Jul. 2009, Volume 8, No.7 (Serial No.73) Chinese Business Review, ISSN 1537-1506, USA
Socio-economic influences of population density∗
Yuri A. Yegorov (Department of Industry, Energy and Environment, University of Vienna, Vienna A-1210, Austria)
Abstract: While population density represents an important socio-economic parameter, its role is rarely studied in the economic literature (contrary to natural sciences). Population density plays an important role in harvesting societies, i.e. those that depend on agriculture and natural resources. With the development of industry and services and emergence of urban areas, population density becomes less economically important unless we consider aspects related to pollution. There exists a phase transition between rural and urban area which makes population density less important in urban area contrary to rural. However, the economic influence of population density in harvesting societies is also not straight forward. Too high population density decreases the natural endowment per capita, but eases the development of infrastructure, leading to existence of an optimal population density for economic growth. It also influences the demand for a monopolistic product, where too little density can lead to non-survival of a monopoly. Emergence of ethnic communities is based on more cooperative behavior in the case of low cultural and physical distances. At the same time, higher probability of large projects (like infrastructure) leads to development of cooperative behavior in the society. Elaboration along these lines leads to the conclusion that population density positively correlates with individualistic (non-cooperative, non-altruistic) behavior, through less time spent in cooperative infrastructure projects and higher frequency of meetings between individuals that with some probability lead to non-cooperative games. Key words: population density; economic development; optimization; cooperation
1. Introduction
Countries differ not only in purely economic parameters (like GDP per capita, capital investment, etc.) but also in geographical characteristics that also influence economics. The development of GIS in recent years allows for measurement of not only aggregate macroeconomic characteristics of a country, but also of spatially distributed parameters. Population density and its spatial pattern is one of such characteristics. It plays an important role not only on economic but also on social aspects of life. First, potential influences of population density and associated heterogeneity will be outlined. Then, the corresponding economic models will be presented. Finally, the economic consequences will be analyzed and some country examples will be provided. 1.1 Discussions in literature Despite the fact that continuous spatial structures (and only such models can deal with population density) do not play major role in contemporary economic studies, such models were important in 1930-ies, starting from spatial oligopoly by Hotelling (1929) and models of monopolistic competition in space by Chamberlin (1933). A
∗ The work of Yuri A. Yegorov on this paper was partly financed by Austrian National Bank through the Jubiläumfonds project (No. 12826). Yuri A. Yegorov, Ph.D., Department of Industry, Energy and Environment, University of Vienna; research fields: economics and business.
1 Socio-economic influences of population density good survey of such models was done by Beckmann and Thisse (1986). Although new economic geography (see works of Krugman) claims to describe spatial economies, in most of its models it reduces geographical space to only two points, making it impossible to discuss the role of population density. Even telecom coverage (and thus efficiency) depends on distribution of population in space. Covering metropolitan areas is low per capita investment, and average density of population plays here less important role than urban-rural split. Here Krugman may be right that population density is not so crucial, but there are many other socio-economic activities where the situation is opposite. This article will focus on them. Population density is important not only for production activities, but also for social behavior. Wirth (1938) suggests that an increase in population density puts stress on humans, causing increased levels of social disorder, like crimes. Ladd (1992) studies the effects of population density on local public spending. While most planners argue that population density is good due to economies of density in the production of certain services, she had found empirically J-shaped curve of public spending per capita. It is clear why at low population densities costs per capita are high and why they decline as population density grows. However, after reaching some threshold density (she found it to be 250 people per square mile) per capita costs of public safety start to grow again. Westlund (1999) studies the factors that influence interregional cooperation. While natural factors (geographical, physical) have slow influence on change, cost and technical-logistical factors can generate rapid change in