Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Alexandre Manuel da Rocha Freitas was born in Guimarães, on 27 October 1992. In. 2010, aware of his passion for the area, initiated a Bachelor (BSc) degree ...
Typology: Summaries
1 / 50
This page cannot be seen from the preview
Don't miss anything!
Alexandre Manuel da Rocha Freitas was born in Guimarães, on 27 October 1992. In 2010, aware of his passion for the area, initiated a Bachelor (BSc) degree in Economics at the School of Economics and Management of the University of Porto (FEP), that was completed in June 2013, with a final average of fifteen (15) points out of twenty (20). During this period, he was co-founder and finance director of an association created within the University of Porto, called Academia de Politica Apartidária, which aims to connect college students to aspects of politics and policies aside from any party institution. Also, in the third and final year, he had the opportunity to study abroad, in Bucharest, Romania. In September 2013, he continued his studies in the Master of Science (MSc) in Economics at the same institution. In the first year, he finished the curricular part of the course, with an average of sixteen (16) points in twenty (20). Alongside, he gained experience in volunteering, tutoring children in the school domain, but also foreign students in the adaptation process to a new cultural setting.
i
Recently, thanks to new techniques of economic modeling, a renewed literature emerged in the treatment of spatial aspects of economic activity in an area known as new economic geography. We contribute to the field by developing a core-periphery model that assumes CES preferences, rather than a Cobb-Douglas utility function as in the original model of Krugman (1991). The main purpose of this work is to articulate the widely-studied agglomeration and dispersion equilibria with the study of changes in the elasticity of sub- stitution between agricultural and industrial goods, which is made possible by the gener- alization of the utility function. Through numerical simulations, mainly conducted in a core-periphery state, complemented by a section dedicated to the economic interpretation, we develop an analysis that was not previously possible. In general terms, an increase of the elasticity of substitution promotes agglomeration (and a decrease, dispersion) because qualifying the two types of goods as substitutes (or complements) changes the share of expenditure on industrial goods (i.e., the demand) differently in the two regions, which, ultimately, also modifies the magnitude of the effects discussed in the literature: market- size, cost-of-living and market-crowding effects. However, these considerations are based on a price index of industrial varieties significantly lower than the price of agricultural goods, which, if tested inversely, leads to different conclusions.
Keywords: new economic geography; core-periphery model; agglomeration; dispersion; constant elasticity of substitution
JEL Classification Numbers: R10 R12 R
iii
Recentemente, graças a novas técnicas de modelação económica, uma literatura renovada emergiu no tratamento de aspetos espaciais da atividade económica numa área conhecida como nova economia geográfica. Com o intuito de enriquecer o campo, foi desenvolvido um modelo centro-periferia que assume preferências CES, em vez de uma função de util- idade Cobb-Douglas como no modelo original de Krugman (1991). O principal objetivo deste trabalho é articular os equilíbrios de aglomeração e dispersão com o estudo de al- terações na elasticidade de substituição entre bens agrícolas e industriais, que surge pela generalização da função de utilidade. Através de simulações numéricas, realizadas so- bretudo numa economia de centro-periferia, complementada com uma seção dedicada a interpretação económica, desenvolvemos uma análise que não era possível ser provi- denciada anteriormente. Em termos gerais, um aumento da elasticidade de substituição promove a aglomeração (e uma diminuição, a dispersão), porque ao qualificar os dois tipos de bens como substitutos (ou complementares) alteramos a percentagem de despesa em bens industriais (isto é, a procura) diferentemente nas duas regiões, o que, em última análise, modifica também a magnitude dos efeitos discutidos na literatura: market-size, cost-of-living e market-crowding effects. No entanto, estas considerações têm por base um índice de preços do setor industrial significativamente mais baixo que o preço de bens agrícolas, que, se testados de forma inversa, originam conclusões diferentes.
