Y R increases.

Suppose now that as time passes, R’s income improves at a growth rate g and P

improves at a growth rate l (the letter “ell”). Furthermore, suppose that these increases for R require that consumption increases. As time passes and the P agents' real incomes decline, P agents consume (or wish to consume) a larger and larger portion of their income. Over time the gap between desired and actual consumption opens. We can represent these events as follows:

Suppose that P's political utility function is log linear so that

PPR P P R P UYYE( , , ) DJ ln Y+ ln Y ln E. (1.50)

(Note that the “H” parameter can be thought of as the degree of humanitarianism that the poor

exhibit toward the rich and reflects the positive or negative potential for this aspect of political

utility.)

Also, the expected future income is

1KK EYPP ªºªº Y Rln E P (1KK ) YY PR (1.51) ¬¼¬¼ .

(Note that K is the weight that the poor give to the way in which the income level of the rich influences theirs.) Combining terms we can represent Poor's political utility as a function of Y P ,

Y R , and t .

UYtYttPP (), R (), (DJ (1 K )lnYtP () + (JK )ln YtR () (1.52)

89 At time zero (recall we begin with identical endowments in this section)

PR YYY(0) (0) , (1.53)

and R's income grows at a constant rate g while P's grows at rate l :

Plt P Rgt Yt() Ye and where l 0 so that Yt() Y ; Yt() Ye. (1.54)

Now suppose that Kc 0 if gl!0 ; that is, over time, P's expectations for enhanced well

being as a result of R's good fortunes declines if the gap between their income and consumption

is increasing. Imagine that the function is

ht K()te K where hgl . (1.55)

We see that as h becomes a larger negative number (that is as h gets larger or the difference between g and l gets larger), the weight K()t that the poor agents assign to the rich’s income growth with respect to theirs declines.

Using (1.54), and (1.55) to rewrite (1.52), we see that the poor agent's political utility at time t is

Phtht U() t ln Y (DJDJK$+ )lt ( (1 e )) gt ( JK e ). (1.56)

Taking the derivative with respect to t, we have the differential equation

x UtPh()((1)()()() lDJ K et lthe JKhth + g JK e th gthe JK t (1.57)

with the initial condition of

x P Ul(0) (D+ J JK ) g ( JK ) . (1.58)

90 Thus political utility is positive at time zero as long as +JK !0 . But can this situation

persist?

Note that a positive + indicates that the poor agent is pleased with the rich agent's income growth, and a negative + indicates displeasure. (As noted above, think of + as a

measure of humanitarianism or altruism toward the rich.) Suppose that the poor realize that

growth in the rich's income only widens the gap between their desired consumption level and

wC p x their actual consumption level. Thus, as C p is increasing, (i.e., the gap between desired wt and actual consumption for the poor is growing), at some point the sign of + becomes

w+ negative. In other words, the poor agents use history to set the sign on + , and x 0 . w C p

Finding the solution for the differential equation is unnecessary to reach a conclusion. If

we simply go to the limit, as time gets large, we see that if gl! then limK (t ) 0 and thus tof

that

wU p lg()D ++ (1.59) wt which, if l is small, zero (or negative!), and + is negative, shows that the poor’s political utility

is decreasing with time. Note that if l is positive but smaller than g, and D is large enough, political utility may not be decreasing. In the context of this model that would suggest that the

wU p poor are content with their falling income. If is negative, then the poor agents see that in wt real terms that they are not only going nowhere; they are being left behind. So as t gets larger,

P's political utility declines toward limUtP ( ) f; that is, the poor agent becomes infinitely tof

91 miserable. Note that if the poor are made better off by the rich agent's gains enough to begin closing the gap, and thus that gl 0 and Kc ! 0 , then they share in the asymptotic infinite

happiness of the rich as t of (the concept of infinite happiness is looked at in detail in

Chapters Two and Three). If we assume that the poor agents are backward-looking in determining their current political utility, then history really does matter, and utility is not

"expected" in the sense of rational expectations but is expected in that only current and past actions, not promises of future changes, mean anything to the poor agents.

We can now specify the explicit form for the zealotry parameter:

P 2 F 1arctan(()() Ut S (1.60) so that F goes to either zero or two as political utility goes to rf . Thus, F is a function of the change in the gap in income (and thus consumption) between rich and poor. It should be noted that the term “zealotry” as used herein does not imply a connection to a religious cult, nor does it imply irrationality. The term as used in this model is an embodiment of a rational response to growing inequality.

Suppose that the poor agents’ political utility is declining and they consider revolt. In the process of revolt, some proportion of the economy's capital,1\ , 01 \ ,will be destroyed. The size of \ , the leftovers after conflict, is inversely related to the resources that the rich apply to guard labor and guard capital (armies, police, security efforts, security perimeters, jails); that is, if bigger armies and better defenses are created, it will require that a higher level of destruction is necessary (smaller leftovers) to accomplish revolt. Suppose that

1 G()Z , where 01 Z measures the proportion of wealth allocated to guard labor with \

92 Gc ! 0 . Resources applied to guard labor and capital, however, reduce resources available for accumulation and bequests. We can rewrite equation (1.44) as

irE hZAhtt1 max{1; (JZ ) } . (1.61)

Thus, if Z increases over time, then the rich will reduce consumption and/or bequests eventually to zero, will lose all accumulated wealth, and will become identical to the poor. In this case the guard labor accumulates the economy's wealth and power.

We will lay out a sequence of timing below which will allow a decision process by which the poor will choose not to revolt in the first place or, if revolt is chosen, they will win. If a revolt happens, then after the overthrow, the poor will gain all the remains, and the rich will have nothing. Thus after the revolution each poor agent's share of output will be

AH\ t (1.62) O .

So by this specification, if the current income of the poor members of the society is less than

(1.62), then all poor agents will be willing to participate in an overthrow of the government.

Finally we specify the form of the revolution function. Assume that the function is

based on zeolotry (which is based on the poor’s political utility) and is augmented by the level of

communications infrastructure. That is, 5(,GF ) FG . Thus for a given level of zealotry,

revolution is more likely as communication infrastructure improves. This makes more intuitive

sense if we allow that, with poor communication, a higher level of zealotry is needed to reach a

given level of revolution technology. As will be more fully developed in the last part of this

section, because we assume that the rich know the level of the threat, it follows that an

economy with more advance communication monitoring tools will respond more rapidly to a

93 growing threat of revolution, P() , and thus that revolution is less likely in a more developed

country.

In order to analyze the model developed above, a stylized sequence of events is defined.

The sequence of events in any time t are as follows:

1. The bequests are received.

2. The elite decide whether or not to allow the poor to vote democratically. We

assume that if given the right to vote, all of the poor will vote.

3. The poor decide whether or not to revolt. If there is no revolution then:

4. A decision is made with regard to the tax rate by either the rich agent if there is

no democracy or the median poor agent if there is.

5. Capital is allocated between A and B processes.

6. Capital receives its wage.

7. Consumption and savings decisions are made.

This sequence disallows the potential of promises not being kept. Note that the elite cannot

avoid a revolution simply by setting a favorable tax rate. Also note that once democracy is

started, it becomes permanent.

Autocracy and Democracy

In all of the cases below, the elite will begin in power and will be able to accumulate at

rr 1 time zero. That is, hhss !!0 ()J A. In other words, the rich always begin with an endowment such that the level of capital at time zero is less than the steady state level (thus growth will occur) and is greater than the share of the wage given to the succeeding generation; thus assuring that a residual will exist.

94 (Benabou, 1996, develops a more general specification for intertemporal utility using a stochastic model to determine income distribution, a specification for political power gained from wealth, and progressive taxes. Although at very low levels of inequality the conclusions are different due to the U-shaped nature of the welfare function, at moderate to higher levels, the dynamics he develops are similar to the basic model outlined above and further developed below.)

In order for revolt to occur, what the poor agents get with revolution must be greater than what the poor agents get without revolution. Also, all of the agents scale the after-conflict value of the economy with the degree of revolution technology. That is, if F G !1, then the

poor agents will be more likely to revolt given the same after-conflict value. Conversely, if

F G 1, then revolt becomes less likely. Thus

rp p ªºAhh\O[(1 )tt O ] G Aht ! «» F (1.63) O ¬¼, which simplifies to

hr O\F(1 G ) t d (1.64) h p \FG (1 O ) t ,

which must be false if revolt is to occur.

Note that all else held constant, the higher the proportion of poor to rich (i.e., the

greater is O ), the less likely a revolt since a small proportion of rich provides a smaller pie to divide up after the revolt. Note also that as \ , the leftover from conflict, decreases (that is as the stakes of conflict rise due to larger allocations of wealth by the rich toward armies, etc. through an increasing G()Z ), all else held constant, the threat of revolution lessens. Finally

95 note that an increase in zealotry (enhanced or degraded by better or poorer communication infrastructure) increases the likelihood of revolt.

p 1 p 1 Two possibilities exist: hA0 ()J or hA0 ! ()J . That is, either the poor are stuck due to initial levels of human capital and technological skills that are below the threshold, or they are not. In our simple economy, being stuck is the result of a harsh dictatorship. The alternative, in which the poor are able to increase their human capital, is the result of a benevolent dictatorship.

p 1 Under the first condition, hA0 ()J , if there were no revolt, the poor would have

pp rrEEr hhtt1 1. The rich would have hZett1 ( (ZJZ )) Z (( ) Aht ) . The unique steady state solution for the rich is given by

1 hAZ ((JZ ) )E 1E (1.65) ss ,

which, if Z is small and fixed in time, reveals that hss !1. If we compare the income of the

rr yAhttr rich and the poor, we see that p ht . Since the initial state is one and steady state is yAt

dyr greater than one, over time dhr ! 0 . Thus, t dhr !0 and we see that inequality will t dy p t t , increase over time to the steady state.

The poor will revolt at some point in time if

O\F(1 G ) h A ! (1.66) ss \FG (1 O ) where the superscript denotes autocracy. The rich, however, can increase the value of the right hand side of (1.66) by decreasing \ (increasing Z ) . If the decrease is a one-time change, the

96 steady state level will be lower. If, however, over time as F G increases and the rich respond by decreasing \ (which means that Z increases), at some point, the assets accumulated by the

rich will begin a decline as shown in Figure 17 below. It is possible that revolt will never happen

as the guard labor inherits the nation's wealth (assuming that the foundations of the nation's

economy remain intact).

Accumulation

Time

Figure 17. Accumulation over time of the rich.

If we assume that the police and army that inherits the country's wealth is a third party in this exercise, we can show that the steady state aggregate income in this economy will be

ªº1 one E 1E YAss «»(1OJZ ) (( ) Z O (1.67) ¬¼ where the superscript on Y indicates case “one” in this analysis (there are several other cases below).

We see that the rich can prolong their hold on power by keeping their ranks limited and their wealth concentrated. They can also prolong their hold by consistently counteracting the growth in zealotry (and controlling the flow of information). Less obvious is how the cultural benchmark for desired consumption may be manipulated so that even though the poor's absolute ability to consume is decreasing, the gap between the desired and actual level of

97 x p consumption is not increasing; that is, C d 0 even though accumulation is static and real

wealth is changing negatively. Note, however, that this technique for prolonging the grip on

power, like the others noted above, is only transitory. As long as the gap between the incomes

of the rich and poor is increasing, at some point in time, there will either be revolt, the economy

will be relinquished to the military, or successful tax redistribution schemes will be adopted and

the direction of change in the gap will be reversed.

p 1 rp 1 The second condition, hA0 ! ()J , where hh00!!()J A , implies that the poor are

endowed with the skills at time zero so that their wage is sufficient for a surplus. In this case

both the rich and poor will converge to the same steady state identical to (1.66). The gap

between incomes will be decreasing; thus the need for guard labor (assuming away the rest of

the world and the problem of inter-country inequality) will not materialize, and the threat of

revolution will not materialize either. Note that the steady state aggregate level of income is

1 two E 1E one YAAZYss ()J !ss (1.68)

and that the outcome here is preferable. There is an equalizing trend in income distribution and

an overall higher level of aggregate output. Of course, this case implies that all agents can consume at their desired level and still have a surplus for the subsequent generations.

Suppose that (1.64) is about to be falsified (that the elite and the poor know that in the

next period it will switch to a pro-revolt signal). The elite will, by the timing imposed on this society, allow the majority poor to vote on a tax scheme. Democracy will occur if the benefits of taxing the aggregate economy outweigh the benefits of revolt. Thus if

rp rpªºAhh\O[(1 )tt O ] G WOOAhh (1 ) tt t«» F (1.69) ¬¼O

98 holds, no revolt will occur. The rich perceive that they will either lose everything or must settle for an equal share; thus they will extend power to the poor majority.

The case of democracy is not so simple, however, since assets available for redistribution from tax are based only on the proportion of agents participating in the formal

AB economy. Recall that the tax rate will be W A , so the larger the number of agents that are

being taxed, the more the optimal tax rate falls. Now the equations for accumulation are

hZrr max{1, ((JZ )[(AB ) AhhBh ( p )r ])E tt1 A tt (1.70) hZpr max{1, ((JZ )[(AB ) AhhBh ( p )p ])E tt1 A tt.

p 1 If the poor accumulate from the initial condition hA0 ! ()J , then the need for taxation will

decline over time. That is, the poor will benefit from the effects of growth.

p 1 If hA0 ()J , then the rich will converge to the unique steady state

11 hAZAD ªºªº[((JZW ) )EE ]11EE [(JZ )(BZ )] (1.71) ss ¬¼¬¼, and the poor will be unable to accumulate. Imagine that even with the subsidy there is insufficient income to derive a surplus as the potential surplus is consumed in a quest to move toward the desired level of consumption. Thus revolt will occur at some time if

1 O\F(1 G ) ªº[(JZ )(AB )]E Z1E ! (1.72) ¬¼G \F(1 O ) .

We can see as before that if the elite increase the proportion of their assets devoted to

the creation of guard labor and guard capital, they can postpone the revolution. Note that the

higher the level of non-market production (or for the rich the higher the level of expatriation of

wealth) the less likely is revolt, all other things held constant. The intuition here suggests that,

99 for a given level of income after transfer, the poor are less likely to revolt if they are taxed less.

But it also suggests that a survival strategy for the elite in a democracy with a large poor sector is to expatriate as much wealth from the country as possible. The result is a lower aggregate value for the economy and a smaller pie to divide up after revolt, thus, in effect, providing the

same effect as raising the level of guard labor.

Note also that the aggregate income in this economy will be

ªº1 three E 1E one two YABss ()(1)(()«» OJZ Z O YYss ss (1.73) ¬¼.

This says that if there is a tax scheme but the poor cannot accumulate, then the economy converges to a lower steady state.

D Revolt many not occur if on the path to hss at some point redistribution will

become sufficient to allow inequality to decline: i.e., if

JOO[(AB! )((1 ) hD ] 1; where h p 1 (1.74) ss 0 .

That is, if the sum of the total per capita transfer plus the poor agents' human capital will at some point in time be greater than one; then after that point in time, poor agents will be able to accumulate. Assuming a small enough B (both a small non-market sector and limited wealth expatriation), if the tax scheme is implemented early enough (i.e., the elite understand and care about the long-run folly of the military option), then inequality will increase until the level of

rp hhtt is sufficient to switch the value of (1.74) to >1. Then inequality will decline, and the

economy will eventually converge to (1.68). Here we require the poor majority to know that

democracy is permanent and thus be willing to wait until the rich are rich enough to have a

100 surplus. (Obviously this case presents a host of more realistic scenarios for moving forward in time toward the switchover to accumulation for the poor.)

If the initial conditions are such that for the poor if

rp JOO[(AB! )((1 ) h00 h ] 1 (1.75) holds, then inequality will decrease. (1.75) shows that at time zero, the sum of the net transfer from the rich plus the after-tax net wage of the poor must be greater than one. If this is not true, then the economy converges to (1.73). If (1.75) is true, then the economy converges to

(1.68) .

The most favorable outcomes are clearly those in which the poor have the ability to accumulate from time zero. The most favorable is that condition under autocracy. But that autocracy requires a “good” dictator willing to optimally distribute for the long-run outcome.

Perhaps Singapore is an example of the “good” dictator case. It has experienced fast growth with declining inequality and fairly low country risks (Economist Country Statistics, 2007).

Perhaps some of the central African nations currently may be an example of the worst autocratic disasters in which the poor receive nothing yet are a large sector of the society. But, most troubling, we may consider current world events as a by-product of a rising level of perception regarding the relationship between the levels of consumption of the United States and the rest of the world. This is feeding the revolution constraint developed above.

The theory suggests that in all cases, it appears that the economic mechanisms channeled through the ability of agents to consume at their desired level of consumption is the key point at which the outcomes of growth are determined. So far, this analysis has concentrated on a closed economy. Suppose now we allow trade to enter into the problem.

101 Trade and the Patterns of Growth

This first part of this section’s analysis will focus on the wage response of a typical

worker in a world of increasing capital mobility. The premise is that if there are positive

movements in the wage but at the cost of significantly increased volatility, then the poor agent's

utility may decline. The second part will inspect the effects transportation costs and labor

mobility (or the lack thereof) on income distribution.

Using the Heckscher-Ohlin trade model as a foundation, it can be shown that the

"demand for any factor (labor for example), becomes more elastic when other factors (capital

for example) can respond to changes in the economic environment with greater ease (by

moving offshore for example)" (Rodrik, 1997, p. 17). Suppose that the initial labor market

equilibrium is at some point A. Suppose that there is a change in labor standards in the home

country (like raising workplace standards). From the point of view of the employer this is like a

tax on employment, and the labor supply schedule shifts the amount of the vertically. Both the

worker and the employer must bear some of the cost of the change. In a closed economy wages fall. In an open economy the wages fall farther, and the reduction in employment is larger.

Thus in an open economy higher employment costs (perhaps higher safety standards) cost the

worker more in both wages and jobs. If footloose capital is to be prevented from leaving the

country, the workers must reject the higher standards. Of course, nations can purchase higher

standards through taxes or can actively control the exchange rate to nullify any competitiveness.

But, particularly in the context of the model presented above, these options seem unlikely if the

political power of workers is low relative to that of employers. Depending upon the regime, the

workers (i.e., poor) must suffer the consequences or be buffered by a policy of redistribution.

Following in the logic above, it is likely that opening a country to trade exposes the less

skilled to increased uncertainty. This is more obvious if a technology shock is introduced. The

102 labor demand schedule shifts, and, for the open economy, for a given shift, wages and jobs change more. Openness magnifies the effects on worker’s wages and jobs (Jean, 2000).

Using a model developed by Rodrik ( 1997), we can show below that an increase in openness makes domestic capital more responsive to changes in international prices and also magnifies the amplitude of fluctuations in real wages at home. The poor majority may or may not experience a drop in wages but will be more exposed to risk. If the government wants to maintain the expected utility of the workers to the reservation level, they can increase taxes and thus increase transfers. If the government does not act, the process developed in the sections above unfolds with the added negative effects of real wage risk beyond the workers’ control. If the government does act, as long as the compensation is not too great and capital is not too mobile, the negative effects can be nullified. Beyond a point, however, the flight of capital and the erosion of real wages doubly accelerate the growth of inequality.

Suppose that the export sector's production function is fkl(,)with the usual well

behaved first and second order conditions (i.e., fffk!!0, l 0, kk 0, ff ll 0, kl ! 0 ). Also let

the fixed labor endowment of the economy be set at unity so that fk()fully describes the

production function. The domestic fixed capital stock is k0 which is not the same as the total capital used at home since capital can move into and out of the country. If p is the relative price of the export, then

rpfk k ()W (1.76)

* rr O() k0 k (1.77)

wpfk l () (1.78)

103 The domestic return to capital, r is the marginal value product of capital minus the domestic tax.

The international trade in capital requires that that rate equal the international return r* minus the cost of moving capital abroad (that is, the degree of globalization, which increases as O falls). For example, a capital outflow that lowers home stocks would lower the rate of return to domestic capitalists to (1.77). Note that if globalization were such that capital mobility were costless, then r= r*. The last equation is simply the wage rate equaling the value of the marginal product of labor.

Using these three equations to describe the system, we can show that the equilibrium level of capital employed at home is a function of kp(,,)WO. Figure 18 below shows that the higher the degree of globalization, the flatter the upward sloping line (equation 1.77) and that with fluctuations in price, the entire downward sloping line (equation 1.76) shifts as the domestic return to capital for a given k changes.

Figure 18. Capital to return on capital based on capital mobility.

Suppose that initially, kp(,,)WO k0 . Setting (1.76) and (1.77) equal and totally

dk kk 0 dw differentiating, . Using (1.78) to get pflk , we can see also that dpfOOkk dk

104 dw kk pf 0 . Both are zero if kk and changes in the degree of globalization would kl 0 , dpfOOkk

have no effect. But now suppose p drops. As the diagram shows, the higher the degree of

dk f globalization, the bigger the change in the domestic capital stock. That is, k !0 , dpO pfkk and it is decreasing with O . We can also imagine that the poor become more anxious as the value of the marginal product of labor falls. And the more globally free capital is, the more

dw fpff responsive is the wage change to a change in relative prices: lkkk!0 which is dpO pf kk ,

also decreasing with O .

Recalling from the model regarding revolution above that taxes are the source stable

outcomes for growing nations, we can see that globalization can confound this solution if a

source of tax revenue is from a tax on capital. (This can be generalized to expatriated non-taxed

income, the B technology from earlier.) Suppose that the unskilled poor worker has an income

Iwtk . (1.79)

Then income fluctuates not only due to changes in wages, but also with changes in the tax base

as capital chases the higher returns. Differentiating (1.79) and holding p constant, we have

dI dw dk k W (1.80) dddWWW.

Substituting in from total differentials of (1.76), (1.77), and (1.78), we have

dI W pf k kl (1.81) dpfWO kl .

105 This is increasing with O , suggesting that a tax on capital works better when global mobility is

dI limited. But more interesting is that as O gets small, becomes unambiguously negative. dW

f (Set O 0 , and derive k kl ) This suggests that an increase in the tax on capital will f kk .

actually reduce workers’ incomes when capital is more globally mobile.

So generally, more openness exposes the workers to increased income volatility and also reduces the government's ability to use fiscal policy to ameliorate the effects of differing factor intensities vis-à-vis endowments on wage changes.

Work by Diego Puga (1996) brings an added dimension into the discussion of the ways in which globalization will create changes within nations. His work, following on Krugmam and

Venables (1995), develops a model in which higher or lower transportation costs create growth patterns in which either firms agglomerate or spread out. For the purpose of this section, we will review the conclusions of Puga's work as they will impact how global integration will affect the income distribution over time. This consideration will be revisited in Chapter Two.

As globalization opens business channels between nations, the ability of workers to move both within nation and across boundaries in response to income differentials is important to the way in which growth affects the nation. The relationships between firms, workers/consumers, and intermediate markets generate forces that will tend to draw labor and firms into clusters and potentially separate regions as well as nations. In general, firms will spread out across regions to meet final consumer demand if transport costs are high and labor is immobile and will tend to agglomerate as transport costs fall and labor is more willing to move.

If the relationship of transport costs to prices is above some critical value, firms tend to set up production close to their suppliers and workers. Workers will prefer to live close to the markets

106 where more goods are available locally. Thus cost linkages are developed. Also, firms tend to go where there are relatively many firms and workers demanding their output, and workers

tend to migrate to where more firms demand their labor. Therefore demand linkages evolve.

Cost and demand linkages create externalities that tend to cause firms and workers to

agglomerate. Puga (1996) develops a model that tracks the shift from spread-out to

agglomerated industry as a function of transport costs.

Interestingly, he finds that the point at which agglomeration is triggered is different

depending upon whether or not workers can move across regions and boundaries. More

relevant to the focus of this research, he finds that the evolution of industrial location and

wages is different if workers are more willing to migrate. The agglomeration of industry tends

to raise local wages in locations with relatively many firms. If higher wages lead workers to

relocate towards more industrialized regions, agglomeration intensifies, and wage differentials

decline. If on the other hand, workers cannot move across regions or boundaries, wage

differentials persist, and firms become increasingly sensitive to wage differentials as

transportation costs decline. In this case industry will tend to spread out.

What is predicted by his analysis that is pertinent to this paper is a tendency for

inequalities to decline between some countries but to increase within all countries as global

networks increase the efficiency of the movement of goods. The analysis suggests in the

aggregate, some peripheral nations will converge with the developed core, but others will keep

falling behind. Chapter Two presents data that confirm this.

Furthermore, it does not bode well for the lower classes of any nation, but particularly the poor of the developed nations, for whom, without a social policy of redistribution that preserves the globally competitive nature of the markets for capital and labor, the change is

107 most stark. Finally, his dynamic analysis suggests that during intermediate stages of integration, wage disparities will increase even for regions and nations that will later improve.

Conclusion

This section has developed an analysis in which the dissatisfaction of the poor is integral to the stability of relationships with a nation and among nations. If development occurs such that poverty and the size of the gap between rich and poor increase, then at some point in time, the nation will experience crisis. Furthermore, we have shown that the tendency for global development to allow for increased capital mobility and for increased mobility of the inputs and outputs of production, in most cases, brings the crisis point closer to the present. We have also shown that responding to increasing social unrest with increased guard labor is not a sustainable solution in the long-run. We have also briefly outlined how redistribution schemes, although potentially able to cure the problem, are also vulnerable to the effects of freely mobile resources and may even be counterproductive in the case of taxes on capital. In fact, "a source of potentially serious problems for the international trade regime is the growing inability of governments at home to sustain their part of the social compact on which postwar international liberalization has hinged" (Ruggie, 1994, qtd. in Rodrik, 1997).

We have seen that, placed within the framework of growth and inequality developed above, developed nations, it would appear, will experience a stronger negative effect on civil stability as the middle and lower classes begin to compete with global labor willing to relocate into industrial concentration zones; the rise of a sort of migrant industrial labor force following capital and production into the zones of highest return. As noted above, a tax on capital will not work to solve the problem. Perhaps higher income taxes would solve the problem, but that schema would require that the elite agree to a much more skewed progressiveness in the tax

108 framework and a willingness to take on a national, even an international, morality regarding accumulation in the face of poverty.

Given the obvious rise in zealotry on the world stage, we need to concern ourselves with understanding the hurdle we face. But, as Lummis (1991, p.58) suggests, "Development does not bring people freedom from want; rather it operates to keep people in a state of perpetual domination by want." So the long-run socially stable solution may be considerably more radical than laws limiting capital mobility or taxing income. If democracy is the rational outcome in this section’s model (that is, the rich know that the next period, given no change in guard labor, will transgress the revolution constraint, and thus they know that a democratically determined redistribution is the only alternative), then perhaps the supra-rational outcome is found in the problem of reconciling the actual and desired levels of consumption. Without a black hole utility function driving an ever-expanding frontier of the per capita demand (and thus creating perpetual dissatisfaction), a concept of common wealth (to replace wealth) could transform social progress from the history we know (cycles of warfare and détente) to one of trust. If we are to leap the hurdle, we must change the foundations the system.

As we have seen, the assumptions that lead to a stable outcome include the possibility of revolt, the possibility of military dictatorship, or the possibility of convergence into a commonwealth either with democracy or without. The path that becomes our history may be a blend of all of the above.

In the next chapter of this work the heart of this chapter’s gloom (unequal per capita consumption growth) will be shown to be an inevitable outcome of growth under free-market capitalism if the parameters that govern decision making remain as they are today.

109

CHAPTER TWO

MODERN GROWTH THEORY: A CLOSE LOOK AT THE THE DETAILS AND THE LONG-RUN

PREDICTIONS – CLASSIC VIEWS EXPLORED AND MODIFIED WITH NON-TRADITIONAL TWISTS

“Well it’s a matter of continuity. Most people’s lives have ups and downs that are

gradual, a sinuous curve with first derivatives at every point. They’re the ones who never

get struck by lightning. No real idea of cataclysm at all. But the ones who do get hit

experience a singular point, a discontinuity in the curve of life – do you know what the

time rate of change is at the cusp? Infinity, that’s what! And right across the point it’s

minus infinity! How’s that for sudden change, eh?” (Pynchon, 1973, p. 664)).

Maxwell’s demon, Smoluchowski’s demon, Gödel’s demon, and Ehrenfest’s demon all do

not work. They are each blocked by a censor. Further demons and their corresponding

censors deserve to be uncovered. For to recognize and understand limitations is even

more important that to be completely free of them” (Rössler, 1998, p. 53)).

Introduction

The history of economic thought and, in particular, the history of modern growth theory is a dynamic process. For a long time a regime exists, and the world is supposed to run that way while great effort is made to explain the unexplained contradictions. Then the discipline is advanced, and what was once a contradiction becomes a normal and expected outcome. We

110 engage in research because we fully expect that what is today a mystery will be tomorrow just another expected outcome. Of course, the reality we want to understand is a moving target with a complex process at the core generating fundamental change. We, at the frontier, try to get a grip on something stable, even as our efforts to get a grip and the knowledge we acquire change the core and make certainty a myth. But, as this work posits, there is a certainty in the very-long-run: there will be an end to growth.

The quest to understand economic growth has focused great minds; the path of understanding that leads us to today’s wisdom provides great insight into the embedded assumptions that mask the fallacy of endless growth. Endless growth will end. This chapter will show how, within modern growth theories, hiding even from those that have developed the theory are the hidden harbingers of that end.

The simplest way to envision the core of the problem is to look at exponential growth.

If we assume a constant growth rate of about 3% per year going forward, the chart below with

data and a forecast for England suggests that we can expect to be very well off in real terms by

the end of this century:

111 source: Gregory Clark Real Income Per Capita 2800 2700 2600 2500 2400 2300 1870 = 100 2200 2100 2000 1900 1800 1700 1600 1500 1400 1300 1200 1100 1000 900 800 700 600 500 400 300 200 100 0 1240-9 1260-9 1280-9 1300-9 1320-9 1340-9 1360-9 1380-9 1400-9 1420-9 1440-9 1460-9 1480-9 1500-9 1520-9 1540-9 1560-9 1580-9 1600-9 1620-9 1640-9 1660-9 1680-9 1700-9 1720-9 1740-9 1760-9 1780-9 1800-9 1820-9 1840-9 1860-9 1880-9 1900-9 1920-9 1940-9 1960-9 1980-9 2000-9 2020-9 2040-9 2060-9 2080-9 2100-9

Figure 19. Real income per capita 1200-2100 (Clark, 2007).

Of course we cannot be sure that we will have continuous 3% per year growth for the next century or so. But we can be certain in saying that in the current economic paradigm, if growth were to go to zero (or below!) for an extended time, we would expect exceedingly difficult times. Without any need for further evidence (there is much below), we can see that

continuous growth is necessary for the dominant world system to remain healthy. “Healthy” is

a term that in the previous sentence is determined from within a framework that is sustaining

the core assumptions of accumulation. Healthy from within this framework, as we will see,

requires a positive return on investment. . .period!

But can that framework be sustained? The typical argument for the limits to growth is

based on the ecological constraints that are presented by a finite carrying capacity of the planet

(Daly, Meadows, and others). And indeed at the heart of this chapter’s thesis is the expectation

that exponential growth will lead to carrying capacity constraints in terms of an absolute limit to

the number of people that can exist on the planet. In other words, population growth must

stabilize at some point in the future. Already zero (or even negative) population growth

112 concerns have begun to be perceived as serious future issues (although not in the terms that his chapter will describe).

Figure 20. Population of Japan (National Institute of Population and Social Security Research,

2006).

The sources of economic growth, as we have seen in the previous chapter, are simply

population growth and the growth of productivity. If population growth reaches a limit, then the only source of growth will be productivity growth. Although more rigorously shown in the section in this chapter discussing the Solow model, we can, in words also, illustrate the fallacy of endless productivity growth. If we assume a stable population and continuous productivity growth, the implications are for ever-increasing per capita income (just as we have now as illustrated in Figure 19). However, even if we assume that the carrying capacity of the planet is not violated in terms of resource needs and waste accumulation (more on this below as these concerns are indeed limiting), the implications are for the accumulation and consumption of

113 more and more goods and services per capita (doubling every 36 years at a 2% annual rate of growth). At some point a limit to real per capita consumption is reached. So just as population growth will stabilize, per capita consumption will also stabilize. At that point, as productivity growth continues, the average person will have to work less and less (or fewer people will work the same amount) to produce the demanded goods and services. At the limit, everyone works one second a day, or only one person works!

The long-run will yield an equilibrium at which the sources of growth balance the stable

demand of a stable population: the production of goods and services will be essentially the

same every period, and the world will be in a zero growth regime. This thesis will be proven

with increasing rigor as this chapter progresses.

Most of this chapter will explore the implications of this outcome through the lens of

modern economic theory. We will take a tour that begins with Solow (1956), then explores the

evolution of successive theoretical models that takes us to current thought. At each step we will

ask basic questions regarding assumptions of the models. Where appropriate we will extend

the models to show the long-run implications that are there but are ignored by a growth

addicted system.

The limits to growth literature is well established, but the underlying concerns are

founded on ecological constraints. What is different about this work is that it stays within the

confines of economic theory, showing that even without the constraints of resource depletion,

waste accumulation, and accelerated change that the path forward will converge to zero

growth.

114 A Closer Look at Accumulation, Production, and Innovation

What is the core of the capitalist system? In three words: return on investment. The energy that drives the economic engine is the quest for profits. All the models discussed in this chapter are linked to the core metrics that define the success or failure of economic activity.

The measure of the return on investment, a ratio typically interpreted as an interest rate

(or a marginal product of capital), shows how well capital has been employed in the production of goods and services and, most importantly, the creation of more capital. The expectation of a larger demand in the future provides an incentive to invest in the expansion of the means of production and in the improvement in the skills and efficiency of human and physical capital. In all cases below, the return on investment, over the long-run, equates to the long-run growth rate of the aggregate output of the products of production. And, although apparently obvious, revenues must be greater than costs for the system to work. But, as we will see, this seemingly simple prescript has deep implications.

Growth theory, as we will see below, has evolved along a path that has, for the most part, been defined by a quest to explain the empirical record. The view can take several perspectives. In a closed system what are the determinates of growth (and thus a sustained expectation for a positive return on investment)? In an open system what are the dynamics that define the changes in relative well-being between countries, in terms of per capita’s share in the economy, over time?

The patterns of the observed historical measures of economic activity (usually centered around GDP per capita and the growth of that metric) are the motivation for seeking an explanation to the past and for seeking insights into what the future will bring and, perhaps, how to influence that future in positive ways. Of course, “positive ways” implies growth.

115 All of the models share some similarities. There are people who provide labor and own assets (including firms that produce). These people earn income and choose to consume and save some ratio of that income. There are firms that employ labor and capital to produce goods for sale to the people and to other firms. Some technology is used to transform the inputs to outputs. Finally, the consumers and producers meet in a market in which the supply and demand for outputs determines the relative value (prices) of the goods and inputs. In some cases the models discussed in detail below use utility maximizing representative agents and in other cases they abstract to generations of agents acting in aggregate. The vector by which the choices are made does not impact overarching insights of this chapter.

The transformation of inputs into goods in the economic models relies on production functions. But the use of the aggregate production function in growth theory (and in all economic theory for that matter) is not without controversy. The long history of production functions, beginning with :ŽŚĂŶŶǀŽŶdŚʒŶĞŶŝŶƚŚĞϭϵϰϬ͛Ɛ and chronicled up to the present, is nicely presented by Mishra (2007). Some of the issues that were argued by, for example

Robinson and Sraffa in the 1950’s and carried into this millennium, will be revisited in some of the sections below. But it is worth noting as a preview that Joan Robinson wrote in 1953 that

“… the production function has been a powerful instrument of miseducation (p. 81)”.

More formally, there is a fundamental inconsistency between the Inada conditions that underpin all of the modern analyses of growth and the algebraic formulation of the production function with respect to returns to scale. This is shown in the short note by Fare and Primont

(2002). Their logic was extended by Baumgärtner (2004). That extension is particularly relevant to the zero-growth outcome at the core of this work. He states in the introduction:

This paper formally explores one particular implication that the

thermodynamic law of conservation of mass, the so-called materials-balance-

116 principle, has for modeling production. It is shown that the marginal product as

well as the average product of a material resource input will be bounded from

above. This means that the usual Inada conditions (Inada 1963), when applied

to material resource inputs, can be inconsistent with a basic law of nature. This

is important since the Inada conditions are usually held to be crucial for

establishing steady state growth under scarce exhaustible resources. While the

advocates of a thermodynamic-limits-to-economic-growth perspective (e.g.

Boulding 1966; Georgescu-Roegen 1971; Daly 1977/1991) usually stress the

universal and inescapable nature of limits imposed by laws of nature, pro-

economic-growth advocates usually claim that there is plenty of scope for

getting around particular thermodynamic limits by substitution, technical

progress and ‘‘dematerialization’’ (e.g. Stiglitz 1997; Beckerman 1999; Smulders

1999). The latter therefore often conclude that, on the whole, thermodynamic

constraints are simply irrelevant for economics. (p. 308)

Essentially a part of the argument that is relevant to the zero-growth outcomes derived below is that production is a function of the combination of capital, labor, and materials, and a fraction of the input is contained in the output. This fraction can be reduced by technological progress and productivity improvement (dematerialization), but the fraction must always be greater than zero. Whatever enters the process has to come out as either output or waste.

There is therefore an upper bound to output if one acknowledges that the planet has a finite resource stock. This argument is formally presented in Baumgärtner (2004).

In the section of this chapter discussing endogenous growth models, the inconsistencies of the Inada assumptions will be used as a basis for deconstructing some of the most recent

117 growth models. The path from some of the older models to the most recent ideas has been the quest to explain what is observed.

The real world has exhibited some patterns that were codified as stylized facts by Kaldor

(1963). This list, which is recounted in most growth texts,25 has motivated researchers to extend and complicate the economic growth models so as to fit (or refute) the predictions of the models to these stylized facts. The extensions, as we will see, are based on how consumers optimize utility, how producers get better at production, and how we might have escaped from the law of diminishing returns by providing new and better goods.

But at the core of all of these simplified views of reality is the assumption or requirement that what is good is growth and what is bad is no growth. Certainly in the world today the relative differences between the wealthy and poor are large. And certainly in the world today, convergence in well-being per capita is the desired outcome over time. (Or is it?

More on that in the following pages.) This would imply that growth for the rich would be slower than growth for the poor until some idealized equality of well-being is reached.

As was discussed in Chapter One, to achieve this outcome suggests either a change in the way in which policy is made or face the consequence of revolution. Clearly, from the chart below (Clark, 2007)), we can see that convergence is in fact divergence, suggesting, given the continuous growth in inequality, that the future will not be like the past.

25 Kaldor’s facts are as follows: 1. per capita output grows over time, and its growth rate does not tend to diminish; 2. physical capital per worker grows over time; 3. the rate of return to capital is nearly constant; 4. the ration of physical capital to output is nearly constant; 5. the shares of labor and physical capital in national income are nearly constant; 6. the growth rate of output per worker differs substantially across countries.

118 Per Capita Income by Rich and Poor Sectors

Figure 21. Long view of per capita income (from data in Clark, 2007).

Interestingly, the predictions of convergence in modern growth theory can easily be discarded

using a modern extension of the simplest (and arguably seminal) theory of economic growth:

the Solow-Swan model. Indeed, the predictions of continuous endless growth can also be seen

to be fallacious within that framework as well. That discussion is next.

The Solow-Swan Model and Extensions

It is not within the scope of this work to work through the details of the derivations and proofs of the historical models. The reader can find any number of texts that provide the details.26 This section and the sections that follow will review the key components and insights and focus on those parameters that drive the growth predictions in the models.

26 See Economic Growth by Barro and Sala-i-Martin (2004) for a comprehensive review and proofs of the details of these historical models.

119 The model developed by Solow and Swan (1956) excludes markets and firms. This is the basic Robinson Crusoe scenario in which the owner of the inputs transforms these into outputs.