inter-regional interactions. Monnesland and Westlund (1999) evaluate Interreg programs between Sweden and Norway. They focus on population density and distance as factors influencing potential for interaction between regions in space. The factor of population density plays a crucial role in the mechanism of urban-rural split. As it was shown in the paper (Yegorov, 2005a), farming activity is possible in homogeneous space. When industrial technology emerges, it requires some minimum number of workers to cover at least fixed costs, and thus it starts first in one location. When the location of a city is chosen, it will create such rental price of land in space that new agricultural location rent will emerge. Land will be more expensive closer to the city, and thus land lots will be of less size there. Why the markets will be located in cities? Because they represent points with maximal concentration of population, and total transport cost that society pays will be minimal if they are located there. Finally equilibrium will emerge, where net income per farmer is exactly equal to net income per worker, and everybody consumes equal proportion of agricultural and industrial good. Population density can also influence the optimal country size. In the paper (Yegorov, 2005b), country is modelled as uniformly populated square with side a, and population density ρ. The revenue is assumed to be proportional to the territory: TR=αa². The total cost of running a country has several components: communication costs-the number of citizens multiplied to the average distance to the centre and unit transport cost; costs of protecting borders, which is proportional to the length of borderline, and cost of having government. The country’s objective depends on political regime. In the case of democracy the surplus per capita is maximized, while in the case of dictatorship—overall surplus. In both cases population density influences an optimal spatial size of a country. 1.2 Paper structure This is a theoretical paper using some abstract set up that can have some difference with reality. For example, there are no countries with uniform spread of population over space, but such an abstraction may be better than spaceless model. Moreover, it does not use any fixed spatial grid (typical for all CGE models) but compare structures that can exist on different grids if we deform the space. Thus, we can compare countries that are
2 Socio-economic influences of population density identical in all other economic parameters except for population density. Here are several fields where the role of population density seems to play an important role. 1.2.1 Low versus high population density Suppose that population density is uniform. We know that this is never the case (it is enough to contrast urban and rural areas), but it is convenient to start comparison from simple cases. If natural resources are spread evenly over space, then lower population density implies higher per capita endowment in natural resources. But to do harvesting, it is important to build network of infrastructure (to bring them to production centre, or to export). Typically transport cost per unit of resources to reach world market or a plant using them as input is higher when population density is lower. What factor would prevail? The paper shows that there exists some optimal population density, when production per capita is maximized and economic growth can be the highest (Yegorov, 2005a). 1.2.2 Spatial heterogeneity I: Rural-urban split Every spatial structure has some natural resources on it and also some centres (cities, industrial complexes), where some concentration takes place due to some scale economies. In this environment we have few more parameters: (a) average city size, (b) average distance between cities, (c) share of rural population (implying rural population density; relevant for agriculture). Rural-urban split has been considered in Yegorov (2005a). A line-land was considered there: equidistant cities on a line with heterogeneous population density between cities. There was a balance between production of industrial and agricultural good, and farmers in different locations were indifferent to reach the markets located in the closest city (like in von Thünen model). 1.2.3 Spatial heterogeneity II: Developed versus undeveloped land Here we focus on countries with large size having a fraction that is little developed. Examples include north of Canada and Siberia, desert centre of Australia, Amazon area of Brazil. It is possible to consider a country as a square with one-dimensional symmetry, where only the distance to its (let say, to western or southern) border plays a role. A model with such spatial structure (with application to forest development) was considered in Yegorov (2007b). In a dynamic setting, there exists a unique optimal development path converging to a steady state with some finite depth of infrastructure development for given values of parameters (world price of output, unit distance transport cost, etc.). It is possible to make some model extensions considering different version of spatial topologies.
