The mystery of and the role of models in Explaining growth: Allen’s model Explaining stagnation: Malthus’ model Summary

Principles of Economics1 2. Technological Change, Population, and Growth

Giuseppe Vittucci Marzetti2

SCOR Department of Sociology and Social Research University of Milano-Bicocca

A.Y. 2018-19

1These slides are based on the material made available under Creative Commons BY-NC-ND © 4.0 by the CORE Project , https://www.core-econ.org/. 2Department of Sociology and Social Research, University of Milano-Bicocca, Via Bicocca degli Arcimboldi 8, 20126, Milan, E-mail: [email protected] Giuseppe Vittucci Marzetti Principles of Economics 1/37 The mystery of economic growth and the role of models in economics Explaining growth: Allen’s model Explaining stagnation: Malthus’ model Summary Layout

1 The mystery of economic growth and the role of models in economics The Industrial revolution Economists, historians, and the Industrial Revolution Economic models Four key ideas of economic modeling

2 Explaining growth: Allen’s model Modeling technology Firm’s choice: isocost lines and cost minimization Relative prices, innovation and profit Innovation incentives in the British Industrial Revolution

3 Explaining stagnation: Malthus’ model Production function and diminishing average product of labor Malthusian economics The Malthusian trap Escaping the Malthusian trap

4 Summary

Giuseppe Vittucci Marzetti Principles of Economics 2/37 The mystery of economic growth and the role of models in economics The Industrial revolution Explaining growth: Allen’s model Economists, historians, and the Industrial Revolution Explaining stagnation: Malthus’ model Economic models Summary Four key ideas of economic modeling Real wage and population in Britain over seven centuries Rapid growth in real wages and population in the last 2 centuries Stagnation in the centuries before that.

Figure: Real wages over seven centuries: Wages of craftsmen (skilled workers) in London (1264-2001), and the population of Britain

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New (general-purpose) technologies introduced in textiles, energy and transports (e.g. James Watt’s steam engine) in Britain in the middle of the 18th century and its cumulative character led to the Industrial revolution. This marked the beginning of the permanent technological revolution, that is behind the recent rapid, sustained increase in income and living standards, in spite of the striking increase of the population. These major changes started very suddenly, 200 years ago. How did the technological revolution start? Why did it happen first in the 18th century, on an island off the coast of Europe? The Industrial Revolution was a complex combination of inter-related intellectual, technological, social, economic and moral changes.

Giuseppe Vittucci Marzetti Principles of Economics 4/37 The mystery of economic growth and the role of models in economics The Industrial revolution Explaining growth: Allen’s model Economists, historians, and the Industrial Revolution Explaining stagnation: Malthus’ model Economic models Summary Four key ideas of economic modeling Explanations of the Industrial Revolution Mokyr (2004), a historian of technology, stresses the role played by Europe’s scientific revolution and its Enlightenment century, which brought the development of new ways to transfer and transform elite scientific knowledge into practical advice and tools. Landes (2006), a historian, emphasizes the political and cultural characteristics of nations: Europe ahead of China because the Chinese state was too powerful and stifled innovation, and Chinese culture at the time favored stability over change. Clark (2007), an economic historian, also attributes Britain’s take-off to culture: along the lines of (1905), success due to cultural attributes such as hard work and savings. Pomeranz (2000), a historian, claims that superior European growth after 1800 was mainly due to the abundance of coal in Britain and Britain’s access to agricultural production in its New World colonies fed the expanding class of industrial workers. Allen (2011), an economic historian, gives a central role to the relatively high cost of labor, coupled with the low cost of local energy, in Britain at the time. Giuseppe Vittucci Marzetti Principles of Economics 5/37 The mystery of economic growth and the role of models in economics The Industrial revolution Explaining growth: Allen’s model Economists, historians, and the Industrial Revolution Explaining stagnation: Malthus’ model Economic models Summary Four key ideas of economic modeling Economists, historians, and the Industrial Revolution

Scholars will probably never completely agree about what caused the Industrial Revolution. Different explanations not necessarily mutually exclusive. Historians and economists disagree about the relative importance of the different factors: Historians (e.g., Pomeranz, 2000) tend to focus on peculiarities of time and place: the Industrial Revolution happened because of a unique combination of favorable circumstances (although they may disagree about which ones). Economists (e.g. Allen, 2011) are more likely to look for general mechanisms that can explain success or failure across both time and space. Historians vs. Economists: Often historians’ arguments are not precise enough to be testable using a model. Historians may regard economic models as simplistic, ignoring important historical facts.