As such there are only two inputs to production: physical capital, K(t) and labor, L(t). As yet, the technology for transforming capital and labor into output is not explicit and is assumed fixed at a point in time. (This will be augmented later in this section.) Consistent with our view of capitalism as an engine of accumulation, the output in the Solow model is a good that can be consumed, C(t) or invested, I(t) to make new units of physical capital.27 There is no other

economy, so this system is closed.

The production of goods is simply

(ݐ), ݐ] . (2.1)ܮ ,(ݐ)ܭ]ܨ = (ݐ)ܻ

The fraction of goods that are not consumed are saved. This fraction is the savings rate, ݏ(ȉ). In this model, the savings rate is exogenous and positive but less than one. The model also assumes that capital depreciates at a constant rate ߜ >0. There is also an assumed production

.0< ܣ and 1>ן>where 0 ן1െܮןܭܣ = ܻ ,function; typically of the Cobb-Douglas form

The economy’s capital thus changes according to

(2.2) . ܭݐ) െߜ ,ܮ ,ܭ)ܨȉݏ =ܭെߜܫ = ሶܭ

In some of the models reviewed later the growth of population will be explicitly modeled along the lines discussed in Chapter One, but in the Solow-Swan model, population growth is exogenous and positive. Thus labor also grows over time. To simplify the model, the

ܮሶ growth rate of the population, ൗܮ = ݊ >0, is normalized so that at time zero there is 1 person

27 The prototypical example is farm animals. They can either be eaten or “invested” to make more animals.

120 and that person’s work intensity is also 1 and fixed (the intensity will be augmented below with

a productivity parameter). The population (and labor force) at time ݐ are described by

(ݐ) = ݁݊ݐ . (2.3)ܮ

The Solow-Sway model is reduced to per capita terms (i.e., ratios of output and capital

ܭ ܻ Thus the key .((݇)݂ = ܮwhich implies that ൗؠݕ , ܮto labor where, for example, ݇ؠ ൗ equation of the model is

݇ሶ = ݏȉ݂(݇) െ (݊ + ߜ) ȉ݇ (2.4)

The implications of the model are well known. Within the constraints of the model’s

assumptions no matter a given level of technology, savings rate, population growth rate, and

depreciation rate, the steady state growth rates of per capita output, capital, and consumption

are all zero. (This is a major shortcoming of this simple model as it does not explain growth in

per capita consumption, etc. The model does, however, predict constant absolute growth as

the population grows.) It is also easy to derive the “golden rule” savings rate. That is, the

ȉ (ݏ1െ)= כܿ savings rate that maximizes consumption. Consumption in the steady state is

then , כߜ) ȉ݇ + ݊)= (כ݇)ȉ݂ݏ Since steady state is where .[(ݏ)כ݇])݂

(2.5) .( ݏ)כെ (݊ + ߜ) ȉ݇ [(ݏ)כ݇]݂ = (ݏ)כܿ

And to maximize 2.5 for consumption, we set the derivative equal to zero and find that

Ԣ ݂ ൫݇݃݋݈݀ ൯ = ݊ + ߜ . (2.6)

121

Figure 22. The golden rule of Solow-Swan.

The implication for settling on the golden rule level of consumption is that consumers are willing to care for future generations. The dynamics of the situation in which savings are below the golden rule, ݏ1 in the illustration above, requires that consumers experience a lower level of per capita consumption in the transition to the golden rule level. The movement from

ݏ1 to ݇݃݋݈݀ requires a trade off that may or may not be consistent with observed trends in the savings rates of world (see chart below). Note that if savings are above the golden rule level, ݏ2

in the illustration, then a reduction in savings both increases current consumption and increases

the steady state consumption per capita, a natural path that does not require altruistic

tendencies.

122 The Ramsey model, reviewed in the next section, will look more closely at how

generations care about the future. One might wonder, however, if current observed trends in

the savings rates of the developed nations vis-à-vis the developing nations carries a message?

48 Savings as a % of GDP 43 source: IMF

38 Developing Asia World

33 Developed Nations

Figure 23. Savings rates (International Monetary Fund, 2007).

Letting the issue of low savings and the implications for future generations sit for a bit

(not long), let’s follow the evolution of the model so that we can understand the role of

technological progress in the production function. The unrealistic (and anti-historical since the industrial revolution as shown in the first chapter) short-run predictions of the model above in terms of constant per capita variables are resolved by augmenting the inherent diminishing returns to inputs of the production function with a labor augmenting technological progress parameter. The general characteristics of the model are very similar to that already shown except that equation 2.4 is now

(ݐ)] െ (݊ + ߜ) ȉ݇ , (2.7)ܣ ,݇]ܨȉݏ = ሶ݇

123 ሶ(ݐ) ൒ 0. Noting that effective labor is labor times its efficiency, thenܣ with the assumption that

෠ ݇ ݐ) grows at the rate ݔ (where ݔ is the rate of)ܣ ݐ)], and, noting that)ܣȉܮ]ܭ = (ݐ)ܣൗ = ݇ technological change or productivity improvement), we can plot the relationship between the exogenous “growth” parameters and the investment relationship. The chart below shows that the growth rate of capital per effective worker is proportional to the distance between the investment relationship and the “growth” parameters (sometimes referred to as the effective depreciation parameters) which, in addition to the population growth rate and depreciation, now include the growth rate of technological progress.

Figure 24. Solow-Swan steady state.

is constantly increasing, and כ݇ ,With labor augmenting technological progress, in steady state

.the per capita variables, ݇, ݕ, and ܿ all grow at the exogenous rate of technological progress

The long-run implications of this model are a reminder of the issues in the core thesis of this research: endless growth driven by population growth and technological progress

(productivity improvement). As long as the population growth rate and the technological progress growth rate have a positive value, the world will experience increasing consumption

124 per capita. (Note that the rate of convergence to the steady state is not constant but is a function of the distance between the two curves in the chart above. This outcome of the model is typically used to explain how the developed world and less developed world will eventually converge to similar per capita values. Later in this section in which we extend the Solow-Swan model we will investigate convergence more closely.) We can also see that for a given set of exogenous parameters, the golden rule consumption rate steadily increases over time at the rate of technological progress. The model explicitly shows that technological progress is the driver of per capita growth, but this implicitly requires that population growth remain constant.

If the population growth rate falls, the per capita rates increase proportionally.

Are there limits to growth in this model (notwithstanding issues of resource constraints)? Suppose population growth falls to zero, as it must at some point in the future. As long as productivity growth is positive, per capita output, consumption, and capital stock increase. Is there a limit to per capita consumption in real terms? If population is constant,

then, at the limit, each person would have to consume an infinite quantity of goods (see the

graphical representation of this in Figure 26). Simple logic says that there is a limit. How then

would a world described by this model be altered? If there is some asymptotic limit to per

capita consumption, then there is also a limit to output and capital stock per capita. In other

words, there are limits to growth strictly in economic terms as long as we accept limits to

population levels.

Also, although not explicit in the typical presentation of this model, there is an implied

interest rate for investment that is a function of the “growth” parameters if return on

investment (ROI) is defined as the ratio of money or capital gained or lost on an investment

relative to the amount of money or capital invested then in the zero growth condition, ROI is

125 zero since there is no net increase in capital stock, output, or consumption in absolute terms

(capital letter versions of the parameters).

These conditions can be illustrated with a numerical example. If we normalize ܮ to an

ܭ initial condition of 1, ݇ = ൗܮ to 4, ܣ to 1, and assume that capital’s share in the production

is .33 (using a Cobb-Douglas form of the production function) we can see what ,ן ,function happens to per capita consumption and output over time. First let’s look at the base case, in which we assume that the key parameters of the model generally represent current real-world

.aggregate conditions. That is, we will assume that ݔ =.02, ݊ =.01, ߜ =.05, and savings =.1

We can see in the chart below that real output and consumption per worker rise

exponentially:

x = 0.02 D Per Capita

n = 0.01 s = 0.1 y c G

0 0 50 100 150 200 250 Units of Time

Figure 25. Numerical example of growth in output and consumption.

With population growth set to zero, we see a similar (and slightly steeper) increase in the per

capita values:

126 x = 0.02 D Per Capita

n = 0 s = 0.1 y c G

0 0 50 100 150 200 250 Units of Time

Figure 26. Numerical example of growth in output and consumption (zero population growth).

Now suppose that at levels of per capita consumption almost 60 times higher than the

initial condition, there begins a diminishing payoff to continued sustained growth in

technological progress at ݔ =.02. Although arbitrarily picked for this example, as noted above that at the limit consumers would have to consume an infinite number of goods, there is some multiple of current per capita consumption at which satiation is reached. That is, if we believe that diminishing marginal utility in our model of consumer choice is rational, then we must assume that diminishing marginal utility to increasing per capita consumption is rational. In the

Solow-Swan model, the reaction to a diminishing demand (which is not explicit at all in this model) would be that either fewer of the fixed population works ( every member of the population works less), or the way in which inputs are converted to outputs stabilizes so that

127 labor intensity is fixed to provide full employment. In this example, we will use the latter case which, in this simple model means that the rate of growth of technological progress declines.28

For simplicity, let us have the growth rate of technological progress jump to zero. If the new time units begin at the jump, we see the following:

x = 0 D Per Capita

n = 0 s = 0.1 y c G

700

600

500

400

300

200

100

0 0 50 100 150 200 250 Units of Time

Figure 27. Numerical example of growth in output and consumption (convergence to zero

growth).

The Solow-Swan model predicts, in the long-run, a convergence to a zero growth regime

if we simply allow consumer choice to vary with time and thus have demand follow.

Furthermore, if the depreciation rate is higher or the savings rate is lower, the long-run absolute

level of consumption per worker is smaller. Eventually the savings rate will equal the

depreciation rate.29

28 In the first or second cases, the limits will never be reached since they are absurd (one person left working or everyone working one second per day!). So even in those cases, there is some bound within the production function that will stabilize output to match demand (measured as per capita consumption which cannot reach infinity due to decreasing marginal utility of per capita consumption). 29 This can be seen by setting the growth rate of per capita capital to zero and solving the equation .at the zero growth point ݏ ݐ)] െ (ݔ + ݊ + ߜ) =0for)ܣ ,݇]ܨȉݏ = ሶ݇

128 But the serious consequences of this outcome strike right at the heart of capitalism. The net change in capital investment, as shown in the chart below, converges to the depreciation rate (barely above zero). But the return on investment, shown on the second chart below, goes rapidly to zero.

Net Change in k Net Change in k 25

0 0 50 100 150 200 250

Figure 28. Numerical example of growth in output and consumption (net change in capital investment).

129 ROI ROI 9.00%

8.00%

7.00%

6.00%

5.00%

4.00%

3.00%

2.00%

1.00%

0.00% 0 50 100 150 200 250

Figure 29. Numerical example of growth in output and consumption (ROI).

The so-called AK model is another method of eliminating diminishing returns, doing so

without the need for technological progress. The key outcome of the simplest form of the

model is

(െ (ݔ + ݊ + ߜ) (2.8 ܣݏ = ߛ݇

where ߛ݇ is the per capita growth rate of capital. Even if ݔ and ݊ are zero, as long as savings are

greater than depreciation, there will be positive growth in per capita capital and thus output

(noting that the production function in the “AK” model is ܻ = ܣܭ). But, as above, the economic

limits to growth assert themselves via the absurdity of infinite consumption per capita which

drives the savings rate to equal the depreciation rate: thus, zero growth.

Several extensions of the basic AK model actually predict zero growth explicitly under

similar conditions. Using a constant elasticity of substitution production function (Arrow et al.,

130 1961) one can derive an outcome in which the growth rate of per capita capital is negative for all levels of per capita capital all the way to a zero growth rate. As above, this outcome depends on the savings rate being less than the depreciation rate (plus the population growth rate in the normal exposition of this outcome). The sensitivity of the model to changes in that inequality depends on the elasticity of substitution between labor and capital: the more inelastic, the more dramatic that transition.

Perhaps the most interesting (and very recent) extension of the Solow-Swan model involves using concepts of thermodynamics and entropy. This extension recognizes that with two dimensional factors interacting (labor and capital, or rich and poor), that the form of mathematics that would be most appropriate is calculus in two dimensions. This is common in thermodynamics but not in economics.

In economic terms, imagine that the sum of production and consumption (and thus savings) is path dependent. For example, in an economy are different types of laborers with different skills, and in a given year they will produce capital that will differ for each group depending on the number of laborers and the productivity of each group. If they are shifted into differing areas from their specialty, there will be different outcomes. A simple two-good basic microeconomic production possibilities frontier captures the essence of this premise.

What is different in the following are the mathematics to capture this concept and the use of entropy as the source of economic growth.

Solow-Swan and a Thermodynamic View of Economic Activity

Based on material in Mimkes (2006, 2007) we will present the Solow-Swan model in a

way that will provide valuable insight into the building of the simulation that is the cornerstone

of chapter three. The foundation of the following logic was developed by Jürgen Mimkes but

many of the insights and the numerical simulation have been developed for this research. To

131 follow the template of Solow-Swan, we will develop a production function based on capital and labor, using the excess of output minus consumption (savings) to create time dynamics.

One of the basic concepts in thermodynamics is entropy and the cyclic nature of work.

The first and second laws of work relate energy input to the mean energy per particle

(temperature). In economics we can transform this relationship into the law of economic production: in economic terms, work is now production, energy input is now capital produced by labor, and mean energy per particle is analogous to mean capital per worker (or the standard of living). In the physics and economic cases an entropy parameter pressures the system to lose energy or have capital dissipate (or, in per capita terms, to have the standard of living degrade).

Only an input of energy (labor making new goods and capital) can prevent the system from

“cooling off.” So in this view of production, output (new capital) is a function of the change in existing capital (which is produced by labor as shown below) and depleted by entropy. More formally (and following thermodynamic theory),

ܻ = ܭെܲߪ (2.9) where Y is output (or income), K is capital, P is the standard of living in terms of the mean share of capital per worker, and ߪ is the entropy parameter. Entropy is determined by a probability that is a function of how labor is allocated (more on entropy and labor below). In any given time cycle, unless capital is replenished, if the standard of living increases then output will fall.

Capital is produced by labor. If there are ݊ types of laborers and sectors producing ܭ in a given period, then

ܮ݅ ܭ = σ ܮ݅ ݇݅ = σ( ൗܮ)݇݅ (2.10)

ݐ݄ where ki is the productivity of the workers in the ݅ sector.

132 The entropy parameter is a function of the possibilities for the putting ܮ people to work

ܮ! in ݅ different sectors of production. The number of possibilities is ܲ = . Using ܮ1!ܮ2!…ܮ݊ !

Sterling’s approximation,30 entropy is thus

ܮ ܮ ߪ = ݈݊ܲ = െܮ σ ݊ ln༌( ݊ ) . (2.11) ܮ ܮ

ܮ For simplicity, let ݔ = ݅ and σ ݔ =1. Thus, plugging into equation 2.9, production is ݅ ܮ ݅

(σ ݔ݅ ݇݅ െܲσ ݔ݅ ݈݊(ݔ݅ )]. (2.12]ܮ = (ܮ ,ܭ)ܻ

In the plot of this function below we see that for a given ܲ, ݇݅ , and ܮ, as the production entropy

parameter ݔ݅ increases, the growth rate of production decreases. This is analogous to the predictions of the Solow-Swan model’s production function, telling a story of efficiency gains from seeking an optimal division of labor and specialization. Production

0.00 0.05 0.10 0.15 0.20 0.25 Production Factor x

Figure 30. Plot of production versus production factor x.

݊ 30 ݊!=ට2ߨ ȉ ቂ݊ቃ ݊ ݁

133 However, if we allow this economy to subdivide into an even larger number of sectors we see that production eventually declines in absolute terms.

Developed Market Sysetm

Less Centrally Production Developed Planned Market Market System System

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 Production Factor x

Figure 31. Plot of production versus production factor x beyond the optimal x.

There is clearly an optimal number of laborers for each of the production sectors. The

production function can be maximized on the production factor to derive a solution:

߲ܻ (ln༌(ݔ݅)+1)] =0 (2.13)ܲ + ݅݇]ܮ = ߲ݔ݅

െ(ܲ+݇݅) (ݔ݅ = ݁ ܲ . (2.14

A well developed market economy should be near the optimal labor allocations for production

sectors (a sort of “golden rule” in this framework). The more primitive the economy, the more

fragmented and inefficient is production. To the right of the optimal area in Figure 31 the production system suffers from inefficiency due to too many workers allocated into production sectors.

134 In the Solow-Swan model, production is only part of the story. The Solow-Swan story also requires that production leads to some level of savings in order to invest in capital and engender economic growth. Economic systems in general must gain more than they expend

(costs and consumption) to grow. That is, ܻെܥ= ܵ >0. To again relate physics to economics, a business collects a high amount of capital (energy) from labor. The business then pays out a lower amount of capital (energy) in the form of costs. The difference is profits which are invested. This is a cycle that is driven by the differential between the prices for the capitalist and the prices for labor (that is prices versus costs/wages).

This is analogous to the Carnot cycle model of a heat engine. A thermodynamic cycle occurs when a system is taken through a series of different states and finally returned to its initial state. In the process of going through this cycle, the system performs work on its surroundings. This is a description of a heat engine.

A heat engine acts by transferring energy from a warm region to a cool region of space and, in the process, converting some of that energy to mechanical work. Using this model to describe an economy, the cycle reduces entropy with the production process (and inputs of labor) and increases entropy with the consumption/cost process. The “mechanical work” is the profits that produce savings and growth. As noted above, what drives this capitalist engine is not a temperature differential but a price differential. The capitalist engine draws capital and income, initially from the environment, and at each layer of the system captures profits.

The diagram below is straight from the Carnot cycle for a heat engine with modifications to relate to an economic concept of the first and second laws of thermodynamics. The red section is the base level of capital. As we have shown, over time this will increase, and therefore over time both ܲ2 and ܲ1, a measure of the mean prices around which the cycle runs, will

135 increase. The mean prices, ܲ2 and ܲ1, plotted against the entropy of goods and money, also

measure capital intensity and the standard of living.

Figure 32. The economic cycle in thermodynamic terms.

Figure 32 is similar to the circular flow diagram so often seen in a principals of

economics course but viewed through the lens of the first and second laws of thermodynamics.

Note that thermodynamic efficiency is defined as the ratio of the work done by a heat engine to

the total heat supplied by the heat source. Here, profits and accumulation are the results of

economic “efficiency.” As we will see later, this “efficiency” is necessary for capitalism to

function. The inner clockwise flow shows how production lowers entropy: (1) to (2) adds value;

(2) to (3) puts the goods into the market, where they are used and depleted raising entropy, (3)

to (4); and finally the cycle begins again with the retained surplus that is invested into

production. The outer counterclockwise flow shows how from (4) to (3) the entropy of money

136 distribution is lowered (concentrated), and industry earns ܲ2 times the change in entropy. From

(2) to (1) some of those earnings are distributed (dispersed), and the labor earns ܲ1 times the

change in entropy. The “work” generated is the accumulation of capital and the accumulation

of profits.

Whereas Solow-Swan have aggregate savings fixed (this is relaxed in the next section),

here we are interested in the accumulation or profits of one entity vis-à-vis the profits of a

counterparty. This relationship is embodied in the difference in the aggregate incomes to the

producer and labor. That is, the share of savings (the income distribution) that each party

receives drives the dynamics of growth in this model. This concept can be generalized beyond

the firm level to the relationship between capital and labor, or even more generally into the

relationship between the developed world and the less developed world. All that is necessary is

the differential between prices and costs, ܲ2 and ܲ1 in Figure 32.

If we consider the costs, ܥ, to be the income of the third world and the production, ܻ, as

the income of the developed world, then we can simulate several scenarios in which the shares

of the of the net profits are reinvested for growth. (We could also think of this relationship as

that between the rich and the working class within a country, or between owners and workers

within a firm.)

Using equation (2.12) and generalizing the production and costs, the functions for

income and costs are identical in this conception except in the intensity of capital, ܲ, the

efficiency of capital, ݇, and the efficiency of labor allocation, ݔ. The producer’s ܲ2 is higher than

the worker’s ܲ1 , and capital and money are more concentrated. The efficiency of capital and of the labor allocation will be assumed to be such that the rich (developed world), ݎ, are more

efficient than the poor (third world), ݌:

ݎ ݎ ݎ (σ ݔ݅ ݇݅ െܲ2 σ ݔ݅ ln༌(ݔ݅ )] (2.15]ܮ = (ܮ ,ܭ)ܻ

137 ݌ ݌ ݌ (ൣσ ݔ݅ ݇݅ െܲ1 σ ݔ݅ ln༌(ݔ݅ )൧ (2.16ܮ = (ܮ ,ܭ)ܥ

Aggregate profits ߨ (savings) are simply the difference between ܻ and ܥ.

Now suppose that the poor (the third world or the workers) get a share of the aggregate

profits, ݌ , and the rich (the developed world or the employers) get a share (1 െ݌). (How these

profits are divided, that is, the value of ݌, was a subject of Chapter One’s discussion of the

scenarios available for growth.) If each group reinvests the excess ݌(ܻെܥ) and (1 െ݌)(ܻെ

ܥ) , then each group will experience an increase in their standard of living over time. That is,

(ݐ (2.17݀(ܥݐ) = ݌(ܻെ)ܥ݀

(ݐ. (2.18݀(ܥݐ) = (1 െ݌)(ܻെ)ܻ݀

In other words, we have an interdependent dynamic system in which each group’s growth is

determined by the how the two groups share in the output of the economic engine. Also

important are the efficient uses of capital and labor. The transmission of knowledge and its

effect on relative growth is the subject of a later section in this chapter.

Solving the system of differential equations (2.17) and (2.18) yields

(1െ2݌)ݐെ1)݁)( ܥ݌(ܻ െ+ ܥ (ݐ) = 0 0 0 (2.19)ܥ 1െ2݌

(1െ2݌)ݐെ1)݁)( ܥ1െ݌)(ܻ െ)+ ܲ (ݐ) = 0 0 0 (2.20)ܻ 1െ2݌

for ݌്0.5.

For ݌ =0.5 the solution is

1 (ݐ (2.21( ܥെ ܻ) + ܥ = (ݐ)ܥ 0 2 0 0

1 (ݐ. (2.22( ܥݐ) = ܻ + (ܻ െ)ܻ 0 2 0 0

138 Thus for a given set of efficiency parameters that determine the initial conditions, ܻ0 and ܥ0, we can explore potential growth paths. Later in this chapter, after exploring the more complex mainstream growth models, we will extend this model to allow the production efficiency and capital efficiency parameters in the two groups to change with time also.

ݎ ݎ If we assume that ݔ݅ is near optimal and ݇݅ is .33 (the same as ߙ in the Cobb-Douglas form in Figure 25 through Figure 29) and assume lower values for the parameters for the less developed counterparty, we can set ܲ such that the rich begin with an income/output of 2 and the poor begin with an income/output of 1 (ܲ2 =4.95 and ܲ1 =2.98). The difference in the standard of living (i.e., the incomes per capita) powers the economic engine. Over time, as the shares of the profits are reinvested, we would expect to see growth. As such, both ܲ2 and ܲ1

should grow, and the standards of living for both counterparties should improve. As we will see

in the scenarios below, this is not necessarily true.

We will first look at how this model predicts growth using the actual division of world

GDP and of world GDP/capita. The share of the aggregate output to the rich world is 65%.31

This suggests the following:

31 This is the share of world GDP to North America and Europe versus Asia, Africa, and South America in 2006 (IMF, April, 2007).

139 8 Relative GDP per Capita 7 Rich Share 0.65 6

Y Rich 5 Y Poor 4

0 Time ------>

Figure 33. Growth of rich and poor with 65% to the rich.

Both rich and poor share exponential growth, but the rich continue to grow at a higher

exponential rate. This suggests that as long as this general income distribution persists,

divergence rather than convergence will describe the income paths of the developed and less

developed nations.

However, the paths may be more divergent than that. Based on the United Nations

Human Development Report, 2006, GDP per capita (at $PPP) for the top 1/3 of countries is

$24,806; for the middle 1/3 it is $4,269, and for the poorest 1/3 it is $1,184. The rich world has

a per capita GDP that is 20 times greater than that of the poor world. Giving the rich a 95%

share produces the chart below.

140 35 Relative GDP per Capita

30 Rich Share 0.95

25 Y Rich

20 Y Poor

0 Time ------>

Figure 34. Growth of rich and poor with 95% to the rich.

Over the same period, both rich and poor do better in absolute terms (the poor reach a

GDP per capita of 2.78 in this scenario versus 1.81 in the previous scenario). However, the rich

are more than 10 times better off whereas the poor are about 50% better off. The poor do

benefit from the interaction with a rapidly growing rich world, but they also see that the gap

between their well-being and the well-being of the rich world grows. As Chapter 1 showed, this

trend will lead to violent outcomes.

Figure 21 at the beginning of this section shows that poor nations have not grown in

absolute terms in recent history (since the industrial revolution and the colonization of the third

world). If our model is set to have the rich exploit the poor (that is, the poor side has only

losses) we can see a pattern that is similar to Figure 21. Setting the rich share to 1.25%, we have

the following:

141 7 Relative GDP per Capita

6 Rich Share 1.25

5 Y Rich

4 Y Poor

0 Time ------>

Figure 35. Growth of rich and poor with 125% to the rich.

Figure 36 below shows the actual data for GDP per capita from 1920 to 2003. The US growth

has been exponential (note R2 and fit equation in the chart). China has only recently joined the exponential growth path. Africa as a continent (data from 57 countries) has remained flat.

However, culling data from the poorest countries, we can see a pattern in Figure 37 that is

similar to that predicted by Figure 34.

142 35,000 GDP per Capita, 1990 $ 30,000 United States y = 4985.e0.021x Western Europe R² = 0.957 25,000 China

Africa 20,000

15,000

10,000

source: Angus Maddison, 2007

5,000

Figure 36. Actual GDP per capita – US, Europe, China, Africa (from Maddison, 2007).

2,500 GDP per Capita, 1990$

2,000 Djibouti Somalia 1,500 Angola Madagascar 1,000 Sierra Leone Niger

500 Central African Republic Zaire

Figure 37. Actual GDP per capita – poorest nations (from IMF, 2007).

There is a variety of reasons for the failing growth of per capita GDP in the poor African nations, but the heart of the matter, as in the simulation, is a failure to share and reinvest in the

143 value added to the output of the country. Exploitation, within country or between countries, benefits some and harms many.

This entropic form of the Solow-Swan model also shows the implications of endless exponential growth. In this form of the model, what will support endless growth is the sustained differential between the value created in the economic engine and the costs of that creation. That is, as long as ܲ2 > ܲ1 or as long as ܻ > ܥ, growth will continue. Yet several unsustainable outcomes arise. As discussed above in this section, at some point, satiation of real per capita consumption will create an asymptotic convergence on a long-run limit to the per capita standard of living.

But more likely to occur before that long-run constraint is, as we demonstrated in

Chapter One, that the continued divergence of standards of living becomes unsustainable: social unrest, terrorism, and revolution will change the divergent exponential paths at some point with a new regime in which the allocations of the value added are distributed differently. This same model that developed the paths in Figures 33 through 34 can provide insight into those potential time paths.

Suppose that there are significant changes in how the poor are allocated a share of the aggregate output such that now, instead of the poor getting 35% as in Figure 33, they get the

65% share that the developed world was getting, while the developed world gets 35%. Figure

38 below shows the example in which starting with an allocation of 1 to the poor and 2 to the rich, the growth of per capita GDP declines to a zero growth level.

144 3.5 Relative GDP per Capita

2.5 Rich Share 0.35

1.5 Y Rich

Y Poor 1

0.5

0 Time ------>

Figure 38. Growth of rich and poor with 35% to the rich.

The dynamics behind this convergence do not require any satiation of real per capita

consumption but occur within the framework of the thermodynamic model. Using the heat

engine example, if there is no difference between the energy in a cold reservoir and a hot

reservoir (in this case hot and cold are not appropriate terms since both are the same!) then the

engine cannot produce work. In our economic system, if there is no difference in the standards

of living between rich and poor (again they are the same, so there is no distinction between rich

and poor) then the economic engine cannot produce an excess accumulation of capital. Simply

stated, if income and costs are the same, there is no profit, and there is nothing to reinvest. At

the convergence point, the only required economic activity is the replenishment of capital

depleted by entropy (depreciation).

The real return on investment (ROI) provides an interesting insight into what might

motivate the rich counterparty to maintain a high share of the aggregate value added (most

145 likely against the wishes of the poor counterparty with the use of, as shown in Chapter One,

police and armies).

The real growth rate of the economy determines the real rate of return on capital

investment in the long-run.32 Short-run fluctuations in a real economy will raise and lower both the real and expected return on investment as is witnessed daily in the world’s stock exchanges.

But over time, the geometric mean long-run real rate of return on capital investment will equal the geometric mean long-run real growth rate of the economy. In our thermodynamic economic model, the interplay between the rich and poor allow long-run (but ultimately unsustainable) differences between the growth rates of the two counterparties.

The return on investment in this scenario is based on the efficiency calculation in

ȴW thermodynamics. The theoretical calculation for the efficiency of a heat engine is ɻ = ȴQH where ȴW is the work done by the system (in economic terms, the accumulation of capital) and

ȴQH is the heat or energy entering the system (the capital invested into the system). The equation for the efficiency of the heat engine equates to the return on investment in our model, which is a function of the difference in standards of living and thus revenue and costs.

ȴW T െT Rearranging the efficiency equation, ɻ = = H C , we can see that efficiency is increased ȴQH TH more by lowering the cool temperature than by increasing the high temperature by the same amount.

The efficiency of our economic model is measured in a similar way, and the resulting

(ݐܥȴߨ (ܻݐ െ ݎ is the net ܭݐ = = where ȴܫܱܴ ratio measures the return on investment. Thus ݐ െܻݐെ1ܻ ܭȴ

invested capital. Note that since ROI is a function of Y and C, then ROI is also a function of the differential between Y and C. As in the thermodynamic example, the return on investment (or

32This is a well established empirical fact and is established in Faugere and Erlach (2003, 2006) and Liu, et al. (2005).

146 the growth rate of the rich) would increase more by lowering the standard of living of the poor

(lowering C) than by increasing the standard of living for the rich (raising Y) by the same amount.

Although not explicitly modeled in the examples so far in these simulations (we have held the internal parameters of the production function constant), we will illustrate the effects by showing the short and long-run effects of first lowering the poor’s standard of living and holding the rich’s fixed, and then doing the opposite by the same amount.

However, in the first chart below we look at the prediction using a 65/35 rich/poor allocation with ܲ2 and ܲ1 at the base values ܲ2 =4.95 and ܲ1 =2.98 and the other parameters also held constant.

5.40% Real Return on Investment

5.30% Rich Share 0.65

5.20%

5.10%

5.00% ROI

4.90%

4.80% Time ------>

Figure 39. Real return on investment – rich get 65%.

In this case, the real rate of return on investment declines to a floor. The prospect of declining future returns could be seen as a motivator to alter the relationship between the

147 counterparties (if possible33) in a way that would change that dynamics in favor of the richer

(and most likely more powerful) counterparty. In our model this is easily accomplished by increasing the share of aggregate output to the rich. We can see the effect of this by changing the share of the rich from 65% to 95% (as we did in Figure 34). The figure below shows the results.

14.00% Real Return on Investment

12.00%

Rich Share 0.95 10.00%

8.00%

6.00%

4.00% ROI

2.00%

0.00% Time ------>

Figure 40. Real return on investment – rich get 95%.

The outcome of an increased share not only increases current ROI but also provides an

expectation of a rising return on investment in the future.

Suppose there are also mechanisms that influence the standards of living independent of altering the share of aggregate income. For example, the rich could have a well managed monetary policy whereas the poor could be exposed to an erosion of purchasing power in the

33 We have not discussed the strategies that have allowed the employer/worker or rich nation/poor nation to gain or lose advantage in a historical sense. In the conclusion to this work we will discuss potential strategies for paths forward. At this point in the discussion we are simply looking at the implications of changes in the structures of theoretical models of the economy, not how those structures might change.

148 home currency due to high inflation. If a social planner were to have a choice of either raising the standard of living of the rich or lowering the standard of living of the poor by the same amounts and the objective were to maximize the current rate of return, the planner would choose to lower the standard of living of the poor. As noted above in thermodynamic terms, it is better to make the cold reservoir colder than to make the hot reservoir hotter by the same amount.

In Figure 40 the rich have a 95% share of the aggregate accumulated profits and have an initial ROI of 8.31% and a ceiling over time of 12.53%. In the two cases in the charts below

(these cases assume a onetime shift at time zero), we hold the share at 95%, first raising the standard of living of the rich while holding the poor fixed, then doing the opposite.

149 14.00% Real Return on Investment

12.00% Rich Share 1.1

10.00% Raise standard of living for rich 8.00%

6.00%

4.00% ROI

2.00%

0.00% Time ------>

14.00% Real Return on Investment

12.00% Rich Share 1

10.00% Lower the standard of living for the poor. 8.00%

6.00%

4.00% ROI

2.00%

0.00% Time ------>

Figure 41. Real return on investment – changes in the initial standard of living.

The case in which the rich’s standard of living increases (top chart) results in an increase

in the initial rate of return from 8.3% to 11.5%, an increase of 3.2%. The case in which the poor’s standard of living is lowered by the same amount that the rich’s was raised (bottom chart) results in the rate of return moving from 8.5% to 12.5%, an increase of 4.0%. The

150 terminal value of one dollar invested after ten years is $3.04 if the poor are less well off and is

$2.80 if the rich are better off.

The key point is that convergence in standards of living is counter to a strategy of maximizing return on investment. This point is further illustrated by looking at the time path of the rate of return for the case shown in Figure 38. If somehow the allocation of the aggregate output were 35% to the rich and 65% to the poor, as Figure 38 shows, the world converges to a per capita ceiling: identical standards of living and zero growth. The ROI time path is as shown below:

3.50% Real Return on Investment

3.00% Rich Share 0.35

2.50%

2.00%

1.50%

1.00% ROI

0.50%

0.00% Time ------>

Figure 42. Return on investment – rich get 35%.

Over a ten year horizon, the ROI drops to 0.18%. At 30 years it is 0.0005%. Eventually it

is zero.

The fundamental fuel of capitalism is the growth in capital. If there is zero growth and

zero return on investment, what is that economic system called? That question will remain

unexplored for now as there are other models to explore before we have a more complete

understanding of potential futures and how to simulate them.

151 Thus far, we have shown that the Solow-Swan framework (both in the traditional model and in the thermodynamic version), while missing components of economic thinking such as utility maximization, the spread and growth of knowledge, and innovation,34 predicts endless growth under the assumption that per capita consumption has no upper limit. In the traditional model there is a golden rule level of investment and savings that yields an optimal capital to labor ratio, maximizes consumption forever, and supports endless growth. In the more modern presentation of the Solow-Swan framework, the golden rule still exists within the production function in determining the optimal capital to labor ratio, but, since there are two counterparties between which a profit dynamic exists that drives the growth of consumption per capita, the golden rule is perverted into excluding the counterparty. That is: “Do unto others (our future generations) as long as they are in our group; otherwise, exploit forever as much as possible.” Data since 1960 seems to suggest that our scenario for the rich taking a steadily increasing share of the aggregate output and its effects on standard of living is plausible. The first chart below shows the relationship between the mean and the median GDP of 140 countries since 196035.

34 Utility maximization based models of growth will be explored in the next section. Growth models that incorporate the diffusion of knowledge will also be looked at in a later section. But perhaps the most interesting dissection of growth models will come when looking at how innovation is modeled. One can foresee an argument that says that innovation will prevent an end to growth as the creation of new products will insure an endless sustained growth in per capita demand. We will take a very close look at how models of innovation forecast the very long run and will show that, barring an innovation that allows us to expand beyond the earth is such a way that moving goods to the next planet is like putting freight on a ship, the economic limits to growth will still bring a future of zero growth and a real return on investment that is zero. 35 IMF, 2007, data from 140 countries with data from 1960: Afghanistan, Albania, Algeria, Angola, Argentina, Australia, Austria, Bahrain, Bangladesh, Belgium, Benin, Bolivia, Botswana, Brazil, Bulgaria, Burkina Faso, Burma, Burundi, Cambodia, Cameroon, Canada, Cape Verde, Central African Republic, Chad, Chile, China, Colombia, Comoro Islands, Congo, Costa Rica, Côte d'Ivoire, Cuba, Czechoslovakia, Denmark, Djibouti, Dominican Republic, Ecuador, Egypt, El Salvador, Equatorial Guinea, Eritrea and Ethiopia, Finland, France, Gabon, Gambia, Germany, Ghana, Greece, Guatemala, Guinea, Guinea Bissau, Haïti, Honduras, Hong Kong, Hungary, India, Indonesia, Iran, Iraq, Ireland, Israel, Italy, Jamaica, Japan, Jordan, Kenya, Kuwait, Laos, Lebanon, Lesotho, Liberia, Libya, Madagascar, Malawi, Malaysia, Mali, Mauritania, Mauritius, Mexico, Mongolia, Morocco, Mozambique, Namibia, Nepal, Netherlands, New

152 350,000 GDP in 1990$ millions 300,000 mean (140 countries) y = 55047e0.0368x median R² = 0.9917 250,000

200,000

150,000

100,000

50,000

Figure 43. GDP of 140 countries – mean and median (from IMF data, 2007).

The divergence between the mean and median shows that the distribution of world

income is becoming increasingly skewed to the rich tail. In fact, Figure 43 looks very similar to

Figure 34 (the 95% to the rich scenario). And, as the simulation predicts, the divergence is

exponential (shown by the dotted line, the fit equation, and the R-squared statistic).

The requirement for a strong and constant or growing return on investment that yields the growth imperative supporting capitalism also, as noted above, would be supported by a lowering of the standard of living for the poor or an increase in the standard of living for the rich

(or both).

Zealand, Nicaragua, Niger, Nigeria, North Korea, Norway, Oman, Pakistan, Panama, Paraguay, Peru, Philippines, Poland, Portugal, Puerto Rico, Qatar, Reunion, Romania, Rwanda, São Tomé and Principe, Saudi Arabia, Senegal, Seychelles, Sierra Leone, Singapore, Somalia, South Africa, South Korea, Spain, Sri Lanka, Sudan, Swaziland, Sweden, Switzerland, Syria, Taiwan, Tanzania, Thailand, Togo, Trinidad and Tobago, Tunisia, Turkey, Uganda, United Arab Emirates, United Kingdom, United States, Uruguay, Venezuela, Vietnam, West Bank and Gaza, Yemen, Yugoslavia, Zaire, Zambia, Zimbabwe.

153 The chart below shows the poorest 20th percentile nations’ per capita GDP as a percentage of the total of the poorest and richest 20th percentile per capita GDP.

GDP per Capita Share of Poor Nations 18.00% (140 countries) 20th pctl P/(20th pctl R + 20th pctl P)

16.00%

14.00%

12.00%

10.00%

8.00%

6.00%

Figure 44. GDP per capita – poor 20th percentile versus rich 20th percentile (from IMF data,

2007)

The standard of living of the poorest quintile relative to the richest quintile has, as the

simulation suggests, diverged.

In the version of the Solow-Swan view of growth developed in this essay, the engine of

capitalism applies a production function to poorly paid workers or nations and sells the output

for a significant multiple of that cost to the relatively rich customers or nations. Since the world economic system needs growth to operate and growth is optimized in this model by a sustained spread between rich and poor standards of living, the motivation is to avoid convergence. A convergence to a common steady state, with or without endless growth (original Solow-Swan versus the version developed in this section) would pull the rug from under the system as the return on investment plunges to zero. The system is addicted to growth and, as in a more

154 general addiction model, the system has a disconnection between long-run well-being and short- run satisfaction. This conclusion refutes most of the mainstream interpretations of this early growth model (see Barro and Sali-i-Martin, 1991) but is not refuted by the data.