2. Homogeneous land: Harvest, population density and growth
The first model shows the influence of population density on production of agricultural or mining type that is spread in space. The initial dispersion of population in space comes from land-intensive activity (farming, forestry, hunting, mining) which historically has been a dominant source of economic output. It is still important, especially in countries with low population density (Russia, Canada, etc.). A space uniformly populated by small identical farms producing everything would be the optimal spatial infrastructure, since it would involve minimal transport costs. This model was partly published in Yegorov (2005a). The influences of geographic factors on macroeconomic performance are largely neglected by modern economic theory. While these factors are extensively considered by economic historians, they still play negligible role in policy advice. The present article builds a simple theoretical model which captures the effect of differences in spatial densities across countries which are assumed to be identical in other economic parameters. While the model formally deals with road
3 Socio-economic influences of population density network, it can be applied to different types of infrastructure, like distribution networks for natural gas. 2.1 Assumptions of the model (1) Countries are assumed to contain homogeneous area S with population N. The population density is ρ=N/S. Land per capita is l=S/N=1/ρ. (2) A country has access to capital K. The capital per capita is k=K/N. Different countries may differ in area S, population N and capital K, but they have identical technology Y= N ka lb, 0
4 Socio-economic influences of population density transport cost TTC = FTC+VTC+WRTC=(δ f /ε+A B t+ B ε T)S/2. 2.3 Optimal road network The problem of minimization of total transport costs was considered by Weber, who was looking for an optimal firm location, and by Kantorovich, who was optimizing traffic flows across existing network. Here the problem is formulated as the problem of selecting an optimal road network. Consider the expression for transport cost as a function of exogenous variables A, B, t, T, f, δ and endogenous variable ε. The optimal road network is one for which the total transport costs are minimal. Differentiating the expression for TTC with respect to ε, we get the answer: ε*=(δ f/BT)1/2. 2.4 Profits of export-transport firm Assume that transport-export firm is monopoly controlled by state. Then it is possible to consider the following scenario. This monopoly maximizes profits in the environment where it can only control the costs related to transportation. It pays c to the producers for each unit of output and sells at price p in the world market. The state controls c, so that each worker gets the marginal value of his labour and capital gets its rent. Further, population can be assumed as shareholders of this monopoly, so that per capita profit, Π1=π y1, where π=p-c-TQ (here TQ=TTC/Y), can be also introduced: a -b a -b Π1=k ρ [p-c-TQ] = k ρ [p-c- (δ f /ε + A t + ε T)/2]. Substitution of formulae for B and for ε* gives the expression for profits at the optimal road network: a -b a/2 -(1+b)/2 1/2 Π1=k ρ (p-c-At/2) - k ρ (δ f T) . 2.5 How profits depend on population density
Let us analyze the obtained expression for profits Π. The firm’s profit is just NΠ1. Both expressions are optimized in the same point. Given the density ρ, the production function is Cobb-Douglas in labour and capital. This implies that the optimal capital-labour ratio is k=K/N=aw/(1-a)r. It is assumed that this ratio is fulfilled, and the firm pays c=w L1+rK1 for each unit produced, where L1, K1 are amounts of labour and capital required for one unit of output. The other parameters, p, f, t, T, δ are taken as exogenous. While population density ρ is also an exogenous factor; it is useful to consider it as the main argument. The following proposition can be formulated: Proposition 1 (1) Under conditions specified above (including 0
(2) Taking the first order condition dΠ1/dρ=0, it is easy to find a maximum: 2/(1-b) ρ2=(C2(1+b)/bC1)
5 Socio-economic influences of population density
For very high densities the negative term is of smaller asymptotic order than the positive term, while positive -b term is also vanishing to zero. Thus, profits at ρ→∞ behave asymptotically as C1ρ . 2.6 Influence of population density on growth Export-led growth is a typical pattern for developing countries. As it was shown before, not for all densities positive profits from export are available. This happens due to high cost of building and maintaining road infrastructure. Instead, countries may rely on heterogeneous development of their areas when high population density in one area is able to overcome fixed costs. The phenomenon of huge metropolitan areas along with poverty in the remote rural area is a typical pattern for many of developing countries. Now we will focus on growth paths consistent with homogeneous population density model, considered earlier. The term c being a negative term in a balance account for transport-export firm is not lost; it contributes to country’s GDP through the income of producers. Assumes that there exists an alternative sector of the economy
(services, for example) where the profit Π1 can be invested. Let this sector be of A-K type: investment creates GDP proportional to them. Formally, we postulate the growth rate as the ratio of profits to net GDP of the country, GDP=pY. Then the growth rate of a country, γ, is just a mark-up of export-transport firm:
γ=Π1/py1=1–c/p–(At+εT+δf/εB)/(2p) Assume that the cost of adjustment to optimal road network during growth is neglected. Then, using A=S1/2, the growth rate is equal to: γ=1–c/p–t S1/2/(2p)–(δfT)1/2 k-a/2 ρ(b-1)/2. Proposition 2 The growth rate negatively depends on the country spatial size S, because of higher variable transport costs, and positively depends on population density, since per capita cost of maintaining transport infrastructure is lower.