Palavras-chave: nova economia geográfica; modelo centro-periferia; aglomeração; dis- persão; constant elasticity of substitution
Códigos JEL: R10 R12 R
iv
1 Introduction
This dissertation falls within the recent strand of neoclassical models developed in the field of new economic geography. Nevertheless, concepts such as distance or space have remained, surprisingly, on the outskirts of Economics until very recently, and it was only following Krugman (1991) that mainstream economists placed geography at the center of economic activity analysis. These theoretical advances, in regard to the well-established ideas developed in traditional location theory, were made possible due to a number of modeling tricks and numerical and computational methods, which enabled the new liter- ature to embrace models of general equilibrium, “and in which spatial structures emerge from invisible-hand processes” (Krugman, 1998, p. 9). Economic Geography is the field that is responsible for the study of the spatial orga- nization of economic activities and the intrinsic reasons behind it. Despite the emergence of so-called core-periphery models in the last two decades, it is important to remember the roots of location theory, the authors and the grounds that justify their position as an economic model.
Johann Heinrich von Thünen is, according to Walter Isard (1956, p. 27), the father of loca- tion theorists, which is the same as saying that economic geography is rooted in The Iso- lated State (1826). In a scenario of a single isolated town (market), with homogeneously fertile land and able to generate several cultures, von Thünen showed that competition among farmers leads to an increase in land costs from the outside limit of cultivation, where rent is nil, to the center. As shipping costs differ between cultures, agricultural goods subject to a higher cost of transportation will be closer to the city. The result is a pattern of concentric rings of production and a study that marked the first ever location theory. However, the work of von Thünen, conducted at the beginning of the Industrial Rev- olution in Germany, was focused on agricultural land use, getting barely within concepts such as industry or agglomeration. Thus, it was only in the end of the nineteenth cen- tury and the first part of the twentieth century, that a number of economists studied more thoroughly aspects related to the location of industry. In the late nineteenth century in England, Alfred Marshall in chapter 10 of the fourth book of Principles of Economics (1890) analyzed the reasons for the concentration of specialized industries in distinct locations. According to Marshall (1890, p 225.) “(...) if one man starts a new idea, it is taken up by others and combined with suggestions of their own; and thus it becomes the source of further new ideas”. Marshallian externalities, as
In 1991, Paul Krugman wrote Increasing returns and economic geography. Developing an abstract model seeking to explain the agglomeration of economic activity, the author managed to draw the attention of mainstream economists to the treatment of spatial as- pects of economics. His work in the early 90s demonstrated that agglomeration can be achieved without exogenous regional asymmetries or external economies, or even without being related to climate or to resource endowments (the so-called first-nature geography, where the traditional neoclassical literature focused on). According to Krugman (1998, p.7), “This [new] approach inevitably has much in common with older approaches. Nev- ertheless, it also has a number of distinctive features that do qualify as a new departure”. The structure of the reminder of this section is taken from Krugman (1998).
(i) Modelling Principles
There is no doubt that some of the ideas of Von Thünen, Christaller and Lösch are in- corporated in new economic geography. Incidentally, in this sense, Krugman adds very little with respect to concepts and theories: the traditional literature is simply updated, and “the so-called new theories do not add any new variables, nor do they establish differ- ent relations or reach original interpretations” (Ruiz, 2001). Krugman’s real asset is the flaw of the others. As mentioned above, some of the most influential works neither take into account the decisions of individuals and firms, the “microagents”, nor explained the process of emergence of spatial structures. In new economic geography, however, indi- viduals choose location maximizing their welfare given what other individuals are doing (Krugman, 1998). The result is the emergence of spatial structures arising from invisible- hand processes, a self-organizing system in which the “micromotives” of the agents are the key (Ruiz, 2001).