Perhaps this extreme conclusion will be mitigated by more advanced models. In our thermodynamic model, we held the capital labor ratio fixed. In both the traditional and the entropic models consumption per capita was explicitly used as a metric for optimization and did not have savings (or forgone current consumption) influence current choices. In the next section we will explore the mainstream theoretical approach to broadening the basis for optimization from consumption to utility. In a later section we will look at how knowledge diffuses from those with high human capital to those with low human capital so that technology improves and labor is more productive. We will also see if innovation can save the future from entering into an economic system that does not provide a return on investment.

But as a starting point, from either the 1950’s perspective of Solow and Swan or from the current perspective of the economic system as a physical entropic process, this framework provides a benchmark for reference. The insights of the traditional model lead to a conclusion of endless growth unless the savings rate declines to the depreciation rate. The insights of the second model lead to a conclusion that the fundamental motivations of capitalism will extract from the poor into the rich. Both models break down in the long-run through satiation of real per capita consumption or from the divergence of rich and poor. And as was shown in Chapter

One, such a sustained and growing divergence portends a sustained and growing support for violent remedies.

Growth with Consumer Optimization – Ramsey and Beyond

The models described in the last section have several shortcomings. One of these is the failure to recognize the forward-looking nature of current decisions in terms of consumption

155 and competition. As a result, the savings rates and thus the investment in capital formation were detached from expectations of what the future will bring.

In this section we will investigate classic growth models that describe a consumption path determined by optimizing households that do not make choices in isolation from the producers. Beginning with Ramsey (1928) and advanced by others, the central concept that drives this section is utility maximizing households (infinitely lived or multi-generational) that face not only a current period budget constraint but also consider future income as well. This framework was the foundation of the story told in Chapter One about the transition from the

Malthusian trap to the era of continuous growth in per capita income.

The ability to accumulate assets and pass on an endowment to the next generation is at the heart of this section’s architecture. In the previous section population growth was exogenous. At this point in the discussion, the growth rate of the family is also exogenous and grows at the rate ݊ (unlike in the model in Part Two of Chapter One). Endogenous population growth will be revisited later in this section.

If the population begins at unity, then at time ݐ the size of the family is

(ݐ) = ݁݊ݐ . (2.23)ܮ

ݐ) , then we can set up a utility)ܮ/(ݐ)ܥ = (Also, if consumption per adult at time ݐ is ܿ(ݐ function that each household will maximize:

(׬ ݑ[ܿ(ݐ)] ȉ݁݊ݐ ȉ݁െߩݐ ݀ݐ. (2.24 = ܷ

Equation (2.24) says that utility is maximized based on the flow of consumption per person

added up by all of the family members and that there is a time preference, as long as ߩ >0, for

156 consumption sooner than later. Although this specification is simplistic,36 particularly when

contrasted to the model developed in Chapter One, it is important to look at this model to

understand the evolution of growth models. In fact, some of the assumptions and predictions of

this model, as we will see, are embedded into the development of thought on economic growth.

The households earn by working and by receiving a return on accumulated assets.

Households deplete per capita assets with consumption and with growth in the size of their

population. That is, the flow of earnings (assets per capita, ܽ(ݐ)) is described by

(െ ܿ െ ݊ܽ , (2.25 ܽݎ + ሶ = ݓܽ

where w is the wages per unit of labor and r is the interest rate. (Note that the time subscripts

are omitted for simplicity.)

The Ramsey model requires a condition to eliminate a Ponzi scheme. That is, if

households borrow (the assets can be loaned so that some households have negative assets)

they can continuously roll over increasingly larger loans forever. Household debt rises at the

interest rate with no limit. The condition prevents the debt per capita (negative values of ܽ)

from rising as fast at the interest rate. This is a typical restriction and we will take a closer look

at the implications of this condition vis-à-vis the time path of interest rates in a numerical

simulation later in this section.

The utility function, (2.24), is maximized subject to the budget constraint (2.25) and the

condition preventing the Ponzi scheme. As in the previous section, we will not detail the

derivation of the key points. After a present value Hamiltonian is set up and the first order

conditions for maximizing utility and a transversality condition are derived, the first outcome

that is of interest is as follows:

36 For example, the discount parameter must be greater than the growth rate of the family. Also, the discount rate for the current generation is identical to that of future generations; more on that assumption follows.

157 ݑԢ /݀ݐ ݑԢԢ ȉܿ ܿሶ݀ ݎ = ߩെቀ ቁ = ߩെቀ ቁȉ . (2.26) ܿ ݑԢ ݑԢ

This says that households choose some level of consumption that is a function of the rate of

time preference plus the marginal utility of consumption times the rate of growth in per capita

consumption so that the sum of these rates equal the interest rate on assets. The term in

parenthesis on the right side of (2.26) is the consumption elasticity of utility. This shows the

sensitivity of the household’s desire for current compensation, ݎ, to the time preference, ߩ.

That is, it determines the premium of the interest rate over the time preference for a given

growth rate in consumption.

Note that if (ܿሶ/ܿ)=0, that is, per capita consumption growth is zero, then the rate of

return on savings equals the rate of return on consumption.

ܿ (1െߠ)െ1 The typical presentation of the Ramsey model also specifies ݑ(ܿ) = so as to (1െߠ) insure that there is a constant elasticity in the steady state. ߠ is greater than zero; thus the elasticity of marginal utility is – ߠ. Using that specification, (2.26) simplifies to

ܿሶൗ 1 ܿ = ൫ ൗߠ൯ȉ(ݎെߩ). (2.27)

So growth in consumption can be positive, zero, or negative, depending on the

relationship between the return on assets and the time preference parameter. If the parents

are very selfish, a high ߩ, or the return on assets is very small, then growth in per capita

consumption could be negative. The larger ߠ (which means a lower willingness to substitute

intertemporally), the slower the response of the per capita consumption rate to a change in the

discount parameters, or the more that households wish to smooth consumption over time.

Since the actors in this model are concerned about both current and future

(consumption, the consumption function must look forward to time ݐ. Whereas equation (2.27

158 determines the growth rate of consumption, to determine the level of ܿ requires the use of the flow of income described in (2.25). The present value of consumption is the sum of current

ҧ(ݐ)െ݊]ݐݎ]ь െ ( ) ,assets, ܽ(0), (wealth) and the present value of wage income, ݓ෥ 0 = ׬0 ݓ(ݐ)݁ ݀ݐ

ҧ(ݐ) is the average interest rate from the present to time ݐ. Consumption is thusݎ where

1 ҧ(ݐ)െߩ]ݐݎ]ቀ ቁ (ݐ) = ܿ(0) ȉ݁ ߠ . (2.28)ܿ

The consumption function is especially sensitive to changes in the expected average

interest rate; this will be demonstrated in the numerical simulation later. Also important is the

value of ܿ(0). Initial consumption is a function of the propensity to consume, ߤ(0), and on the sum of current wealth and the present value of wage income. With a bit of manipulation, it can be shown that

1െߠ ߩ ҧ(ݐ)ȉቀ െ ቁቃݐݎь ቂ ( ) ߠ ߠ+݊ (ߤ 0 = ׬0 ݁ ݀ݐ. (2.29/1

This says that if the average interest rate were to increase, then two offsetting effects

would follow. The positive effect occurs as an income effect. That is, if the average interest rate

rises, consumption is increased for all time. The negative effect occurs as a substitution effect.

That is, if the average interest rate rises then there is a higher penalty for current consumption

versus future consumption. In other words, the altruistic parent would prefer to save a larger

proportion of assets that will become wealth for future generations. Whether the propensity to

consume rises or falls depends on which of these effects dominate. This depends on ɽ, the parameter that determines the willingness of the consumer to smooth their consumption over time. If 0<ߠ <1 , then the substation effect wins: the households do not smooth consumption, so shifting consumption to the future is easy. If ɽ >1 , then ʅ(0) rises with rҧ(t).

159 As noted by equation (2.27), another way to view this is as the effect of a gap between the

ܿሶ . ݐ) െߠ= ߩ)ݎ ,market valuation of time and the consumer’s valuation of time or ܿ

When we review the assumptions of this model, look at some empirical data, and look

at some simulations, we will see how the zero growth outcome arises from this model and specifically from the specifications we have just reviewed. But before we can do that investigation, we need to complete the model by describing the production side.

The specification for the firms is not unlike that of the Solow-Swan model. Firms produce goods, they pay wages for labor, and they incur a cost of capital.37 Technological progress is considered exogenous in this model. Some presentations of the Ramsey model bury that assumption into the effective labor rate. For this presentation we will specify that

ݐ) = ݁ݔݐ . So output is)ܣ ݐ) where the growth rate is constant at ݔ൒0, or)ܣȉܮ = ෠ܮ

ܻ = ܨ(ܭ, ܮ෠). (2.30)

Using notation similar to the Solow-Swan presentation, we will define quantities per effective

෠ so that the production function is nowܮ/ܭ = ෠ and ݇෠ܮ/ܻ = unit of labor, ݕො

(ݕො = ݂(݇෠) . (2.31

In this closed system, the cost of capital (which also equals the return on assets) is ܴ (the marginal product of capital), and the value of capital depreciates at ߜ, so that ݎ = ܴെߜ or

ܴ = ݎ + ߜ. Thus profits are

(ߜ) ȉ݇෠ െݓ݁െݔݐ ൧ . (2.32 + ݎ)෠ൣ݂൫݇෠൯െܮ = ߨ

37 Firms must pay for the use of capital from the households that own the capital.

160 The combination of the households and firms brings competitive market equilibrium.

:Since ܽ = ݇ and therefore ݇෠ = ݇݁െݔݐ , we can derive this system of differential equations

ܿƸ (Ƹሶ = ൣߙ݇෠ߙെ1 െ (ߜ + ߩ + ݔߠ)൧ (2.33ܿ ߠ

ן ሶ k෠ =k෠ െ cොെ(n + x + ɷ)k෠ . (2.34)

As before in the Solow-Swan model, the variables with hats are constant in the steady state, the

grow at the rate ,ܻ ,ܭ ,ܥ ,per capita variables, ܿ, ݇, ݕ, grow at the rate ݔ, and the stock variables

of population growth plus the rate of technological progress. The steady state is

૚ ן (ቀ ቁ૚െࢻ (2.35 = כ k෠ ࢾ+࣋+࢞ࣂ

(െ (݊ + ݔ + ߜ)݇෠ . (2.36 ן(כ෠݇)= כƸܿ

Figure 45 shows the phase diagram with the transitional dynamics to the steady state values of

is to the left of the golden כthe per capita consumption and capital variables. Notice also that ݇෠

rule level from the Solow-Swan model. This is because savings are determined by households

who are somewhat impatient so that they shift consumption to the present and save less. This

is often called the golden rule of utility maximization.

161

Figure 45. Ramsey golden rule.

Note also that the transitional dynamics of the model suggest that if the economy starts at ݇෠0

" ƍ and if the initial savings rate it too high (ܿƸ0) or too low (ܿƸ0), then eventually the economy will

reach the point where the ݇෠ሶ =0 locus crosses the horizontal axis, and undersavings

(overconsumption) will drive the capital per effective unit of labor to zero or the economy moves to the c axis, where output must be zero! As is shown mathematically in Novales et al.

(p.72-78, 2007), the system explodes if the economic actors or the social planner violate the optimality conditions of this model.

But, as noted above, one of the conditions of the model is no Ponzi scheme (that is, that debt cannot grow faster than the real interest rate net of population growth). Yet in the short- run, the real economy can deviate from the stable manifold if savings rates are, for example, too low. But just how long is the short-run, and at what point must debt per capita grow slower than the real interest rate net of the population growth rate? In the numerical simulation below we will see what happens, but first let us look at some actual data for the US:

162 US Savings Rate 16

2 y = 5E-08x3 - 0.000x2 + 0.036x + 6.649 0 R² = 0.878

-2

-4 1959 1960 1961 1963 1964 1966 1967 1968 1970 1971 1973 1974 1976 1977 1978 1980 1981 1983 1984 1985 1987 1988 1990 1991 1993 1994 1995 1997 1998 2000 2001 2002 2004 2005 2007

Figure 46. US Savings Rate (Bureau of Economic Analysis, 2008).

Figure 46 shows the US savings rate with a fitted polynomial function. Below we use that

smoothed savings rate to compute a measure of the change in debt by taking the difference of

the average rate over the last 25 years and each year’s savings rate.38 This is compared to the

real interest rate net of population growth (using Dept. of Health and Human Services data for

the fertility rate and the immigration rates for the US from 1983 to the present).

38 This measure is relative to the savings rate. This measure also picks 1983 due to data in Galbraith et al. (2007) on FED policy regimes. The data in the Galbraith essay shows that the policy regime has been consistent since 1983. Thus the assumption, based on that work, is that the natural real interest rate will be near the average of that period. The average 10-year bond rate minus the CPI (which works out to 4.94%) is used as the benchmark.

163 10.00 Smoothed US Data (percents) 8.00 Relative growth of debt 6.00

Real return net of population growth 4.00

2.00

0.00

-2.00

-4.00

-6.00

Figure 47. Ramsey ponzi violation (Bureau of Economic Analysis, 2008, & Dept. of Health and

Human Services, 2008).

Figure 47 suggests that since 2000 the US has violated the constraints of the Ramsey

model. Clearly, the choice of the benchmark real interest rate matters as to the exact point of

intersection. But no benchmark that is sensible results in a non-violation. It is also true that in

an open economy it is possible for foreign savings to provide short run sustenance to an

undersaving home economy. That supplementary effect (not in the Ramsey model) would be

captured in a measure of the net worth verses the savings of the private sector adjusted by

disposable income. If foreign borrowings are sufficient then, at least locally, the economy will

remain on the Ramsey stable path since the growth in net worth adjusted for after tax income

would offset the low domestic savings. Figure 48 shows the relationship between the ratio of

net worth to disposable income and savings to disposable income.

164 8 12.00%

7.5 10.00%

8.00% 6.5

6 6.00%

5.5 4.00%

5 net worth/disposable income (multiple) 2.00% 4.5 saving/disposable income (percent)

4 0.00% 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

Figure 48. US net worth and savings relative to disposable income (BEA, 2008).

Does the higher net worth measure offset the drop in savings? Figure 49 shows a fitted line between the net worth ratio and the savings rate ratio:

12.00% y = -0.021x4 + 0.561x3 - 5.506x2 + 23.77x - 37.98 R² = 0.867 10.00%

8.00% If savingswere 4.6 times higher than actual 6.00%

4.00%

2.00%

2007 Actual Data Point Personal Savings/Disposable Income (percent) 0.00% 55.566.577.58

-2.00% Net Worth/Disposable Income (multiple)

Figure 49. Scatter plot of Figure 48 data.

165 In order for the 2007 data point to be on the regression line, current savings would have to be 4.6 times higher than they are. The orange square shows the projected relationship if current trends were continued. So by this measure also the US economy is not abiding by the constraints of the Ramsey model. It also suggests that in order to return to the stable path, there will be overshoot (more on this in the simulation below).

So does that mean that the concept of a saddle path, while mathematically appealing, does not actually have real power in the real economy? And therefore are the growth predictions of this model invalid? To try to answer these questions, we will submit a Ramsey39

economy to a simulation, but we will also allow a stochastic component into the simulation in

order to view the effects of surges in technological innovation.

The numerical model follows from the solution shown in equations (2.35) and (2.36). (It

is important to review the mathematics used to set up the simulation in order to understand the

embedded assumptions.)

The steps taken to derive the numerical outputs for the simulation are based on the

following mathematics. The steady state levels of capital stock and consumption can be easily

derived if a Cobb-Douglas production function and a constant relative risk aversion utility

function are assumed. (These are the first two assumptions.) For now, assuming that ܣ =1 and

adding the risk aversion parameter, ߪ40, equations (2.35) and (2.36), with, as before, time

subscripts not shown, can be rewritten as

݀ ln ܿƸ 1 = ൣߙെ(1െߙ)݈݊ ෡݇ െ (݊ + ߜ + ߩ)൧ (2.37) ݐ ߪ݀

39 There are many variants to the original Ramsey model. For example, Caselli and Ventura (2000) allow for household heterogeneity and Barro (1999) allows for non-constant time preference rates. The outcomes are essentially identical to the model as presented so far. We will add government to the simulation in the following pages, but that will not materially alter the model’s dynamics. 1െߪ .Using the constant relative risk aversion form ܷ(ܿ ) = ܿݐ , ߪ >0 40 ݐ 1െߪ

166 ݀ ݈݊ ෡݇ = ݁െ(1െߙ)݈݊ ෡݇ െ݁ln ܿƸെln ݇෠ െ (݊ + ߜ). (2.38) ݐ݀

Based on Novales and Ruiz (2007) it can be shown that this system can be log-linear approximated as

݀ ln ܿො 0 െߟ ln ܿƸ െ ln ܿƸݏݏ (ቆ ݀ݐ ቇ = ቀ ቁ ൬ ൰ (2.39 ݀ ln ݇෡ ᇣെ݄ᇧᇧᇤᇧᇧ0ᇥ ln ݇෠ െ ln ݇෠ ݏݏ ݐ݀ ܦ

(1െߙ)(݊+ߜ)+ߩ 1െߙ ,where ݄ = and ߟ = (݊ + ߜ + ݔߠ) are both greater than zero. The matrix, D ߙ ߪ has a determinant – ߟ݄ <0 so the system is saddle path stable to the steady state. The

eigenvalues of the transition matrix are

ߩ±ඥߩ2+4ߟ݄ ߤ , ߤ = , (2.40) 1 2 2

ln݇෠ െ, ݏݏso that ߤ1 > ߩ >0 and ߤ2 <0. This system can be rewritten where ݔݐ =(lnܿƸ െ ln ܿƸ

ݔݐ orܦso that ݔሶݐ ؆ (ݏݏln ݇෠

ݐܦ (ݔݐ ؆݁ ݔ݋ . (2.41

In order to simulate the transition to the steady state and investigate the implications

for long-run growth, we need to derive from (2.41) an explicit system that can run in a standard

software package (we use Excel but Matlab would work also). The goal is to find a specification

that is a linear combination of the deviations from the steady state values of both consumption

and capital. Not only can we then see the response to one-time changes in key parameters, but

also, as noted above, we can overlay stochastic characteristics and watch the outcomes of

persistent deviations from the saddle path. As long as the stability conditions driving the

dynamics are not violated, there should be pressure to return to the stable path. As we will

show, given those conditions and given some positive rate of the combination of population

167 growth and technology (productivity) growth, we will have the same exponential path in the growth of all key measures of the economy: in other words, endless growth.

Appendix B contains a summary of the logic used to form the numerical simulation. The outcome of that exercise is that the solution can be shown to be

ʅ t ln ܿƸ െ ln ܿƸݏݏ =e 2 (ln c0 െ ln cොss ) (2.42)

ʅ t ln ܿƸ െ ln ܿƸݏݏ =e 2 (ln c0 െ ln cොss ). (2.43)

The path of output is derived from the production function. Given a level of technology, then ln ݕො ݕො = ݇෠ߙ ֜ ln ݇෠ = . Thus the stock of capital and per capita income are proportional at every ߙ

point in time and in steady state. Therefore

ʅ t ʅ t (ln ݕො = (1 െ e 2 ) ln yss +e 2 ln y0, recalling that ߤ2 <0. (2.44

This says that distance to steady state for income shrinks at a rate ߤ2. The convergence speed,

(1െߙ)(݊+ߜ)+ߩ 1െߙ .(ߤ will increase with the value of ߟ݄ where ݄ = and ߟ = (݊ + ߜ + ݔߠ 2 ߙ ߪ

The growth rate of income per capita depends on the distance from steady state. That is, if the economy begins at a point below the steady state, ݇0 < ݇ݏݏ , then the farther away from the steady state, the higher the growth in income. The speed of convergence is increased with larger values of ݊, ߩ, ߜ (population growth rate, the social discount parameter or the utility

of future consumption, and depreciation). The speed of convergence is decreased with larger

values of ߙ, ߪ (the share of capital and the level of risk aversion in the utility function).

Therefore if two economies share the same set of structural parameters, they will

converge to the same steady state but at speeds inversely related to their initial income/output,

thus the well known expectation for poor countries to grow more rapidly than rich countries.

168 However, if the assumption of identical structural parameters is dropped, there can be no conclusion about relative speed or the steady states.

We now have a basis upon which to engage the Ramsey model in simulation and to observe what will happen to several economies. But before comparing the outcomes between a developed and developing country, let us first observe the predictions of the model in terms of long-run growth. Or, more to the point of this research, does this model also foretell endless growth?

The standard presentation shows the steady state prediction for income per capita for a given set of structural parameters. In this case we will set technology, ܣ =1, the growth in technology, ߣ =0, the rate of time preference (the discount rate on future utility), ߩ =.1, capital share, ߙ =.33, population growth, ݊ =0.0, the depreciation rate, ߜ =.05, the risk aversion parameter ߪ =2.0, and consumption smoothing, ߠ =.5.

It will also be useful to observe the half-life for convergence of the capital stock per

1 ln capita back to the steady state value after a positive technology shock, ݐ = 2. If the half-life is ʅ2 longer, then the economy benefits from the change for a longer period. As we will see, based on empirical estimates of the key structural parameters (see, for example, Easterly, 1999, and

Afaro et al., 2005) the poor economy will have a much shorter half-life.

This simulation also includes an exogenous stochastic element. This element is actualized as exogenous randomly sized innovation shocks that, on impulse, influence the short- term steady-state per capita levels of income and capital stock (as well as consumption and investment). (We will look at models of endogenous technology growth in the next section of this paper.) In the first simulation below, technology over the long-run does not change, and the long-run growth rate of the economy is zero. Thus we can see in Figure 50 below how income (and thus the other endogenous variable) may take persistent excursions away from the

169 steady state but will always, in the long-run, return to the steady state. One can think of these excursions as economic cycles. The simulation covers 150 time periods with each period calibrated to be about ¼ of a year (three months) for a total of almost 40 years.

Income (per capita) 0.210

0.205

0.200

0.195

Income 0.190

0.185 Steady State = 0.1957

0.180

0.175

Time

Figure 50. The Ramsey model benchmark with zero population growth and zero technology

improvement.

Population growth, given a fixed level of technology, actually lowers the steady state

level of per capita income. We can consider population growth like a depreciation of physical

capital so that without an improvement in productivity, given higher population growth rate, the

economy will tend to a lower level of per capita income. If population growth increases from

zero to 1% per period (4% per year), then the steady state level in income per capita drops to

0.187 (from 0.196) in this simulation. But more important to the discussion below regarding

growth rates of rich and poor economies, the half-life for capital stock to return to steady state

falls from 6.86 periods with zero population growth to 4.92 periods with 4.0%/year population

growth. Thus the higher population growth rate has the effect of shortening the positive

170 influence of a non-persistent technology innovation. The dramatic negative effects of higher population growth (and other differences between rich and poor) are illustrated below.

The model becomes more interesting when growth from technology improvement is included (that is, the innovation shocks lead to persistent technology improvement and thus continuously increasing steady state values). As we found in the discussion of the Solow model, if we expect to have continuous growth in per capita income, we must face the reality of continuous compound growth.

Income (per capita) 0.700

0.600 Income

0.500

0.400

Income 0.300

0.200

0.100

0.000

Time

Figure 51. Ramsey model with technology growth at 2% per year.

Figure 51 shows the time path under the assumption of a constant growth rate in

technology of 0.5% per period (or 2% per year). In order to highlight the exponential growth

rate, Figure 52 shows the time path at 8% per year for consumption per capita.

171 Consumption (per capita) 16.00

14.00

12.00

Consumption 10.00

8.00

6.00 Consumption 4.00

2.00

0.00

Time

Figure 52. Ramsey model with technology growth at 8% per year.

In this time accelerated version, real consumption per capita grows from about 0.194 to

14.3 in about 40 years. That is 73 times higher than today’s in less than half a century. What

exactly does this mean in words that we today can comprehend? Quite simply, we will have the

equivalent of 73 times more stuff per year! Although it will certainly take longer to get to that

level (with productivity growth certainly less than 8% per year41), this model predicts a remarkable future. So once again, as in the previous section, we have to ask ourselves if there is some limit to the per capita level of consumption, and, perhaps easier to consider in the context of the ecological perspective, is there a limit to the stock of capital? There can be no argument concluding that infinity is attainable. But to keep the analysis within the boundaries of economic theory, the next section will provide a rigorous proof demonstration that this is not possible even if knowledge (human capital) is allowed into the equation.

41 However, the work of Kurzweil (2001) suggests that the world is indeed experiencing an increasing rate of innovation that effectively is yielding an increasing rate of technological change. His conclusion leads to what he calls a technological singularity at which point artificial intelligence literally makes machines smarter than humans.

172 For now, in the context of this model, suppose that the parameter for risk aversion is not fixed over time. Furthermore, does a fixed labor intensity in the production function make sense when there is hypercapital per capita? That is, does 1D remain constant as

YY / of? If capital intensity were to vary in that world, it would increase as labor inputs

became less important. As capital intensity increases, the speed of convergence, ߟ݄ , decreases.

These longer and more persistent fluctuations cause households to become more risk averse,

causing V to increase at an increasing rate that further slows the rate of convergence. Now suppose that this is happening on an excursion below the steady state, and households engaged

in consumption habits that mirror those shown in the data above. If U were to go below zero

(that is, no consumption were postponed, or there were no savings), the systems would implode. That is, ߟ݄ would go below zero. What does this mean in a social context? We explore that just ahead, simulating a system that can lead to chaos (in both the mathematical and social senses). As in the previous section, we have a glimpse of the unsustainability of endless growth.

For the moment excluding the chaotic potential of the model, let us explore a few more of the assumptions that lead to a convergent future. If the rich country is to have such a marvelous future to look forward to (that is, exponential growth in per capita consumption), what about the poor country? The usual convergence story assumes that ultimately both countries will have identical structural parameters and therefore will converge to the same steady state; the farther apart, the more rapid the growth of the poor country. (See Barro and

Sala-i-Martin, p. 111-118, 2004, for a summary of the Ramsey model’s predictions under those assumptions.) As we noted in the previous section, the data is not consistent with that expectation for many countries. In the output that follows, we start the rich country with a higher level of technology (A=2) and also alter some of the structural parameters. For example,

173 it has been shown (Ogaki & Atkeson, 1997) that the intertemporal elasticity of substitution is lower for poorer countries. (This simulation uses 0.30 for the poor and 0.65 for the rich.) This essentially says that the wealthy are willing to postpone a higher proportion of consumption until the future. We also set the social discount factor higher for the poor country (0.10 versus

0.05 poor to rich based on Easterly, 1999). In other words, the poor country is relatively is less concerned about future generations. The risk aversion parameter, which measures the how much a consumer dislikes facing uncertainty, is higher in poorer countries (a higher ߪ means a higher dislike of uncertainty). This is sensible since poor countries tend to have poorly developed credit and insurance markets (Yesuf & Bluffstone, 2007). In this simulation the risk aversion parameter for the rich country is 0.5 and is 1.0 for the poor country. The population growth rates are also different (.02 for rich and .05 for poor). Although the absolute values of parameters can be argued, the relative values are fully consistent with the literature. In the simulation we let both the rich and poor countries experience identical (and random) technology shocks. Capital intensity is also identical for both countries. (We will take a closer look at this below.)

Based on these parameters, Figure 53 below shows the difference in the persistence of an identical technology shock for both the rich and the poor economies.

174 Impulse Responses to a Technology shock

Income Rich Income Poor

Time periods

Figure 53. Ramsey model response to a technology shock.

As can be clearly seen, the rich economy harvests greater and longer lasting benefits from an

identical one-period non-persistent technology shock. These magnitude and persistence

characteristics, when coupled with an accumulation of technology, yield extremely different

growth rates. The time paths for output/income per capita illustrate not convergence but

divergence as Figure 54 below shows:

175 Income (per capita) 7.000

6.000 Income Rich Income Poor 5.000

4.000

3.000

2.000

1.000

0.000 Time

Figure 54. Ramsey model time paths for rich and poor economies.

The Ramsey model (as specified so far) does not recognize the effects of international capital

flows or any variation over time of capital intensity. We will investigate a few extensions of the

Ramsey model below in which attempts are made to extend the model into an open economy

framework. However, within the framework already established, let us look at the effect of an

exogenous change in capital intensity.

There are no direct connections in this model between the rich and the poor (as there

will be in a look at an extension of the model below), but we can compare the effects of an

identical change in capital intensity to both rich and poor and conjecture about the motivations

of the more powerful party as a result. If both rich and poor experience a one-time identical increase in capital intensity, we see the following outcomes for consumption. (Note that the starting stocks of each has been adjusted so that the graph shows the relative change from an identical initial condition.)

176 Response of Consumption to Change in Capital Intensity

Rich

Poor

Time

Figure 55. Capital intensity change for rich and poor.

We see that for a given increase in the intensity of capital in production, the rich’s benefit is

sustained at a greater level in all three measures. In other words, given the differences in

structural parameters described above, convergence will not happen unless either the poor

have a more rapid shift from labor to capital in production or the poor adopt structural

parameters for risk aversion, social discounting, etc. that are stronger in terms of growth

opportunity than those of the rich. Note that the transition to the new steady state requires

that initially consumption falls in order to fund the large increase in investment. Production

increases as the stock of physical capital increases. As the marginal product of capital gradually

decreases, investment also converges to its new steady state. The savings rates also adjust.

Figure 56 shows the relative responses. This gap will be important as the analysis continues a

177 few paragraphs down since, in the context of Figure 48, this requirement of the model is not matched in the measured reality of the US.

Response of Saving to Change in Capital Intensity

Rich

Poor

Time

Figure 56. Capital intensity change effect on savings for rich and poor.

Although this model does not describe a relationship between rich and poor (that is, in

the context of an open economy) as did our thermodynamic model, we might conjecture as to

how this relationship might evolve as growth trends toward zero. As further support for our

contention regarding zero growth as posited and used in the discussion of the Solow-Swan

model, we draw upon the literature on population growth dynamics which clearly recognizes

the unsustainablity of endless population growth (see, for example, Cushing, 2001, 2002) and in

many cases uses the Beverton-Holt equation42 as the foundation for ecological models of population dynamics. The Beverton-Holt relationship results in a time path as shown in Figure

42 1 ݐ , which has very strong ecologicalܻ ܻ ݎ = This difference equation for population growth is ܻݐ+1 െ1) ݐݎ)1+ ܭ implications. In this representation ݎ >1represents the inherent growth rate of population determined by demographic properties such as birth rates, survivorship rates, etc. ܭ >0is the “carrying capacity” characteristic of the environment typically associated with the availability of finite versus sustainable resources and waste by-products.

178 57 below. This growth path is essentially the same as those shown in several parts in Figures 25

and 27.

Time

Figure 57. Beverton-Holt model of population growth.

As can be seen, the population converges to a steady state (zero growth). As is clear by now,

this paper’s work extends this expectation to a more generalized zero economic growth

(contrasted with zero population growth).

In what follows, rather than show again that continuous growth in per capita consumption cannot be permanent (i.e., at some high level of real per capita consumption the aggregate consumer will reach satiation), we will show that, using the Ramsey model as a foundation, as the savings rates of the rich and poor diverge (or as the relative capital intensities diverge) and as population growth converges on a steady state, the time path for capital accumulation can exhibit chaotic characteristics. That is, in socio-economic terms, there is the potential for anarchy. The contention that chaotic outcomes in an economic model are analogous to anarchy requires some discussion before we proceed with this extension of the

Ramsey model.

179 Chaotic systems are determined by processes “that appear to proceed according to chance events though their behavior is in fact determined by precise laws” (Lorenz, 1994, p.4) or more succinctly, the systems exhibit “unruly behavior governed entirely by rules” (Stewart,

2001, p. 174). Although there are rigorous mathematical descriptions for these general statements, we will use the working definition proposed by Cushing et. al. (2003): “A trajectory is chaotic if it is bounded in magnitude, is neither periodic nor approaches a periodic state, and is sensitive to initial conditions (p. 6).”

It has been clearly demonstrated that macrodynamic theoretical models can exhibit chaotic outcomes (Rosser, 2000); but is the possibility of chaos only a laboratory experiment undertaken by “theorists bearing free parameters undisciplined by empirical studies?” (Quoted in Rosser, 2000, p. 195). The answers to Woodford’s criticism have ranged from agreement to disagreement. (See Rosser, 2000, for a review). The idea that a deterministic system can produce fluctuations that look just like random patterns is a bridge between opposite ends of the deterministic/probabilistic views of how the world works. In essence, does it matter whether or not research has been able to rigorously distinguish something that looks random but is not from something that is truly random? As will be shown in the model below, in spite of the ambiguity of mathematical proofs seeking to sift the “noise” from the signal of economic time series, computer simulations using parameters that are realistic (particularly in the context of zero growth) do lead to chaotic results. Furthermore, adding stochastic elements to a deterministic specification that can lead to seemingly unpredictable outcomes, as will be done in Chapter Three, only heightens the urgency concerning the movement of key parameters toward setting the system into chaos.

The implications captured in the last part of Cushing’s definition above regarding sensitivity to initial conditions has been understood since Poincaré wrote (1890): “A very small

180 cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. It may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible (2001, p.404).” Taking these words written in the 1890s and looking at how that general description would apply to the social systems that depend on continuity in economic growth and continuity in the expectations for the returns on investment, is it then not the essence of anarchy when the policy choices of government become irrelevant and the comfort of a known tomorrow evaporates? The simple fact that responses are not necessarily proportional to disturbances and, in fact, might be unexpected and nonintuitive (both in magnitude and in temporal dynamics) does not comfort those that wish that the future is determined, with a mean reverting random property, by today. There is no mathematical argument that refutes this possibility.

We depart now from the traditional macroeconomic analysis in which there is an assumption of linearity in relationships that are intrinsically nonlinear (wherein around the steady state the equilibrium points and the path outcomes of stable node, unstable node, and saddle-point equilibria are “forced” on the system). Taking a “global” view and applying nonlinear dynamical techniques (Medio & Lines, 2001; Lines, 2005), we open the door to the possibility of observing cyclical behavior with regular or irregular periodicity. As we will see, multiple and different results are the result of very small changes in parameter values: chaos and, in a broader context, anarchy!43

43 As alluded to above, the literature testing for chaos in economic time series is fairly large but inconclusive. See, for example, Barnett and Chen (1988); Serletis and Shintani (2006); and Barnett (2006), who says “It is my belief that the economics profession, to date, has no dependable empirical evidence of whether or not the economy itself produces chaos, and I do not expect to see any such results in the near future. The methodological obstacles in mathematics, numerical analysis, and statics are formidable” (p. 255). But in general there is a consensus that, as in any complex system in nature or society, the nonlinear relations will lead to strange dynamics.

181 The time dynamics in this extension of the Ramsey model are motivated from two sources: the Beverton-Holt equation, which forces the growth characteristics to rely on capital intensity and productivity, and a modification of the Ramsey model in which the production function is

ߙ(1+ߟ) (1െߙ)(1+ߟ) (ݐ ݈ݐ (2.45݇ܣ = ( ݕݐ = ݂(݇ݐ, ݈ݐ where ߟ൒0, ܣ >0, 0<ߙ <1, 0<ߟ <1.44 Note that if ɻ =0 , then the function is the standard Cobb-Douglas type. Capital accumulation is according to

(ݐ+1 = ݂(݇ݐ, ݈ݐ ) െܿݐ +(1െߜ)݇ݐ (2.46݇

with the depreciation rate ߜ >0.

Also, the utility function is expanded to include not only consumption but also leisure.

Thus

(ݐ, ݈ݐ ) = ݈݊(ܿݐ)+݉ȉln༌(1 െ݈ݐ) (2.47ܿ)ܷ

where ݉ >0. We have ܿݐ as per capita consumption and ݈ݐ as the time per capita spent

.working. With the time endowment normalized to one, 1 െ݈ݐ is the per capita share of leisure

The parameter ݉ provides weight to leisure versus consumption in the utility function. As we

have noted above, the dynamics of continued growth with constant productivity improvement

provide for less per capita labor and more per capita consumption.

44 The Ramsey model, as we have seen, absent an external shock, will only have a single outcome in terms of long-run stability (for a given set of parameters). However, if the production function is not specified for constant returns to scale, then endogenous cycles are possible. In particular, following Gomes (2006), the production function includes a mutually shared benefit (the economy’s average capital and labor ן1െ ן ߟ ן1െ ן ݐ ) ݇ݐ ݈ݐ and assuming a symmetric distribution soܮ ݐܭ)ܣ = inputs). (2.45) is derived by specifying ݕݐ that Kt =kt and Lt =lt. This approach bypasses some of the typical criticism of nonlinear models leading to chaos in which the model relies upon unreasonably high levels of externalities.

182 The economic interpretation of the modifications in (2.45) and (2.47) are derived from

the effect that ߟ has on output. As specified, ߟ is an externality. In the framework of this analysis, and recalling the discussion in Chapter One regarding the increased use of guard labor to counter the increased propensity for social unrest, the externality is, in fact, the diversion of productive resources from output to the mitigation of social unrest. This parameter is driven, as in the Chapter One model, by the gap between the per capita consumption of the rich versus the poor and is amplified by the continued improvement in communication technology. Thus,

ݐ െܿ݌ݐ ) increases, ߟ increases. So, according to (2.45), as ߟ increases (and concurrently asݎܿ) as

leisure for the rich versus poor increases), more resources are required to offset the growing

unrest. At some point, a saturation point is reached at which no output is generated. However,

on the path to that saturation point, as is shown below, the economy unravels unless, as is also

shown below, the gap between rich and poor is closed. If the endpoint is somehow reached, the

world is at a zero growth state.

This two-equation system can be reduced to the following difference equations in two

dimensions (see Appendix B for the proof and definitions of the new parameters):

ߙ(1+ߟ) (1െߙ)(1+ߟ) ߛ1݇ݐܣ(1+ߟ) ߙ(1+ߟ)[1െ(1െߙ)(1+ߟ)] ݉ܿݐ െ(1െߙ)(1+ߟ)(ן1െ(1െ + ݐ ൤ ൨ െܿݐ݇ ܣ = ݐ+1݇ (1െߙ)(1+ߟ)ߛ2

(െߜ)݇ݐ (2.48 1)

2 ݔ2ݐ±ඥ(െݔ2ݐ) െ4ݔ1ݐݔ3ݐ (ݐ+1 = . (2.49ܿ 2ݔ1ݐ

These equations are the foundation of the following numerical simulation. The per capita values

for the key parameters will respond to the population growth dynamics shown in Figure 57.

Since effects of diverging consumption rates (contained in the guard labor parameter ߟ

are ן that drains the productive capabilities of the economy) and the elasticity of substitution

183 relevant to both the Chapter One story and to the analysis of what happens to this version of the Ramsey model over time, those are two of the parameters that we will explore. As we will

and the consumption/leisure ,כ݈ ,see, it is also important to consider labor’s share in production

weighting, ݉.

Initiating the model with reasonable parameters based on the work of Guo and Lansing

(2002),45 we first see that with growth productivity stable, ߟ =0 and the elasticity of substitution set at .2 (a low capital intensity), we have a stable outcome in the long run (the initial 10,000 iterations of this simulation are excluded from the graph to allow the system to reach a zero growth state) for consumption and capital per capita.

Figure 58. Ramsey model – long-run stability under traditional assumptions.

However, if we set ߟ >0 (in this case to 4.8), we have a different long-run outcome.

כ 45 ݇0 =0.75, ܿ0 =0.5, ߚ = 0.962, ߜ = 0.067, ݉ =.38, ݈ =0.4.

184

Figure 59. Ramsey model – long-run instability with a high level of guard labor.