3. Optimal number of plants—Monopoly in low-populated area
The second model deals with optimal structure of plants in space. Industrial performance during the period of transition was vulnerable to rapid changes in economy, like change of relative prices. The effect is similar to oil price shock. The basic idea behind this reasoning is derivation of the optimal spatial structure as the result of interplay between scale economies and transport costs, with subsequent study of comparative statics. This idea is not new and was used by many researchers of spatial economy: Christaller, Losch, Chamberlin, Salop, Krugman and others. Each of them presented a distinct mathematical model with a similar spatial structure: dispersed consumers in space being served by a set of firms. Absence of scale economies gives no reason for agglomeration. If fixed cost or other scale effects are not involved, it is better to have a small plant producing everything at every farm. In this model the question of optimal number of firms is addressed. The problem is about optimal location, capacity and number of plants, which have to satisfy the given country’s demand in a particular good at minimal cost. It is considered as central planner problem, but monopolistic setting has similar mathematical structure. Assume that a country with given territory S optimizes its production of some industrial good. It has a fixed capital stock (we can think about labour also as some capital stock) and the technology has increasing returns to scale: Y=AK1+α, α>0 The good needs inputs for its production, which are located homogeneously across all territory and then
6 Socio-economic influences of population density distributed to the consumers, which are also located homogeneously. The total transportation cost per 1 km for all inputs and outputs, associated with 1 unit of production, is denoted by b. This transport cost includes both the variable cost and the fixed cost of investment in infrastructure. The social planner has to decide how many plants it is optimal to build in order to maximize production surplus. The price of output is independent on quantity and normalized to 1. The renting cost of capital (alternatively, wage) is r and is also fixed. The social planner is facing the following problem: 1+α Max N [N A(K/N) (1 - b R(N)) - rK] The first term is output minus transportation cost, the second—capital rent, which is irrelevant for the maximization problem, but relevant for the shutdown point of this industry. R(N) is the average distance of transportation. It is easy to show that for uniform demand density R=γ(S/N)1/2, where γ is a constant. Then such a firm would serve an area around it until the equidistant point with neighbouring firm. While population density is not introduced, it is clear that for the same output level the average transport distance will depend negatively on population density. Taking the derivative with respect to N, we get the following value for optimal number of plants: N*=(γb)²S (α+1.5)²/(α+1)² In the limit of very small scale economies α→0, we get N*=9 S γ²b²/4. It means that the optimal number of firms is proportional to the area of the country and proportional to the square of transportation costs. For the low level of transportation costs it might be optimal to have one plant. Clearly, this is a monopoly as thus should be regulated by state, but price p in our model was fixed, and thus regulation is implicit. Now consider the question about shutdown point. The production surplus (profit) is equal to zero, when Y(1- bR) = rK. Thus, for any given N, S, r, A the maximal level of transportation costs that makes the production still profitable is given by: 1/2 1/2 α α bmax = N /(γS )[1 - (r N )/(A K )]. These results are summarized in a following proposition. Proposition 3 For any given IRS technology, value of transportation costs, spatial density of consumers, price of good, physical stock and rental price of capital there exists an optimal number and location of plants, producing this good. Depending on the value of parameters, these plants may have positive or negative profits. It means that under certain conditions a specific industry in specific country might never emerge or be completely shut down, even if decisions are taken optimally by a central planner. Now assume, that initially the optimal number of plants was constructed to satisfy optimality condition at a given b, which probably was different from the world b (it was the case of the USSR, when industrialization took place). Suppose that then the country decides to open its economy in order to introduce the world prices. It can easily occur, that this world level of fuel price will increase transportation costs to such a level, that shutdown of the whole industry will occur. This means that introduction of the world level of energy prices might demand the restructure of the whole industry (at least, construction of new plants), which can never occur in one moment. Thus, the “shock therapy”, which was implemented in Russian economy in 1992, was probably the worst method to stimulate reconstruction and to increase efficiency. Consider such low populated area as Siberia. It may happen that for critically low population density even monopoly is not able to survive, if it faces world level of transport costs. In Northern territories of Canada such productions did not emerge, while they emerged in Siberia because of state subsidy for fuel and transportation.