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Economic theory is essentially a collection of models. (Krugman, 1997)

A model is a particular stylized representation of a phenomenon, i.e. a relatively stable and general feature of the world that is interesting from a scientific point of view. Why do economists use models? What happens in an economy depends on the actions and interactions of millions of people. Economists use models to “see the big picture”. Models necessarily omit many details. This is their feature, not a bug.

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The objective of the most basic physics is a complete description of what happens. ... But most things we want to analyze, even in physical science, cannot be dealt with at that level of completeness. The only exact model of the global weather system is that system itself. Any smaller-scale model of that system is therefore to some degree a falsification: it leaves out many aspects of reality. And how do you know that the model is good? It will never be right in the way that quantum electrodynamics is right. At a certain point you may be good enough at predicting that your results can be put to repeated practical use ...; in that case predictive success can be measured ..., and the improvement of models becomes a quantifiable matter. In the early stages of a complex science, however, the criterion for a good model is more subjective: it is a good model if it succeeds in explaining or Paul R. Krugman rationalizing some of what you see in the world in a way that you might (1953) not have expected. [...] The important point is that any kind of model of a complex system – a physical model, a computer simulation, or a pencil-and-paper mathemat- ical representation – amounts to pretty much the same kind of procedure. Nobel Memorial You make a set of clearly untrue simplifications to get the system down to something you can handle; those simplifications are dictated partly Prize in by guesses about what is important, partly by the modeling techniques Economics 2008 available. And the end result, if the model is a good one, is an improved insight into why the vastly more complex real system behaves the way it does. (Krugman, 1997)

Giuseppe Vittucci Marzetti Principles of Economics 8/37 The mystery of economic growth and the role of models in economics The Industrial revolution Explaining growth: Allen’s model Economists, historians, and the Industrial Revolution Explaining stagnation: Malthus’ model Economic models Summary Four key ideas of economic modeling Building a model

To create an effective model we need to distinguish between: the essential features of the economy that are relevant to the question we want to answer, which should be included in the model; unimportant details that can be ignored Process of model building 1 Construct a simplified description of the conditions under which people take actions. 2 Describe in simple terms what determines these actions. 3 Determine how each of their actions affects each other. 4 Determine the outcome of these actions. This is often an equilibrium (something is constant). 5 Get more insight by studying what happens when conditions change.

Equilibrium Situation that is self-perpetuating. Something of interest does not change unless an external force is introduced that alters the model’s description of the situation.

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“Mathematical translation is itself a substantive contribution to the theory. [...] Mathematics has become the dominant language of the natural sciences not because it is quantitative – a common delusion – but primarily because it permits clear and rigorous reasoning about phenomena too complex to be handled in words.” (Simon, 1957, p. 89)

Economic models often use mathematical equations and graphs as well as words and pictures. Mathematics is part of the language of economics, and can help us to communicate our statements about models precisely to others. A (formal) mathematical model is a particular representation of a phenomenon that allows one to analyze the phenomenon itself by means of math.

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[Models] are to our minds what spear-throwers were to stone age arms: they greatly extend the power and range of our insight. In particular, I have no sympathy for those people who criticize the unrealistic simplifications of model-builders, and imagine that they achieve greater sophistication by avoiding stating their assumptions clearly. The point is to realize that eco- nomic models are metaphors, not truth. By all means express your thoughts in models, as pretty as possible ... But always remember that you may have gotten the metaphor wrong, and that someone else with a different metaphor may be seeing something that you are missing. (Krugman, 1992, How I work)

1 It is clear: it helps us better understand something important. 2 It predicts accurately: its predictions are consistent with evidence. 3 It improves communication: it helps us to understand what we agree (and disagree) about. 4 It is useful: We can use it to find ways to improve how the economy works.