The system, although without any stochastic elements, exhibits seemingly random fluctuations in capital intensity. In fact, the system exhibits classic chaotic symptoms. Plotting in the space of capital and consumption, we can see what is typically called a strange attractor.46

That is, a system that exhibits none of the three outcomes of classic analysis (stable, unstable, saddle-path) but is bounded within the state space. We see in Figure 61 below the attractor of this model (with the first 100,000 iterations excluded and the second 100,000 iterations shown).

46 An attractor is informally described as strange if it has non-integer dimension or if the dynamics on it are chaotic. The term was coined by Ruelle and Takens, 1971.

185

Figure 60. Ramsay Model – attractor of the guard labor externality model with ࣁ set to 4.8.

The attractor also shows a discontinuous (instantaneous) movement from one regime to the other. This is confirmed by observing the map as it is being drawn. It is also interesting to see how the system evolves into this state by observing the relationship between consumption and changes in the guard labor externality and capital intensity.

186

Figure 61. Ramsey model – bifurcation diagram on the guard labor parameter.

Figure 61 shows the bifurcation diagram of the model on changes in the guard labor parameter (and the other parameters fixed as shown in the footnote above). As can be seen, the area in which the model was plotted for the attractor is an area of relative “stability” in that after following a stable path in the early stages of the increase in guard labor, consumption quickly enters a period doubling zone and then explodes into indeterminacy. This essentially suggests that as guard labor increases, there comes a point at which the regime must jump to a much higher level or face true uncertainty. (There are parameter combinations that retain single outcome paths as will be seen below.) This leads to what may seem a paradoxical conclusion: because this model is fully deterministic, forecasting is possible! Clearly the sensitivity to initial conditions of a chaotic system makes long term forecasts highly inaccurate, but there is valuable information in the system’s attractor. In this case, the ruling regime will know that only a leap in the proportion of guard labor to output will provide some bounded

187 certainty. Of course, they should also know that reducing the consumption gap and thus mitigating the need for guard labor will assure that they remain on a fixed point outcome.

With ߟ set to zero or less than the point of the first bifurcation, the model is single

However, setting ߟ =4.5 , we see that .כ݈ outcome stable for any reasonable values of ߙ or capital intensity, ߙ, is also a critical contributor to a loss of predictability.

Figure 62. Ramsey model – bifurcation diagram on alpha.

Figure 62 shows that the economy can in fact make the transition from low to high ߟ

without passing thru the zone of complete indeterminacy shown in Figure 61. This is

accomplished if capital intensity is very low (in this specification, less than about 0.0817). This

condition is sensible in the context of a world in which a growing majority of the people are

excluded from the growth in per capita consumption. At least if most are laboring (thus low

capital intensity), they are less likely to be restive. The rich sector may understand this and

188 might maintain a lower capital intensity and a high guard labor in order to avoid mathematical and social chaos.

Figure 6347 below shows the bifurcation diagram in eta and alpha space (that is, allowing both parameters to vary and thus showing a “three dimensional” view based on the colors in which red “bricks” are single outcome space, white is indeterminate space, and the other shades represent increasing periodicity, to black which is greater than cycles of period 25).

This diagram maps out the levels of capital intensity and guard labor that identify the single outcome space (red “bricks”) in which the ruling regime would prefer to reside. Note that as capital intensity increases (and thus labor is displaced), a higher level of guard labor is required

.0.6= כ݈ to remain in non-chaotic space. This outcome was simulated with

Figure 63. Ramsey model – bifurcation diagram in alpha and eta space.

47 This simulation and the others following each takes about 3.5 hours on a powerful desktop PC!

189 Somewhat less of a policy choice is the level of the average share of labor in production,

As the model is specified, this parameter is exogenous; however, this parameter would be .כ݈

expected to decrease as the economy moves to a zero growth state. Given a low initial value for

the guard labor parameter (0.5) and a capital intensity of 0.3, we see in Figure 64 that the

system is stable in the traditional sense as long as labor’s share is at least greater about 0.2575.

Figure 64. Ramsey model – labor’s share with a low guard labor.

and Ƚ space, we see in Figure 65 below כSetting guard labor to 1.2 and simulating in l that the system is stable for a variety of combinations of the parameters. Note that as labor’s share falls and/or capital intensity increases, the system’s area of stability shrinks. Although not

and Ƚ can be attained, but כshown, if the guard labor parameter is increased, lower levels of l there is still a limit at which the system rapidly shifts into a regime of greater than cycles of 25.

In the context of what we are investigating in this paper, this version of the Ramsey model suggests that as the economy approaches (or is at) zero growth, the effects of mitigating social unrest overwhelm the internal feedback loops of a traditional capitalist system of production

190 and consumption, and, if the direction and characteristics of the systems dynamics are not

altered radically, anarchy ensues even if it is not in the form of revolution.

In fact, drawing upon Chapter One’s insights, revolution might provide a stop gap on

the path to chaos.

Figure 65. Ramsey Model – labor’s share versus capital intensity with guard labor at 1.2.

Figure 66 below shows that with a high labor share, there are a number of parameter

combinations that will yield stability. Note, however, that there is still a limit to which guard labor can prevent anarchy. As capital intensity increases and thus labor input is lowered, there is an interesting pattern that evolves with guard labor and the boundary to anarchy. This pattern suggests that the effectiveness of the armies, police, militias, etc. in preventing chaos

(from both mathematical and social perspectives) declines if capital intensity rises too high and

to be too כ݈ capital does not expropriate enough of the fruits of production (that is, allowing large). What is informative from this simulation is the fact that there are stable zero growth outcomes if and only if the value of ߟ, the need for guard labor to cordon off the rich pockets,

191 moves toward zero. That means that the consumption gap between rich and poor must also move to zero.

Figure 66. Ramsey model – guard labor versus capital intensity with labor’s share high (0.8).

In the context of the zero growth story, once population stabilizes (which in all of these simulations it already has) then as long as technology is improving, labor per capita will fall, and leisure per capita will increase. This would mean a shift in the parameter ݉ in the utility function (2.47).

Figure 67 below shows that the outcome for the simulation that a shift in the choice

set at 0.6 ,כ݈ ,between consumption and leisure and the need for guard labor (with labor’s share and capital intensity, ߙ, set at 0.4) yields a limit to the effectiveness of guard labor. As the preference for maximizing utility shifts toward leisure from consumption, at about 0.357 guard labor becomes necessary to prevent entering the chaotic zone. However, unlike several of the simulations above, the effectiveness is limited to a value of about 1.9 for ߟ. A lower capital

192 allows guard labor to be effective to about ,0.9= כ݈ ,intensity, ߙ =0.2, and a higher labor share

3.1. No set of parameters is stable in the traditional sense if ݉ >0.6. The message for the

ruling class is to consume and let the poor work in order to maximally delay the end of order.

Figure 67. Ramsey model – guard labor versus leisure choice with labor’s share at 0.6.

As we have seen, the Ramsey model has some interesting implications for a zero growth

world. The model as first explored predicts a persistent divergence between the rich and the

poor, showing that even allowing for shocks to technology, the magnitude and persistence of

the effects are more favorable to the rich. The exploration of the Ramsey framework within a

nonlinear difference equation setting shows that the persistent divergence of rich and poor

drives the economic (and social!) system to chaos.

We have seen that small and economically reasonable changes in the specification of

the traditional Ramsey model can lead to the possibility of unpredictable irregular long-run

outcomes for important economic measures. It is important to note that saying that chaos can

be enticed does not imply that chaos is everywhere. As noted above, a large combination of

193 parameter values confined to a space that is typical for solving growth models yields typical results (stability, instability, or saddle point stable). But in this section we have shown that cycles and chaos in economic theory are possible using reasonable parameter values. This is not simply an exercise in math and logic. There is information that can inform policy makers and perhaps even guide decisions with a long-run goal of economic and social stability. At the very least, it should inspire thought (and imagination) into a realm of possibilities in which everything is possible at once. That is, of course, an undesirable outcome, so, perhaps, given the possibility

of that impossibility, the path taken will go to a steady state that works for everyone.

In the next section we will expand the possibilities. We will look at endogenous growth

models with human capital. As we have done so far, we will build upon the traditional

framework and explore zero growth outcomes.

Current Endogenous Growth Models: Knowledge, Education, Diffusion, Innovation, and the

Proliferation of Goods

“The presence of human capital may relax the constraint of diminishing returns to a

broad concept of capital and can lead thereby to a long-term per capita growth in the absence

of exogenous technological progress” (Barro, 2004, p. 240). As has been demonstrated to this

point, without some assumptions regarding how value is created by labor and capital in such a

way as to yield an endless increase in per capita measures of well being, growth models cannot

support endless growth. The consequences of the transitional dynamics under those

assumptions were explored above and the forecasts suggest a difficult future. Some of the

symptoms and by-products of this troubling forecast are already manifesting in the present as

was shown also above. But thus far several critical components of the real world have been

missing from the models.

194 In this section we will explore extensions of growth theory that are quite recent. We will briefly review some of the theory regarding the concept of human capital. However, even when we allow a fixed number of workers (zero population growth) but provide for an increasing quality of the labor function, diminishing per capita returns will eventually manifest themselves. The solution to that problem has been the most recent extensions in growth theory in which continuing advances in methods of production and the types and quantities of products open the escape door from long-run diminishing returns. In fact, it is this solution that is currently being played out in the world system. As Figure 6848 shows, the estimated stock of trademarks is increasing exponentially. The fitted time series forecast shows that by 2020 the stock of active trademarks will be more 3 times greater than in 2000. This suggests an exponentially increasing array of goods that has helped support the growth of the general economy. But can that pattern carry into long-run? That is what this section will investigate.

48 For period 1891 to 1970 the data on registered trademarks is taken from Historical Statistics of the United States: Colonial Times to 1970 (Series W 107 and W 108), US Census Bureau. These series are updated using data from the United States Patent and Trademark Office, US Department of Commerce, Annual Reports. The stock of trademarks is computed based on methodology used by Greenwood and Uysal (2005). Let the time t stock be denoted by St. The stock of trademarks is assumed to evolve in line with St+1 сɷ St + [It + Rt], where It represents new registrations at time t, Rt ŝƐƌĞŶĞǁĂůƐ͕ĂŶĚɷŝƐƚŚĞĚĞƉƌĞĐŝĂƚŝŽŶĨĂĐƚŽƌŽŶ trademarks.

Trademarks need to be renewed roughly every 20 years, but most are not. The mean of Rt /( Rt-20

+ It-20) measures the survival rate on trademarks. The depreciation factor on trademarks is 1/20 therefore given by ɷс΀Rt /( Rt-20 + It-20)]^ .

195 200,000 2,500,000

180,000 Registered - Left Scale R² = 0.9976 160,000 Renewed - Left Scale 2,000,000 Stock - Right Scale 140,000 Time Series Forecast

120,000 1,500,000 Registered 100,000

80,000 1,000,000

60,000 Renewed 40,000 500,000

20,000

0 0 1870 1875 1880 1885 1890 1895 1900 1905 1910 1915 1920 1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Figure 68. The stock of trademarks 1871-2000. (See Footnote 44 for sources.)

Arthur C. Clarke’s third law of technology, “Any sufficiently advanced technology is

indistinguishable from magic” (based on his work from 1972, p. 189) is, as it turns out, prophetic

with respect to how growth theory has used technology to provide for unending growth in per

capita measures of well being. But in order to substantiate that statement, we must first review

the current state of growth theory.

Uzawa-Lucas-Rebelo: Human Capital in Production

The model that we will begin with is based on the Uzawa-Lucas framework with an extension by Rebelo (Uzawa, 1965; Lucas, 1988; Rebelo, 1991). Rather than recreate their work, we will summarize the conclusions of the model. The model is based on Cobb-Douglas production functions as follows:

196 YCK G KAvKuH ()()DD 1 (2.50) HHB G [(1 vK ) ]KK [(1 uH ) ]1

where Y is the output of consumables and gross investment in physical capital; AB,0! are technological parameters; H is human capital; H and K are the change in human and physical

capital based on some investments I and I and a depreciation rate, G . DD,(0dd 1) and K H ,

K,(0ddK 1) are the shares of physical capital inputs in each sector, and vv,(0dd 1) and

uu,(0dd 1) are the fractions of physical and human capital respectively used in production.

Obviously the fractions of physical and human capital used to generate human capital through education are 1 v and 1 u . The implication is that human capital is generated from a

technology different from physical capital. In fact, if K D , then the model says that education

is more intensive in the use of human capital than the production of physical capital. This is an important consideration that we will explore later when looking at the prospects for stability if the opposite is true. The model displays constant returns to scale due to the constraint that

DD12 1 (where in the case of constant returns to scale DD21 1 ). That will be relaxed

farther down. The model also requires that there be a constraint on non-negative gross

investment so that once an investment is made into physical or human capital, it cannot be

reversed.

Following the typical use of the household’s utility function (and using the form

uC() ( C1T 1)/(1)T ) and forming a Hamiltonion

JuCe ()UDDt QG [ AvKuH ( ) ( )1 KC ] (2.51) KK1 PG {BvKuHH [(1 ) ] [(1 ) ] } , it can be shown that the first-order conditions lead to

197 (1D ) CC/(1/)[(/)] TD A vKuH GU. (2.52)

That is, the growth rate of consumption depends on the elasticity of substitution, 1/T , the net marginal product of physical capital in the production of goods (the rate of return),

rA DG(/ vKuH )(1D ) , and the rate of intertemporal substitution, U . A characteristic of the model is that the rates of return for physical capital, regardless to which sector it is allocated, must be the same. This is also true of human capital. That says then that

§·KD§·§·§·vu ¨¸¨¸¨¸¨¸ (2.53) 11KDvu 11 ©¹©¹©¹©¹.

So for a given set of K and D an increase in the production of goods is the result of an increase in the fractions of the two inputs, K and H , that are allocated to the goods sector.

We can express the shadow price of human capital in units of goods by taking the ratios

of the Lagrange multipliers, pH { PQ/ . Using (2.51) and (2.53) and some manipulation yields

the following:

pAB{PQ/ ( / ) ( DK / )KKD [(1 D ) / (1 K )]1 (vKuH / ) K (2.54) H .

This is a differential equation on pH , which is stable only if [(ww pp / )/ p ] 0 , which is only

true if DK! . That is, the relative intensity of physical capital must be greater than the relative

intensity of human capital. This ratio of the marginal product of H in the physical goods sector

(the wage rate) to the marginal product of H in the education sector shows that price is based on the ratio of physical capital employed in the production of goods to human capital employed in the production of goods or Q KH/ P . The instability that arises if the relationship DK!

198 switches would either drive wages (and thus consumption) to infinity or zero in one or the other sector. Farther down we will see what happens if that relationship switches.

The stable version of the system can be shown to lead to several conclusions about endogenous growth (see Uzawa, 1965, and Lucas, 1988). The key insight is that the growth rate of output will rise or fall if human capital is relatively abundant or scarce. In straightforward words, if an economy is below its steady state growth rate due to a catastrophe, the economy will move to a steady state growth rate more rapidly if human capital is preserved. This conclusion is supported in the analysis in Chapter One, in which education leads to growth in per capita income.

However, suppose that this model is subjected to a breakdown in the assumptions about growth within the assumption in the Cobb-Douglas production function regarding returns

to scale. (Recall that these issues were raised in the introduction to this chapter.) The

inconsistency that was referenced in the opening section of this chapter between the Inada

conditions that support the algebraic formulation of the production function and assumptions

on returns to scale that are also essential to the stability of endogenous growth model suggests

that one must be forced to choose one or the other when studying growth.49 In fact, Shephard

(1969) shows that since the production function is essentially a technological relationship that

combines inputs one must accept that it is bounded or expel the notion of diminishing or

constant returns to scale. He shows that the Cobb-Douglas form violates the premise of a

bounded set on technology and thus output. As Fare (2002) showed, the Inada conditions

reinforce this inconsistency.

49 The Inada conditions relevant to this discussion regard the marginal product of capital or labor at the limit if capital or labor goes to infinity and, at the limit, the effects of capital and labor on output. The outcomes imply that that labor is essential and capital is essential.

199 What follows is inspired by their work. We will show that the commonly used foundation for endogenous growth models can lead to zero growth by a simple change in the production function. (By the way, this is the counter to the standard outcome of these models,

which lead to endless exponential growth; we have already looked at in the Solow and Ramsey

frameworks as impossible for a number of reasons.) The change from constant returns is

accomplished by allowing the possibility of the sum of the parameters D1 and D2 to not equal

one. For example, if DD12 1 then the system exhibits diminishing returns to physical capital

(and the same for human capital with K ). In this case we can rewrite (2.50) as:

YCK G KAvKuH ()()DD12 (2.55) HHB G [(1 vK ) ]KK12 [(1 uH ) ]

With this change we can find a condition that will guarantee endogenous positive growth. We first divide the second part of (2.55) by H , take the logarithms of the terms, and differentiate

with respect to time. This yields

** K12JKKY(1)0 J (2.56) where J * is the steady state growth rate of physical, human capital, or consumption, depending on the subscript. Dividing the first part of (2.55) by K and performing the same set of calculations we get

§·CK/ ** ** ¨¸()(1)JJCK D12 JDJKH (2.57) CK/ JG* ©¹K .

* * ** J K must equal J C since if JJCK! , then (2.55) says that the growth rate of capital will go to

** f . Also if JJCK , then at the limit CK/0 . Thus (2.57) simplifies to

200 (1)DJDJ** 0 (2.58) 12KH.

Equations (2.56) and (2.58) can be put into a system of two linear equations with two

* * unknowns, J K and J H . Only if the determinant of the characteristic matrix of the coefficients

is not zero does the system have a solution that provides for endogenous positive growth (so

** that we do not get the outcome JJHK 0 , the dreaded zero growth conclusion). That requires the parameters satisfy

(1KDDK ) (1 ) 0 (2.59) 2121.

Clearly constant returns to both sectors work out (DD12 1 and KK12 1). In fact, this is the only set of parameters that provides for endless positive endogenous growth. The outcome

**** of constant returns to scale says that JJJJKHYC or that K, C, H, and Y must all grow at

the same rate in steady state. Looking at other parameter combinations, D1 0 and K2 0

make no sense (that would say that physical capital has no place in production, and/or human

capital has no place in education). D2 0 and K1 0 can make sense if, for the first, human capital has no purpose in production, and, for the second, physical capital has no purpose in education. The first alludes to a world of only machine workers, and the second is counterfactual and not possible in a developed civilization. Some of the other combinations in

which the parameters sum to more or less than one (but where if DD12!1 then K12dK 1 or the converse) yield outcomes in which K and H grow at different rates and thus KH/ rises or falls forever. That outcome also makes no sense since at the limit the world is all machines or is an idiocracy50. Two long-run predictions of this endogenous growth model are as

50 See the movie by the same name for a good laugh and glimpse of that future.

201 follows: 1. endless balanced growth with ever-increasing consumption per capita; or (if both sectors exhibit diminishing returns to scale as Shephard showed to be a necessary deduction from the logic and algebra of production functions) 2. something that is not acceptable in our vision of the future: eventual zero growth. That is, if both DD 1 and KK 1 then the 12 12 ,

growth rates of both K and C fall to the asymptote of zero, and the world approaches a new

**** steady state in which JJJJKHYC 0.

Recall that all of this is also based on the assumption that the output elasticity of

physical capital must be greater than the output elasticity of human capital,

DD 12t D KKK 12. This is easy to understand in non-mathematical terms in that it says

that as long the goods sector’s share of physical capital is greater than the knowledge sector’s

share of physical capital, then output and consumption will not experience negative growth in

the long-run. If the factor intensities are reversed (that is, the education sector becomes

relatively intensive in physical capital), then (2.54) is unstable, and any departure from the

saddle path would lead to an outcome that caused the time path of the key variables to depart

from the steady state growth rates at a rate that grows over time. This would be manifested by

the part of (2.54), in which the ratio (/vK uH )DK would have an opposite effect from the marginal product of physical capital than expected. Perhaps we can imagine a future that becomes more and more a world that trades in knowledge rather than physical goods. The logic of this model suggests that, given these “unstable” parameters, over time in that world the fraction of human capital used in production will approach zero.

In other words, just as posited earlier in this chapter, either everyone works one second a day, or only one person works. The logic also then says that consumption will approach zero.

202 And striking right at the heart of capitalism (and rigorously supporting the thesis of this research), the logic also says that the return on investment rA DG(/ vKuH )(1D )

will approach the depreciation rate.

Most treatments of this model exclude the conclusions in the last few paragraphs

regarding zero growth by saying that using parameter combinations that lead to unimaginable

outcomes are therefore implausible parameters. But is it implausible to imagine a future in

which human capital becomes the primary stock of capital and physical capital exists to simply

replace depreciated physical assets and food? If not then, at least in the context of the

endogenous model we have just explored, we can imagine a zero growth world.

We are not quite finished, however, with this systematic deconstruction of growth

models. The extensions of the endogenous growth model we have just reviewed have modified

the standard conclusion regarding balanced growth at constant growth rates. In particular, the

declining rate of return that we just identified is a troubling outcome that arises if one

recognizes that DK 1 is not possible in the long-run. That is, the continual accumulation of capital (both physical and human) cannot sustain long-run growth. This has motivated an exploration for logic that could modify the rate of technological progress by, among others,

Romer (1990, 1994), Judd (1992), Aghion and Howitt (1992), and Aghion et al. (2002) to find an escape from the long-run diminishing returns trap.

For the rest of this chapter we will consider models that incorporate technological change both in the form of an expanding variety of products and also in the form of better quality products replacing older products.

203 Endogenous Growth through Innovation and Diffusion

The foundation for the model in which there is a variety of products (that is, new products are added to the menu for the households to choose from) are producers, inventors, and consumers. The models differ in their treatment of patent duration and the cost of innovation (cost in terms of goods or labor) but in general have similar conclusions to the AK type models we have already looked at. What follows is a summary of those models.

Using a typical formulation, the quantity of output for the ith firm (producer) is described

11DDD YALNXNii () i (2.60)

where D plays its traditional role in the production function, L is labor input, X is an intermediate good to production, N is the number of varieties of goods, and A is the overall

measure of productivity. This function, however, leads to diminishing returns as, if NX i increases, the benefits of X are spread thinner. The way out of that is to see that the term

N 1D , by spreading intermediates over a more final goods, performs a sort of technological progress role. As long as N increases for a given X , diminishing returns are avoided, and endogenous growth in engendered.

The inventors have to assess that the net present value of the profits of an invention justifies the cost of the invention. They also have to find the optimal price for the new goods that they will sell to the producers of final output. The cost of invention is, in this model, K units of output Y . This suggests a potential problem for long-term growth in this context. If we

think of the ability to invent new ideas becoming more difficult as the world proliferates with

goods, then K()N (that is, the cost of invention is a function of the number of goods) would

204 suggest that Kc()N ! 0. If the net present value of the profits is denoted at Vt() , then at

some point if Vt() K (which says that since the net present value is less than the cost), no resources would be devoted to inventing. From that point forward, the number of goods, N would remain constant. This would lead to diminishing returns and eventually zero growth. The typical presentation of this model has a statement that excludes this outcome with a non- mathematical disclaimer in which only the outcome with positive R&D is considered (see, for

c example, Barro and Martin, 2004, p. 294). Perhaps this is also true because if K ()N ! 0, then

the interest rate, rt() (SK / ), also goes to zero, and this is anathema to the endless growth

assumption.

The third party in this model is the households who maximize utility over an infinite

horizon according to

1T f §·c 1 Ut Ue ¨¸dt (2.61) ³0 1T ©¹.

Population growth is assumed to be zero. Since the growth rate of consumption is

CC/(1/)() TU r , (2.62)

then if interest rates go to zero, the growth rate of consumption also goes to zero. By the way, as interest rates fall, then, although not explicitly modeled in the math, we can imagine that the household preference parameters T and U would increase as households save less; this would accelerate the transition to zero growth. This effect and the effect of an increasing K can be seen in the solution for the growth rate:

205 ªº1/(1DD ) §·1 D 2/(1 ) JT (1 / ) (LA / K ) ¨¸ DU (2.63) «»D ¬¼©¹ .

Extensions of this model by Peretto (1998), Segerstrom (1998), and Jones (1999)allow

for Kc()N ! 0. The solutions yield a saddle-path stability trajectory that yields only long-run

growth if L grows at the rate of population growth. These extensions find that non-zero long-

run per capita output growth requires endless population growth, and that is impossible. The

only way out of a zero growth outcome is if the cost of invention declines forever. Romer (1990)

and Grossman and Helpman (1991) followed this path by assuming that the cost of invention

declined over time as more ideas were accumulated. Data from the United States does not bear

this out as shown below.51

R&D Total Expenditures US constant 2000 $millions $350,000

$300,000

$250,000

$200,000

$150,000

$100,000

$50,000

$0 1953 1955 1957 1959 1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005

Figure 69. Real total R&D expenditures in the US (National Science Foundation, 2007).

Figure 68 (NSF, 2007) shows that total R&D spending, in real dollars, has been increasing at a steady rate. If Romer’s assumption is correct, productivity should be rising at a faster rate.

51 Frantzen (2000) also shows this for a cross section of 21 developed countries.

206 But as the chart below (NSF, 2007 and Bureau of Labor Statistics, 2008) shows, there appears to be no increasing return to R&D investment.

Annual Change in R&D Spending and Net Total Multifactor Productivity 35.00%

30.00% R&D

productivity 25.00%

20.00%

15.00%

10.00%

5.00%

0.00%

-5.00% 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006

-10.00%

Figure 70. Change in R&D spending and net total multifactor productivity (NSF, 2007, and BLS,

2008).

Ha and Howitt (2007) confirm that there is no upward trend in productivity growth

against a variety of measures of R&D investment. It would appear that the pessimistic forecast

for zero growth has been excluded from this growth model framework’s long-run by nothing

other than psychological denial.

Some researchers understood this and found that rather than seeing a future with an

inevitable finite number of goods , they would envision and model a future in which the quality

of existing goods were continuously improved upon (beginning with Aghion and Howitt, 1992).

In this framework there is a process of “creative destruction” (Schumpeter, 1934) by which,

when a technology or good is improved, the better technology or good replaces the old one.

207 This contrasts with the previous model’s discussion in that the inventors of improved things now will eliminate the perpetual profits of the inventors of old things (that were a part of the production of an endless accumulation of goods in the previous model). As in the last model, there are three sectors: producers, inventors (R&D firms), and consumers.

Inventors invest resources to engage in research to develop improvements in quality.

They essentially face a world in which the number of unique goods has reached a growth limit and are now only concerned with making “new” goods by replacing old goods with better versions. We have taken a look at some data on trademarks and a short term projection of the growth in trademarks in Figure 68. The series that identifies “renewed” trademarks is flat versus the total stock series, suggesting that the current system is supported to a great degree by creative destruction. But there is also a continued proliferation of what might be called quality differentiated goods. (There is certainly a connection here to consumerism, but that is another story.) However, as will be argued below, there is a consideration regarding both the degree of differentiation and quality leap of the relative “improvement.”

Inventors do not know how long they will have monopoly rights on their ideas so that the calculation of the net present value of the returns on their investments has uncertainty. The details of deriving the model that will be used as a foundation for discussion can be reviewed in

Aghion and Hewitt (1992).

The assumptions used on the path to finding the model’s predictions that are relevant to this discussion concern how the uncertainty is assumed to play out and the degree to which an improvement changes quality. Both of these considerations appear in the equation for expected net present value of the return on the inventor’s investment:

NDj /(1 D ) EV[(NNjj )] g q /[ r p ( )] (2.64)

208 1/(1DD ) §·1D 2/(1 ) SN()jjpEV () N [()] N j where gA ¨¸ D L , r , D plays its usual role ©¹D EV[(N j )]

as a determinate of factor intensity, N j is the R&D firm in sector j , and q is the improvement

in quality. p()N j is the probability per unit of time that there will be a successful innovation

(better than what exists) by the inventor in sector j . Note that g says that there is some flow of value that is constant with a given population L (that is when there is no innovation).

SN()jjj Pq () Zk () where P is the same across all sectors and is a function of quality, and

Zk()j is the cost (defined more fully below) of innovation. As generally modeled, the duration

of the monopoly profits is based on the probability of a successful research effort; that is

assumed to be generated from a Poisson process. (Of course, for a sufficiently large number of

occurrences the Poisson distribution becomes a normal distribution.) The random process is a

function of R&D effort in the particular sector j . To avoid diminishing returns in that process, it

is assumed that the probability of success is proportional to the investment in R&D and is not

negatively related to the level of quality. (That is, there is a linear reward for investment even

as quality improves that is symmetrical around the probability distribution.) There are two

fallacies embedded in that assumption.

First, recent data suggests that the cost of innovation is increasing, and second, the

distribution is not normal. The following charts52 with data from a cross section of 14 key US

sectors illustrate the first problem with the assumptions. Figure 71 below shows the aggregate

ratio of R&D spending to output (both in real 2004 dollars and normalized to an index) with a

52 Data is from the Bureau of Economic Analysis/National Science Foundation 2007 Research and Development Satellite Account, Tables 5.2 and 7.1a, Sept. 28, 2007. Industries selected are from North American Industry Classification System codes 325, 3254, 3251-53, 3255-56, 3259,334, 3341, 3342, 3344, 3343, 3346, 336, 3361-63, 3364, 3365-66, 3369, 5112, 5415, and 5417.

209 simple ARIMA time-series forecast 10 years forward (1987 is indexed to 1.0 or 100 in the following charts).

Ratio of R&D to Output for all Industries 6.00

R² = 0.9621 5.00

4.00

3.00

2.00

1.00

0.00

Figure 71. Ratio of R&D to output. (See Footnote 48 for sources.)

Since many of the foundations of Schumpeterian growth models were developed in the

1990’s, one can see how the data for the US supports a linear relationship assumption. But

there is break point (confirmed with a Quandt-Andrews breakpoint test) in 1996. Looking at a

few specific sectors in Figure 72 below, the divergence is clearly illustrated. Chemical manufacturing is near the median, communications is the maximum extreme, and software is at the minimum extreme. Note that the median sector in Figure 72 below, in 2004, invested almost 6 times in real dollars in research (compared to 1987) for an output that was about double that of 1987. The forecast suggests 14 times the input for less than 3 times the output in

2015.

210 Chemical manufacturing Output 1600

1400 Chemical manufacturing Output Chemical manufacturing R&D 1200 Output TS Forecast 1000 R&D TS Forecast

800

600

400

200

Communications equipment manufacturing Output 3500

Communications equipment manufacturing Output 3000 Communications equipment manufacturing R&D

2500 Output TS Forecast

R&D TS Forecast 2000

1500

1000

500

(Third chart on next page.)

211 Software publishers Output 4000

3500 Software publishers Output Software publishers R&D 3000 Output TS Forecast

2500 R&D TS Forecast

2000

1500

1000

500

Figure 72. R&D and output for three specific sectors. (See Footnote 48 for sources.)

The data suggests that the assumption of a one-to-one relationship is incorrect since the

breakpoint in 1996.

The following charts, which show data for the R&D to output ratios overlaid with a best

fit probability distribution (based on the minimum Kolmogorov-Smirnov statistic tested on a full

menu of probability distributions), test the assumption of normality in the random

characteristics of p()N j , the probability of a successful innovation. If the assumption is correct, the ratio of the R&D investment to the output of the sectors should center on the mean.

212 Figure 73. Probability distribution of R&D to output data – 1987 to 1996. (See Footnote 48 for

sources.)

Figure 73 shows that the decade to 1996 had a normal distribution, and the mean and median are close. Skewness is very small. Of more interest is the proportion of ratios that are less than one. 80.0% of the data showed a net positive relationship between the growth of R&D and the growth of output (that is, a given growth in R&D generated a larger growth in output, a ratio of less than one).

213 Figure 74. Probability distribution of R&D to output data – 1997 to 2004. (See Footnote 48 for sources.)

Figure 74, showing the data since the breakpoint, however, shows that the distribution is

anything but normal.53 The data since the breakpoint suggests that there is an increased risk to the payoff of an investment with an almost exactly reversed (totally coincidental!) proportion of ratios now showing a net negative relationship between the change in R&D and output. (That is, a greater change in R&D is needed for a given change in output, a ratio greater than one).

The large skewness illustrates the increased need to pump R&D into the production function to keep output growing. The typical role for standard deviation in financial applications is as a measure of risk. In this case, the uncertainty of a positive result has increased by about 8 times.

53 The best fit is a type V Pearson distribution with a density function of .

This density function best fits data with a large skewness.

214 This increased risk, along with the other contradictions outlined above, in the context of an R&D investment choice based on (2.64), has consequences.

Clearly the probability of success for an innovator is related to the R&D expenditure. So what happens in endogenous growth models that relay on innovation if the risk of innovation is increasing over time and the marginal benefit is decreasing? In other words, suppose that an increasing expenditure in R&D is required to maintain a constant growth rate. And suppose that that condition is overlaid with a market in which the required rate of return for increasing risk should be increasing.

Following the typical evolution of this model class (but with variations based on the insights above), if the aggregate flow of resources in sector j by a potential inventor for the purpose of increasing the quality, q of a good from N to N 1 is denoted by Z()N , then j j j

the probability of success for the inventor would be

q pZ()NNIGjjj ()() k (2.65)

§·1 (1)k where I()kq j is the cost is a function that embodies the relationship j ¨¸ ©¹KN Z()j

between the level of quality for that good in that sector and the cost of innovation, and G is a

measure of the variance in success as quality increases. 01 K scales the cost effect. Since

both terms in IN()j are decreasing with improvements in quality over time, the only way that

p()N j can remain constant or increase is for Z()N j to grow at an increasing rate (just as we

have seen in the data above). But as q increases, IN()j o 0 , and thus p()N j o 0. The

marginal increase in quality, N , becomes insufficient to support profits. That is, the price

increase is insufficient to offset the cost increase, i.e., ww S /0q , and diminishing returns set

215 in. The economy will have no escape from the diminishing returns to scale modeled in prior models. As the probability of success falls, a feedback loop accelerates the convergence to zero.

So rather than an asymptotical convergence, this extension of the model suggests a crash to

SN()jjpEV () N [()] N j zero. Recall that SN()jjj Pq () Z ()N , and r . By simply EV[(N j )] discarding the assumptions that mandate positive growth forever and injecting currently observed reality into the model, we have again thrust a death blow to the heart of capitalism with profits and interest rates crashing to zero in the long-run.

This can be illustrated by a derivation of the system’s dynamics which shows aggregate quality and consumption growth rates loci, QQ / CC / . Since consumption growth and overall growth are the same, this analysis shows the growth rate of the economy. Following the usual mathematics (and using the specification for the households’ consumption smoothing used earlier in this chapter), we can see that CC /(1/)() TU r (at zero population growth). Aggregate quality is the sum of all of the sector’s q ’s and is thus

§·Q DD/(1 ) Epkq¨¸ ()( 1). Solving for the intercepts and slopes yields the following: ©¹Q

216

Figure 75. CC and QQ locus for endogenous growth with innovation.

As q increases, the slope of the QQ / locus gets more negative. In the story told by this model in the literature, the increase in the intercept is at least large enough that the growth rate (and interest rate) does not decline from the decreasing slope. This is assured by the assumption that the marginal return on investment in innovation is greater than one and that profits do not fall. But as we have just shown, if those assumptions are altered to allow the model to reflect an increasing cost to maintain growth, then as q increases, S o 0 , and both the slope and intercept in figure 75 take the equilibrium growth rate of the economy to zero.

We have almost concluded our deconstruction of growth models. The rest of the extensions in the literature focus not on the determinates of fundamental growth but on the ways in which the benefits of invention diffuse or labor migrates. Starting with Nelson and

Phelps (1966) to Krugman (1979) and extending more detailed investigations of assumptions in

Aghion, et al. (2001) and Acemoglu et. al. (2004), the general outcomes of the foundational models are not challenged vis-à-vis long-run optimism for continued growth (and also

217 convergence between leading and following economies toward a flat world, a conclusion that we have refuted earlier in this chapter as counter to the underlying motivations of capitalism’s quest to maximize return on investment). The details of the diffusion models, such as agglomeration, intellectual property, communication, supply chain integration, fertility choice, government intervention, and labor/leisure choice only change the conclusions about convergence. Still lurking at the foundations of these investigations are the assumptions that lead to endless growth. Therefore, we will not review the details of these models.

Certainly there is a large and credible literature advocating for limits to growth, but that literature typically relies on ecological arguments (which to this writer make exceptionally good sense). But, as we have shown with increasing rigor, the mainstream economics literature, when it sees a potential pathway to zero growth, assumes parameters or specifications that exclude that possibility. Some of the more recent literature (see Ponzi, Yasutom,and Kaneko,

2003, and Gomes, 2006, for examples) find pathways to instability and chaos from within the mainstream models. But they, like this chapter, have removed the blinders that have hidden the scary stories that, if told, will reveal the Ponzi pyramid that props up capitalism.

Conclusion

This chapter has reviewed growth theory from the simple models that relied on exogenous parameters developed more than a half a century ago to the most recent endogenous growth models. Interestingly, all of the models, including the endogenous models, use parameters that have assumed (and usually fixed) roles to play. In the pages above we have focused on how assumptions that are made in the name of making models supposedly congruent with the so-called stylized facts of economic growth (and also mathematically stable) are often very much ad-hoc or, worse, fly in the face of recent data.

218 We have demonstrated from a common sense perspective the fallacy of endless growth by extending the logic of the diminishing marginal utility to increasing consumption per capita to

its limit. We have also shown theoretically that the underlying “engine” of capitalism contains

contradictions with respect to convergence and have demonstrated that the data reveals trends

that support our analysis. This troubling prediction connects with Chapter One’s story regarding

the dangers of unequal growth and also connects with our extension in this chapter of the

growth models in such a way as to test for chaotic outcomes. But we have also rolled up our

sleeves and shown that the mathematics, when decoupled from the restrictions of parameter

and model specification assumptions that have no grounding in empirical trends, yield outcomes

that prove our thesis for a future of zero growth.

That conclusion cannot be avoided. If our developed civilization can survive every

challenge that it faces,54 the challenge that will be left will be the transition from capitalism into some post-capitalistic world. What that world will look like and the full story of that transition will be part of the subject of the work that will extend this project into a fuller exploration of the futures that lie ahead and how to get there. But that work is not a part of this paper. What is a part of this paper is the material in Chapter Three that will provide clues for the navigational challenges ahead.

This last part of this document uses the models and the relationships that have been worked out so far to construct a computer simulation. That simulation will show how the current path has no happy ending unless critical assumptions that we now regard as axiomatic are altered. But in no way will the future be what we think it will be.

54 This is a huge “if,” considering the ecological by-products of global development, the competition for finite primary inputs, the propensity for violence at a scale that has the potential to distort the future into something we cannot imagine, the general growth in complexity in every system we can define that has already moved the understanding of systems beyond a human mind’s capacity… . The list could fill pages.

219

CHAPTER THREE

WHERE WE HAVE BEEN, HOW WE GOT HERE, AND WHERE WE MIGHT GO

“There is no bound to the prolific nature of plants or animals but what is made by their crowding and interfering with each other’s means of subsistence” Thomas Malthus, An

Essay on the Principles of Population, 1798, p. 152.

“It’s tough to make predictions, especially about the future.” Yogi Berra.

“Linearity is a trap. The behavior of linear equations – like that of choirboys – is far from typical. But if you decide that only linear equations are worth thinking about, self- censorship sets in. Your textbooks fill with triumphs of linear analysis, its failure buried so deep that the graves go unmarked and the existence of the graves goes unremarked.

As the 18th century believed in a clockwork world, so did the 20th in a linear one”

(Steward, 1989, p. 83).

“And it ought to be remembered that there is nothing more difficult to take in hand, more perilous to conduct, or more uncertain in its success than to take the lead in the introduction of a new order of things. Because the innovator has for enemies all those who have done well under the old conditions, and lukewarm defenders in those who may do well under the new. This coolness arises partly from fear of the opponents, who have the laws on their side, and partly from the incredulity of men, who not readily believe in

220 new things until have had a long experience of them. Thus it happens that whenever

those who are hostile have the opportunity to attack, they do it like a partisan, whist the

others defend lukewarmly” (Machiavelli, 1515, p. 27).