7 Socio-economic influences of population density
4. Population density and cooperation
Economists and sociologists understand different issues under the concept of cooperation. While in economics, game theorists consider a class of cooperative games, where all agents are absolutely selfish but think how to divide the surplus that can be obtained from potential coalition. In sociology, following McClintock, altruistic component in preferences complement self-regarding. Contrary to economics, it is normal to consider that agents have some positive altruistic component. In fact, it was measured empirically for different societies (Henrich, Boyd, Bowles, et al., 2001). Yegorov (2007a) considers potential mathematical formalizations of corresponding preferences that correspond to non-liberal societies (nationalistic and Marxist). Yegorov (2000) considers two games (hunting big and small animal). While the second game does not require cooperation, in the first game only cooperative behavior allows obtaining higher total benefit. How can agents learn to cooperate? A simple evolutionary model is set, and the society can turn to be more or less cooperative depending on fractions of both types of games (Yegorov, 2000). Spatial clusters of altruistic behavior are considered and the process of their formation is studied analytically (Yegorov, 2007a). What can be the role of population density for the development of cooperation? If the density is low, agents have fewer possibilities to quarrel as they meet other agents less frequently. At the same time, they are more involved in building infrastructure projects (It was shown above, that low population density implies higher cost per capita for infrastructure projects). 4.1 Hypothetical comparison of two countries Consider two lands, the first with high land fertility and the second with low land fertility. Let the first land be in relatively South and the second in North. In the pre-historical period, this Northern land had low population density, since the land could not give enough food for many people. Contrary, Southern land could be more densely populated. It was not before industrial revolution that farming could bring some additional product to be traded. Still, in the North, farmers had to work on more land per person and spend more hours working to produce food necessary for the survival than in the South. Hence, it happened that even before industrial revolution not all of Southern population had to be farmers. Simply, one unit of Southern land required work of only a fraction of Southern population that could be fed from the harvest on this land. Such situation before industrial revolution had two consequences. First, population density in Southern territories became larger. Second, a fraction of this population was not needed to work on land. An interesting consequence was observed in Spain. If there were three sons in a family, only one inherited land, while others could be priests or soldiers. In other Northern countries, land was divided into smaller plots with generations. There were also additional occupations, related to art, trade, and services. Extra population not required for farming was moving to cities. Cities had two roles, military protection through walls and space-saving constructions to save more land for agriculture. As population density was growing, people met other people more frequently and had more frequent arguments, starting from bargaining in trade market and ending with the development of robbery. These things made people more individualistic and less cooperative. Arguments were solved using law. Now let us consider Northern population. Land was abundant there, but one has to develop a lot of land to survive. This traditional agriculture gave little additional product in Russia even in the 19th century. Hence, there was low population density. Moreover, it was difficult to collect the product for export, as more roads per capita were required to cover all arable territory. However, agricultural innovations raising land productivity could have
8 Socio-economic influences of population density important consequences. With lower land per capita required for survival, population density could grow. And indeed, Russian population grew 5 times in the 19th century, from 30 to 150 million people. It could grow more in the 20th century, but the process was perturbed by wars and revolution rather than by natural restrictions. If people had to develop more land per capita, they had to work more hours. Also, they had to invest more hours for equal technology in infrastructure development. This required cooperative work on common infrastructure projects. People simply had no time for learning cheating and dirty tricks. The society was developed as moral with lower criminality and less experience in playing games or arguing. Clearly, both in North and South, there were religious institutions talking about morality, but Northern people had less possibilities and experience to make sins. Moral behavior, and not one regulated by law, was naturally developing in these societies. 