(ii) Modelling Tricks
Paul Krugman in a conversation with Masahita Fujita, in The new economic geography: Past, present and the future (2003), describes the model with a peculiar slogan: "Dixit- Stiglitz, icebergs, evolution and the computer" (p. 142). Dixit-Stiglitz is relative to the monopolistic competition model by Avinash Dixit and Joseph Stiglitz (1977), adopted nowadays by various fields of study. According to Krugman, “it has the virtue of pro- ducing in the end a picture of an economy, in which there are increasing returns [and existence of monopoly power], (...) not get into the fascinating but messy issues posed by realistic oligopoly.” (Fujita & Krugman, 2003, p.143). The expression icebergs concerns a transportation model by Paul Samuelson (1952), in which the costs are introduced by
imagining that a fraction of the product melts in the road. This avoids the analysis of the transportation service as an isolated industry, while it simplifies the perception of com- panies’ costs when setting their monopoly price. On the behalf of agents’ behavior, the evolution slogan refers to the decision not to assess location by future expectations, but solely on current conditions. Finally, computer is no more than the use of new numerical and computational methods, as models of new economic geography “turn out to be a bit beyond the reach of paper-and pencil analysis” (Krugman, 1998, p.11).
(iii) Modelling Strategy
Above all, Krugman’s framework represents a tension between forces that promote and forces that oppose agglomeration, i.e, between centripetal and centrifugal forces, respec- tively. In the introduction of Increasing returns and economic geography, Krugman first stresses that, due to economies of scale, the production of each industrial good will be limited to a small number of locations. Ceteris paribus, the location of these production plants will be next to markets with high demand, in order to minimize transportation costs. Then he asks where that demand will be higher. Since part of consumption of manufac- tured goods is directed for industrial workers, the demand will be bigger the larger the sector. This is a clear example of the theory of circular cumulative causation of Myrdal (1957): industrial production tends to concentrate where there is greater demand, but the market will be bigger as more concentrated the industry is (market-size effect). The circularity created by backward linkages is reinforced, in turn, by forward link- ages: other things equal, it is more pleasant to live in the center, where the goods are not subject to shipping costs (Krugman, 1991). It is known as the cost-of-living effect, and is more beneficial (for the locals) the more crowded the region. This brings us to the last property, the only one that acts against agglomeration, the market-crowding effect. The market-crowding effect is the benefit of the region with a smaller industry, which, by having a smaller number of firms and workers, faces for the local market less competition than if it was located in the other region. Obviously, the effect is felt more when workers are concentrated in one region, because by moving they are able to get a clear comparative advantage over goods imported from the other region. The outcome of these three forces, which determines the location of industry, depends on a number of parameters that arise from the modeling of the main actors in the economic geography.
workers who are considering to move will be, since the share of industrial goods that need to be imported is also higher, but nevertheless, from the firm’s point of view, the demand in the peripheral region increases. Finally, the elasticity of substitution between industrial varieties also plays an impor- tant role on centrifugal and centripetal forces. At equilibrium, (^) σσ− 1 is equal to the ratio between average and marginal cost, a common measure of economies of scale (Krugman, 1991). A low elasticity of substitution can give rise to significant economies of scale, making it less attractive to serve the peripheral market locally. In short, with reduced transport costs (low τ), a dominant industry sector (high μ) and important economies of scale (lower σ), agglomerations become more robust (Schmut- zler, 1999).
While Krugman’s model captures important aspects of the development of spatial pat- terns, it is based on various assumptions which, if relaxed, lead to additional insights, as Schmutzler (1999, p.364) indicates. As Krugman points out in What’s new about new economic geography (1998), be- yond the desire of firms to serve the periphery, there are other centrifugal forces of ag- glomeration that are not incorporated in the base model. Barkman et al. (1994) modifies Krugman’s model by introducing effects of congestion. The study concludes that, in the presence of a negative externality, a complete concentration rarely occurs because pro- duction in the core becomes too costly. Assuming n-regions, the results are complex and show, most of the time, multiple agglomerations as equilibrium (Schmutzler, 1999). With only one more region, such as Castro et al. (2012) shows, a model with three regions favors concentration in relation to the initial setup. A work by Krugman and Livas-Elizondo, in 1996, extended the analysis of a multiple regions’ model in order to study the spatial distribution as a function of the degree of openness to trade. In addition, they introduce urban rents and commuting costs, which represents an additional centrifugal force. This occurs because the agglomeration of industry causes an increase in the size of the city, resulting in the growth of rents and commuting costs, which ultimately reduces the likelihood of agglomeration.