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In building a model to help explain the circumstances under which new technologies are chosen, we use four key ideas of economic modeling: Ceteris paribus: simplification that involves “holding other things (in/outside the model) constant”. Incentives: economic rewards or punishments, which influence the benefits and costs of alternative courses of action. Relative prices help us compare alternatives. Economic rent: the benefit received from a choice, taking into account the next best alternative(reservation option or opportunity cost). Cost-benefit principle: economic rent forms the basis of how agents make choices.

Giuseppe Vittucci Marzetti Principles of Economics 12/37 The mystery of economic growth and the role of models in economics The Industrial revolution Explaining growth: Allen’s model Economists, historians, and the Industrial Revolution Explaining stagnation: Malthus’ model Economic models Summary Four key ideas of economic modeling Ceteris paribus and simplification

As is common in scientific inquiry, economists often simplify an analysis by setting aside things that are thought to be of less importance to the question of interest (holding other things constant or ceteris paribus). These ceteris paribus assumptions, when used well, can clarify the picture without distorting the key facts. E.g. When we study the way a capitalist economic system promotes technological improvements we assumed: Prices of all inputs are the same for all firms. All firms know the technologies used by other firms. Attitudes towards risk are similar among firm owners.

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Agents respond to economic incentives.

All economic models have something equivalent to gravity, and a description of the kinds of movements that are possible. The equivalent of gravity is the assumption that, by taking one course of action over another, people are attempting to do as well as they can (according to some standard).

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Many economic models are often interested in ratios of things, rather than their absolute level. Economics focuses attention on alternatives and choices. Relative prices are simply the price of one option relative to another. We often express relative price as the ratio of two prices. E.g. If you are deciding where to shop, it is not the corner shop prices alone that matter, but rather the prices relative to those in the supermarket and relative to the costs of reaching the supermarket.

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Economic rent A payment or other benefit received above and beyond what the individual would have received in his or her next best alternative.

When taking some action (call it action A) results in a greater benefit to yourself than the next best action (call it action B), we say that you have received an economic rent: Economic rent = Benefit from option A - Benefit from option B The best alternative (action B) is often called reservation option or fallback option. Economic rent gives us a simple decision rule: If an action A would give you an economic rent: do it. If you are already doing action A, and it earns you an economic rent: carry on doing it. Innovation rents are a form of economic rent. This decision rule motivates our explanation of why a firm may innovate by switching from one technology to another.

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5 different ways to produce 100 meters of cloth, using labor (number of workers) and energy (tonnes of coal) as inputs. E-technology is relatively labor-intensive; A-technology is relatively energy-intensive. Giuseppe Vittucci Marzetti Principles of Economics 17/37 The mystery of economic growth and the role of models in economics Modeling technology Explaining growth: Allen’s model Firm’s choice: isocost lines and cost minimization Explaining stagnation: Malthus’ model Relative prices, innovation and profit Summary Innovation incentives in the British Industrial Revolution Inferior technologies

Firms choose between technologies (specific combinations of inputs) to produce outputs. Some technologies (e.g. C) are dominated by others (e.g. A). Giuseppe Vittucci Marzetti Principles of Economics 18/37 The mystery of economic growth and the role of models in economics Modeling technology Explaining growth: Allen’s model Firm’s choice: isocost lines and cost minimization Explaining stagnation: Malthus’ model Relative prices, innovation and profit Summary Innovation incentives in the British Industrial Revolution Cost minimization

Firms aim to maximize their profit. This entails producing cloth at the least possible cost. Firms’ choice of technology depends on economic information about relative prices of inputs. C = w × L + p × R |{z} | {z } | {z } Total cost Wage×Workers Price of a tonne of coal×Tonnes of coal

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Isocost lines Combinations of inputs that give the same cost.

We can derive it from the cost equation by re-arranging it: C w R = − L p p The slope is equal to the relative price of inputs.

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The firm will choose the least-cost technology.

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Technology was labor-intensive before the Industrial Revolution (technology B). Increase in wages relative to coal price in Britain create the incentive to innovate more capital-intensive technologies (technology A).