4.2 Economy with low population density Let ρ=N/S is population density. Then 1/ρ is an average endowment of land per capita. Assume that land and labor L (not capital) are the main production inputs for agricultural and mining technology, and that production function for individual activity (harvesting) is of Cobb-Douglas type, Y=σ L1-b ρ-b, where σ is land productivity. There was a historical period, when only fertile land zones have been populated. In those zones, population was growing with the development of technology that first made land more productive and later invented non-land production activities, like manufacturing and services. Initially low productive land was not occupied by population, if one could not produce enough harvest to survive. But with the technological progress, it became possible to produce an output Y>Y*, (Y*=σ (s*)b is survival minimum, where s* is land per capita) using inelastic labor supply, L=1, and some land s>s*. Until s*<1/ρ, this low-populated land was sufficient for autarchic development. Thus, in areas with low land fertility σ the zones with low population density ρ have been formed. Population there could grow until s*<1/ρ. This is how traditional societies have been developed. In the time of Great Geographical Discoveries, most of those lands became colonies, and those economies no longer became autarchies. But in cold lands (like Siberia and Canada), it was still a challenge to develop those territories even under growing technology. There were two problems: (a) to make it accessible to world markets by building infrastructure (road network), (b) to raise individual productivity substantially above survival level, so that some surplus is created. When natural resources are still abundant in more fertile places, world cares little about those autarchic zones that had low population density and low surplus. However, with globalization the interest to integrate those territories into the world economies emerged again. In section 2, those cases are formally considered. The result is that independent growth of those regions required some optimal population density, since too little density is not sufficient to build infrastructure. This was an approach of independent growth. However, with land and capital coming to regions from other countries, this critical density could be effectively reached. Canada did not reach substantial development of its Northern territories until now, since it was prohibitively expensive under world prices for transport and labor. Russia in autarchic state (Iron Curtain of the USSR) was able to do so, using subsidized transport pricing and relatively cheap labor (by world standards), however making domestic incentives for labor by offer of higher than average country salary. However, the goal of this section is to explain emergence of cooperation in low-populated land. 4.3 Development of cooperation in low-populated economies It became a tradition of economic literature, to formalize non-exchange interactions between economic agents as some kind of games. Then, Yegorov (2000) considers two types of games. The game A will be named
9 Socio-economic influences of population density
“cooperative”: if two agents meet and both play the same strategy T (stylized sign for telling truth, being cooperative, having high moral standards, etc), they both win surplus of some value; let us normalize it to 4. In the case of complementary strategy L (telling lie, playing dirty tricks, deceiving, having not moral behavior) none of participants get any surplus. If only one side plays L, it is also no win strategy with payoff equal to zero. Formally, game A can be represented as a matrix (Table 1):
Table 1 Payoffs (a, b) for “cooperative” game A for (row, column) strategies Game A T L T (4,4) (0,0) L (0,0) (0,0)
The complementary game B will be named “non-cooperative”. It has the same set of strategies (T, L) that have the same interpretation in moral terms as game A. However, under game B strategy T is no longer winning for both. Contrary to game A, it is zero-sum game, with sum of payoffs equal to 2 under any pair of chosen strategies. But here the agent playing “non-morally” (choosing L) wins over a partner choosing morality (T). The game B has the following payoffs (Table 2):
Table 2 Payoffs for “non-cooperative” game B Game B T L T (1,1) (0,2) L (2,0) (1,1)