Introduction

Can we keep doing what we are doing and keep getting what we got? The answer depends on whom you ask.

The limits-to-growth literature shows how the human footprint is squashing the ecosystem. “Finitude, entropy, and complex ecological interdependence… combine to provide the biophysical limits to growth” (Daly, 1991, p 114). Finite resources have combined with the second law of thermodynamics, and thus depletion and pollution are disordering the natural

feedback loops that have sustained this planet until now. From that literature and its simulation modeling we can see that if we keep doing what we have done, the future will definitely not be what we want it to be. The relationships between the economy and the world environment in models such as the seminal World Model developed by Meadows and other simulation models

that followed55 explicitly tell a story in which the economy, in conjunction with natural resource

limits and energy constraints, crashes.

Much of the mainstream economics literature, as we have shown, is strangely devoid of

concerns regarding limits to growth. In general, logic that leads to uncomfortable conclusions

regarding the future is shunted or is nudged back onto a nice saddle path to a well defined

outcome that fits into the paradigm of endless growth.

55 See Meadows, 2004, for the most recent update to the 1972 World Model. Also see Nordhaus, 1991; Fiddaman, 1996, 1997, 1998; Gerhagh and van de Zwaan, 2003; Manne and Richels, 2004; Warr and Ayers, 2002, 2006; and Ayers and Warr, 2005.

221 We have shown in a progression of models in the previous chapter that limits do exist if the logic is liberated from the axioms that permeate the foundations of thought. We also showed in Chapter One that the logical outcomes of unequal growth can introduce destabilizing feedbacks. This was incorporated into a growth model in Chapter Two, and chaos followed. But all of the models and simulations that have preceded this chapter have more or less stood in isolation to each other. Furthermore, the forecasts were based on exogenously modifying key parameters such as the rate of technological progress, the factor intensities, or shares of the rich and poor as time passed.

This chapter will unify what we have discovered into a single simulation in which there are no exogenous inputs. The model that follows builds upon the complex systems models noted in the footnote above. In particular, we use the variation on the neoclassical production function that Reiner Kummel pioneered.56 The integration of the components of neoclassical theory, the insight from the thermodynamic interpretation of economic activity, the non- productive demand for guard labor, and natural constraint of the limits to labor (population) are at the heart of what follows. Although the model needs to explicitly consider energy use (and waste) in the production function, we decouple ourselves from any limits to energy sources or concerns with ecological imbalances. The purpose of this research is to look forward into the world that would be ours if there were no ecological constraints–a world, if we could keep doing what we have done, with endless growth.

The experiments that follow the description of the simulation will evaluate the prospects for our future. After the end of endless growth perhaps there is one.

56 See Kummel, 1989, and Lindenberger and Kummel, 2002.

222 The Background for the Model

At the heart of the model is output. That is, after all, what we do. We combine materials, knowledge, labor, and energy to make stuff. The stuff is “worth” more than the sum of the cost of the individual parts; thus we have capitalism. As we have seen, along with capitalism has come, in the aggregate, a dramatic increase in the standards of living. How to explain this within a simulation requires that we first can credibly replicate empirical data before we can credibly forecast the future.

Therefore we need to specify a core set of relationships that explain the inputs to output so that simply normalizing the beginning of time to one we can generate a history that matches what really happened. The real challenge is to avoid any assumptions in the production relationship or to rely on macroeconomic time series data to drive the model. Of course empirical data needs to be used to calibrate the model, but, in the end, the model must generate history without assumptions. We use data from the US since it is fairly complete and accurate back to 1900.

The choice of a production function specification can be limiting or liberating. As we reviewed in Chapter Two, liberation has not been typical in the development of growth theory.

Indeed, combining capital and labor have long been seen as the source of growth. Ever since

Adam Smith’s invisible hand, the notion of equilibrium and markets clearing has guided thought.

Since Walras’s competitive equilibrium postulate was proven by Arrow and Debreu (1954), mainstream theory has assumed that the real economy is at or near equilibrium. But even prior to the 1950s, that assumption underpinned the mathematics. The Harrod model (1939), which gave capital a premier role in development and was influential in policy in the post-World War II era, did not withstand empirical scrutiny. Then Solow and Swan, whose model we have looked at carefully in Chapter Two, introduced the aggregate production function which relies on

223 capital stock to combine with labor and create output. There was still a problem with matching the data on per capita growth to the theory, and the substantial Solow residual became technological progress.

The explanation of technological progress is the goal of the theory that we deconstructed in the second half of Chapter Two. However, “the so-called Solow residual

(technological progress) remains to be explained. The neo-classical paradigm as articulated by

Solow and others does not allow for ‘real’ material flows. Production and consumption are abstractions, linked only by money flows, payments for labor, payments for products and service, savings and investment. These abstract flows are governed only by equilibrium-seeking market forces (the invisible hand). There is not a deep fundamental connection between the physical world and the economy” (Ayres and Warr, 2002, p. 3). Even incorporating knowledge in the form of human capital, there is still the problem of explaining economic growth from a quantifiable measure of what that means. As we saw in Chapter Two, R&D fails.

The search for a production function specification for this simulation model needs to go outside of the limits of Cobb-Douglas forms and the linear assumptions that facilitate mathematical optimization. These conventions are convenient for Hamiltonian systems modeled on classical dynamics but are not reflective of the growing understanding of the complex nonlinear world in which we operate.

If one looks at the history of growth, a potential candidate for a key role in explaining growth is the increasing energy flows used to achieve the substitution of machines for animals and people (machines that consume fossil fuel, we should note). However, it is also important to account for the actual services that are performed by the energy. That is, how efficiently is energy converted to useful work? As we will see, that is the heart of technological progress.

224 The quantity used and the efficiency of the conversion of natural resources into output has changed over time. This suggests a further shortcoming in the use of a production function with fixed factor intensities. Although impossible to solve mathematically, time varying factor intensities can be built into a numerical simulation model.

The empirical view of the data is in part based on a dataset developed by Ayres et.al.

(2003). They compiled historical data on capital, labor, and total energy production and use

from a variety of sources. That dataset has been updated from where they left off (1998) to the

present for this research.57 The data is in Appendix C. The quantification of the energy produced and used in the economy allows us to work out the efficiency of the conversion to actual output (and also the waste produced in the process). The increase in efficiency and decrease in waste per capita, it turns out, do a very good job of quantifying the mysterious technological progress part of explaining the history (and therefore the future) of growth. In fact, it turns out that the problems of understanding the proliferation of goods, such as the endogenous growth models reviewed in Chapter Two, show as a foundation for sustained growth, are subsumed into the relationship between capital, labor, and resource flows if the functional form of the relationship is liberated from the Cobb-Douglas form and is instead determined from the data with no a priori assumptions. In our quest to unmask the distortions that underlie the assumptions that create our expectations for the future, an entirely endogenously determined model is a good thing.

To connect energy efficiency to technological progress requires some discussion. It is

straightforward to state that technological progress arises from improvement and invention.

57 See the appendix of Ayres et. al, 2003 and 2005, for details on the sources and methods. In brief, the first step is to allocate energy inputs among various types of work. For example, the uses of coal for locomotives and steam engines in the early part of the 20th century and then for electricity production and coke production, domestic heat, etc., must be allocated. Then the conversion efficiencies for each source of energy over time are used to find work outputs. The aggregate of inputs to work outputs yields an aggregate thermodynamic efficiency of the conversion of natural resources (for example, oil) into useful work (for example, electricity).

225 And it is uncontroversial to state that human capital is at the core of the process that leads to improvement and invention. The motive for improvement and invention is the potential for a fall in unit cost and therefore an economic gain. Investment is the cost of finding or sustaining a way to transform material, energy, and knowledge into forms that are closer to a goal of minimum cost. The knowledge that is gained does have a cumulative effect, but, since knowledge is not homogenous (i.e., different sectors may require entirely different knowledge),

technologies will have limits. Some will expire as new technologies arise. If minimizing unit cost

is the goal and raw material costs are somewhat independent of knowledge (and in fact may rise

with scarcity) the objective is to minimize the cost of adding value. This means an efficient use

of energy. In other words, the economy is a system that converts materials and energy into

output. How energy is consumed is both a consequence of growth and a driver of growth, and, just as human and physical capital accumulates, so does the ability to convert natural resources into useful work in the production of economic activity.58

“Technology can be considered as knowledge combined with the appropriate means to transform materials, carriers of energy, or types of information from less to more desirable forms” (Ayres, 1994, p. 6). If we are to liberate ourselves from an exogenous assumption on the growth of productivity, technological progress needs to be measured directly rather than be derived as a residual. We can measure by using the ratio of the useful work delivered divided by the primary natural resource supplies of energy.

F. G Tyron (1927) noted that, “Anything as important in industrial life as power deserves more attention than it has yet received from economists. The industrial position of a nation

58 The useful work is the service provided from the use of energy. The value of energy services is derived from a thermodynamic perspective. It is the amount of actual work done in contrast to the potential work. The calculation is done using data on the consumption of coal, crude oil, natural gas, nuclear, wood, and other forms of energy versus the consumption by the end users of the refined energy, typically via combustion, into heat, electricity, and motive power. The difference is waste created by inefficiency.

226 may be gauged by its use of power. The great advance in material standards of life in the last century was made possible by an enormous increase in the consumption of energy, and the prospect of repeating the achievement in the next century turns perhaps more than on anything else on making energy cheaper and more abundant. A theory of production that will really explain how wealth is produced must analyze the contribution of this element of energy

(p.271).” As we will see, he was correct. Technological advances in the past century can be proxied (and therefore measured) by the improvements in the conversion of primary energy resources to output.

Naturally one assumes that output is derived from capital and labor. But if we are to use energy as an input to the production function (or more precisely, the work derived from the conversion of raw energy), are we able to assume that changes in energy consumption cause changes in economic growth? Perhaps energy consumption is a consequence of economic growth. Most of the literature is inconclusive. For example, regarding the US, Kraft and Kraft

(1978) responding to the oil shocks found evidence of unidirectional causality running from GDP growth to energy consumption. But Stern (2000) found evidence running in the opposite direction. Soytas and Sari (2006), in a study of the G-7 testing of the efficacy of pollution reduction through energy efficiency, found that it depended on the country.

For this research, the data on GDP, capital, labor, and the value of useful work delivered

(energy services) was subjected to a Granger causality test. (A unit root test on the log transformed first differenced data found that the variables are order of integration one, I(1).)

The Granger causality test output is as follows:

Pairwise Granger Causality Tests

227 Sample: 1900 2008

Null Hypothesis: Obs F-Statistic Prob.

ENERGY does not Granger Cause CAPITAL 107 5.93594* 0.0036

CAPITAL does not Granger Cause ENERGY 0.74273 0.4784

GDP does not Granger Cause CAPITAL 107 5.33551* 0.0063

CAPITAL does not Granger Cause GDP 1.03241 0.3598

LABOR does not Granger Cause CAPITAL 107 2.53352 0.0844

CAPITAL does not Granger Cause LABOR 3.29249 0.0411

GDP does not Granger Cause ENERGY 107 1.98053 0.1433

ENERGY does not Granger Cause GDP 5.37699* 0.0080

LABOR does not Granger Cause ENERGY 107 2.82483 0.0640

ENERGY does not Granger Cause LABOR 2.24293 0.1114

LABOR does not Granger Cause GDP 107 1.59234 0.2085

GDP does not Granger Cause LABOR 2.14926 0.1218

The results are convincing for energy Granger-causing GDP and capital, and GDP

Granger-causing capital. (The null is rejected at >99% in those cases.) Labor is bi-directional with capital and energy services. Therefore, the use of energy services as an input to the production function (and GDP for capital formation) appears valid.

228 The relationship between the values of end use energy to the raw energy put into the economy (that is, the efficiency of converting raw resources to useful work) is shown below with the actual data and a fitted line.

Technological Efficiency of Energy Conversion to Work 30.0% y = -3E-07x3 + 6E-05x2 - 0.0003x + 0.0468 R² = 0.9944 25.0%

20.0%

15.0%

10.0%

5.0%

0.0% 1900 1904 1908 1912 1916 1920 1924 1928 1932 1936 1940 1944 1948 1952 1956 1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008

Figure 76. Technological efficiency of energy conversion to work.

The chart shows that since 1900 the US has seen energy service per unit of raw input

improved from 4.0% to 23.6% in 2007. Less waste (higher efficiency) has led to the decline in

the price of power delivered to the user, which has been the prime motivator for the

substitution of machines for people and animals. This feeds back to the cost of goods in general

and the consumption of new products that rely on low cost power. The chart also would appear

to suggest that the bounty that has been derived from this technological progress is beginning

to plateau. This will be considered in more detail when experimenting with the simulation. But

it is worth noting that even if raw energy sources are unlimited, the technological efficiency of

229 conversion in the aggregate has limits. The next chart shows the energy59 intensity of output

(GDP) and shows the efficiency trend. We have clearly become more efficient at creating output from a given amount of energy.

Energy Intensity of Output 1900 = 1 1.2

0.8

0.6

0.4

0.2

0 1900 1904 1908 1912 1916 1920 1924 1928 1932 1936 1940 1944 1948 1952 1956 1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008

Figure 77. Energy Intensity of output.

The Model’s Underpinning

Following the logic above, we can envision a production process that combines capital and labor in the traditional sense but also consumes energy to produce the measured output of the economy. As the calibrated simulation will show, the history of the past 100+ years is simulated accurately using these three inputs (actually four, as will be shown below). The data

59 In thermodynamics, the “exergy” of a system is the maximum work possible during a process that brings the system into equilibrium. Exergy is then the energy that is available to be used. After the system and surroundings reach equilibrium, the exergy is zero. In general, it is more correct to use this term when referring to the amount of energy that actually does work. The term has become somewhat common in the ecological economics literature, but we will use the term “energy services” as the useful output.

230 used in the simulation is based on the calculated aggregate energy services (in exajoules), labor

(man-hours employed), and capital (accumulated investment less depreciation).60

The production function is of the typical implicit form: YfKLU (,,) where Y is output (GDP in $), K is capital (the value of the stock of capital in $), and U is the value of useful energy employed (energy services in exajoules). Normalizing each variable to the starting

year of the time series so that yYY / 0 etc., and differentiating the production function with

respect to time, yields

dy§·wwww y dk §· y dl §· y du y ¨¸ ¨¸ ¨¸ (3.1) dt©¹wwww k dt ©¹ l dt ©¹ u dt t .

Dividing by y yields

dln y dk dl du DEJ (3.2) dt dt dt dt where

ky§·w dyln D ¨¸ yk©¹w dkln ly§·w dyln E ¨¸ (3.3) yl©¹w dlln uy§·w dyln J ¨¸ yu©¹w duln .

The marginal productivities (output elasticities) are functions of the log derivatives of their

arguments. Following a solution to this system by Kummell et. al. (2008), we can note that since

capital, labor, and energy services (which are a result of technological improvement) represent

60 Bureau of Economic Analysis, NIPA tables, Economic Report of the President.

231 all of the factors of production, then DEJ 1. Since this is true, we can eliminate one of the three elasticities. Eliminating J , we have the partial differential equation

DD kklluu(/)(/)(/)0w wwww D D w (the equation for E has the same structure).

The coupling equation is lkkk(/)(/)wwDE ww. The solution of this system of partial

differential equations requires knowledge of the boundary conditions for D and E in klu,,

space. The simplest solution that is non-constant can be found by assuming an asymptotic limit

that is meaningful in reality. The outcome derived in the 2008 paper referenced above was

based on the best empirical fit. That solution is as follows:

§·1 u D a¨¸ ©¹k ªº§·ll E ab«»¨¸ (3.4) ¬¼©¹uk JDE 1 .

The parameter a weights the degree to which the ratios of labor to capital and technological progress to capital contribute to the productive power of capital. The parameter b scales the technological improvement that displaces labor. Note that E o 0 as u and k get large.

Inserting (3.4) into (3.2) yields our production function:

ªº§·§·lu §· l yu exp«» a¨¸ 2 ¨¸ ab ¨¸ l (3.5) ¬¼©¹©¹ku ©¹

This production function has only two parameters, which can be estimated from normalized

empirical data using constrained optimization.

The role of communications (and thus information transfer) is also important to the

growth of output. The proportion of capital invested in information and communications

232 technology (ICT) has increased rapidly in the last half century. The data contained in Jorgenson and Stiroh (2000) from 1959 to 1998 provided a basis for estimating the fraction of ICT versus total capital from 1900 to 2007. The chart below shows this time series with the actual data in middle and the fitted line supplementing the data at each end.

Information and Communication Technology as a Fraction of Total Capital 5.00%

4.50% y = 4E-08x3 - 1E-06x2 + 7E-05x + 0.001 4.00% R² = 0.9983

3.50%

3.00%

2.50%

2.00%

1.50%

1.00%

0.50%

0.00% 1900 1904 1908 1912 1916 1920 1924 1928 1932 1936 1940 1944 1948 1952 1956 1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008

Figure 78. ICT as a fraction of total capital (using data from Jorgenson and Stiroh, 2000).

The production function was calibrated without this input, and then the production

function was modified to use this fourth factor of production. The fit to the historical GDP was

significantly improved for the later part of the last century by including this factor. The factor is

k specified with a third relationship and parameter as c ICT . Inserting into (3.2) and solving the k system we now have the production function

k c ICT §·llk ªº§· §·ul §· yu ¨¸ exp«»a 2 ¨¸ abl ¨¸ (3.6) uku¨¸ ©¹¬¼©¹ ©¹ ©¹.

233 Using this production function, we model the output of the economy as a materials production system, adding value from physical capital, ICT capital, labor, and the technological proxy, energy services. The growth rate of ICT investment is also derived from the data.

Calibration of the simulation also includes provisions for structural breakpoints. Those breakpoints and the other parameters are derived from a constrained nonlinear optimization process for fitting the historical data to (3.6). There are a number of parameters that are estimated other than those for the production function with respect to the fitting the time series for labor, capital and energy. All of these will be shown below.

After the model is calibrated satisfactorily and we explore the base case, we will add the

effects of a diverging rich and poor and the effects of social unrest.

The Simulation Model

The model is built with a systems dynamics approach using Vensim Professional.61 A

very general schematic of the model’s structure is shown below. Not shown in the schematic

are the feedback loops from GDP growth to investment decisions and energy demand. Those

will be shown in more detail below.

61 http://www.vensim.com.

234

Figure 79. Schematic of simulation model structure.

The simulation model has three key input modules and one module containing the production function. The three input modules determine physical capital, labor, and work from energy. The determination of ICT capital is based on the growth rate estimated from historical data and is determined in the module that combines the three inputs. All of the modules are interconnected. The schematics for each of the modules follow as well as discussion of the optimized parameters and the fit between the empirical data and the simulated values. In the schematics, the boxes are stocks or levels, the double arrows are flows, the single arrows move information or quantities, the words are variables, and the little clouds are the boundaries of the model (that is, the sources and sinks for the flows are assumed to be unbounded). The terms in brackets are inputs from the other modules. Wherever arrows originate or terminate,

235 there are mathematical relationships defined that combine the information, quantities, and parameters. Some of the more trivial relationships are hidden.

Figure 80. Capital module.

Capital

The growth of physical capital is a proportion of the GDP determined by the savings rate, minus depreciation. In fitting the data to the simulation, the simulated time series for net capital was optimized to the historical series by including a structural shift in both the savings rate and the depreciation rate. (Note that all of the optimizations were done on the complete model, not just on each module independently. Therefore all of the parameters in all modules were included in each optimization run.) The optimization was tested with up to 5 breaks for savings and depreciation, and there was no significant improvement in the fit for more than one break. SR1 is 1970 and DR1 is 1930. The net savings rates are 8.096% before 1970 and 7.419% after. The depreciation rates are 5.903% before 1930 and 10.644% after. This model does not distinguish the source of the savings. In order to fit the data, net savings (including perhaps net foreign inflows) must equal those values.

236 Capital 20

2 15 1

2 1 2 10 1 1 2 1 2 5 2 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2 0 1 2 1 2 1900 1912 1924 1936 1948 1960 1972 1984 1996 2008 Time (Year) Capital : MacroEnergyData6 1111111111 Capital : Calibr ation 22222222222

Figure 81. Simulation versus empirical data for capital.

As the figure above shows, the calibrated simulation for more than 100 years has a very good fit between the data (MacroEnergyData) and the simulation (Calibration). The mean absolute percentage error (MAPE) is 3.59%.

Labor

The labor supply is pretty straightforward. Later feedback will added to have the stock of labor stabilize. This simple specification needs to have the parameters change several times during the calibration to fit the 107 years of historical data.

237

Figure 82. Labor module.

The growth rates of labor hours employed switched two times from the starting value of

12.47% to 13.653% and then to 14.897% in 1965 and 2002.5 respectively. The decay rates changed from the starting value of 10.886% to 10.967% and then to 12.297% in 1913.5 and 1940 respectively. MAPE is 4.36%.

Labor 4 2 1 2 3 1 2 1 1 2 1 2 2 1 2 1 1 1 1 2 2 2 2 1 2 1 2 2 1 2 1 2 1 1

0 1900 1912 1924 1936 1948 1960 1972 1984 1996 2008 Time (Year) Labor : Calibr ationGDP4 11111111111 Labor : MacroEnergyData2 2222222222

238

Figure 83. Simulation versus empirical data for labor.

Energy Services

The specification for the consumption of energy for work (energy service) is quite a bit

more complex than that for capital and labor. The general decline in intensity (that is, the more

efficient use of energy resources) has been punctuated by several structural events. The charts

that follow show this history as a relationship between primary energy and capital, and primary

energy and output.

Primary Energy Intensity of Capital 12 Great Depression End of WW II 11 Oil Shocks 10

7 Index of Exergy/Capital 6

4 1900 1904 1908 1912 1916 1920 1924 1928 1932 1936 1940 1944 1948 1952 1956 1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008

Figure 84. Energy intensity of capital.

239 Primary Energy Intensity of Output 1.2 Great Depression End of WW II 1 Oil Shocks

0.8

0.6

0.4 Index of Exergy/Capital

0.2

0 1900 1904 1908 1912 1916 1920 1924 1928 1932 1936 1940 1944 1948 1952 1956 1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008

Figure 85. Primary energy intensity of output.

There are several steps in the simulation of the production of useful work from primary energy resources. The central goal of this module is both to fit the data on the proxy measure of the stock of technological knowledge and to model the growth of the stock of knowledge though innovation. The following schematic shows the general architecture.

240

Figure 86. Schematic of energy module.

The primary demand for energy is based on GDP. The intensity by which that is applied to the production of energy has shown a steady decline, so the first portion of the module models that relationship. The following chart shows the actual and simulated values for the data in Figure 86:

241 Primary Energy Intensity of Output 2

1.5

1 1 2 1 2 1 2 1 2 2 1 1 2 1 0.5 2 1 2 1 221 1 2 1 2 1 2 1 2 1 2 0 1900 1912 1924 1936 1948 1960 1972 1984 1996 2008 Time (Year) Primary Energy Intensity of Output : Calibration 1111111111 Primary Energy Intensity of Output : MacroEnergyData6 222222222

Figure 87. Simulation versus empirical data for energy intensity of output.

The parameters that the constrained optimization determined will be reviewed after the full

module is discussed. This section of the model is as follows:

Figure 88. Production section of energy service module.

The efficiency by which primary resources are converted to useful services depends on

innovation. The module models innovation as a process of invention and obsolescence.

Technological improvements have continued to advance the efficiency of conversion, but as

242 efficiencies begin to move toward asymptotic limits, the marginal increase in the stock of conversion knowledge (incremental technology improvements) declines. The intensity measure can never go beyond unity. (Beyond unity would say that more useful work is derived from primary energy than it contains.) Eventually, the technology for conversion will reach a steady state asymptotic to the limits of efficiency. (As we will see, this comes into play for our future.)

The fit between the actual data and simulated data has been optimized with the choice of the functional forms for the growth and decay rates of the stock of knowledge and the parameters within those forms that best calibrated the model to the historical data. After some experimentation–and guidance from Arrow (1962), Felipe and Fisher (2003), and Kummell et. al.

(2008)–the growth rate of the stock of knowledge is modeled as follows:

ªº1 1 «». The parameter growthinvention is determined in the ¬¼exp(growthinvention ( T index 1))

optimization and the technology index, Tindex is endogenously determined. The technology

index is the ratio of the current efficiency to the maximum efficiency (unity). The “forgetting”

(see Benkard, 2000) of the stock of knowledge is based on an exponential function on the

B technology index with three parameters, ACTindex . The final specification was the result of experimentation to fit the growth history of efficiency to the simulated series.

The motive for the specification is to replicate the growth of the stock of knowledge in terms of its value in the conversion of raw materials into useful work. Thus, although the model uses energy as the measured variable, the model is really creating the value of the Solow residual endogenously.

The results of the simulation compared to the actual data that are shown in the next chart suggest a far amount of success in modeling the growth of efficiency vis-à-vis energy. A

243 few pages hence the value of the input of useful work into the production function is demonstrated.

Efficiency of Primary Energy Conversion 0.2

2 1 1 0.15 1 2 2 1 2 2 1 2 1 0.1 1 1 2 1 2 1 2 0.05 2 1 2 2 1 2 1 1 2 1 0 1900 1912 1924 1936 1948 1960 1972 1984 1996 2008 Time (Year) Efficiency of Primary Energy Conversion : Calibration 111111111 Efficiency of Primary Energy Conversion : MacroEnergyData6 222222222

Figure 89. Simulation versus empirical data for efficiency of energy conversion.

The MAPE is 3.72%. The module design for this section is as follows:

Figure 90. Innovation section of the energy service module.

244

The final part of the energy services module combines the efficiency of conversion with the production of primary energy to derive the delivered energy services. The calibrated simulation values and the actual values for energy service are shown in the following chart.

Energy Services 60

2 45 1

1 2 30 1 2 dmnl 2 1 2 2 1 15 1 1 2 2 2 1 1 1 2 1 2 0 112 2 1 2 1 2 1900 1912 1924 1936 1948 1960 1972 1984 1996 2008 Time (Year) Energy Services : Calibration 1111111111 Energy Services : MacroEnergyData6 22222222

Figure 91. Simulation versus empirical data for energy services.

The MAPE is 11.34%.

245

Energy Service Intensity of Output 4

2 2 2 1 2 1 1 1 2 1 2 1 2 1 2 1 2 1 2 2 1 2 2 1 2 2 1 1 1 2 1 1

0 1900 1912 1924 1936 1948 1960 1972 1984 1996 2008 Time (Year) Energy Service Intensity of Output : Calibration 1111111111 Energy Service Intensity of Output : MacroEnergyData6 222222222

Figure 92. Simulation versus empirical data for energy service intensity of output.

The chart above shows a sort of energy services Kuznets curve based on the efficiency of the use of energy services to produce output. The economy reached a turning point between

1970 and 1980. The first energy shock matches well with the turning point. This relationship differs from that in Figure 87 (the primary energy intensity of output) because the economy is shifting from manufacturing to service industries. The primary intensity fell steadily as more efficient manufacturing processes and prime movers were invented. But that in turn caused industrialization to grow and that effect, in the first 3/4 of the century was more positive than the increase in efficiency was negative. However, since the mid-1970s the value added in the US has been shifting from manufacturing to service (Schettkat and Yocarini, 2003). That is, from capital that is highly energy intensive to capital that is less energy intensive.

246

The parameters for the energy services module are Loss Parameter A, -0.0203, Loss

Parameter B, 3.01, Loss Parameter C, 23.9848, Decay Rate Past, 0.012, and Growth Past, 12.0.

The full module is as follows:

Figure 93. Energy services module.

The Production Function

The final part of the model is for providing the inputs that have been derived above into the production function. The schematic and a comparison between the actual and simulated GEDP are below.

247

Figure 94. The production function module.

Gross Domestic Product 40

30 2 1 2 20 1 1 2 2 1 2 1 10 2 1 2 2 1 1 2 1 2 1 1 2 0 1 2 1 2 1 2 1 2 1900 1912 1924 1936 1948 1960 1972 1984 1996 2008 Time (Year) Gros s Domestic Produ ct : Calibr ation 111111111 Gross Domestic Product : MacroEnergyData6 222222

Figure 95. Simulation versus empirical data for GDP.

248

The output of the model results in a mean absolute percentage error of 4.19%. The primary sources of error are from the Great Depression through the WWII period. The model is also accurate in simulating the monetary value of GDP in actual dollars (1992$).

Monetary Value of Output 10,000 2 1

7,500 2 1

2 1 5,000 1 2 1 2 2,500 1 2 1 2 2 1 2 1 1 1 0 1 1 1 2 1900 1912 1924 1936 1948 1960 1972 1984 1996 2008 Time (Year) Monetary Value of Output : Calibration 111111111 Monetary Value of Output : MacroEnergyData7 22222222

Figure 96. Monetary value of output.

The Vensim code and the normalized economic data used in the simulation are in

Appendix C.

Simulating the Future

With the simulation well calibrated, we now look into the future. The first simulation is

“doing what you did gets you what you got.” That is, there are no changes to the model other

than to see where we will be in 2050 if nothing changes. The simulation outputs still show the

empirical data up to 2007.

249

Gross Domestic Product 400

300

200 1

100 1 1 1 1 0 2 1 2 1 2 112211221 2 1 2 1 2 1 1900 1920 1940 1960 1980 2000 2020 2040 Time (Year) Gross Domestic Product : FutureNoC hange 1111111 Gross Domestic Product : MacroEnergyData2 222222

Figure 97. Doing what we did until 2050 – GDP.

We see that our old friend exponential growth is with us. Recall that both measures

were normalized to unity in 1900. The GDP index rises from 27.36 in 2007 to 105.62 in 2050.

That is nearly four times larger. The labor hour index increases from 3.64 to 10.71. The output

per labor hour index increases from 7.52 to 9.86, reflecting the increased efficiency of converting capital and energy inputs to output. Another way to view this is to look at labor intensity in output. The chart below shows this relationship.

250

Labor Intensity of Output 1 1 2 1

2 1 0.75 2 1 0.5 2 1

2 1

2 0.25 1 2 1 2 1 2 1 2 1 1 1 1 0 1 1900 1920 1940 1960 1980 2000 2020 2040 Time (Year) Labor Intensity of Output : FutureNoC hange 1111111 Labor Intensity of Output : MacroEnergyData5 222222

Figure 98. Doing what you did to 2050 – labor intensity of output.

The model shows a period of plateau that is a function of the last set of parameters used to work out the stock of labor. The simulation does not capture the volatility of the Great

Depression and the WW II rebound. However, the curve fitted to the simulation rates shows that the overall effect is accurate. But it is also clear that the final value for net labor growth may not reflect the future trend.

251

Net Labor Growth Rates 8.00%

6.00% 4-Year Moving Avg.

4.00%

2.00%

0.00%

Simulation Rates -2.00%

4 Year Moving Average of Actual Rates -4.00% Fitted Polynomial -6.00%

-8.00% 1905 1908 1911 1914 1917 1920 1923 1926 1929 1932 1935 1938 1941 1944 1947 1950 1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007

Figure 99. Net labor growth rates.

Allowing the growth rate to vary randomly (normal distribution around the long term trend)

beginning in 2002, we can see that labor intensity declines more or less monotonically.

FutureNoC hange MacroEnergyData5 50% 75% 95% Labor Intensity of Output 1

0.75

0.5

0.25

0 1900 1938 1975 2013 2050 Time (Year)

Figure 100. Labor intensity with uncertainty.

252 This is a problem. Labor intensity cannot go to zero or we have the condition that was discussed in Chapter Two: productivity increases to the point to where labor hours converge on zero. As noted in Chapter Two, this leaves us with the absurd conclusion that either everyone works one second a day or only one person works (and that is just before labor intensity goes to zero). And based on this simulation, we see this coming sooner than later.

The model predicts several impossible outcomes if allowed to proceed to the point at which the system explodes (nearly infinite GDP). Recall that this is the “doing what you did” scenario. That is, we remain on the path that has carried us to today for the last 107 years. If we do that, in 2080 very strange things happen. Given that the growth rate of labor is stable, the labor intensity of output goes to 0.0034 (not much labor needed), and the exponential growth of normalized output takes it to 2,487 (from 26.71 in 2007). Consumption per labor hour goes from 7.526 (that is 7.5 times higher than in 1900) in 2007 to 289.39; a 38.45-fold increase. So whereas we have seen an increase in our standard of living by a factor of about 7.5 in the last 107 years, we can expect to see about 5 times that (38.45 fold increase) in the next 70 or so years.

253 Energy Service Intensity of Output 4

2 2 1 2 1 1 2 1 1 2 2 1 1 2 1 1 2 2 1 1 1 1 1 2 1 1

0 1900 1923 1946 1969 1992 2015 2038 2061 2084 Time (Year) Energy Service Intensity of Output : FutureLaborTrend 111111111 Energy Service Intensity of Output : MacroEnergyData6 222222222

Figure 101. Doing what you did until 2080 – energy services intensity of output.

Perhaps most incredible is the energy service “Kuznets” curve shown above. In effect, this says that infinite output is possible due to infinite efficiency. It is obvious that this scenario cannot happen. Sometime between 2083 and 2084 the model crashes. For the simulation there are not enough decimal points in the floating point processor. For reality, there is the impossibility of creating output with nearly zero energy services inputs.

But, even though this analysis is not going to focus on carrying capacity problems, it is relevant to show that there is a problem with energy. Though efficiency is extremely high in

2083 (so that output can be made with infinitesimal energy services inputs) the exponential GDP growth curve is primary energy hungry as the growth rate of the economy is a few steps ahead of efficiency growth. Note in the chart below that the scale is exponential.

254

Primary Energy Demand 1000

283.16

100

Simulated Primary Energy Demand

: MacroEnergyData6

6.95

1 1900 1906 1912 1918 1924 1930 1936 1942 1948 1954 1960 1966 1972 1978 1984 1990 1996 2002 2008 2014 2020 2026 2032 2038 2044 2050 2056 2062 2068 2074 2080

Figure 102. Doing what you did to 2080 – primary energy demand.

In 2007 the US used 6.95 times more primary energy than in 1900. In 2080 it will

require 283.16 times more than in 1900. That is a 40.74 times increase from 2007. The usual

limits-to-growth analysis would impose a finite limit on energy production as well as consider

other by-products of growth to tell a story about exceeding the carrying capacity of the planet.

A part of that story is about waste. In our model so far, waste is created but, in this scenario,

efficiency is increasing so that at the limit (2083 or so), there is no waste! We again see that if

the future is to be what is assumed in both economic theory and in the minds of business and

political decision makers, there are outcomes that violate possibility.

Suppose that there is a slower growth in technological improvement. As the charts

below show, a decline in the growth rate of technology brings challenging times. If the labor

pool continues to grow at trend levels but there is a flattening in the increase of the efficiency of

255 primary energy conversion to energy services, then the economy enters a prolonged contraction. The charts that follow show this scenario.

Efficiency of Primary Energy Conversion 0.4

0.3

1 1 1 1 1 0.2 1 2 1 2 1 2 1 1 0.1 2 1 1 2 1 2 2 1 2 0 1 1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 Time (Year) Efficiency of Primary Energy Conversion : FutureProductivityStable 11111111 Efficiency of Primary Energy Conversion : MacroEnergyData7 222222222

Figure 103. Future with lower technology growth but labor growing – conversion efficiency.

Gross Domestic Product 80

1 60 1 1

40 1 1 1 2 1 20 1 2 1 2 1 2 1 2 1 0 1 2 1 2 1 2 1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 Time (Year) Gross Domestic Product : FutureProductivityStable 1111111 Gross Domestic Product : MacroEnergyData7 222222222

Figure 104. Future with lower technology growth but labor growing – GDP.

256

The good times erode as the labor intensity of output increases. The growing population with less technological growth results in a return to a more labor intensive world.

Labor Intensity of Output 2

1.5 1

1 1 2 1 2 1 1 2 0.5 1 2 1 1 2 1 2 1 2 1 1 0 112 1 1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 Time (Year) Labor Intensity of Output : FutureProductivityStable 1111111 Labor Intensity of Output : MacroEnergyData7 22222222

Figure 105. Future with lower technology but labor growing – labor intensity of output.

This scenario is a glimpse into an outcome modeled in Chapters One and Two in which

there was growing inequality. One can imagine the minority power elite fighting for control of

the energy services that are increasingly scarce while the rest of the world gets increasingly

excluded from benefits of growth (that is, as we have showed, until they revolt). As the chart

below shows, if the empirical data follows the forecast (and it is giving us a hint that it is), and if

the models in Chapters One and Two regarding revolution and chaos are potentially correct,

then as capitalism implodes, violence explodes.

257

Energy Services per Unit of Labor 20

1 2 1 1 2 2 10 1 1 1 1 2

5 1 2 1 1 2 2 1 2 1 1 0 1 1 1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 Time (Year) Energy Services per Unit of Labor : FutureProductivityStable 11111111 Energy Services per Unit of Labor : MacroEnergyData7 222222222

Figure 106. Future with lower technology but labor growing – energy services per unit of labor.

In the calibrated model, the investment/depreciation rate is based on parameters that

are derived from the historical data. They do not vary in the future but are fixed at the levels

that they were at the end of 2007. In the output shown in the following charts, the model is

altered so that the investment rate is a function of savings and that is a function of output per

unit of labor. Labor growth is also stabilized.62 The outcome is similar to that shown above but

delayed (see the charts below, the first of which compares the two cases). The stable stock of

labor allows the growth of GDP to be more equally spread. However, as time passes, capital

intensity increases, and labor once again is marginalized. Capital intensity increases because

even though productivity growth is stable, the stock of primary energy is still growing, as is

shown in the third chart, in a world of stable population.

62 For these simulations, labor hour growth trends to zero between 2008 and 2050. The choice of when and how quickly labor hours change does not change the outcomes, only the timing of the outcomes.

258

Output per Unit of Labor 20

2 15

2 10 2

2 3 2 2 3 1 3 2 3 1 2 3 3 5 1 2 3 3 1 2 3 1 3 1 2 3 2 2 0 1 2 3 1 2 3 3 1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 Time (Year) Output per Unit of Labor : MacroEnergyData7 11111111 Output per Unit of Labor : FutureProductivityStable2 2222222 Output per Unit of Labor : FutureProductivityStable 3333333

Figure 107. Future with lower technology and capital and labor stable – output per unit of labor.

Labor's Share and Capital Intensity

8 1 1 8 2 1 1 2 1 2 2 4 1 3 3 4 3 2

0 3 1 3 3 0 2 4 3 4 3 443 3 3 1 1 2 0 1 2 1 0 1 1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 Time (Years) Output per Unit of Labor : FutureProductivityStable 111111 Output per Unit of Labor : MacroEnergyData7 2222222 Capital Intensity of Output : FutureProductivityStable 33333 Capital Intensity of Output : MacroEnergyData7 444444

Figure 108. Future with lower technology and capital and labor stable – comparing output per unit of labor and capital intensity.

259

Primary Energy Aggregate Production 40,000

2 30,000 2

2 20,000 2 2 10,000 2 2 1 1 2 1 2 1 2 0 1 2 1 2 1 2 1 2 1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 Time (Year) Primary Energy Aggregate Production : MacroEnergyData7 111111111 Primary Energy Aggregate Production : FutureProductivityStable2 22222222

Figure 109. Future with lower technology and labor and capital stable –primary energy.

This scenario also results in a much deeper decline in aggregate output than that above

in which only productivity growth slowed. By 2100 the economy will have reached a level about

the same as it was in 1973.