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Because relative prices of inputs changed, a firm that switches to the new cost-minimizing technology has an advantage over its competitors. Profit = Revenue - Cost The change in profit is equal to the fall in costs associated with adopting the new technology. This is the innovation (or Schumpeterian) rent. The first adopter is called an entrepreneur. Innovation rents will not last forever: Other firms, noticing that entrepreneurs are making economic rents, will eventually adopt the new technology. As more firms introduce the new technology, the supply of cloth increases and the price starts to fall. The process continues until everyone is using the new technology and no one is earning innovation rents. The firms stuck to the old B-technology are unable to cover their costs at the new lower price and they go bankrupt.

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The economist Joseph Schumpeter made the adoption of technological improvements by entrepreneurs a key part of his explanation for the dynamism of capitalism. Schumpeter called creative destruction the process by which old technologies and the firms that do not adapt are swept away by the new, because they

cannot compete in the market. Joseph Alois The branch of economic thought known as Schumpeter evolutionary economics trace its origins to (1883-1950) Schumpeter’s work, as well as most modern economic modeling that deals with and innovation.

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One of the first sectors to undergo technological change was textiles. Before the Industrial Revolution, making clothes for the household were time-consuming tasks. By the late 19th century, a single spinning mule operated by a very small number of people could replace more than 1,000 spinsters. These machines were powered by water wheels and later coal-powered steam engines instead of using human labor.

Old technology New technology Lots of workers Few workers Little machinery Lots of capital goods Require only human energy Require energy (coal) Labor-intensive Labor-saving Capital-saving Capital-intensive Energy-saving Energy-intensive

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(a) Wages relative to energy price (early (b) Wages relative to the cost of capital 1700s) goods (late 16th to the early 19th century)

English wages were higher than wages elsewhere, and coal was cheaper in Britain than in the other countries.

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The combination of capacity to innovate and changing relative prices of inputs led to a switch to energy-intensive technology.

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We need a different model to explain the stagnation in population and living standards before 18th century. Malthus provided a model of the economy that predicts a pattern of economic development consistent with the flat part of the GDP per capita hockey stick. His model introduces concepts that are used Thomas Robert widely in economics. Malthus One of the most important concepts is the idea of (1766–1834) diminishing average product of a production factor.

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Production function gives maximum output for a given set of inputs (production factors). Average product (or productivity) of an input: total output divided by the quantity used of the input. E.g. average product of labor: Output per worker: total output divided by the number of workers; Output per worker per hour: total output divided by the total number of hours of labor put in. Law of diminishing average product of labor: If we hold the other inputs fixed, and expand labor, the average output per worker is going to fall.

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Simplifying assumptions: Agricultural economy producing just one good: grain. Grain production involves only farm labor and land. The amount of land is fixed. The production function shows how the number of farmers working the land translates into grain produced in a given period.

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The diminishing average product of labor entails that living standards depend on population size. Malthus also argues that population expands if living standards increase: with living standards above the subsistence level, population grows. below the subsistence level, population decreases (death rates increase and birth rates fall) Population expands if living standards increase, but the law of diminishing average product of labor implies that, as more people work on the land, their income will inevitably fall. In equilibrium: Living standards are at the subsistence level; Population and income stay constant.

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The model predicts a self-correcting response to new technology. In the long run, an increase in productivity will result in increased population, but not increased wages.

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Source: The CORE Project, Allen (2001).

Figure: Wages and population in England (1280-1600)

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Giuseppe Vittucci Marzetti Principles of Economics 34/37 Source: The CORE Project. The mystery of economic growth and the role of models in economics Production function and diminishing average product of labor Explaining growth: Allen’s model Malthusian economics Explaining stagnation: Malthus’ model The Malthusian trap Summary Escaping the Malthusian trap Escaping the Malthusian trap

Conditions required to stay in the Malthusian trap: 1 Diminishing average product of labor. 2 Rising population in response to increases in wages. 3 Absence of improvements in technology to offset the diminishing average product of labor. The permanent technological revolution meant that third condition no longer holds, and explains why Britain was able to escape the Malthusian trap.

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Source: The CORE Project.

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Introduction to economic models Less is more: use simplifying assumptions e.g. ceteris paribus Used models for insights on the technological revolution Model of a firm: high wages (relative to capital, including energy) motivated technological innovation; Malthus’ model: permanent technological change enabled economies to escape economic stagnation.

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