Now consider the real cases when life situations resemble game A. Suppose, two hunters meet a large animal (like bear) in the forest and only their cooperative behavior ensure successful hunt. Another situation is related to cooperation in some infrastructure project (like building a road, although this may require cooperation of more than 2 agents) when one participant has no resources for project completion. In all of these cases prize emerges if and only if cooperation takes place. In low populated economies, agents are self-sufficient in many cases. But sometimes they need cooperation, having too little individual resources to complete necessary project. Now let us use some analogy with statistical physics. In low-density society agents have to spend almost all of the time working on low-fertile land. In their free time (which is not abundant), they also do not meet so many agents. Because of low density, the average distance between agents is large, and if they move with constant speed in their leisure time (1-L), the probability to meet somebody is proportional to ρ. Assuming that each agent has at least one cooperative project in mind during a day, every first meeting results in cooperative game of type A, and only 2nd and further meetings result in no game. For population density sufficiently small, practically all meetings between agents will bring game A into place, and they will evolve to play strategy T as one giving benefit. The game B emerges in other situations. Here some value is already created and no new value emerges during interaction. The simplest example is card game that requires some kind of deceiving rival as pre-condition for “win”. The games linked to “honest gambling” I would not put to this type, while “dishonest gambling” is clearly of this type. “Market for lemons” is another example: one needs to convince buyer in false information about the value of the product he buys. Typically, these games of type B develop in societies with high population density. In this case meeting partner rarely creates surplus, because this event is not seldom, like in low-populated territories. Enough population density is also a pre-condition for survival of “professional cheater”, because cheating twice on the same agent may be dangerous.
10 Socio-economic influences of population density
4.3.1 High population density Consider densely populated societies. If land is highly fertile, it is enough to have small land spot and to work on it relatively small fraction of time endowment in order to survive. In this case, it was quite possible to have a society with equal land endowments, working small fraction of a day on land slot and enjoying the rest of the time. However, as we know from history, such cases have been described in fantastic literature but rarely took place in reality. As it was shown by K. Marx, a possibility to create additional product above survival minimum leads to historical formations with exploitation: slavery, feodalism and later capitalism. In such societies with exploitation, morality of cooperation would be unstable. Indeed, most of the projects that can create surplus from cooperative behavior of two randomly meeting agents would be named “firms” and owned by somebody. Those who have less wealth in this society and will not have a chance to become richer due to the lack of capital or power have a clear incentive to invent tricky games so that richer agents can be “deceived” and pass them some of their value. If the return to such “dishonest” activity is higher that to honest labor (or if there is no chance to apply honest labor; think of landless peasants, or unemployed workers), there is a clear sign that such types of game B will be developed in such society. So, contrary to low-populated area, in high-density area there will emerge games of type B. 4.3.2 Intermediate case Considering finally an intermediate case of population density, when both types of games (A and B) are present, the analysis will be done in the framework of bounded rational evolutionary games. Any agent randomly meets another and they do not know what game they are playing, A or B. They also cannot observe their type, but at any time, each agent knows that he will play now T or L. This is predetermined by his initial education, and later may be revised depending on average payoffs from playing strategy T or L at time t. In other words, people may learn at school to be moral (play T), so they play T initially. But if they observe that those around them who play L, get higher expected payoff, they will revise behavior, and the strength of pressure to revise depends on the payoff difference, dP(t)=PT(t)-PL(t). Let h(t) denotes the fraction of population playing strategy T at time t, and let α (t) be the probability to play game A at time t. The expected payoffs of playing strategies T, L depends on α(t) and h(t) in the following way:
PT(t)= 4h(t) α(t) + h(t)(1- α(t)),