260

Gross Domestic Product 200

150 2

100 2

2 2 50 2 2 1 2 1 2 2 0 2 1 2 1 2 1 2 1 2 1 2 1 1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 Time (Year) Gross Domestic Product : MacroEnergyData7 11111111 Gross Domestic Product : FutureProductivityStable2 22222222

Figure 110. Future with lower technology and labor and capital stable – GDP.

Output per capita does not show a very different story. The following chart normalizes

the actual and simulated output by the actual and predicted population. That is, it shows output

per capita. The population growth in the past 100 years has been almost linear (0.9851 R-

squared), adding about 2.0878 million people per year. That growth is carried out to about

2050 (where labor hours stabilize in the simulations above), at which point the US population is

about 30% larger than in 2007.

261

Output per Capita Stable Population Growth after 2050 8

7 Simulated Output per Capita 6 Actual Output per Capita

1 Actual

0 1900 1906 1912 1918 1924 1930 1936 1942 1948 1954 1960 1966 1972 1978 1984 1990 1996 2002 2008 2014 2020 2026 2032 2038 2044 2050 2056 2062 2068 2074 2080 2086 2092 2098

Figure 111. Future with lower technology and labor and capital stable – GDP per capita.

Since the key macroeconomic measures in the simulation are entirely endogenously determined (starting at “one” in 1900) the model shows what can be expected based on what has happened. For example, as discussed earlier, the three parameters that drive the production function are determined from constrained optimization on the historical data. Thus the production function is “hard wired” to expect that the dynamics of the production of labor, capital, and innovation through the improvements in energy efficiency (the key inputs to production) will remain, more or less, as they have been. Based on our simulations, in which the key parameters of the production function are held constant, several unsettling conclusions arise. In trying to avoid the impossibility of exponential growth (and the accompanying impossibility of perfect efficiency), it seems that no matter how the future is altered, the prediction is for a prolonged decline to aggregate output levels that are near or below current levels. These declines would be expected to also engender increasing conflict for increasingly scarce energy services and output per capita.

262

Inequality and Social Unrest

Continuing, for now, to use history as a guide to the future, we will explore the potential

for social unrest. As we showed in Chapter One, as the ability to consume is more highly

concentrated, the likelihood of social unrest grows. Furthermore, recall that the tipping point

for revolution was a function of a growing gap in real consumption per capita, the amount of

guard labor/capital, and the ability of the poor to communicate. The improving ability to

communicate is shown in the simulation as the fraction capital that goes into information and

communication technology; that is a direct input into the production function. If we assume

that the rich will do what it takes to maintain income levels associated with the peak output per

unit of labor, then all we need to do is add the rich’s response to growing unrest to the

simulation in order to see what happens to the economy as the poor get poorer and rich build

bigger fences with bigger armies. As in Chapter Two, the use of guard capital will be input into

the production function as a negative effect on investment’s contribution to capital growth.

That is, a choice is being made to invest in a bigger army rather than in the machinery of

production. The parameter a in the production function is thus separated so that the effect can

be isolated on capital’s role in production:

ªº§·§·lu §· l yu exp«» a12 2 ¨¸ ab ¨¸ l (3.7) ¨¸ku ¬¼©¹©¹ ©¹.

As the output per unit of labor falls, the rich apply more investment into the armies. This shows

up in the production function as parameter a1 which weights the degree to which the ratio of

labor to capital contributes to the productive power of capital.

263 Using the beginning in 2015 as the high water mark, the need to sidetrack investment into non-productive uses grows every year as the rich attempt to maintain that level of consumption as the aggregate average level of consumption falls. In the simulation, the rich are unwilling to take any decline in per capita income; thus the need for guard labor and capital grows very quickly. As the chart below shows and as was shown in Chapter Two, the system eventually becomes chaotic. In the chart below, which shows the relationship between GDP and the same variable one time period back, there is a period in which GDP for the next period is well predicted by GDP in the prior period (the dots that connect into a straight line). This period is 1900 to about 2016. The effects of lost physical capital investment cause the “hook” in the trend as the lagged values predict a decline. After 2031 the relationship between GDP in the current period and the next appears to be random. But there are no random inputs to this model.

When Guard Labor/Capital Goes too Far 80

0 0 8 16 24 32 40 48 56 64 72 One Period Back GDP GDP

Figure 112. When guard labor/capital goes too far.

264 Another way to show how this can occur is to isolate how the investment in capital and the use of guard labor and capital works inside the production function. Capital is a function of investment. Thus we can show63 that the capital formation process is

wKGtc1 DJ KGKtct() K t. (3.8) wKIt

This simplified version of the simulation model will not show any growth since the function is in

steady state for “normal” levels of guard capital investment and it does not have feedback from

G any production function. The chart below shows that for low ratios of c , capital from the last I

period predicts capital for the current period. (It is a very simple map of one point.)

63 Let output be a generalized function of capital, the technology for conversion, and the cost of guard capital. (The productive labor input is held constant at unity for simplicity, but that does not change the results as long as guard labor grows more rapidly than productive labor, as it will if investment in guard wy capital is increasing.) Then yKGK DJ()where D and J are from equation (3.3). Note that wu c

D and J are dynamic under growth conditions but do not change with no growth. Gc t 1 is the cost of guard capital, and ()GKc measures the negative effect of guard capital. Since the value of the effect of wy the improvement in output due to increased efficiency, is a function of investment I , then we can wu

wKGtc1 DJ write KGKtct() K t. wKIt

265 Steady State Capital from Last Period Capital 0.75

0.625

0.5

0.375

0.25 0.25 0.35 0.45 0.55 0.65 0.75 Last Period Capital Capital : Current

Figure 113. Capital formation with simplified production function – “normal” guard to physical

capital ratio.

As the ratio increases, the dynamics change. At a ratio of 3.0 the system shows a

dampening oscillation that still shows a predictive outcome. The next chart shows that a

pattern of dampening oscillations are the result of a period doubling event and that they

converge from the initial conditions to two points as the oscillations eventually reach a constant amplitude.

266

Steady State Capital from Last Period Capital 0.8

0.7375

0.6750

0.6125

0.55 0.550 0.600 0.650 0.700 0.750 0.800 Last Period Capital Capital : Current

Figure 114. Capital formation with simplified production function – higher guard to physical capital ratio.

Finally, if the ratio gets beyond 3.57 in this specification, the system shows no tendency

to converge on two, four, eight, or any specific predictable set of oscillation peaks and valleys.

Steady State Capital from Last Period Capital 1

0.75

0.5

0.25

0 0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1 Last Period Capital Capital : Current

Figure 115. Capital formation with simplified production function – chaos.

267 Since this simplified model does not have growth, the attractor in Figure 112 is well defined. In Figure 115 the attractor shows the effects of increasingly large (but seemingly random) oscillations. In fact, the scenario that produced Figure 115 explodes in the year 2234 after one absurd excursion from a GDP of 8.520 in the year 2223 to 82,107 in the year 2224 (yes, in one year). The chart of GDP for that scenario is below. The scale is so distorted that the seemingly random oscillations that precede that date are mostly hidden.

Gross Domestic Product 100,000

75,000

50,000

25,000

0 1900 1937 1974 2011 2048 2085 2122 2159 2196 2233 Time (Year) Gross Domestic Product : FutureGuardLabor Gross Domestic Product : MacroEnergyData7

Figure 116. When guard labor/capital goes too far – time series of GDP.

What we see therefore is that an increasingly costly diversion of investment from

physical capital to guard capital (and therefore labor) can buy the minority rich some time. But

the consequences are an unavoidable, sudden, and rapid lost of stability (again, both in the

mathematical and social meanings of the word). We did not simulate the outcome of an

insufficiency of guard capital (and thus certain revolution). However, as was shown in Chapter

One, the higher the investment in guard capital, the larger the drop in the aggregate value of

268 the economy as a result of the revolt. The purpose of this scenario is to illustrate the dead- endedness of “doing what you did.”

Finding a Path to a Stable Future

In this last section, we will see if there is a way forward that does not end a future in which we regress to output per person levels seen in the mid to early 1900s, or into chaos. The tactic is straightforward. We take the original simulation conditions that showed infinite output and perform constrained optimization on an idealized future path for GDP. The result is to “re- hardwire” the production function by altering its and other parameters with the objective of a sustainable future in terms of output per unit of labor.

The choice of an objective is entirely arbitrary. The following chart shows the objective as a level of GDP about 100 times greater than in 1900 and about 3.71 times greater than in

2008.

Ideal GDP Path 120

100

0 1900 1909 1918 1927 1936 1945 1954 1963 1972 1981 1990 1999 2008 2017 2026 2035 2044 2053 2062 2071 2080 2089 2098 2107 2116 2125 2134 2143 2152 2161 2170 2179 2188 2197 2206

Figure 117. Looking for a future – ideal GDP path.

269 Constrained optimization on the production function parameters could only fit a portion of the ideal path. The following chart shows that very quickly the simulation begins an exponential growth pattern that leads to a floating point error in mid-century.

Gross Domestic Product 200

150

100 2 2 2 22 2 2

50 2 1 2 1 2 1 2 0 1 2 1 2 1 2 1 2 1900 1944 1988 2032 2076 2120 2164 2208 Time (Year) Gross Domestic Product : FutureOptimizedStableGrowth 111111111 Gross Domestic Product : MacroEnergyDataFuture 2222222222

Figure 118. Looking for a future – the limits of the production function.

Very small changes in the parameters lead to an opposite picture in which GDP crashes.

270

Gross Domestic Product 200

150

100 2 2 2 22 2 2

50 1 2 1 2 1 2 1 2 0 1 2 1 2 1 2 1 2 1900 1944 1988 2032 2076 2120 2164 2208 Time (Year) Gross Domestic Product : FutureOptimizedStableGrowth3 111111111 Gross Domestic Product : MacroEnergyDataFuture 2222222222

Figure 119. Looking for a future – the limits of the production function again.

Letting capital, labor, and energy intensity growth continue as they have for the past

107 years, the inability of the production function to follow any path that is not exponential or

crash, and the sensitivity to small changes, leads to two conclusions: 1. if capital and labor and

energy services continue on paths as they have, the production function is invalid for a

sustainable future; 2. stable outcomes in the future with this production function will become

increasingly less likely. It is as if the knife edge on the saddle path is getting thinner until there is

no edge, and we have to fall off.

Recall that the specification for the parameters in the production function and the other

relationships in the model are empirically determined from the data over the past 107 years. In

other words, although the simulation model is built from data with no assumptions regarding a

theoretical economic growth model, embedded in the data are the patterns that built the 20th century. So what drives capitalism drives this model. And this model therefore contains the

271 axiomatic assumptions that govern economic (and policy) decision making. So just as in Chapter

Two, we have discovered that expectations for the future, based on what we think is the normal course, are unjustified.

Can new relationships be imposed on the model that can lead to a reasonable outcome?

Next the optimization was extended to the investment (savings) and depreciation parameters, the growth and decay rates of the labor supply, and the parameters controlling innovation (the efficiency of the conversion of primary energy to energy services). The simulation results are illustrated in the following chart.

Gross Domestic Product 200

150

100 2 2 2 22 2 1 2 1 50 1 2 1 2 2 1 1 2 2 1 0 1 111 1 2 1 2 1 2 1900 1944 1988 2032 2076 2120 2164 2208 Time (Year) Gross Domestic Product : FutureOptimizedStableGrowth5 111111111 Gross Domestic Product : MacroEnergyDataFuture 2222222222

Figure 120. Looking for a future – the limits of the model.

The optimized capital, labor, and the growth and decay of innovation lead to a

simulation that follows the ideal path farther along until 2096, and then it collapses. The

parameter changes lead to very interesting outcomes vis-à-vis the foundations of capitalism. In

order to ride the ideal path for another 45 years from the previous specification, the aggregate

stock of labor and capital has to stabilize. Both can have zero growth – or one can grow, but

272 then the other must fall. Meanwhile, innovation continues unabated; that is how the economy continues to grow.

Efficiency of Primary Energy Conversion 0.8

1 0.6 1 1 1 0.4 1 1 1 1 0.2 1 1 1 2 1 2 1 2 2 0 1 2 1 1900 1944 1988 2032 2076 2120 2164 2208 Time (Year) Efficiency of Primary Energy Conversion : FutureOptimizedStableGrowth1 1111111 Efficiency of Primary Energy Conversion : MacroEnergyDataFuture 22222222

Figure 121. Looking for a future – innovation continues.

What throws the economy off the path is an increasing sensitivity to very small changes

in the continued growth in the ability to get useful work out of primary energy. As the chart

below shows, the model continues to extract more and more useful work out of a given quantity

of primary energy. This is sensible to a point, but eventually the marginal increase in useful

work is insufficient to power growth. The second chart shows the decline in the marginal

productivity of energy services.64

64 ªlu§· l l º Calculated from (3.4c) as 1(aab )¨¸ ()()) «»kuk ¬¼©¹ .

273

Primary Energy Intensity of Output 2

1.5

1 1 2

1 2 1 0.5 2 1 2 1 2 1 1 1 1 0 1 1 1 1 11 1900 1944 1988 2032 2076 2120 2164 2208 Time (Year) Primary Energy Intensity of Output : FutureOptimizedStableGrowth1 1111111 Primary Energy Intensity of Output : MacroEnergyDataFuture 222222222

Figure 122. Looking for a future – the limits to efficiency.

Marginal Productivity of Energy Services 1

0.85

0.7

0.55

0.4 1900 1944 1988 2032 2076 2120 2164 2208 Time (Year) Marginal Productivity of Energy Services : FutureOptimizedStableGrowth1

Figure 123. Looking for a Future – the decline in the marginal productivity of energy services.

The solution to this simulation challenge lies in maintaining the marginal productivity of energy services. So, although there are no limits to the accumulated stock of energy used (that

274 is, no limits to growth from finite resources) in this simulation, limits on the amount of useful work that can be extracted from that primary energy are necessary. By shifting the decay rate of primary energy intensity so that there is a higher limit to the primary energy intensity of output, we have the following outcome:

Gross Domestic Product 200

150

22 100 2 1 2 1 2 1 2 1 1 2 1 50 1 2 1 2 1 2 1 2 0 1 2 1 2 1 2 1 2 1900 1944 1988 2032 2076 2120 2164 2208 Time (Year) Gross Domestic Product : FutureOptimizedStableGrowthComplete 11111111 Gross Domestic Product : MacroEnergyDataFuture 2222222222

Figure 124. Looking for a future – stable long-run growth – GDP.

275

Marginal Productivity of Energy Services 1

0.85

0.7

0.55

0.4 1900 1944 1988 2032 2076 2120 2164 2208 Time (Year) Marginal Productivity of Energy Services : FutureOptimizedStableGrowth1

Figure 125. Looking for a future – stable long-run growth – marginal productivity of energy

services.

We can also compare this scenario to Figure 111 in which output per capita peaked and declined. As the chart below shows, the need for guard capital is mitigated.

Output per Unit of Labor 20

11 15 1 1 1 1 10 1

1 1 2 1 1 5 2 1 2 2 1 0 1 2 1 1900 1944 1988 2032 2076 2120 2164 2208 Time (Year) Output per Unit of Labor : FutureOptimizedStableGrowth5 111111111 Output per Unit of Labor : MacroEnergyDataFuture 2222222222

Figure 126. Looking for a future – stable long-run growth – sustained per unit of labor output.

276

This scenario (which is following an entirely arbitrarily chosen path to zero growth so that the timing of the transition and the magnitude of the goal could be quite different) shows that there is a possible way forward even using the production function specification derived from the 20th century. But recall that both labor supply and the stock of physical and ICT capital have to reach a stable level for this to occur. Ultimately the long-run stability around the output per unit of labor (which, with stable capital, implies stable consumption per person) is dependent upon there being limits to the intensity of energy services in output. We can see in the chart below that the stable path requires a stable relationship between output and the amount of useful work required.

Energy Service Intensity of Output 4

2 2 1 1 2 1 1 2 1 2 1 1 1 1 1 111 1 1 1 2

0 1900 1944 1988 2032 2076 2120 2164 2208 Time (Year) Energy Service Intensity of Output : FutureOptimizedStableGrowth5 1111111 Energy Service Intensity of Output : MacroEnergyDataFuture 222222222

Figure 127. Looking for a future – stable long-run growth – energy services intensity of output.

277

CONCLUSION

We asked at the beginning of the last chapter, “Can we keep doing what we are doing and keep getting what we got?” The empirical model that we built in that chapter says no. We have shown that the foundations upon which we the last century’s growth were based cannot work for another century. And that is notwithstanding the limits to natural resources and the ability of the planet to process or absorb waste. When this research began, the expectation, even through Chapter Two’s exposure of the flaws in economic theory, was that the ecological constraints that have been essentially excluded from this analysis would motivate change long before the endless growth issues elucidated in Chapter Two arrived. But Chapter Three suggests that that future may be closer than we think.

The disruptions in the energy markets that are occurring as this is being written, while obviously a product of finite resources facing potentially infinite demand, can be directly

connected to the simulation in Chapter Three. First, lurking below the surface of the current oil

shock are the uncomfortable realities of what happens as the growth curve steepens; the denial

of the consequences of endless growth are more difficult when the price signals are so strong

(see the second chart below). At the production level in the simulation, the production function

requires a level of energy services production that is a function of primary energy production

and the efficiency of primary energy conversion. Mess up either of those inputs, and the system

encounters strong and persistent fluctuations. For example, a 12% drop in primary energy

production that lasts for two years and then returns to normal after six years looks like the chart

below. The second chart shows the clear price signal, in terms of the marginal productivity, with

relative prices for energy inputs reverting to 1960s levels. (Note that there is no empirical data

for the marginal productivity series, so it is entirely simulated.)

278 Gross Domestic Product 40 1 2 30 1 2 3 2 1 3 20 2 1 2 3 1 3 2 10 3 1 2 3 1 1 2 2 3 1 2 3 1 332 1 2 3 0 112 3 2 3 1 2 1 1900 1912 1924 1936 1948 1960 1972 1984 1996 2008 2020 Time (Year) Gros s Domestic Produ ct : Calibr ation 111111111 Gros s Domestic Produ ct : Calibr ationOilShoc k 222222 Gross Domestic Product : MacroEnergyData5 3333333

Figure 128. Current events – oil shock – recession.

Marginal Productivity of Energy Services 1

0.9

1 2 1 2 0.8 2 1 1 1 2 2 1 1 2 2 0.7 1 2 1 1 2 2 1 2 1 2 1 2 1 2 0.6 1 2 1900 1912 1924 1936 1948 1960 1972 1984 1996 2008 2020 Time (Year) Marginal Productivity of Energy Services : CalibrationOilShock 11111111 Marginal Productivity of Energy Services : Calibration 222222222

Figure 129. Current events – oil shock – price shock.

279

Chapter Three has revealed the fragility of the system that is expected to deliver a growing and prosperous future. Chapter One showed that unequal growth would lead to

revolution. Chapter Two showed that endless growth is impossible but that the axioms that shape our decision making processes drive us to believe it is possible. Chapter Two also demonstrated that some of the by-products of the motives for maintaining endless growth are disincentives for economic convergence. The consequences of that, developed in detail in chapter one, were played out using endogenous growth theory in Chapter Two and in the

Chapter Three simulation. In both cases the consequences, at best, deny the maximization of return on investment, and at worst, lead to a rapid transition into a future that is unpredictable

(and therefore uncontrollable).

So we are left wondering how civilization can make it. It can, but not in the way we

think it should. At a 1994 conference organized by the author of this paper at the University of

New Hampshire and titled “Why is the future not what it was supposed to be?” the focus was

the developing world.

In contrast, the focus here is on the world developing. But to get there will require a fundamental change in how we literally do business. Bypassing concerns for ecological sustainability and accepting that exponential growth in impossible to sustain, and, even more in the present, accepting that the paradigm that sustained the 20th century will not work going forward for much longer, we are faced with a need to radically overhaul the fundamental motives for business. More is not going to become better for long. And that means that eventually a steady state must be reached in which the return on investment is no more than the rate of depreciation of our steady stock of efficient and long lasting capital. This is not only an overhaul of how we do business, but is also a shift in what living and working is all about.

280 It is very hard to imagine a non-capitalistic world. Perhaps that reality will never happen as we try to balance on the ever-narrowing saddle path by doing what we did, or we fall into a police state heading for economic and social chaos, both leading to unpleasant endings. But imagine it we must if we are to see a future in which there are semblances of the comforts that we, as civilized people, have defined as good and necessary.

That imagining will be the next phase of this work. Think about it, and send your thoughts.

“Heavier than air flying machines are impossible” (Lord Kelvin, Royal Society, 1895.) 65

“There is no likelihood that man can ever tap the power of the atom. The glib

supposition of utilizing atomic energy when our coal has run out is a completely

unscientific Utopian dream, a childish bug-a-boo.” (Robert Millikan, Nobile Laureate,

Physics, 1923).

"There is not the slightest indication that nuclear energy will be

obtainable." (Albert Einstein, 1932)

65 These quotes are common in many narratives but there are no direct sources.

281

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296 Appendix A - The CC Locus

i The economy crosses from subsistence consumption when the potential income, zt is

ab greater than the critical level, z for all individuals, iab , . We know that for all time zztt! ,

b so the crossing must happen when zzt . Thus

b CC{{( gtt , x ) : z t z } . (A.1)

bbD Since zxhgtt () t1 and zc /(1J ) , then the CC locus can be explicitly described as

CC CC b 1/D G x xg(tt ){ ( c / [(1J ) hg ( )]) . It follows that ! 0 ; thus the CC locus is upward G gt

CC 1/D sloping. Note also that at gt 0 , xc(0) ( /[1!J ]) 0 so that the CC locus has a positive intercept.

The XX Locus

The XX locus is all the points at which the effective resources per efficiency unit of labor,

xt are in steady state given a level of q . Thus the XX locus is

XX{{( gtt , x ; q ) : x t x t1 } . (A.2)

From (1.39), along the XX locus, xtttttt111 [(1 g ) / (1 u )] xxxgxq { ( ,t ; ) . The growth rate of the efficiency units of labor and technological progress are equal along the XX locus: i.e.,

ugxq(;)(;)tt ggt q.

Three characteristics arise from this relationship.

1. The XX locus is vertical in the range above the CC locus. This follows by substituting

(1.27) and 1.33) into (1.38) and Conclusion One and thus noting that

wug(,,) x q tt 0 for all xzhg! [/ b ( )]1/D (The partial is greater than zero for all wx tt.

297 b 1/D xzhgttd [/ ( )] . The point at which that partial switches is the value where

ggqt ˆ(). )

wug(,,) x q 2. Since as noted above tt ! 0 for the interval [0,gqˆ ( )] , then wx

XX wxgq(;)t [(;)ggqgt ugxq gtt (,,)]/( ugxq xtt )0!; that is, the XX locus has a wgt

XX n 1/D positive slope when ggqt ˆ(). Also, since xc(0,0) ( /[1W ]) ! 0 , then

the vertical intercept is positive.

3. Since JW. n , then xcXX (0, 0) ( / [1WJn ])1/DD xcCC (0, 0) ( / [1 ])1/ , which

means that the CC locus is above the XX locus in the interval [0,gqˆ ( )].

From the properties outlined above we can see that from xt to xt1 the system will

°!!0 if gt gˆ move towards the XX locus as follows: xxtt1 ® °! 0 if g gˆ ¯ t .

The GG Locus

The GG locus is described as

GG{{( gtt , x ; q ) : g t g t1 . (A.3)

From (1.36) it is clear that the GG locus is unaffected by the effective resources per efficiency

unit of labor, xt , and is therefore vertical.

The GG loci exist as determined by the nodes shown in Chart C. Thus for qq ˆ there

are three separate vertical lines corresponding to the steady state level of

g:{(), gLU qg (), qg H ()} q . For qq! ˆ only the last of the three exists; thus there is only one

vertical GG locus corresponding to the steady state level gqH ().

298 The system moves towards the GG locus as over time as follows:

L °! 0 if gt g For gg ˆ , ggtt1 ® H ¯°!!0 if gt g

H °! 0 if gt g For gg! ˆ , ggtt1 ® H ¯°!!0 if gt g

Assumptions

These conclusions require that several assumptions be made with respect to how the growth rate of efficiency units of labor, u , respond to changes in technological progress, g . In particular, we have to assume that for a given ratio of types of individuals, u changes negatively

(or not at all) with respect to g . Also, at the limit as gt of, then u is negative. Finally, it is

necessary that, for a given q , when all of the driving variables are zero, then ug! . This is true

if u ! 0 at the Malthusian frontier. This is a crucial assumption since it assumes continuous growth in population.

299 Appendix B - The Math behind the Ramsey Simulations

Using spectral theory to apply a decomposition66 to the Ramsey economic system, we

dlncො dt let ȳ be a matrix with the right eigenvectors of the matrix D in equation (2.39), ቆ dlnk෡ ቇ = dt

െʅ 11 2 െ1 0 െɻ ln cොെln cොss െ1 ɻ ɻ ቀ ቁ ൬ ൰. Thus ȳ = ቆെʅ1 െʅ2ቇ and ȳ = ቌ ቍ. Now, using the ෠ ෠ ʅ െʅ ʅ1 ᇣെᇧᇧh0ᇤᇧᇧᇥ ln k െ ln kss ɻ ɻ 1 2 1 D ɻ

Dt ,spectral decomposition of D for the matrix exponential function, equation (2.41), xt ؆ e xo

ݐ െ1ٿ െ1 ٿ Dt can be written as xt ؆ e xo = ൫ȳ݁ ȳ ൯ݔ0 = ȳ݁ ȳ ݔ0. Written out this is

െʅ 11 2 െ1 ln ܿƸ െ ln ܿݏݏƸ ɻ eʅ1t 0 ɻ ln c0 െ ln cොss ൬ ൰ = ቆെʅ1 െʅ2ቇቀ ቁቌ ቍ൬ ൰ or ෠ ෠ ʅ െʅ ʅ t ʅ1 ෠ ln ݇ െ ln ݇ݏݏ 1 2 ɻ ɻ 0e2 1 ln k0 െ ln kss ɻ

ʅ t ʅ t ln ܿƸ െ ln ܿƸݏݏ =e 1 b11 +e 2 b12

ʅ t ʅ t ln ݇෠ െ ln ݇෠ݏݏ =e 1 b21 +e 2 b22

where

1 ෠ ܾ11 = െ ൣʅ2(ln c0 െ ln cොss ) + ɻ(ln k0 െ ln kss )൧, ʅ1െʅ2

1 ෠ ܾ12 = ൣʅ1(ln c0 െ ln cොss ) + ɻ൫ln k0 െ ln kss ൯൧, ʅ1െʅ2

ʅ1 ෠ ܾ21 = ൣʅ2(ln c0 െ ln cොss ) + ɻ൫ln k0 െ ln kss ൯൧, (ʅ1െʅ2)ɻ

1 ෠ ܾ22 = െ ൣʅ1(ln c0 െ ln cොss ) + ɻ(ln k0 െ ln kss )൧. (ʅ1െʅ2)ɻ

Recall that the system must obey the “no Ponzi” rule. That means that ܾ11 =0 , and ܾ21 =0

ʅ t ʅ t because if they did not, then both e 1 b11 and e 1 b21 would cause the system to explode. One can imagine that everyone knows that the world will end at some time T ; therefore they will not

ٿ Ȟെ1, withٿȞ = ܣ is defined as the factor product ,ܣ ,A spectral decomposition of a square matrix 66 being a diagonal matrix with elements equal to the eigenvalues of ܣ and Ȟ being a matrix that has the right eigenvectors of ܣ as columns. The spectral decomposition of the exponential of the same square matrix is .Ȟെ1ٿȞ݁ = ܣ݁

300 want to leave any assets when they die. Thus the initial stock of capital in any time period

෠ would be zero. By setting ܾ21 to zero we see that ʅ2(ln c0 െ ln cොss ) + ɻ൫ln k0 െ ln kss ൯ =0 or

ɻ that stability requires that ln c0 =lncොss െ (ln k0 െ ln k෠ ss ). Using that condition, the solution ʅ2

to the system is

ʅ t ln ܿƸ െ ln ܿƸݏݏ =e 2 (ln c0 െ ln cොss )

ʅ t ln ݇෠ െ ln ݇෠ݏݏ =e 2 ൫ln k0 െ ln k෠ ss ൯.

The Numerical Simulation with Chaos

For the Ramsey model with the guard labor externality and leisure explicitly in the utility

function, the solution to the system follows an optimal control technique for dynamic systems.

Using a technique pioneered by Gomes (2006), we first define the Hamiltonian:

ߙ(1+ߟ) (1െߙ)(1+ߟ) ݐ ݈ݐ െܿݐ െߜ݇ݐ ቃ݇ܣݐ, ݈ݐ , ݇ݐ, ݌ݐ ) = ݈݊ܿݐ + ݉ȉ݈݊(1 െ݈ݐ) + ߚ݌ݐ+1 ቂܿ)ܪ

where ݌ݐ is a co-state variable. The first order conditions are

1 (݅) ߚ݌ݐ+1 = 0֜= ܿܪ ݐܿ

(1െߙ)(1+ߟ)െ1 ݉ (݅݅) (0݈֜ݐ (1 െ݈ݐ ) = ߙ(1+ߟ= ݈ܪ ݐ݇ܣെߙ)(1 + ߟ)ߚ݌ݐ+1 1)

ߙ(1+ߟ)1 (1െߙ)(1+ߟ) (݅݅݅) ݐ ݈ݐ݇ܣߚ݌ݐ+1 െ݌ݐ = ߜߚ݌ݐ+1 െߙߚ݌ݐ+1

and the transversality condition that

ݐ (lim ݌ݐߚ ݇ݐ = 0 . (݅ݒ ݐ՜ь

Using (i), (ii) becomes

1െߙ)(1+ߟ)െ1 ݉ܿݐ) (ݐ (1 െ݈ݐ ) = ߙ(1+ߟ) . (v݈ ݐ݇ܣ(1െߙ)(1+ߟ)

In order to isolate the labor input as a function of only the parameters we have to use a Taylor-

will be of כ݈ The values of the parameter) .1> כ݈>series expansion to linearize (v) around 0

interest in the simulation.) This yields

301 (1െߙ)(1+ߟ)െ1 (ݐ (1 െ݈ݐ ) ൎߛ1 + ߛ2݈ݐ (ݒ݈݅ where

(1െߙ)(1+ߟ)כ כ 1െߙ)(1+ߟ)െ1)כ ߛ1 = [2 െ (1 െߙ)(1+ߟ)]݈ (1 െ݈ ) + ݈

1െߙ)(1+ߟ)െ1)כ כ 1െߙ)(1+ߟ)െ2)כ ߛ2 = [(1 െߙ)(1+ߟ) െ 1]݈ (1 െ݈ ) + ݈ .

Putting (vi) into (v) yields the labor input in explicit terms:

ݐ ߛ1ܿ݉ (ݐ = ߙ(1+ߟ) െ (ݒ݈݅݅ ߛ2 ߛ2݇ݐܣ(െߙ)(1 + ߟ 1)

Combining (i), (ii), and (vii) into (iii) derives

2 (ݔ1ݐ ܿݐ+1 െݔ2ݐ ܿݐ+1 + ݔ3ݐ = 0 (ݒ݅݅݅ where

1 ߙ(1 + ߟ) ݉ ݔ1ݐ = ݉൤ + ȉ ൨ ߚܿݐ (1 െߙ)(1 + ߟ) ݇ݐ

ߙ(1+ߟ) [(ߛ1 + ߛ2)݇ݐ+1 െ[1െߙ(1+ߟ)ܣ(െߙ)(1+ߟ 1) ߛ1݇ݐ+1ܣ݉(ݔ2ݐ = ݉(1 െߜ) + + ߙ(1+ߟ ߚܿݐ

ߙ(1+ߟ) . ߛ1 + ߛ2)(1 െߜ) ݇ݐ+1)ܣ(ݔ3ݐ = (1 െߙ)(1+ߟ

Solving (viii) for ܿݐ+1 and using (vii) in the capital accumulation constraint yields (2.48) and

(2.49).

302 Appendix C - Vensim Code and Economic Data

The following pages contain the Vensim dynamic modeling software code that was used to construct the simulation. Following that are the normalized time series data used in the simulations.

Growth Past= 12 ~ ~ |

Growth Parameter A= IF THEN ELSE(Time<=2008, Growth Past ,Growth Future ) ~ ~ |

Decay Rate Future= 0.012 ~ ~ |

Growth Future= 12 ~ ~ |

Decay Rate of Intensity Reduction= IF THEN ELSE(Time<=2008, Decay Rate Past ,Decay Rate Future) ~ ~ |

Decay Rate Past= 0.012 ~ ~ |

Fractional Growth Rate= 1-(1/(1+EXP(Growth Parameter A*(Efficiency Index-1)))) ~ ~ |

Information and Communication Fraction of Capital= Information and Communication Capital Growth Rate*(Aggregate Accumulated Monetary Value of Output\ /7315.2) ~ ~ |

Capital Intensity of Output= Capital/Gross Domestic Product ~ ~ |

Labor Intensity of Output= Labor/Gross Domestic Product ~

303 ~ |

Marginal Productivity of Labour= Production Function parameter a*((Labor+Energy Services)/Capital) ~ ~ |

Gross Domestic Product= ACTIVE INITIAL ( Energy Services*((Labor/Energy Services)^(IF THEN ELSE(Time <=1980,0,Production Function Parameter c\ )*Information and Communication Fraction of Capital))*EXP( Production Function parameter a\ *(2-((Labor+Energy Services)/Capital))+Production Function parameter a*Production Function parameter b\ * ((Labor /Energy Services)-1)), 1) ~ ~ |

Production Function Parameter c= -0.408142 ~ ~ |

Information and Communication Capital Growth Rate= 0.00105 ~ ~ |

Energy Service Intensity of Output= Energy Services/Gross Domestic Product ~ ~ |

Marginal Productivity of Energy Services= 1-(Production Function parameter a*((Labor+Energy Services)/Capital))-(Production Function parameter a\ *(Production Function parameter b*((Labor/Energy Services)-(Labor/Capital)))) ~ ~ |

Monetary Value of Output= Gross Domestic Product*"Reference Output t=1900" ~ ~ |

Marginal Productivity of Capital= Production Function parameter a*(Production Function parameter b*((Labor/Energy Services\ )-(Labor/Capital))) ~ ~ |

Loss Parameter A= -0.0203 ~ ~ -0.0203786 |

Labor Decay Rate=

304 IF THEN ELSE(Time<=Structural Shift Time D, Labor Decay Rate A*Labor, Labor Decay Rate B\ *Labor ) ~ ~ |

Labor Intensity of Capital= Labor/Capital ~ ~ |

Loss Parameter B= 3 ~ ~ 3 |

Fractional Efficiency Loss Rate= Loss Parameter A+Loss Parameter C*Efficiency Index^Loss Parameter B ~ ~ |

Loss Parameter C= 23.8718 ~ ~ 23.8718 |

Technical Efficiency Limit= 1 ~ ~ |

Energy Service Intensity of Capital= Energy Services/Capital ~ ~ |

Energy Service Intensity of Labour= Energy Services/Labor ~ ~ |

Primary Energy Intensity of Capital= Primary Energy Demand/Capital ~ ~ |

Primary Energy Intensity of Labour= Primary Energy Demand/Labor ~ ~ |

Energy Services Production= Efficiency of Primary Energy Conversion*Primary Energy Production ~ ~ |

305 Primary Energy Production= Primary Energy Demand*"Reference Primary Energy Production t=1900" ~ ~ |

Labor Decay Rate A= 0.10913 ~ ~ |

Labor Decay Rate B= 0.117186 ~ ~ |

Labor Growth Rate A= 0.124721 ~ ~ |

Labor Growth Rate B= 0.1277 ~ ~ |

Efficiency of Primary Energy Conversion= INTEG ( Efficiency Growth Rate-Efficiency Loss Rate, Initial Efficiency of Primary Energy Conversion) ~ ~ |

Efficiency Index= Efficiency of Primary Energy Conversion/Technical Efficiency Limit ~ ~ |

Initial Efficiency of Primary Energy Conversion= 0.0259 ~ ~ |

Structural Shift Time C= 1937.54 ~ ~ |

Structural Shift Time D= 1920 ~ ~ |

"Reference Primary Energy Cumulative Production t=1900"= 24.89 ~ ~ |

Efficiency Loss Rate= Fractional Efficiency Loss Rate*Efficiency of Primary Energy Conversion

306 ~ ~ |

Labor Growth Rate= IF THEN ELSE(Time<=Structural Shift Time C, Labor Growth Rate A*Labor, Labor Growth Rate B\ *Labor) ~ ~ |

Labor= INTEG ( Labor Growth Rate-Labor Decay Rate, 1) ~ ~ |

Efficiency Growth Rate= Fractional Growth Rate*(Primary Energy Aggregate Production/"Reference Primary Energy Cumulative Production t=1900"\ ) ~ ~ |

Capital= INTEG ( Investment-Depreciation, 1) ~ ~ |

Depreciation Rate Two= 0.106435 ~ ~ Determined by optimization. |

Depreciation= Capital*Depreciation Rate ~ ~ |

Depreciation Rate= IF THEN ELSE( Time<=Structural Shift Time DR1, Depreciation Rate One, Depreciation Rate Two\ ) ~ ~ |

Depreciation Rate One= 0.0590329 ~ ~ Determined by optimization. |

Savings Rate= IF THEN ELSE( Time<=Structural Shift Time SR1,Savings Rate One , Savings Rate Two) ~ ~ Fraction of output invested (savings rate). |

Savings Rate One=

307 0.0809601 ~ ~ Determined by optimisation. |

Savings Rate Two= 0.0741895 ~ ~ Determined by optimisation. |

Structural Shift Time DR1= 1930 ~ ~ |

Structural Shift Time SR1= 1970 ~ ~ |

Production Function parameter a= 0.129312 ~ ~ |

Energy Services= ACTIVE INITIAL ( (Energy Services Aggregate Production-Last Years Energy Service Production)/"Reference Energy Services Production t=1900"\ , 1) ~ dmnl ~ |

Energy Services Aggregate Production= INTEG ( Energy Services Production, 1) ~ ~ |

Initial Primary Energy Intensity of Output= 1 ~ ~ |

Investment= Gross Domestic Product*Savings Rate ~ ~ |

Last Years Energy Service Production= DELAY FIXED (Energy Services Aggregate Production, 1, 0) ~ ~ |

Production Function parameter b= 3.44985 ~

308 ~ |

"Reference Energy Services Production t=1900"= 0.65 ~ Ej ~ |

Primary Energy Aggregate Production= INTEG ( Primary Energy Production, 24.89) ~ ~ |

Primary Energy Demand= Primary Energy Intensity of Output*Gross Domestic Product ~ ~ |

Primary Energy Intensity of Output= INTEG ( -Rate of Intensity Reduction, Initial Primary Energy Intensity of Output) ~ ~ |

Rate of Intensity Reduction= Decay Rate of Intensity Reduction*Primary Energy Intensity of Output ~ ~ |

"Reference Primary Energy Production t=1900"= 24.89 ~ ~ |

Aggregate Accumulated Monetary Value of Output= INTEG ( +Monetary Value of Output, 7315.2) ~ billion 1992$ ~ |

"Reference Output t=1900"= 354 ~ billion 1992$ ~ |

******************************************************** .Control ********************************************************~ Simulation Control Parameters |