An analytically solvable model
Forslid & Ottaviano in An analytically core-periphery model (2003) address a major lim- itation of Krugman’s core-periphery model. By considering that mobile skilled workers are a fixed cost in the industrial sector, while immobile unskilled workers are the variable
input in the industrial sector (as well as the single input in agriculture), the model allows an analytical treatment that is not possible in Krugman’s setting, while maintaining the properties of the original work. This model is, as well, the starting point for obtaining the model explored in this dissertation.
The theoretical field known as new economic geography studies issues related to the lo- cation of industry, in a core-periphery model in which it is frequently assumed that agents have preferences of Cobb-Douglas type. Given that Cobb-Douglas can be seen as a par- ticular case of a CES (constant elasticity of substitution) function, we investigate if the aspects described in the literature persist in the more general case of a model using a CES utility function. We also address the impact of the elasticity of substitution between agricultural and industrial goods (ρ, a new parameter) on the long-term stability of the traditional agglomeration and dispersion equilibria. The methodology of this investigation combines analytical and computational treat- ment. We generalize the Forslid & Ottaviano (2003) model to obtain the relevant equa- tions when consumers have CES type preferences, later implemented in a numerical computing software, MatLab. Here, the work partitioned in ensuring that the behavior observed for a Cobb-Douglas value appears in the new model when ρ tends to zero, be- yond the illustration of the model’s behavior for positive and negative values of ρ, which unfolds new insights. In a core-periphery economy, regarding the elasticity of substitution between agri- cultural and industrial goods, we found that, when the elasticity is positive, its increase promotes agglomeration, when compared to the Cobb-Douglas setup. This is because the increase of substitution between agricultural and industrial goods raises the demand for industrial goods more proportionately in the core than at the periphery, while the cost of living is lower. The ratio of utilities increases in favor of the central region, and therefore, of agglomeration. On the contrary, when the elasticity is negative, the consumption of industrial goods decreases more strongly in the central region. An agent in the periph- eral region increases its relative utility by consuming a greater share of industrial goods (even with transportation costs), acting against concentration. However, the latter case only reveals itself a force of dispersion given the marked difference in prices between agricultural and industrial cheaper goods. Finally, the results of the model also differ when the price of the agricultural good is lower than the price of manufactured goods. Negative values of ρ increase the share of expenditure on industrial goods more in the peripheral region, which given the higher price of industrial goods in relation to agricultural goods, affect the consumption in this
7
2 The model
This core-periphery model is based on two regions, each with two sectors, agriculture and industry. Based on the framework of Forslid & Ottaviano (2003), there are two factors of production, skilled (H) and unskilled labour (L), both employed in manufactured produc- tion. Unskilled workers are perfectly mobile between sectors but spatial immobile and assumed to be evenly distributed across regions (Li = L/2, i = 1 ,2), unlike skilled ones that are geographically mobile and therefore choose to reside in the region that offers a higher well-being (H = H 1 + H 2 ).