PL(t)= (1-α(t))(1 + h(t)). If the number of agents is large, then the evolution of type’s shares becomes asymptotically deterministic. If c is the speed of learning, dh(t)/dt =c (1-h) dP(t), if dP(t)>0. In stationary case of α(t)=const, this dynamics ensures convergence to T-society, if the probability of game A is above the threshold: α > α* =1/(1+4h(0)). In the opposite case there is convergence to L-society. However, for any positive h(0) there always exists a neighbourhood [α*, 1] in game probability space, where convergence is to T-society. Let us relate probability α with population density ρ. In two-dimensional space, uniformly occupied by residents (they need land to work to it, so cannot concentrate in cities) the average distance between agents, r, is of order ρ-1/2. If every agent has to build a road from his house to some common road, its length will be also r. So, all road network that is necessary for connection of all production places with world market, is of order ρ-1/2. In other words, per capita cost of infrastructure grows to infinity as population density vanishes to zero. Assuming that building infrastructure requires cooperation across agents, the demand for cooperative behavior (and emerging games of type A) will be very high for small ρ. At the same time, for these small densities agents simply have no free time to participate in games of type B, and they will not emerge in this society. If we introduce
11 Socio-economic influences of population density relatively small fraction of agents of complementary type, they will not perturb convergence to T-society. Hence: Proposition 4 For small population densities there is always a convergence to T-society. Moreover, this society is resistant to small infection of B-games (coming from migrants, for example). As time goes, technological development reduces the labor time and population density also grows (as less land is necessary for survival, if land productivity σ grows because of new technologies). Under these conditions, probability of A game declines, and of B game increases. At some moment, α=α*, and this society no longer converges to T-state. For higher densities it will converge to L-state. The vulnerability to infections in form of L-type migrants is also larger in this society. Territories with low population density are often developed more efficiently under autarchies. For example, in a globalized world with free trade, Siberia has a difficulty to develop competitive agriculture. Moreover, low density implies larger distance to bring product to the world market, and thus higher share of transport cost. In the Soviet time, Siberian agriculture was developed more as autarchy, for local consumption. Subsidized transport, on the other hand, made harvesting in Siberia more competitive. What can liberalization bring? Return to no development, like Canadian territories in similar conditions. This is unlikely to be an efficient equilibrium.
5. Conclusions
Firstly, this paper investigates an influence of such geographical factor as population density on economic performance and social life. Despite the beliefs of many economists about vanishing and almost negligible role of geography in globalized world this does not seem to be true. The paper provides several examples that represent different areas of economic and social life where the role of population density is still important. Secondly, the first important case is resource-rich economy with moderate or low population density. Under these conditions, there exists a relation between population density, profitability and economic growth potential. Some intermediate level of population density, when resource endowment per capita is still high while per capita investment in infrastructure is not so high, becomes optimal. Thus, low populated territories, like Siberia, can gain in profitability if population density will grow. Thirdly, another model shows that scale economies do not lead to unbounded growth of plant in the environment of spatial economy with transport cost. Moreover, in low populated economies even a monopoly may not survive. In the case of Russia, setting world prices for fuel (and hence, transport) inside a country has put such industries located in low-populated zones to permanent shock. Setting transport subsidy can be the optimal remedy to escape de-industrialization. At last, uniform population density becomes unstable when technologies with low land intensity (industry, services) emerge. This leads to urban-rural split or separation of space to attractors with low and high population density. However, urban concentration of population has potentially negative effects, not only via depopulation of rural areas but also because of rising cost of providing some public services in dense areas (Ladd, 1992). This paper considers another social influence of population density: on honesty and cooperativeness of population. It is shown that low-populated territories were the cradles of more honest and cooperative populations. (to be continued on Page 47)
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