FINAL TIME = 2008 ~ Year ~ The final time for the simulation. |

INITIAL TIME = 1900 ~ Year

309 ~ The initial time for the simulation. |

SAVEPER = TIME STEP ~ Year ~ The frequency with which output is stored. |

TIME STEP = 1 ~ Year ~ The time step for the simulation. |

\\\---/// Sketch information - do not modify anything except names V300 Do not put anything below this section - it will be ignored *Economy $192-192-192,0,Times New Roman|12||0-0-0|0-0-0|0-0-255|-1--1--1|-1--1--1|96,96,5,0 10,1,Aggregate Accumulated Monetary Value of Output,1182,728,137,34,3,131,0,9,0,0,0,0,160-160-160,0-0- 0,|14||0-64-0 12,2,48,698,720,10,8,0,3,0,9,-1,0,0,0,160-160-160,0-0-0,|14||0-64-0 1,3,6,1,4,0,0,23,3,0,0,0-0-0,|12||0-0-0,1|(971,730)| 1,4,6,2,100,0,0,23,3,0,0,0-0-0,|12||0-0-0,1|(698,730)| 10,5,"Reference Output t=1900",703,788,56,20,8,131,0,9,0,0,0,0,160-160-160,0-0-0,|14||0-64-0 11,6,556,892,730,6,8,34,3,0,1,1,0,0,0,160-160-160,0-0-0,|12||0-0-0 10,7,Monetary Value of Output,892,758,61,20,40,131,0,9,-1,0,0,0,160-160-160,0-0-0,|14||0-64-0 10,8,Gross Domestic Product,933,603,85,24,8,131,0,41,0,0,0,0,160-160-160,0-0-0,Bookman Old Style|16||0-64-0 1,9,8,6,1,0,0,13,3,64,0,0-0-0,|12||0-0-0,1|(905,670)| 10,10,Labor,875,456,24,11,8,3,0,9,0,0,0,0,160-160-160,0-0-0,|14||0-64-0 10,11,Capital,1059,445,27,11,8,3,0,9,-1,0,0,0,160-160-160,0-0-0,|14||0-64-0 1,12,11,8,1,0,0,13,3,64,0,0-0-0,|12||0-0-0,1|(1022,553)| 1,13,10,8,1,0,0,13,3,64,0,0-0-0,|12||0-0-0,1|(908,511)| 10,14,Production Function parameter a,621,519,93,31,8,131,0,25,-1,0,0,0,160-160-160,0-0-0,|14|I|0-64-0 1,15,14,8,1,0,0,13,3,0,0,0-0-0,|12||0-0-0,1|(757,589)| 10,16,Production Function parameter b,657,643,86,32,8,131,0,25,-1,0,0,0,160-160-160,0-0-0,|14|I|0-64-0 1,17,16,8,1,0,0,13,3,0,0,0-0-0,|12||0-0-0,1|(756,653)| 10,18,Energy Services,749,460,32,20,8,3,0,9,-1,0,0,0,160-160-160,0-0-0,|14||0-64-0 1,19,18,8,1,0,0,13,3,64,0,0-0-0,|12||0-0-0,1|(813,541)| 12,20,0,838,341,59,19,8,4,0,49,-1,0,0,0,160-160-160,0-0-0,Futura Md BT|14|B|0-64-0 Analysis of the US Economy 10,21,Labor Decay Rate,864,378,58,20,8,2,9,25,-1,0,0,0,160-160-160,0-0-0,|14|B|0-64-0 1,22,21,10,0,9,0,13,1,0,0,0-0-0,|12||0-0-0,1|(868,412)| 10,23,Labor Growth Rate,982,379,65,20,8,2,9,25,-1,0,0,0,160-160-160,0-0-0,|14|B|0-64-0 1,24,23,10,1,9,0,13,1,0,0,0-0-0,|12||0-0-0,1|(937,418)| 10,25,Depreciation,1115,372,61,14,8,130,2,35,-1,0,0,0,160-160-160,0-0-0,Futura Md BT|12||0-64-0 1,26,25,11,1,2,0,13,1,0,0,0-0-0,|12||0-0-0,1|(1095,405)| 10,27,Investment,1262,373,52,11,8,130,2,9,-1,0,0,0,160-160-160,0-0-0,|14||0-64-0 1,28,27,11,1,2,0,13,1,0,0,0-0-0,|12||0-0-0,1|(1162,418)| 10,29,Energy Services Aggregate Production,720,366,87,20,8,130,2,9,-1,0,0,0,160-160-160,0-0-0,|14||0-64-0 1,30,29,18,0,2,0,13,1,0,0,0-0-0,|12||0-0-0,1|(731,403)| 10,31,Last Years Energy Service Production,511,437,78,20,8,2,2,9,-1,0,0,0,160-160-160,0-0-0,|14||0-64-0 1,32,31,18,1,2,0,13,1,0,0,0-0-0,|12||0-0-0,1|(642,460)| 10,33,"Reference Energy Services Production t=1900",524,367,76,30,8,2,2,9,-1,0,0,0,160-160-160,0-0-0,|14||0-64-0 1,34,33,18,1,2,0,13,1,0,0,0-0-0,|12||0-0-0,1|(644,423)| 10,35,Information and Communication Fraction of Capital,1329,570,147,25,8,131,0,9,0,0,0,0,160-160-160,0-0- 0,|14||0-64-0 1,36,5,7,1,0,0,13,3,64,0,0-0-0,|12||0-0-0,1|(802,803)| 1,37,1,35,1,0,0,13,3,64,0,0-0-0,|12||0-0-0,1|(1332,665)|

310 10,38,Production Function Parameter c,1196,650,92,31,8,131,0,25,-1,0,0,0,160-160-160,0-0-0,|14|I|0-64-0 1,39,38,8,1,0,0,13,3,64,0,0-0-0,|12||0-0-0,1|(1045,652)| 1,40,35,8,0,0,0,13,3,64,0,0-0-0,|12||0-0-0,1|(1109,587)| 10,41,Information and Communication Capital Growth Rate,1284,447,125,26,8,131,0,9,0,0,0,0,160-160-160,0-0- 0,|14||0-64-0 1,42,41,35,1,0,0,13,3,64,0,0-0-0,|12||0-0-0,1|(1328,496)| 12,43,0,1022,366,95,24,8,4,0,57,-1,0,0,0,160-160-160,0-0-0,Futura Md BT|10|B|0-64-0 Factors of production are normalised to 1900 values making them dimensionless. 10,44,Time,1054,540,31,11,8,2,1,9,-1,0,0,0,160-160-160,0-0-0,|14||0-64-0 1,45,44,8,0,1,0,13,1,64,0,0-0-0,|12||0-0-0,1|(1014,560)| \\\---/// Sketch information - do not modify anything except names V300 Do not put anything below this section - it will be ignored *energy $192-192-192,0,Times New Roman|12||0-0-0|0-0-0|0-0-255|-1--1--1|-1--1--1|96,96,5,0 10,1,Initial Primary Energy Intensity of Output,618,105,79,28,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 10,2,Primary Energy Intensity of Output,828,127,62,30,3,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 12,3,48,1272,135,10,8,0,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 1,4,6,3,4,0,0,14,3,0,0,0-0-0,|12||0-0-0,1|(1139,128)| 1,5,6,2,100,0,0,14,1,0,0,0-0-0,|12||0-0-0,1|(947,128)| 11,6,48,1011,128,6,8,34,3,0,0,1,0,0,0 10,7,Rate of Intensity Reduction,1011,152,77,16,40,131,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 1,8,2,7,1,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(920,191)| 10,9,Decay Rate of Intensity Reduction,1312,256,71,28,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 1,10,9,7,1,0,0,14,3,64,0,0-0-0,|12||0-0-0,1|(1080,150)| 10,11,Primary Energy Demand,784,257,65,19,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 1,12,2,11,1,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(802,209)| 10,13,Gross Domestic Product,620,196,99,21,8,130,0,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|10||128-128-128 1,14,13,11,1,0,0,14,1,0,0,0-0-0,|12||0-0-0,1|(662,248)| 10,15,Primary Energy Aggregate Production,881,357,81,35,3,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 12,16,48,638,351,10,8,0,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 1,17,18,16,100,0,0,14,1,0,0,0-0-0,|12||0-0-0,1|(667,354)| 11,18,48,692,354,6,8,34,3,0,0,1,0,0,0 10,19,Primary Energy Production,692,380,57,18,40,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 1,20,11,18,1,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(762,284)| 1,21,18,15,4,0,0,14,1,0,0,0-0-0,|12||0-0-0,1|(749,354)| 10,22,"Reference Primary Energy Production t=1900",496,294,69,27,8,3,1,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 10,23,"Reference Energy Services Production t=1900",1271,758,82,28,8,3,1,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 10,24,Energy Services Aggregate Production,1053,837,81,35,3,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 12,25,48,638,777,10,8,0,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 1,26,28,24,4,0,0,14,1,0,0,0-0-0,|12||0-0-0,1|(899,838)| 1,27,28,25,100,0,0,14,1,0,0,0-0-0,|12||0-0-0,1|(638,838)| 11,28,48,821,838,6,8,34,3,0,0,1,0,0,0 10,29,Energy Services Production,821,864,60,18,40,3,0,32,1,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 10,30,Energy Services,1240,861,35,19,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 10,31,Last Years Energy Service Production,1152,933,78,19,8,3,2,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 1,32,24,31,1,2,0,14,1,64,0,0-0-0,|12||0-0-0,1|(1051,885)| 1,33,23,30,1,1,0,14,1,64,0,0-0-0,|12||0-0-0,1|(1260,832)| 1,34,31,30,1,2,0,14,1,64,0,0-0-0,|12||0-0-0,1|(1248,881)| 1,35,24,30,1,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(1185,832)| 10,36,Efficiency of Primary Energy Conversion,1077,467,78,34,3,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 12,37,48,731,462,10,8,0,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 1,38,40,36,4,0,0,14,1,0,0,0-0-0,|12||0-0-0,1|(944,466)| 1,39,40,37,100,0,0,14,1,0,0,0-0-0,|12||0-0-0,1|(809,466)| 11,40,48,883,466,6,8,34,3,0,0,1,0,0,0 10,41,Efficiency Growth Rate,883,502,73,28,40,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 12,42,48,1336,466,10,8,0,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0

311 1,43,45,42,4,0,0,14,1,0,0,0-0-0,|12||0-0-0,1|(1278,467)| 1,44,45,36,100,0,0,14,1,0,0,0-0-0,|12||0-0-0,1|(1183,467)| 11,45,48,1221,467,10,8,34,131,0,0,1,0,0,0 10,46,Efficiency Loss Rate,1221,503,60,28,40,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,47,Efficiency Index,930,654,81,19,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,48,Technical Efficiency Limit,843,564,81,19,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,49,"Reference Primary Energy Cumulative Production t=1900",545,428,69,27,8,3,9,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,50,Initial Efficiency of Primary Energy Conversion,1229,395,86,28,8,3,2,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 1,51,15,40,1,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(881,420)| 1,52,49,40,1,8,0,14,1,64,0,0-0-0,|12||0-0-0,1|(717,418)| 1,53,36,46,1,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(1092,495)| 1,54,36,47,1,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(950,558)| 1,55,48,47,1,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(880,618)| 10,56,Fractional Growth Rate,561,500,84,28,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,57,Fractional Efficiency Loss Rate,1189,590,84,19,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,58,Growth Parameter A,602,662,55,19,8,3,0,48,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12|I|0-0-0 10,59,Loss Parameter A,1079,667,55,19,8,3,0,48,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12|I|0-0-0 10,60,Loss Parameter B,1210,660,54,19,8,3,0,48,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12|I|0-0-0 10,61,Loss Parameter C,1372,656,79,18,8,131,0,48,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12|I|0-0-0 1,62,47,57,1,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(1008,596)| 1,63,59,57,1,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(1101,632)| 1,64,60,57,1,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(1200,630)| 1,65,61,57,1,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(1332,604)| 1,66,58,56,0,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(585,595)| 1,67,56,41,1,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(717,500)| 1,68,57,46,1,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(1178,515)| 1,69,47,56,1,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(767,629)| 10,70,Efficiency of Primary Energy Conversion,904,755,98,28,8,2,0,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128-128-128 1,71,70,28,1,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(863,797)| 10,72,Primary Energy Production,734,751,61,18,8,2,0,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128-128-128 1,73,72,28,1,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(769,789)| 1,74,22,18,1,1,0,14,1,64,0,0-0-0,|12||0-0-0,1|(593,309)| 10,75,Decay Rate Past,1126,246,57,19,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,76,Decay Rate Future,1176,323,57,19,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,77,Time,1378,164,35,11,8,2,0,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128-128-128 1,78,75,9,0,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(1201,249)| 1,79,76,9,0,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(1225,298)| 1,80,77,9,1,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(1380,195)| 10,81,Growth Future,482,608,41,19,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,82,Growth Past,463,687,41,19,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 1,83,81,58,0,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(531,630)| 1,84,82,58,0,0,0,14,1,64,0,0-0-0,|12||0-0-0,1|(515,677)| 10,85,Time,517,749,35,11,8,2,0,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128-128-128 1,86,85,58,0,0,0,14,1,0,0,0-0-0,|12||0-0-0,1|(547,716)| 1,87,1,2,0,0,0,0,1,64,1,0-0-0,|12||0-0-0,1|(724,115)| 1,88,50,36,0,0,0,0,1,64,1,0-0-0,|12||0-0-0,1|(1165,425)| \\\---/// Sketch information - do not modify anything except names V300 Do not put anything below this section - it will be ignored *Capital $192-192-192,0,Times New Roman|12||0-0-0|0-0-0|0-0-255|-1--1--1|-1--1--1|96,96,5,0 10,1,Capital,940,439,40,20,3,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 12,2,48,650,440,10,8,0,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 1,3,4,2,100,0,0,23,3,0,0,0-0-0,|12||0-0-0,1|(705,438)| 11,4,48,756,438,6,8,34,3,0,0,1,0,0,0 10,5,Investment,756,457,47,11,40,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0

312 12,6,48,1234,439,10,8,0,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 1,7,8,6,4,0,0,23,3,0,0,0-0-0,|12||0-0-0,1|(1162,440)| 11,8,48,1094,440,6,8,34,3,0,0,1,0,0,0 10,9,Depreciation,1094,459,54,11,40,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 10,10,Savings Rate,852,577,48,19,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 10,11,Time,955,674,35,11,8,2,0,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|10||128-128-128 1,12,11,10,1,0,0,13,1,64,0,0-0-0,|12||0-0-0,1|(914,623)| 1,13,10,5,1,0,0,13,1,64,0,0-0-0,|12||0-0-0,1|(859,516)| 10,14,Depreciation Rate,1047,577,55,19,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 10,15,Gross Domestic Product,780,338,74,23,8,130,0,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|10||128-128-128 1,16,15,5,1,0,0,13,1,64,0,0-0-0,|12||0-0-0,1|(766,358)| 1,17,14,9,1,0,0,13,1,64,0,0-0-0,|12||0-0-0,1|(1000,510)| 1,18,11,14,1,0,0,13,1,0,0,0-0-0,|12||0-0-0,1|(999,619)| 1,19,4,1,4,0,0,23,3,0,0,0-0-0,|12||0-0-0,1|(831,438)| 1,20,8,1,100,0,0,23,3,0,0,0-0-0,|12||0-0-0,1|(1034,440)| 10,21,Savings Rate One,648,538,47,19,8,3,0,48,0,0,0,0,0-0-0,0-0-0,Futura Md BT|10|I|0-0-0 10,22,Savings Rate Two,626,627,47,19,8,3,0,48,0,0,0,0,0-0-0,0-0-0,Futura Md BT|10|I|0-0-0 10,23,Depreciation Rate One,1224,539,56,19,8,3,0,48,0,0,0,0,0-0-0,0-0-0,Futura Md BT|10|I|0-0-0 10,24,Depreciation Rate Two,1225,617,56,19,8,3,0,48,0,0,0,0,0-0-0,0-0-0,Futura Md BT|10|I|0-0-0 1,25,21,10,1,0,0,13,1,64,0,0-0-0,|12||0-0-0,1|(768,520)| 1,26,22,10,1,0,0,13,1,64,0,0-0-0,|12||0-0-0,1|(718,582)| 1,27,23,14,1,0,0,13,1,64,0,0-0-0,|12||0-0-0,1|(1123,518)| 1,28,24,14,1,0,0,13,1,64,0,0-0-0,|12||0-0-0,1|(1139,582)| 10,29,Structural Shift Time SR1,786,667,64,19,8,3,0,48,0,0,0,0,0-0-0,0-0-0,Futura Md BT|10|I|0-0-0 10,30,Structural Shift Time DR1,1094,662,63,19,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|10||0-0-0 1,31,29,10,1,0,0,13,1,64,0,0-0-0,|12||0-0-0,1|(811,626)| 1,32,30,14,1,0,0,13,1,64,0,0-0-0,|12||0-0-0,1|(1072,616)| 1,33,1,8,1,0,0,13,1,64,0,0-0-0,|12||0-0-0,1|(1023,403)| \\\---/// Sketch information - do not modify anything except names V300 Do not put anything below this section - it will be ignored *Labour $192-192-192,0,Times New Roman|12||0-0-0|0-0-0|0-0-255|-1--1--1|-1--1--1|96,96,5,0 10,1,Labor,922,419,40,20,3,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 12,2,48,702,421,10,8,0,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 1,3,5,1,4,0,0,13,1,0,0,0-0-0,|12||0-0-0,1|(836,420)| 1,4,5,2,100,0,0,13,1,0,0,0-0-0,|12||0-0-0,1|(745,420)| 11,5,48,785,420,6,8,34,3,0,0,1,0,0,0 10,6,Labor Growth Rate,785,447,54,19,40,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 12,7,48,1163,419,10,8,0,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 1,8,10,7,4,0,0,13,1,0,0,0-0-0,|12||0-0-0,1|(1109,420)| 1,9,10,1,100,0,0,13,1,0,0,0-0-0,|12||0-0-0,1|(1008,420)| 11,10,48,1060,420,6,8,34,3,0,0,1,0,0,0 10,11,Labor Decay Rate,1060,447,59,19,40,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,12,Labor Growth Rate A,708,550,76,19,8,3,0,48,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12|I|0-0-0 10,13,Labor Growth Rate B,749,620,76,19,8,3,0,48,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12|I|0-0-0 10,14,Labor Decay Rate A,1165,550,76,19,8,3,0,48,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12|I|0-0-0 10,15,Labor Decay Rate B,1119,620,76,19,8,3,0,48,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12|I|0-0-0 10,16,Structural Shift Time C,873,578,64,19,8,3,0,48,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12|I|0-0-0 10,17,Time,921,518,35,11,8,2,0,34,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128-128-128 1,18,17,6,1,0,0,13,1,64,0,0-0-0,|12||0-0-0,1|(861,510)| 1,19,17,11,1,0,0,13,1,64,0,0-0-0,|12||0-0-0,1|(987,506)| 1,20,1,6,1,0,0,13,1,64,0,0-0-0,|12||0-0-0,1|(868,457)| 1,21,1,11,1,0,0,13,1,64,0,0-0-0,|12||0-0-0,1|(955,448)| 1,22,12,6,1,0,0,13,1,64,0,0-0-0,|12||0-0-0,1|(740,503)| 1,23,13,6,1,0,0,13,1,64,0,0-0-0,|12||0-0-0,1|(784,567)| 1,24,14,11,0,0,0,13,1,64,0,0-0-0,|12||0-0-0,1|(1119,505)| 1,25,15,11,1,0,0,13,1,64,0,0-0-0,|12||0-0-0,1|(1062,469)| 1,26,16,6,1,0,0,13,1,64,0,0-0-0,|12||0-0-0,1|(829,537)|

313 10,27,Structural Shift Time D,1001,578,64,19,8,3,0,48,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12|I|0-0-0 1,28,27,11,0,0,0,13,1,64,0,0-0-0,|12||0-0-0,1|(1026,521)| \\\---/// Sketch information - do not modify anything except names V300 Do not put anything below this section - it will be ignored *Intensity Measures $192-192-192,0,Times New Roman|12||0-0-0|0-0-0|0-0-255|-1--1--1|-1--1--1|96,96,5,0 10,1,Capital,947,352,32,11,8,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,2,Depreciation,672,287,40,20,8,2,9,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128-128-128 1,3,2,1,0,9,0,0,1,0,0,255-128-0,|12||0-0-0,1|(806,318)| 10,4,Investment,667,367,40,20,8,2,2,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128-128-128 1,5,4,1,0,2,0,0,1,0,0,255-128-0,|12||0-0-0,1|(804,359)| 10,6,Energy Services,1326,534,59,10,8,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,7,Energy Services Aggregate Production,665,401,65,27,8,2,2,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128-128-128 1,8,7,6,0,2,0,0,1,0,0,255-128-0,|12||0-0-0,1|(996,467)| 10,9,Last Years Energy Service Production,662,445,74,18,8,2,2,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128- 128-128 1,10,9,6,0,2,0,0,1,0,0,255-128-0,|12||0-0-0,1|(994,489)| 10,11,"Reference Energy Services Production t=1900",661,495,74,27,8,2,2,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128-128-128 1,12,11,6,0,2,0,0,1,0,0,255-128-0,|12||0-0-0,1|(994,514)| 10,13,Gross Domestic Product,760,283,68,20,8,131,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 1,14,1,13,0,2,0,0,1,0,0,255-128-0,|12||0-0-0,1|(872,324)| 1,15,6,13,0,2,0,0,1,0,0,255-128-0,|12||0-0-0,1|(1060,416)| 10,16,Labor,674,590,44,11,8,2,2,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128-128-128 1,17,16,13,0,2,0,0,1,0,0,255-128-0,|12||0-0-0,1|(713,447)| 10,18,Production Function parameter a,674,555,62,19,8,2,2,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128- 128-128 1,19,18,13,0,2,0,0,1,0,0,255-128-0,|12||0-0-0,1|(714,426)| 10,20,Production Function parameter b,669,626,62,19,8,2,2,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128- 128-128 1,21,20,13,0,2,0,0,1,0,0,255-128-0,|12||0-0-0,1|(712,461)| 10,22,Labor,1137,436,31,11,8,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,23,Labor Decay Rate,807,621,55,19,8,2,2,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128-128-128 1,24,23,22,0,2,0,0,1,0,0,255-128-0,|12||0-0-0,1|(972,527)| 10,25,Labor Growth Rate,788,640,60,19,8,2,2,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128-128-128 1,26,25,22,0,2,0,0,1,0,0,255-128-0,|12||0-0-0,1|(962,537)| 10,27,Efficiency of Primary Energy Conversion,1133,294,81,27,8,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,28,Efficiency Growth Rate,783,698,73,28,8,2,2,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128-128-128 1,29,28,27,0,2,0,0,1,0,0,255-128-0,|12||0-0-0,1|(953,500)| 10,30,Efficiency Loss Rate,764,717,60,28,8,2,2,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128-128-128 1,31,30,27,0,2,0,0,1,0,0,255-128-0,|12||0-0-0,1|(943,510)| 10,32,Energy Service Intensity of Capital,1146,528,67,18,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,33,Labor Intensity of Capital,947,436,70,19,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,34,Energy Service Intensity of Labour,950,527,66,18,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 1,35,6,32,0,2,0,0,1,64,0,255-128-0,|12||0-0-0,1|(1246,531)| 1,36,6,34,0,2,0,0,1,64,0,255-128-0,|12||0-0-0,1|(1148,530)| 1,37,22,33,0,2,0,0,1,64,0,255-128-0,|12||0-0-0,1|(1068,436)| 1,38,1,32,0,2,0,0,1,64,0,255-128-0,|12||0-0-0,1|(1036,431)| 1,39,22,34,0,2,0,0,1,64,0,255-128-0,|12||0-0-0,1|(1056,474)| 1,40,1,33,0,2,0,0,1,64,0,255-128-0,|12||0-0-0,1|(947,383)| 10,41,Primary Energy Demand,1319,600,57,18,8,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 1,42,13,41,0,2,0,0,1,0,0,255-128-0,|12||0-0-0,1|(1034,439)| 10,43,Primary Energy Intensity of Output,1301,665,69,18,8,2,2,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128- 128-128 1,44,43,41,0,2,0,0,1,0,0,255-128-0,|12||0-0-0,1|(1307,639)| 10,45,Primary Energy Intensity of Output,760,600,64,18,8,3,0,32,-1,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,46,Rate of Intensity Reduction,733,622,49,28,8,2,2,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128-128-128

314 1,47,46,45,0,2,0,0,1,0,0,255-128-0,|12||0-0-0,1|(746,610)| 10,48,Primary Energy Intensity of Labour,947,600,66,18,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,49,Primary Energy Intensity of Capital,1137,600,67,18,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 1,50,41,48,0,2,0,0,1,64,0,255-128-0,|12||0-0-0,1|(1144,600)| 1,51,22,48,0,2,0,0,1,64,0,255-128-0,|12||0-0-0,1|(1051,509)| 1,52,41,49,0,2,0,0,1,64,0,255-128-0,|12||0-0-0,1|(1240,600)| 1,53,1,49,0,2,0,0,1,64,0,255-128-0,|12||0-0-0,1|(1034,466)| 10,54,Information and Communication Fraction of Capital,760,315,68,19,8,2,1,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128-128-128 1,55,54,13,0,1,0,0,1,0,0,255-128-0,|12||0-0-0,1|(760,306)| 10,56,Production Function Parameter c,760,315,59,19,8,2,1,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128- 128-128 1,57,56,13,0,1,0,0,1,0,0,255-128-0,|12||0-0-0,1|(760,306)| 10,58,Capital Intensity of Output,760,352,71,19,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,59,Labor Intensity of Output,760,437,70,19,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,60,Energy Service Intensity of Output,760,524,64,18,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 1,61,13,58,0,1,0,0,1,64,0,255-128-0,|12||0-0-0,1|(760,311)| 1,62,1,58,0,1,0,0,1,64,0,255-128-0,|12||0-0-0,1|(880,352)| 1,63,13,59,0,1,0,0,1,64,0,255-128-0,|12||0-0-0,1|(760,353)| 1,64,13,60,0,1,0,0,1,64,0,255-128-0,|12||0-0-0,1|(760,397)| 1,65,6,60,0,1,0,0,1,0,0,255-128-0,|12||0-0-0,1|(1052,529)| 1,66,22,59,0,1,0,0,1,0,0,255-128-0,|12||0-0-0,1|(975,436)| 10,67,Marginal Productivity of Labour,761,734,61,28,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,68,Marginal Productivity of Capital,947,743,61,28,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,69,Marginal Productivity of Energy Services,1148,745,76,18,8,3,0,32,0,0,0,0,0-0-0,0-0-0,Futura Md BT|12||0-0-0 10,70,Production Function parameter a,571,605,62,19,8,2,1,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128- 128-128 10,71,Production Function parameter b,558,660,62,19,8,2,1,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128- 128-128 1,72,70,67,0,1,0,0,1,64,0,255-128-0,|12||0-0-0,1|(652,661)| 1,73,70,68,0,1,0,0,1,64,0,255-128-0,|12||0-0-0,1|(747,669)| 1,74,71,68,0,1,0,0,1,64,0,255-128-0,|12||0-0-0,1|(746,699)| 1,75,1,67,0,1,0,0,1,0,0,255-128-0,|12||0-0-0,1|(861,528)| 1,76,6,67,0,1,0,0,1,0,0,255-128-0,|12||0-0-0,1|(1066,625)| 1,77,22,67,0,1,0,0,1,0,0,255-128-0,|12||0-0-0,1|(965,572)| 1,78,1,68,0,1,0,0,1,0,0,255-128-0,|12||0-0-0,1|(947,532)| 1,79,6,68,0,1,0,0,1,0,0,255-128-0,|12||0-0-0,1|(1158,626)| 1,80,22,68,0,1,0,0,1,0,0,255-128-0,|12||0-0-0,1|(1051,575)| 1,81,1,69,0,1,0,0,1,0,0,255-128-0,|12||0-0-0,1|(1041,538)| 1,82,6,69,0,1,0,0,1,0,0,255-128-0,|12||0-0-0,1|(1245,630)| 1,83,22,69,0,1,0,0,1,0,0,255-128-0,|12||0-0-0,1|(1141,580)| 10,84,Production Function parameter a,1144,712,62,19,8,2,1,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128- 128-128 1,85,84,69,0,1,0,0,1,0,0,255-128-0,|12||0-0-0,1|(1144,722)| 10,86,Production Function parameter b,1144,712,62,19,8,2,1,35,-1,0,0,0,128-128-128,0-0-0,Futura Md BT|12||128- 128-128 1,87,86,69,0,1,0,0,1,0,0,255-128-0,|12||0-0-0,1|(1144,722)| 10,88,Initial Efficiency of Primary Energy Conversion,1137,377,86,28,8,2,0,3,-1,0,0,0,128-128-128,0-0-0,|12||128- 128-128 1,89,88,27,0,0,0,0,0,64,1,-1--1--1,,1|(1135,342)| 10,90,Initial Primary Energy Intensity of Output,758,655,73,19,8,2,0,3,-1,0,0,0,128-128-128,0-0-0,|12||128-128-128 1,91,90,45,0,0,0,0,0,64,1,-1--1--1,,1|(758,633)| 10,92,Time,903,282,26,11,8,2,0,3,-1,0,0,0,128-128-128,0-0-0,|12||128-128-128 1,93,92,13,0,0,0,0,0,64,0,-1--1--1,,1|(859,282)| \\\---/// Sketch information - do not modify anything except names V300 Do not put anything below this section - it will be ignored *Notes $192-192-192,0,Times New Roman|12||0-0-0|0-0-0|0-0-255|-1--1--1|-1--1--1|96,96,5,0