(i) Demand Side
Preferences are defined over two final goods, agricultural (a homogenous good, A) and manufactured (a differentiated good, X). Unlike Krugman (1991), the preference ordering of the representative consumer in region i = 1 ,2 is captured by a constant elasticity of substitution (CES) utility function:
Ui =
μX (^) iρ + (1 − μ) A iρ ρ ,^ (1) where Xi is the consumption of the manufactures aggregate, Ai is the consumption of agricultural products, μ ∈ (0,1) is the strength of preference for manufactured goods rela- tively to the agricultural good and ρ ∈ (−∞,1) is a measure of the elasticity of substitution between agricultural and manufactured goods^1. The first order condition for the problem of maximizing Ui with respect to xi (the demand of a representative consumer), subject to Pi xi + PAai = y, gives us:
Pi xi = y 1 + ( 1 −μμ ) 1 −^1 ρ P 1 ρ−ρ i
where Pi is the local price index of manufactures and y each consumer’s income. Define μ¯i ∈ (0,1), different between regions, as the share of expenditure in manufactured goods:
μ¯i = 1 1 + ( 1 −μμ ) 1 −^1 ρ P 1 −^ ρρ i
The calculations leading to (3) are given in Appendix A. It is also important to stress that, relatively to Krugman (1991) or Forslid & Ottaviano (2003), the percentage of expen- diture on industrial goods is no longer a parameter. The consumption of the manufactures (^1) Note that the standard Cobb-Douglas utility function is recovered for ρ → 0. The elasticity of substi- tution is represented by (^1) −^1 ρ.
aggregate, Xi, is defined by:
Xi =
s∈N
di (s) σ σ− 1 ds
) (^) σσ− 1 , (4)
where di (s) is the consumption of variety s of good X, N is the mass of varieties (N = ni + nj ) and σ > 1 is the elasticity of substitution between any two varieties of good X. Demand by residents in location i for a variety produced in location j is:
d (^) ji (s) = pji (s)−σ P i^1 −σ μ ¯iYi, i, j = 1 , 2 , (5)
where pji is the consumer price of a variety produced in j and sold in i and Y (^) i the local income consisting of skilled (wi) and unskilled wages (wiL ), defined by:
Y (^) i = wi Hi + wiL
The local price index of manufactures Pi associated with (4) is:
Pi = * ,
s∈ni
pii (s)^1 −σ^ ds +
s∈nj
pji (s)^1 −σ^ ds 1 −^1 σ +
The representative consumer in region i has the following budget constraint when maxi- mizing utility (1):
Yi =
s∈ni
pii (s)dii (s)ds +
s∈n j
pji (s)d (^) ji (s)ds + piA Ai (8)
(ii) Supply Side
Firms in the industrial sector are monopolistically competitive and employ both skilled and unskilled workers under increasing returns to scale. The total cost of production of a firm, in location i, is:
TCi (s) = wi α + wiL βxi (s), (9)
meaning that in order to produce x(s) units of variety s, a firm must employ α units of skilled labour (fixed cost) and a marginal input of βx units of unskilled labour. Trade of manufactures is subject to a transportation cost, modeled as iceberg costs (1 ≤ τ < +∞)^2. Given the fixed input requirement α, skilled labour market clearing implies that in equilibrium the number of firms is determined by: (^2) Differently to Krugman (1991), where 0 < τ ≤ 1
(12), (13) and (16), we can determine the output of firms in both regions:
xi = σ βσ^ −^1
μ¯iYi ni + φnj^ +^
φ μ¯jYj φni + nj
Using (9) and (13), (17) can be equivalently written as:
wi = (^) σ^1
μ¯iYi Hi + φHj^ +^
φ μ¯jYj φHi + Hj
Plugging expression (6) into (18) generates a system of two linear equations in wi and wj , that can be solved to obtain the equilibrium skilled wages as explicit functions of the spatial distribution of skilled workers Hi, whose expression is obtained in Appendix B and displayed as:
wi = 2 Lσ
φHi ( ¯μi + μ¯j ) +
μ¯i − μ¯i σ^ μ¯ j+ (1 + μ σ¯i ) ¯μj φ^2
Hj φ(H i^2 + H^2 j ) − (H i^2 μ¯i + H^2 j μ¯j ) (^) σφ +
1 + (^) σ^12 − μ¯i^ + σ^ μ¯j+ (1 − μ¯ σi^ μ¯ 2 j)φ^2
Hi Hj
for i, j = 1 ,2. The ratio between the equilibrium skilled wages, defining h = H 1 /H as the share of skilled workers that reside in region 1, is:
w 1 w 2 =^
φh( ¯μ 1 + μ¯ 2 ) +
μ¯ 1 − μ¯^1 σ^ μ¯ 2 + (1 + μ σ¯^1 ) ¯μ 2 φ^2
(1 − h) φ(1 − h)( ¯μ 1 + μ¯ 2 ) +
μ¯ 2 − μ¯^1 σ^ μ¯ 2 + (1 + μ¯ σ^2 ) ¯μ 1 φ^2
h
It is important to emphasize that this expression, despite being formally very similar to the equivalent (17) in Forslid & Ottaviano (2003), underlies a major distinction. The share of expenditure in manufactured goods ¯μi, i = 1 ,2, before just a parameter, depends on the elasticity of substitution between agricultural and manufactured goods ρ and on the region’s price index.^3 The indirect utility, i.e., the maximal utility attainable in region i for given prices and wages, is:
Vi = μ^
(^1) ρ Pi
1 − μ μ
) (^1) −^1 ρ P 1 −^ ρρ i
1 −ρρ wi, (21)
or, simply, Vi = μ^ ρ^1 μ ¯
1 −ρρ i
( (^) wi Pi
(see Appendix C). Finally, the ratio between the indirect utilities
gives us a starting point to study agglomeration and dispersion patterns:
V 1 V 2 =^
μ¯ 2 μ ¯ 1
) 1 −ρρ w 1 w 2 (22) (^3) This will have implications in the analytical treatment of the long-run equilibrium patterns.
3 Long-run equilibria
Let us start the study of agglomeration and dispersion equilibria, focusing our analysis on the ratio between indirect utilities (22), an indicator that triggers the mobility of skilled workers between regions (see also Section 3.1). The utility of any skilled worker in re- gion i = 1 ,2 will depend on his wage (wi), on the price index associated (Pi) and on the share of expenditure in manufactured goods, ¯μi. Contrary to the original model, the latter depends not only on μ (that now only represents a measure of preference for manufac- tured goods relatively to the agricultural good), but also on the elasticity of substitution between agricultural and manufactured goods, ρ, and on the region’s price index. In- deed, Pi incorporated in ¯μi makes fixed cost, α, marginal cost, β, and number of skilled workers, H, that on Krugman’s model were eliminated by choice of units, parameters relevant to our study. Finally, and to complete the description of all the parameters that affect the model’s behavior, the ratio of indirect utilities also depends on the elasticity of substitution between industrial varieties, σ, and on transportation costs, τ. Assuming symmetry regarding the production factors, the immobility of unskilled workers makes them evenly split between regions. The issue has to do then with industry and skilled workers: in the long term, the industry can be fragmented between the two regions, or concentrated in one, creating an economy divided between an industrial center (or core) and an agricultural periphery. Herein, we need to introduce the concept of long- term equilibrium (from now on, just equilibrium), as the distributions of skilled workers that remain unchanged over time. An equilibrium is stable, as Gaspar (2012, p.11) ex- plains, “if after occurrence of some small exogenous migration of skilled workers to any of the regions, the spatial distribution of skilled workers is pulled back to the initial one.” Thereby, a dispersion equilibrium is observed when the skilled workers are equally divided and is stable if, after a small migration, the economy returns to a symmetry of industries. By moving, for example, from region i to region j, a skilled worker causes the real wage of region j to become comparatively lower than the one in region i, and consequently, a different skilled worker will do the opposite movement. On the other hand, an agglomeration equilibrium is stable when the real wage of the region in which all entrepreneurs are located is larger than the real wage in the region without manufacturing. To determine when we have a stable or unstable equilibrium, let us analyze both situations from the analytical and numerical point of view.
As explained before, workers are short-sighted and choose their location by maximizing their indirect utility. According to Forslid & Ottaviano (2003, p.234), skilled worker