315 Labor 1978 2.25 1947 1.63

2008 3.72 1977 2.17 1946 1.6

2007 3.64 1976 2.1 1945 1.58

2006 3.60 1975 2.03 1944 1.67

2005 3.52 1974 2.07 1943 1.69

2004 3.44 1973 2.06 1942 1.63

2003 3.35 1972 1.99 1941 1.52

2002 3.28 1971 1.92 1940 1.4

2001 3.18 1970 1.91 1939 1.33

2000 3.15 1969 1.92 1938 1.27

1999 3.09 1968 1.88 1937 1.39

1998 3.02 1967 1.85 1936 1.31

1997 2.95 1966 1.84 1935 1.21

1996 2.89 1965 1.81 1934 1.15

1995 2.82 1964 1.76 1933 1.17

1994 2.79 1963 1.72 1932 1.18

1993 2.7 1962 1.69 1931 1.34

1992 2.65 1961 1.66 1930 1.46

1991 2.63 1960 1.66 1929 1.56

1990 2.66 1959 1.65 1928 1.53

1989 2.66 1958 1.6 1927 1.52

1988 2.61 1957 1.67 1926 1.53

1987 2.56 1956 1.69 1925 1.48

1986 2.5 1955 1.67 1924 1.43

1985 2.45 1954 1.61 1923 1.46

1984 2.42 1953 1.68 1922 1.35

1983 2.31 1952 1.68 1921 1.26

1982 2.27 1951 1.66 1920 1.4

1981 2.31 1950 1.61 1919 1.38

1980 2.3 1949 1.58 1918 1.43

1979 2.31 1948 1.64 1917 1.44

316 1916 1.41

1915 1.31

1914 1.32

1913 1.35

1912 1.34

1911 1.3

1910 1.28

1909 1.24

1908 1.18

1907 1.23

1906 1.2

1905 1.16

1904 1.1

1903 1.12

1902 1.09

1901 1.04

1900 1

317 Energy Services Production 1978 16.61547789 1947 4.361299936

2008 30.00574381 1977 16.02133175 1946 3.864469744

2007 29.50017554 1976 15.52539244 1945 3.958552706

2006 28.73631957 1975 14.47012874 1944 3.99467991

2005 27.69302003 1974 14.94440703 1943 3.759980814

2004 26.79517831 1973 15.20002288 1942 3.482812683

2003 25.7615890 1972 14.12331949 1941 3.302785712

2002 24.97470672 1971 13.24003138 1940 2.952179022

2001 24.21588370 1970 12.93050564 1939 2.597427118

2000 23.94580714 1969 12.37266025 1938 2.250389485

1999 23.4153327 1968 11.57505857 1937 2.654987153

1998 23.02087127 1967 10.71640772 1936 2.382078694

1997 22.83019001 1966 10.43706445 1935 2.033490149

1996 22.45302569 1965 9.753049103 1934 1.874139993

1995 21.59269705 1964 9.239261639 1933 1.727281481

1994 20.82033071 1963 8.546351033 1932 1.548379487

1993 20.22400235 1962 8.017917707 1931 1.841237196

1992 19.80239284 1961 7.742261483 1930 2.216209511

1991 19.30011345 1960 7.440356289 1929 2.473947374

1990 19.35353306 1959 7.035219742 1928 2.246336416

1989 18.86778246 1958 6.500144285 1927 2.108412969

1988 18.4290446 1957 6.690825119 1926 2.117060548

1987 17.441821 1956 6.496443157 1925 2.015890837

1986 16.63114685 1955 6.183131415 1924 1.885932317

1985 16.58738069 1954 5.383605352 1923 2.011449595

1984 16.8462622 1953 5.581487946 1922 1.554027207

1983 15.70475628 1952 5.191844542 1921 1.346581716

1982 15.39450902 1951 5.227957173 1920 1.711927765

1981 16.34008847 1950 4.767787367 1919 1.49200306

1980 16.70833536 1949 4.256107516 1918 1.656379162

1979 17.02096468 1948 4.6579867 1917 1.63112297

318 1916 1.616209172

1915 1.387799011

1914 1.234697036

1913 1.355586727

1912 1.289756316

1911 1.13550035

1910 1.168900016

1909 1.10920803

1908 0.900479075

1907 1.053628958

1906 0.990606661

1905 0.922854211

1904 0.788454344

1903 0.785895537

1902 0.758669112

1901 0.699841534

1900 0.645593554

319 Gross Domestic Product 2178 101.59 2147 99.91

2208 102.01 2177 101.55 2146 99.83

2207 102.01 2176 101.52 2145 99.74

2206 102.01 2175 101.49 2144 99.65

2205 102.01 2174 101.45 2143 99.56

2204 102.01 2173 101.41 2142 99.46

2203 102.01 2172 101.37 2141 99.37

2202 102.01 2171 101.34 2140 99.26

2201 102.01 2170 101.29 2139 99.16

2200 102.01 2169 101.25 2138 99.05

2199 102.01 2168 101.21 2137 98.94

2198 102.01 2167 101.16 2136 98.83

2197 102.01 2166 101.12 2135 98.71

2196 102.01 2165 101.07 2134 98.59

2195 102.01 2164 101.02 2133 98.47

2194 101.99 2163 100.97 2132 98.34

2193 101.97 2162 100.92 2131 98.2

2192 101.95 2161 100.87 2130 98.07

2191 101.93 2160 100.81 2129 97.93

2190 101.91 2159 100.75 2128 97.79

2189 101.89 2158 100.69 2127 97.64

2188 101.86 2157 100.63 2126 97.48

2187 101.84 2156 100.57 2125 97.33

2186 101.82 2155 100.51 2124 97.17

2185 101.79 2154 100.44 2123 97

2184 101.76 2153 100.37 2122 96.83

2183 101.74 2152 100.3 2121 96.65

2182 101.71 2151 100.23 2120 96.47

2181 101.68 2150 100.15 2119 96.29

2180 101.65 2149 100.08 2118 96.1

2179 101.62 2148 100 2117 95.9

320 2116 95.69 2085 82.99 2054 56.77

2115 95.48 2084 82.31 2053 55.96

2114 95.25 2083 81.6 2052 55.16

2113 95.02 2082 80.88 2051 54.37

2112 94.78 2081 80.14 2050 53.58

2111 94.52 2080 79.38 2049 52.81

2110 94.26 2079 78.59 2048 52.04

2109 93.98 2078 77.79 2047 51.27

2108 93.69 2077 76.97 2046 50.52

2107 93.39 2076 76.12 2045 49.77

2106 93.08 2075 75.26 2044 49.03

2105 92.76 2074 74.37 2043 48.3

2104 92.42 2073 73.47 2042 47.58

2103 92.07 2072 72.54 2041 46.86

2102 91.7 2071 71.61 2040 46.15

2101 91.32 2070 70.69 2039 45.45

2100 90.93 2069 69.77 2038 44.76

2099 90.52 2068 68.85 2037 44.07

2098 90.1 2067 67.94 2036 43.4

2097 89.66 2066 67.04 2035 42.73

2096 89.2 2065 66.15 2034 42.07

2095 88.73 2064 65.26 2033 41.41

2094 88.24 2063 64.38 2032 40.77

2093 87.73 2062 63.51 2031 40.13

2092 87.2 2061 62.64 2030 39.5

2091 86.66 2060 61.78 2029 38.88

2090 86.09 2059 60.93 2028 38.26

2089 85.51 2058 60.08 2027 37.65

2088 84.91 2057 59.24 2026 37.06

2087 84.29 2056 58.41 2025 36.46

2086 83.65 2055 57.59 2024 35.88

321 2023 35.3 1992 17.64 1961 6.54

2022 34.73 1991 17.17 1960 6.39

2021 34.17 1990 17.33 1959 6.24

2020 33.62 1989 17.12 1958 5.81

2019 33.07 1988 16.57 1957 5.87

2018 32.53 1987 15.96 1956 5.76

2017 32 1986 15.5 1955 5.65

2016 31.47 1985 15.04 1954 5.28

2015 30.95 1984 14.52 1953 5.31

2014 30.44 1983 13.57 1952 5.08

2013 29.94 1982 13.05 1951 4.9

2012 29.44 1981 13.34 1950 4.55

2011 28.95 1980 13.04 1949 4.18

2010 28.47 1979 13.08 1948 4.21

2009 27.99 1978 12.72 1947 4.03

2008 27.53 1977 12.07 1946 4.06

2007 27.21 1976 11.53 1945 4.61

2006 26.63 1975 10.94 1944 4.69

2005 25.89 1974 10.99 1943 4.38

2004 25.11 1973 11.06 1942 3.87

2003 24.23 1972 10.46 1941 3.43

2002 23.64 1971 9.92 1940 2.95

2001 23.27 1970 9.6 1939 2.72

2000 23.09 1969 9.59 1938 2.51

1999 22.28 1968 9.3 1937 2.64

1998 21.33 1967 8.89 1936 2.51

1997 20.54 1966 8.67 1935 2.2

1996 19.76 1965 8.14 1934 2

1995 19.1 1964 7.65 1933 1.84

1994 18.67 1963 7.23 1932 1.87

1993 18.05 1962 6.93 1931 2.2

322 1930 2.38

1929 2.65

1928 2.48

1927 2.47

1926 2.47

1925 2.33

1924 2.15

1923 2.16

1922 1.92

1921 1.66

1920 1.82

1919 1.9

1918 1.97

1917 1.76

1916 1.74

1915 1.62

1914 1.63

1913 1.71

1912 1.69

1911 1.6

1910 1.56

1909 1.52

1908 1.3

1907 1.42

1906 1.4

1905 1.25

1904 1.17

1903 1.18

1902 1.13

1901 1.12

1900 1

323 Capital 1978 6.93 1947 2.34

2008 15.93 1977 6.67 1946 2.25

2007 15.48 1976 6.45 1945 2.18

2006 15.03 1975 6.28 1944 2.17

2005 14.59 1974 6.2 1943 2.18

2004 14.17 1973 5.93 1942 2.19

2003 13.75 1972 5.69 1941 2.2

2002 13.34 1971 5.45 1940 2.17

2001 12.95 1970 5.26 1939 2.14

2000 12.56 1969 5.09 1938 2.13

1999 12.18 1968 4.9 1937 2.13

1998 11.81 1967 4.72 1936 2.11

1997 11.39 1966 4.55 1935 2.1

1996 10.97 1965 4.37 1934 2.12

1995 10.55 1964 4.19 1933 2.14

1994 10.3 1963 4.03 1932 2.18

1993 10.08 1962 3.89 1931 2.21

1992 9.89 1961 3.77 1930 2.21

1991 9.74 1960 3.66 1929 2.18

1990 9.6 1959 3.55 1928 2.12

1989 9.39 1958 3.44 1927 2.07

1988 9.17 1957 3.35 1926 2.01

1987 8.94 1956 3.24 1925 1.94

1986 8.7 1955 3.13 1924 1.9

1985 8.45 1954 3.01 1923 1.85

1984 8.19 1953 2.91 1922 1.82

1983 7.94 1952 2.82 1921 1.8

1982 7.77 1951 2.73 1920 1.78

1981 7.62 1950 2.5 1919 1.74

1980 7.41 1949 2.52 1918 1.7

1979 7.2 1948 2.44 1917 1.65

324 1916 1.61

1915 1.59

1914 1.55

1913 1.5

1912 1.46

1911 1.42

1910 1.38

1909 1.34

1908 1.31

1907 1.27

1906 1.22

1905 1.17

1904 1.14

1903 1.11

1902 1.07

1901 1.03

1900 1

325 Capital Intensity of Output 1978 0.54 1947 0.58

2008 0.55 1977 0.55 1946 0.55

2007 0.54 1976 0.56 1945 0.47

2006 0.55 1975 0.57 1944 0.46

2005 0.54 1974 0.56 1943 0.5

2004 0.55 1973 0.54 1942 0.57

2003 0.56 1972 0.54 1941 0.64

2002 0.55 1971 0.55 1940 0.74

2001 0.56 1970 0.55 1939 0.79

2000 0.56 1969 0.53 1938 0.85

1999 0.55 1968 0.53 1937 0.81

1998 0.55 1967 0.53 1936 0.84

1997 0.55 1966 0.52 1935 0.95

1996 0.56 1965 0.54 1934 1.06

1995 0.55 1964 0.55 1933 1.16

1994 0.55 1963 0.56 1932 1.16

1993 0.56 1962 0.56 1931 1.01

1992 0.56 1961 0.58 1930 0.93

1991 0.57 1960 0.57 1929 0.82

1990 0.55 1959 0.57 1928 0.85

1989 0.55 1958 0.59 1927 0.84

1988 0.55 1957 0.57 1926 0.81

1987 0.56 1956 0.56 1925 0.83

1986 0.56 1955 0.55 1924 0.88

1985 0.56 1954 0.57 1923 0.86

1984 0.56 1953 0.55 1922 0.95

1983 0.59 1952 0.56 1921 1.08

1982 0.6 1951 0.56 1920 0.98

1981 0.57 1950 0.55 1919 0.92

1980 0.57 1949 0.6 1918 0.86

1979 0.55 1948 0.58 1917 0.94

326 1916 0.92

1915 0.98

1914 0.95

1913 0.88

1912 0.86

1911 0.89

1910 0.88

1909 0.88

1908 1

1907 0.89

1906 0.87

1905 0.94

1904 0.98

1903 0.94

1902 0.95

1901 0.92

1900 1

327 Primary Energy Demand 1978 5.043668696 1947 2.28160961

2008 7.13 1977 4.904400099 1946 2.137592399

2007 7.04 1976 4.738012773 1945 2.177569787

2006 6.95 1975 4.5053619 1944 2.191808035

2005 6.85 1974 4.587936392 1943 2.104455215

2004 6.72 1973 4.664595173 1942 1.977384222

2003 6.55 1972 4.506601599 1941 1.913287553

2002 6.36 1971 4.303565624 1940 1.77407318

2001 6.2 1970 4.213041653 1939 1.660228182

2000 6.13 1969 4.086956008 1938 1.5312359

1999 6.06 1968 3.93089386 1937 1.675156273

1998 6.001271158 1967 3.739116274 1936 1.535396229

1997 5.948106239 1966 3.620455811 1935 1.395697229

1996 5.919309279 1965 3.451154048 1934 1.399291691

1995 5.718236638 1964 3.319344542 1933 1.379074298

1994 5.645882367 1963 3.191437297 1932 1.381565775

1993 5.560259904 1962 3.115634439 1931 1.528183434

1992 5.428195627 1961 3.008459577 1930 1.676280578

1991 5.356432119 1960 2.994653898 1929 1.788053686

1990 5.25729022 1959 2.906512614 1928 1.729788211

1989 5.277337859 1958 2.771339284 1927 1.717037872

1988 5.199109794 1957 2.752220759 1926 1.709471359

1987 5.08855167 1956 2.717936069 1925 1.656905184

1986 5.061422758 1955 2.636841573 1924 1.646701603

1985 4.984059102 1954 2.464301991 1923 1.698402942

1984 5.021620104 1953 2.504289593 1922 1.531440772

1983 4.826719583 1952 2.453214678 1921 1.486816852

1982 4.774476743 1951 2.471881334 1920 1.649218311

1981 4.994260104 1950 2.375416837 1919 1.542241867

1980 5.027544657 1949 2.237260133 1918 1.652923017

1979 5.101909348 1948 2.350369793 1917 1.63654347

328 1916 1.560863205

1915 1.46377063

1914 1.46357449

1913 1.485199606

1912 1.430188207

1911 1.387387321

1910 1.375607032

1909 1.321392098

1908 1.269078573

1907 1.358571239

1906 1.270830096

1905 1.241652713

1904 1.174279717

1903 1.143033438

1902 1.079477038

1901 1.052261797

1900 1

329 Capital Energy Service Intensity 1979 3.065093063 1948 2.00168706

1978 3.031065286 1947 1.95027995 2008 3.82385 1977 2.992084754 1946 1.869825375 2007 3.8006683 1976 2.972985545 1945 1.834209582 2006 3.7795175 1975 2.926306561 1944 1.832899813 2005 3.7400853 1974 2.942774004 1943 1.822071935 2004 3.695874 1973 2.921275937 1942 1.832604241 2003 3.612807 1972 2.824847037 1941 1.808630291 2002 3.607295 1971 2.779822039 1940 1.763511887 2001 3.60003 1970 2.769201888 1939 1.703282766 2000 3.5900974 1969 2.74014245 1938 1.601292925 1999 3.5802247 1968 2.695097724 1937 1.646006301 1998 3.590963881 1967 2.64315912 1936 1.593490188 1997 3.554304331 1966 2.658131059 1935 1.51217937 1996 3.515145573 1965 2.621356567 1934 1.445224686 1995 3.4926143 1964 2.590456144 1933 1.390155489 1994 3.436667275 1963 2.50138381 1932 1.306960834 1993 3.404621892 1962 2.436272598 1931 1.365124923 1992 3.405074085 1961 2.459548792 1930 1.439637726 1991 3.374517762 1960 2.398208741 1929 1.463842258 1990 3.365703661 1959 2.352463415 1928 1.40068494 1989 3.26750987 1958 2.268645142 1927 1.326863528 1988 3.248502172 1957 2.325376771 1926 1.328866421 1987 3.21286862 1956 2.258572135 1925 1.336194945 1986 3.159945124 1955 2.233286335 1924 1.261337188 1985 3.164435296 1954 2.139314004 1923 1.290564396 1984 3.200772269 1953 2.158804387 1922 1.205480577 1983 3.133014278 1952 2.061214813 1921 1.093601487 1982 3.065479449 1951 2.060063187 1920 1.197555026 1981 3.119759293 1950 2.010056955 1919 1.179748335 1980 3.10551398 1949 1.947292546 1918 1.125594959

330 1917 1.159331256

1916 1.24922459

1915 1.181527688

1914 1.085423974

1913 1.112936674

1912 1.126715054

1911 1.046201925

1910 1.066476624

1909 1.096834852

1908 0.967939391

1907 1.018852801

1906 1.087397624

1905 1.048165052

1904 0.98025709

1903 0.970114754

1902 1.059144483

1901 1.018816107

1900 1

331 Efficiency of Primary Energy 1979 0.134030151 1948 0.07961834 Conversion 1978 0.132347993 1947 0.076793717 2008 0.168 1977 0.131239266 1946 0.072630007 2007 0.165 1976 0.131642898 1945 0.073032375 2006 0.164 1975 0.129030918 1944 0.073220138 2005 0.163 1974 0.130861644 1943 0.071778936 2004 0.164 1973 0.130912572 1942 0.070760375 2003 0.164 1972 0.125903757 1941 0.06935076 2002 0.163 1971 0.123598061 1940 0.066853205 2001 0.161 1970 0.123302201 1939 0.062853094 2000 0.158 1969 0.121622576 1938 0.059042761 1999 0.155 1968 0.118299512 1937 0.063673419 1998 0.15410956 1967 0.115141354 1936 0.062328505 1997 0.154199115 1966 0.115815367 1935 0.058533154 1996 0.152389455 1965 0.113534314 1934 0.053807752 1995 0.151703584 1964 0.111824253 1933 0.050318365 1994 0.148151779 1963 0.107583454 1932 0.045025331 1993 0.146124517 1962 0.103387057 1931 0.048404454 1992 0.146559257 1961 0.103389094 1930 0.053114754 1991 0.144755585 1960 0.099815542 1929 0.055585431 1990 0.1478936 1959 0.097242592 1928 0.052171454 1989 0.143633927 1958 0.094228954 1927 0.04933179 1988 0.142404891 1957 0.097666919 1926 0.049753372 1987 0.137704683 1956 0.096025699 1925 0.048878788 1986 0.132008124 1955 0.094205338 1924 0.046011063 1985 0.133704401 1954 0.08776682 1923 0.047579458 1984 0.134775445 1953 0.089539882 1922 0.040767069 1983 0.130716438 1952 0.085023152 1921 0.036385329 1982 0.129536194 1951 0.084968016 1920 0.041702142 1981 0.131442049 1950 0.080635841 1919 0.038865861 1980 0.133514465 1949 0.076427065 1918 0.040258557

332 1917 0.04004149

1916 0.041599087

1915 0.038089443

1914 0.033891957

1913 0.036668535

1912 0.036229767

1911 0.032880667

1910 0.034137684

1909 0.033723479

1908 0.028505994

1907 0.031157052

1906 0.031315895

1905 0.029859603

1904 0.026974665

1903 0.027622117

1902 0.028235148

1901 0.026719417

1900 0.025936434

333 Aggregate Monetary Value of 1979 134837.2 1948 46210.1 Output 1978 130206.6 1947 44721.5 2008 329372.761 1977 125703.6 1946 43295.3 2007 320341.0448 1976 121430 1945 41857.4 2006 311495.0143 1975 117347.1 1944 40224.7 2005 302832.6048 1974 113473.2 1943 38564.2 2004 294351.7517 1973 109582 1942 37012.6 2003 286050.3904 1972 105665.7 1941 35642.2 2002 277926.4563 1971 101963.4 1940 34428.9 2001 269977.8848 1970 98453.4 1939 33384.2 2000 262202.6113 1969 95055.8 1938 32420.6 1999 254598.5713 1968 91662.2 1937 31533.1 1998 247163.7 1967 88368.3 1936 30598.7 1997 239611.6 1966 85221.1 1935 29710 1996 232341.8 1965 82151.9 1934 28930.4 1995 225347 1964 79270.8 1933 28220.8 1994 218585.3 1963 76562.4 1932 27570 1993 211974.6 1962 74003 1931 26906.3 1992 205585 1961 71548.2 1930 26128 1991 199340.6 1960 69233.9 1929 25284.5 1990 193261.2 1959 66971 1928 24347.3 1989 187124.9 1958 64760.8 1927 23469 1988 181062.9 1957 62703.3 1926 22596 1987 175197.7 1956 60624.8 1925 21722.8 1986 169548.2 1955 58584.6 1924 20897.7 1985 164060.5 1954 56583.5 1923 20136.8 1984 158737 1953 54715.3 1922 19373.7 1983 153596.9 1952 52833.9 1921 18693.4 1982 148793.2 1951 51035.2 1920 18106 1981 144172.9 1950 49301.2 1919 17462.4 1980 139452.2 1949 47689.9 1918 16789.3

334 1917 16090.6

1916 15469.1

1915 14852

1914 14278.8

1913 13700.5

1912 13095.3

1911 12497.2

1910 11931.3

1909 11379

1908 10841.8

1907 10380.2

1906 9877.2

1905 9382.8

1904 8940.4

1903 8527.3

1902 8109.3

1901 7710.3

1900 7315.2

335 Primary Energy Intensity of 1979 0.39 1948 0.56 Output 1978 0.4 1947 0.57 2008 0.265 1977 0.41 1946 0.53 2007 0.26 1976 0.41 1945 0.47 2006 0.265 1975 0.41 1944 0.47 2005 0.265 1974 0.42 1943 0.48 2004 0.27 1973 0.42 1942 0.51 2003 0.27 1972 0.43 1941 0.56 2002 0.275 1971 0.43 1940 0.6 2001 0.275 1970 0.44 1939 0.61 2000 0.27 1969 0.43 1938 0.61 1999 0.28 1968 0.42 1937 0.63 1998 0.28 1967 0.42 1936 0.61 1997 0.29 1966 0.42 1935 0.63 1996 0.3 1965 0.42 1934 0.7 1995 0.3 1964 0.43 1933 0.75 1994 0.3 1963 0.44 1932 0.74 1993 0.31 1962 0.45 1931 0.7 1992 0.31 1961 0.46 1930 0.7 1991 0.31 1960 0.47 1929 0.68 1990 0.3 1959 0.47 1928 0.7 1989 0.31 1958 0.48 1927 0.7 1988 0.31 1957 0.47 1926 0.69 1987 0.32 1956 0.47 1925 0.71 1986 0.33 1955 0.47 1924 0.77 1985 0.33 1954 0.47 1923 0.79 1984 0.35 1953 0.47 1922 0.8 1983 0.36 1952 0.48 1921 0.9 1982 0.37 1951 0.5 1920 0.91 1981 0.37 1950 0.52 1919 0.81 1980 0.39 1949 0.54 1918 0.84

336 1917 0.93

1916 0.9

1915 0.9

1914 0.9

1913 0.87

1912 0.85

1911 0.87

1910 0.88

1909 0.87

1908 0.97

1907 0.96

1906 0.91

1905 0.99

1904 1.01

1903 0.97

1902 0.96

1901 0.94

1900 1

337 Primary Energy Production 1978 125.5438602 1947 56.79240551

2008 190.67 1977 122.077273 1946 53.20761877

2007 186.07 1976 117.9356633 1945 54.20271101

2006 184.11 1975 112.1446626 1944 54.55712063

2005 180.09 1974 114.2000555 1943 52.38278863

2004 175.04 1973 116.1081981 1942 49.21981661

2003 172.6 1972 112.1755205 1941 47.62436223

2002 168.93 1971 107.1216754 1940 44.15912477

2001 161.73 1970 104.8684091 1939 41.32536598

2000 155.92 1969 101.7299637 1938 38.11457041

1999 152.84 1968 97.84536194 1937 41.69694671

1998 149.3799043 1967 93.0717537 1936 38.21812673

1997 148.0565562 1966 90.11813135 1935 34.74082624

1996 147.3397602 1965 85.90397729 1934 34.83029734

1995 142.3347853 1964 82.62305716 1933 34.32705859

1994 140.5337878 1963 79.43926967 1932 34.38907488

1993 138.4025268 1962 77.55243215 1931 38.03859034

1992 135.1152651 1961 74.88470223 1930 41.72493223

1991 133.3289725 1960 74.54105986 1929 44.5071188

1990 130.8611941 1959 72.3471019 1928 43.0568109

1989 131.3602074 1958 68.98245156 1927 42.7394374

1988 129.4130032 1957 68.50656515 1926 42.55109647

1987 126.6610592 1956 67.653172 1925 41.24265198

1986 125.9857832 1955 65.63461831 1924 40.98867078

1985 124.0600953 1954 61.33987047 1923 42.27558832

1984 124.9950403 1953 62.33521697 1922 38.11966997

1983 120.1436979 1952 61.06389197 1921 37.00891915

1982 118.8433017 1951 61.52853076 1920 41.05131511

1981 124.3140122 1950 59.12739658 1919 38.3885241

1980 125.1425106 1949 55.68848593 1918 41.14353035

1979 126.9935502 1948 58.50394116 1917 40.73582088

338 1916 38.85203486

1915 36.43526694

1914 36.43038474

1913 36.96866365

1912 35.59935419

1911 34.53398118

1910 34.24075357

1909 32.89126918

1908 31.5891135

1907 33.8167092

1906 31.63271133

1905 30.90644607

1904 29.22943942

1903 28.45167648

1902 26.86967017

1901 26.19224534

1900 24.89137723

339 Primary Energy Aggregate 1979 4550.379635 1948 1897.783366 Production 1978 4424.835775 1947 1840.990961 2008 8456.162233 1977 4302.758502 1946 1787.783342 2007 8308.961719 1976 4184.822839 1945 1733.580631 2006 8163.096804 1975 4072.678176 1944 1679.02351 2005 8018.56749 1974 3958.478121 1943 1626.640722 2004 7875.373776 1973 3842.369923 1942 1577.420905 2003 7733.515662 1972 3730.194402 1941 1529.796543 2002 7592.993147 1971 3623.072727 1940 1485.637418 2001 7453.806233 1970 3518.204318 1939 1444.312052 2000 7315.954919 1969 3416.474354 1938 1406.197482 1999 7179.439205 1968 3318.628992 1937 1364.500535 1998 7044.264745 1967 3225.557239 1936 1326.282408 1997 6896.208188 1966 3135.439107 1935 1291.541582 1996 6748.868428 1965 3049.53513 1934 1256.711285 1995 6606.533643 1964 2966.912073 1933 1222.384226 1994 6465.999855 1963 2887.472803 1932 1187.995151 1993 6327.597328 1962 2809.920371 1931 1149.956561 1992 6192.482063 1961 2735.035669 1930 1108.231628 1991 6059.153091 1960 2660.494609 1929 1063.72451 1990 5928.291897 1959 2588.147507 1928 1020.667699 1989 5796.931689 1958 2519.165055 1927 977.9282614 1988 5667.518686 1957 2450.65849 1926 935.3771649 1987 5540.857627 1956 2383.005318 1925 894.1345129 1986 5414.871844 1955 2317.3707 1924 853.1458422 1985 5290.811748 1954 2256.030829 1923 810.8702538 1984 5165.816708 1953 2193.695613 1922 772.7505839 1983 5045.67301 1952 2132.631721 1921 735.7416647 1982 4926.829708 1951 2071.10319 1920 694.6903496 1981 4802.515696 1950 2011.975793 1919 656.3018255 1980 4677.373186 1949 1956.287307 1918 615.1582952

340 1917 574.4224743

1916 535.5704394

1915 499.1351725

1914 462.7047878

1913 425.7361241

1912 390.1367699

1911 355.6027887

1910 321.3620352

1909 288.470766

1908 256.8816525

1907 223.0649433

1906 191.432232

1905 160.5257859

1904 131.2963465

1903 102.84467

1902 75.97499981

1901 49.78275447

1900 24.89137723

341 Energy Services 1978 25.73674688 1947 6.755488662

2008 45.06026437 1977 24.81643697 1946 5.985917484

2007 43.97868927 1976 24.04824574 1945 6.131648434

2006 43.30631416 1975 22.41368217 1944 6.187608107

2005 41.94313906 1974 23.14832131 1943 5.824068083

2004 40.98916395 1973 23.54426059 1942 5.394745131

2003 39.74438885 1972 21.87648776 1941 5.115890161

2002 38.90881375 1971 20.50830789 1940 4.572813657

2001 38.58243864 1970 20.02886422 1939 4.023316374

2000 37.26526354 1969 19.1647828 1938 3.485768205

1999 36.45728844 1968 17.92932797 1937 4.112474691

1998 35.65845897 1967 16.59931028 1936 3.68974981

1997 35.3631009 1966 16.16661812 1935 3.149799336

1996 34.77888765 1965 15.10710421 1934 2.902971972

1995 33.44627111 1964 14.31126686 1933 2.67549369

1994 32.24990487 1963 13.23797454 1932 2.398381267

1993 31.3262148 1962 12.4194513 1931 2.852006783

1992 30.6731576 1961 11.99247023 1930 3.432824719

1991 29.89514582 1960 11.52483051 1929 3.83205092

1990 29.97789079 1959 10.89728932 1928 3.479490155

1989 29.22548147 1958 10.06847767 1927 3.265851951

1988 28.54589312 1957 10.36383507 1926 3.279246723

1987 27.0167211 1956 10.06274476 1925 3.122538668

1986 25.76101751 1955 9.577436724 1924 2.921237836

1985 25.69322537 1954 8.339001089 1923 3.115659352

1984 26.09422304 1953 8.645513743 1922 2.407129371

1983 24.32607354 1952 8.041970847 1921 2.085804151

1982 23.84551227 1951 8.097907946 1920 2.651711364

1981 25.31017908 1950 7.38512232 1919 2.311056315

1980 25.88057958 1949 6.592549582 1918 2.56566868

1979 26.36483057 1948 7.21504524 1917 2.526547794

342 1916 2.503446884

1915 2.149648182

1914 1.912499013

1913 2.099752573

1912 1.997783757

1911 1.758847099

1910 1.810581919

1909 1.718121289

1908 1.394808033

1907 1.632031409

1906 1.534412255

1905 1.429466271

1904 1.22128596

1903 1.217322466

1902 1.175149762

1901 1.084028069

1900 1

343 Energy Services Aggregate 1979 390.4262717 1948 93.54272593 Production 1978 373.8107938 1947 89.18142599 2008 1019.282346 1977 357.7894621 1946 85.31695625 2007 988.809543 1976 342.2640696 1945 81.35840354 2006 958.9830676 1975 327.7939409 1944 77.36372363 2005 929.7957193 1974 312.8495339 1943 73.60374282 2004 901.2402982 1973 297.649511 1942 70.12093013 2003 873.3096043 1972 283.5261915 1941 66.81814442 2002 845.9964375 1971 270.2861601 1940 63.8659654 2001 819.2935979 1970 257.3556545 1939 61.26853828 2000 793.1938854 1969 244.9829942 1938 59.0181488 1999 767.6901001 1968 233.4079357 1937 56.36316164 1998 742.7746485 1967 222.6915279 1936 53.98108295 1997 719.9444585 1966 212.2544635 1935 51.9475928 1996 697.4914328 1965 202.5014144 1934 50.07345281 1995 675.8987357 1964 193.2621528 1933 48.34617133 1994 655.078405 1963 184.7158017 1932 46.79779184 1993 634.8544027 1962 176.697884 1931 44.95655464 1992 615.0520098 1961 168.9556225 1930 42.74034513 1991 595.7518964 1960 161.5152662 1929 40.26639776 1990 576.3983633 1959 154.4800465 1928 38.02006134 1989 557.5305809 1958 147.9799022 1927 35.91164837 1988 539.1015363 1957 141.2890771 1926 33.79458783 1987 521.6597153 1956 134.7926339 1925 31.77869699 1986 505.0285684 1955 128.6095025 1924 29.89276467 1985 488.4411877 1954 123.2258972 1923 27.88131508 1984 471.5949255 1953 117.6444092 1922 26.32728787 1983 455.8901692 1952 112.4525647 1921 24.98070616 1982 440.4956602 1951 107.2246075 1920 23.26877839 1981 424.1555718 1950 102.4568201 1919 21.77677533 1980 407.4472364 1949 98.20071263 1918 20.12039617

344 1917 18.4892732

1916 16.87306403

1915 15.48526502

1914 14.25056798

1913 12.89498125

1912 11.60522494

1911 10.46972459

1910 9.30082457

1909 8.191616541

1908 7.291137465

1907 6.237508507

1906 5.246901846

1905 4.324047635

1904 3.535593292

1903 2.749697754

1902 1.991028643

1901 1.291187109

1900 0.645593554

345 Information and Communication 1979 0.017579221 1948 0.006263945 Fraction of Capital 1978 0.017162467 1947 0.006045476 2008 0.035566112 1977 0.017008158 1946 0.005834626 2007 0.036596264 1976 0.017093883 1945 0.00563113 2006 0.037648096 1975 0.016959127 1944 0.005434732 2005 0.03872185 1974 0.016858033 1943 0.005245183 2004 0.039817764 1973 0.016672718 1942 0.005062246 2003 0.040936079 1972 0.016400608 1941 0.004885688 2002 0.042077035 1971 0.015864962 1940 0.004715289 2001 0.043240872 1970 0.015445553 1939 0.004550832 2000 0.044427829 1969 0.014920383 1938 0.004392112 1999 0.045638148 1968 0.014160241 1937 0.004238927 1998 0.033576905 1967 0.013338266 1936 0.004091085 1997 0.03319077 1966 0.012625416 1935 0.003948399 1996 0.032857469 1965 0.011893581 1934 0.00381069 1995 0.031997365 1964 0.011071743 1933 0.003677783 1994 0.031061424 1963 0.010336043 1932 0.003549512 1993 0.030035098 1962 0.009602516 1931 0.003425715 1992 0.02896392 1961 0.008900985 1930 0.003306235 1991 0.027801775 1960 0.008559669 1929 0.003190923 1990 0.026895043 1959 0.008266054 1928 0.003079632 1989 0.026184037 1958 0.008933517 1927 0.002972223 1988 0.025588076 1957 0.008621941 1926 0.00286856 1987 0.025146058 1956 0.008321231 1925 0.002768513 1986 0.024871362 1955 0.008031009 1924 0.002671954 1985 0.024406563 1954 0.007750909 1923 0.002578764 1984 0.023703981 1953 0.007480579 1922 0.002488824 1983 0.022614353 1952 0.007219677 1921 0.00240202 1982 0.021343543 1951 0.006967874 1920 0.002318244 1981 0.019873326 1950 0.006724854 1919 0.00223739 1980 0.01857524 1949 0.006490309 1918 0.002159356

346 1917 0.002084044

1916 0.002011358

1915 0.001941207

1914 0.001873503

1913 0.001808161

1912 0.001745097

1911 0.001684233

1910 0.001625491

1909 0.001568799

1908 0.001514083

1907 0.001461276

1906 0.001410311

1905 0.001361123

1904 0.001313651

1903 0.001267834

1902 0.001223616

1901 0.001180939

1900 0.001139751

347 Labor Intensity of Output 1930 0.613445365 1961 0.253822626

1900 1 1931 0.609090911 1962 0.243867258

1901 0.928571391 1932 0.631016013 1963 0.237897652

1902 0.964601804 1933 0.63586953 1964 0.230065355

1903 0.949152589 1934 0.574999988 1965 0.222358706

1904 0.940170995 1935 0.550000005 1966 0.212226069

1905 0.927999973 1936 0.52191233 1967 0.208098982

1906 0.857142906 1937 0.526515125 1968 0.202150533

1907 0.866197223 1938 0.50597609 1969 0.200208543

1908 0.907692301 1939 0.488970599 1970 0.198958322

1909 0.81578949 1940 0.474576255 1971 0.193548381

1910 0.820512832 1941 0.443148674 1972 0.190248566

1911 0.812499958 1942 0.421188642 1973 0.186256769

1912 0.792899401 1943 0.385844752 1974 0.188353046

1913 0.789473681 1944 0.356076746 1975 0.185557591

1914 0.809815985 1945 0.342733188 1976 0.182133561

1915 0.808641938 1946 0.394088681 1977 0.179784601

1916 0.810344804 1947 0.404466479 1978 0.176886789

1917 0.818181855 1948 0.389548687 1979 0.176605501

1918 0.725888288 1949 0.377990456 1980 0.176380365

1919 0.726315796 1950 0.353846142 1981 0.173163412

1920 0.769230734 1951 0.338775497 1982 0.173946356

1921 0.759036154 1952 0.330708656 1983 0.170228445

1922 0.703125028 1953 0.316384174 1984 0.166666667

1923 0.675925917 1954 0.304924233 1985 0.16289894

1924 0.665116225 1955 0.295575209 1986 0.161290323

1925 0.635193162 1956 0.293402776 1987 0.160400999

1926 0.61943318 1957 0.284497443 1988 0.157513575

1927 0.615384601 1958 0.27538727 1989 0.155373829

1928 0.616935468 1959 0.264423083 1990 0.153491062

1929 0.588679203 1960 0.259780908 1991 0.153174147

348 1992 0.150226768

1993 0.149584496

1994 0.149437598

1995 0.147643973

1996 0.146255064

1997 0.143622197

1998 0.141584622

1999 0.138689399

2000 0.136422697

2001 0.13665664

2002 0.138747887

2003 0.138258356

2004 0.136997211

2005 0.135959833

2006 0.135185881

2007 0.133774356

2008 0.135125316

349 Energy Service Intensity of 1929 1.446056944 1960 1.803572936 Output 1930 1.442363213 1961 1.833710987 1900 1 1931 1.296366642 1962 1.792128719 1901 0.96788225 1932 1.282556806 1963 1.830978441 1902 1.039955578 1933 1.454072646 1964 1.87075382 1903 1.031629257 1934 1.451485991 1965 1.855909541 1904 1.043834174 1935 1.431726945 1966 1.864661846 1905 1.143572998 1936 1.470019813 1967 1.867188895 1906 1.096008779 1937 1.557755589 1968 1.92788479 1907 1.149317951 1938 1.388752323 1969 1.998413261 1908 1.072929312 1939 1.47916042 1970 2.086339907 1909 1.130342968 1940 1.55010625 1971 2.067369784 1910 1.16062948 1941 1.491513098 1972 2.091442414 1911 1.099279432 1942 1.393991088 1973 2.12877569 1912 1.18212054 1943 1.329695872 1974 2.106307701 1913 1.227925507 1944 1.319319438 1975 2.048782797 1914 1.173312316 1945 1.330075567 1976 2.085710923 1915 1.326943323 1946 1.474363954 1977 2.056042866 1916 1.438762531 1947 1.676299881 1978 2.023329183 1917 1.435538592 1948 1.713787503 1979 2.015659799 1918 1.30236982 1949 1.577165089 1980 1.984706984 1919 1.216345476 1950 1.623103734 1981 1.897314728 1920 1.456984279 1951 1.652634258 1982 1.827242302 1921 1.256508594 1952 1.583065222 1983 1.7926362 1922 1.253713199 1953 1.628156992 1984 1.797122741 1923 1.442434775 1954 1.579356131 1985 1.708326192 1924 1.358715263 1955 1.695121466 1986 1.662001087 1925 1.340145351 1956 1.747004287 1987 1.692777046 1926 1.327630271 1957 1.765559717 1988 1.722745518 1927 1.322207262 1958 1.73295658 1989 1.707095771 1928 1.403020167 1959 1.746360525 1990 1.729826321

350 1991 1.741126691

1992 1.738841145

1993 1.735524491

1994 1.727364997

1995 1.751113577

1996 1.760065197

1997 1.721669931

1998 1.671751469

1999 1.636323416

2000 1.613913485

2001 1.658033462

2002 1.645888937

2003 1.640296712

2004 1.632383968

2005 1.620051723

2006 1.626222829

2007 1.616269481

2008 1.636769468

351 Monetary Value of Output 1960 2075 1991 5890

1930 656 1961 2124 1992 6086

1931 614 1962 2252 1993 6248

1932 534 1963 2351 1994 6500

1933 527 1964 2487 1995 6662

1934 584 1965 2647 1996 6909

1935 636 1966 2820 1997 7220

1936 719 1967 2890 1998 7521

1937 756 1968 3030 1999 7856

1938 730 1969 3123 2000 8143

1939 789 1970 3129 2001 8204

1940 858 1971 3234 2002 8335

1941 1005 1972 3405 2003 8545

1942 1191 1973 3601 2004 8856

1943 1386 1974 3583 2005 9127

1944 1498 1975 3576 2006 9389

1945 1482 1976 3767 2007 9595

1946 1318 1977 3941

1947 1306 1978 4160

1948 1363 1979 4291

1949 1356 1980 4282

1950 1474 1981 4389

1951 1588 1982 4305

1952 1649 1983 4499

1953 1725 1984 4822

1954 1713 1985 5022

1955 1836 1986 5196

1956 1871 1987 5371

1957 1909 1988 5593

1958 1891 1989 5791

1959 2025 1990 5900

352 Energy Services per Unit of 1929 2.456443064 1960 6.942669307 Labor 1930 2.351249673 1961 7.224379535 1900 1 1931 2.128363136 1962 7.348787747 1901 1.042334774 1932 2.032526559 1963 7.696496481 1902 1.078119048 1933 2.286746851 1964 8.131401691 1903 1.086895057 1934 2.524323516 1965 8.346466729 1904 1.110259921 1935 2.603139874 1966 8.786205464 1905 1.232298525 1936 2.816602961 1967 8.972599842 1906 1.278676837 1937 2.95861508 1968 9.536877108 1907 1.326854809 1938 2.744699504 1969 9.981658284 1908 1.182040776 1939 3.025049815 1970 10.48631636 1909 1.385581675 1940 3.266295421 1971 10.68141087 1910 1.414517159 1941 3.365717165 1972 10.99320986 1911 1.352959371 1942 3.309659734 1973 11.42925276 1912 1.490883381 1943 3.446194007 1974 11.1827642 1913 1.555372317 1944 3.705154731 1975 11.04122328 1914 1.448862874 1945 3.88079011 1976 11.45154642 1915 1.640952888 1946 3.741198424 1977 11.43614557 1916 1.775494239 1947 4.144471713 1978 11.43855455 1917 1.754547089 1948 4.399417997 1979 11.41334661 1918 1.7941739 1949 4.172499761 1980 11.25242588 1919 1.674678539 1950 4.587032443 1981 10.95678761 1920 1.894079649 1951 4.878257941 1982 10.5046311 1921 1.65540019 1952 4.786887772 1983 10.53076766 1922 1.7830587 1953 5.146139169 1984 10.78273645 1923 2.13401312 1954 5.179503496 1985 10.48703076 1924 2.042823813 1955 5.734992032 1986 10.30440674 1925 2.109823329 1956 5.954286836 1987 10.55340716 1926 2.143298607 1957 6.205889582 1988 10.93712409 1927 2.148586852 1958 6.292798425 1989 10.98702259 1928 2.27417654 1959 6.604417839 1990 11.2698831

353 1991 11.36697495

1992 11.57477571

1993 11.60230192

1994 11.55910576

1995 11.86037971

1996 12.03421711

1997 11.987492

1998 11.80743673

1999 11.79847503

2000 11.83024174

2001 12.13284233

2002 11.86244324

2003 11.86399693

2004 11.915454

2005 11.9156643

2006 12.02953159

2007 12.08205765

2008 12.11297426

354 Output per Unit of Labor 1930 1.630137022 1961 3.939759092

1900 1 1931 1.641791039 1962 4.100591476

1901 1.076923121 1932 1.584745837 1963 4.203488313

1902 1.036697212 1933 1.572649659 1964 4.346590987

1903 1.053571377 1934 1.739130471 1965 4.497237901

1904 1.063636302 1935 1.8181818 1966 4.711956478

1905 1.077586238 1936 1.916030611 1967 4.805405529

1906 1.1666666 1937 1.899280671 1968 4.946808625

1907 1.154471492 1938 1.976377975 1969 4.994791858

1908 1.101694924 1939 2.045112737 1970 5.026178298

1909 1.225806427 1940 2.107142927 1971 5.166666822

1910 1.218749983 1941 2.25657902 1972 5.256281401

1911 1.230769294 1942 2.374233066 1973 5.368932392

1912 1.261194041 1943 2.591715956 1974 5.309178805

1913 1.266666673 1944 2.80838334 1975 5.389162431

1914 1.234848432 1945 2.917721524 1976 5.490476313

1915 1.236641279 1946 2.537499926 1977 5.562211645

1916 1.234042589 1947 2.472392774 1978 5.653333452

1917 1.222222167 1948 2.567073216 1979 5.66233777

1918 1.377622448 1949 2.64556944 1980 5.669565318

1919 1.376811582 1950 2.82608705 1981 5.774891984

1920 1.30000006 1951 2.951807346 1982 5.748898811

1921 1.317460301 1952 3.023809573 1983 5.874458888

1922 1.422222165 1953 3.16071435 1984 6

1923 1.479452075 1954 3.279503207 1985 6.138775375

1924 1.503496625 1955 3.383233677 1986 6.2

1925 1.574324252 1956 3.408284044 1987 6.234375154

1926 1.614379134 1957 3.514970082 1988 6.348659142

1927 1.625000039 1958 3.63124991 1989 6.436090333

1928 1.620915075 1959 3.781818098 1990 6.515037355

1929 1.698718072 1960 3.849397587 1991 6.528516855

355 1992 6.656603304

1993 6.685184785

1994 6.691756391

1995 6.773049941

1996 6.837370073

1997 6.962712062

1998 7.062913927

1999 7.21035641

2000 7.330158557

2001 7.317610053

2002 7.20731695

2003 7.23283589

2004 7.299418661

2005 7.355113503

2006 7.397222185

2007 7.475274258

2008 7.400537762

356 Future GDP 2038 44.76 2069 69.77

2008 27.53 2039 45.45 2070 70.69

2009 27.99 2040 46.15 2071 71.61

2010 28.47 2041 46.86 2072 72.54

2011 28.95 2042 47.58 2073 73.47

2012 29.44 2043 48.3 2074 74.37

2013 29.94 2044 49.03 2075 75.26

2014 30.44 2045 49.77 2076 76.12

2015 30.95 2046 50.52 2077 76.97

2016 31.47 2047 51.27 2078 77.79

2017 32 2048 52.04 2079 78.59

2018 32.53 2049 52.81 2080 79.38

2019 33.07 2050 53.58 2081 80.14

2020 33.62 2051 54.37 2082 80.88

2021 34.17 2052 55.16 2083 81.6

2022 34.73 2053 55.96 2084 82.31

2023 35.3 2054 56.77 2085 82.99

2024 35.88 2055 57.59 2086 83.65

2025 36.46 2056 58.41 2087 84.29

2026 37.06 2057 59.24 2088 84.91

2027 37.65 2058 60.08 2089 85.51

2028 38.26 2059 60.93 2090 86.09

2029 38.88 2060 61.78 2091 86.66

2030 39.5 2061 62.64 2092 87.2

2031 40.13 2062 63.51 2093 87.73

2032 40.77 2063 64.38 2094 88.24

2033 41.41 2064 65.26 2095 88.73

2034 42.07 2065 66.15 2096 89.2

2035 42.73 2066 67.04 2097 89.66

2036 43.4 2067 67.94 2098 90.1

2037 44.07 2068 68.85 2099 90.52

357 2100 90.93 2131 98.2 2162 100.92

2101 91.32 2132 98.34 2163 100.97

2102 91.7 2133 98.47 2164 101.02

2103 92.07 2134 98.59 2165 101.07

2104 92.42 2135 98.71 2166 101.12

2105 92.76 2136 98.83 2167 101.16

2106 93.08 2137 98.94 2168 101.21

2107 93.39 2138 99.05 2169 101.25

2108 93.69 2139 99.16 2170 101.29

2109 93.98 2140 99.26 2171 101.34

2110 94.26 2141 99.37 2172 101.37

2111 94.52 2142 99.46 2173 101.41

2112 94.78 2143 99.56 2174 101.45

2113 95.02 2144 99.65 2175 101.49

2114 95.25 2145 99.74 2176 101.52

2115 95.48 2146 99.83 2177 101.55

2116 95.69 2147 99.91 2178 101.59

2117 95.9 2148 100 2179 101.62

2118 96.1 2149 100.08 2180 101.65

2119 96.29 2150 100.15 2181 101.68

2120 96.47 2151 100.23 2182 101.71

2121 96.65 2152 100.3 2183 101.74

2122 96.83 2153 100.37 2184 101.76

2123 97 2154 100.44 2185 101.79

2124 97.17 2155 100.51 2186 101.82

2125 97.33 2156 100.57 2187 101.84

2126 97.48 2157 100.63 2188 101.86

2127 97.64 2158 100.69 2189 101.89

2128 97.79 2159 100.75 2190 101.91

2129 97.93 2160 100.81 2191 101.93

2130 98.07 2161 100.87 2192 101.95

358 2193 101.97 2199 102.01 2205 102.01

2194 101.99 2200 102.01 2206 102.01

2195 102.01 2201 102.01 2207 102.01

2196 102.01 2202 102.01 2208 102.01

2197 102.01 2203 102.01

2198 102.01 2204 102.01

359