Agglomeration under forward-looking expectations: Potentials and global stability

This paper considers a class of migration dynamics with forward-looking agents in a multi-country solvable variant of the core–periphery model of Krugman [Krugman, P., 1991. Increasing returns and economic geography. Journal of Political Economy 99, 483–499]. We find that, under a symmetric externality assumption, our static model admits a potential function, which allows us to identify a stationary state that is uniquely absorbing and globally accessible under the perfect foresight dynamics whenever the degree of friction in relocation decisions is sufficiently small. In particular, when trade barriers are low enough, full agglomeration in the country with the highest barrier is the unique stable state for small frictions. New aspects in trade and tax policy that arise due to forward-looking behavior are discussed.     

Bifurcations in regional migration dynamics

The tomahawk bifurcation is used by Fujita et al. [Fujita, M., Krugman P., Venables A.J., 1999, The Spatial Economy: Cities, Regions, and International Trade, MIT Press: Cambridge, MA.] in a model with two regions to explain the formation of a core–periphery urban pattern from an initial uniform distribution. Baldwin et al. [Baldwin, R., Forslid, R., Martin, P., Ottaviano, G.I.P., Robert-Nicoud, F., 2003, Economic Geography and Public Policy, Princeton University Press: Princeton, NJ.] show that the tomahawk bifurcation disappears when the two regions have an uneven population of immobile agricultural workers. Thus, the appearance of this type of bifurcation is the result of assumed exogenous model symmetry. We provide a general analysis in a regional model of the class of bifurcations that have crossing equilibrium loci, including the tomahawk bifurcation, by examining arbitrary smooth parameter paths in a higher dimensional parameter space. We find that, in a parameter space satisfying a mild rank condition, generically in all parameter paths this class of bifurcations does not appear. In other words, conclusions drawn from the use of this bifurcation to generate a core–periphery pattern are not robust.     

Tiebout's tale in spatial economies: Entrepreneurship, self-selection, and efficiency

This paper establishes the existence and efficiency of equilibrium in a local public goods economy with spatial structures by formalizing Hamilton's [Hamilton, B.W., 1975. Zoning and property taxation in a system of local governments Urban Studies 12, 205–211] elaboration of Tiebout's [Tiebout, C., 1956. A pure theory of local public expenditures. Journal of Political Economy 64, 416–424] tale. We use a well-known equilibrium concept from Rothschild and Stiglitz [Rothschild, M., Stiglitz, J.E., 1976. Equilibrium in competitive insurance markets: an essay on the economics of imperfect information. Quarterly Journal of Economics 40, 629–649] in a market with asymmetric information, and show that Hamilton's zoning policy plays an essential role in proving the existence and efficiency of equilibrium. We use an idealized large economy following Ellickson, Grodal, Scotchmer and Zame [Ellickson, B., Grodal, B., Scotchmer, S., Zame, W.R., 1999. Clubs and the market, Econometrica 67, 1185–1217] and Allouch, Conley and Wooders [Allouch, N., Conley, J.P., Wooders, M.H., The Tiebout Hypothesis: On the Existence of Pareto Efficient Competitive Equilibria, (2004), mimeograph]. Our theorem is directly applicable to the existence and efficiency of a discrete spatial approximation of mono- or multi-centric city equilibria in an urban economy with commuting time costs, even if we allow the existence of multiple qualities of (collective) residences, when externalities due to traffic congestion are not present.     

Convergence of Bayesian learning to general equilibrium in mis-specified models

A central unanswered question in economic theory is that of price formation in disequilibrium. This paper lays the groundwork for a model that has been suggested as an answer to this question in, particularly, Arrow [Toward a theory of price adjustment, in: M. Abramovitz, et al. (Ed.), The Allocation of Economic Resources, Stanford University Press, Stanford, 1959], Fisher [Disequilibrium Foundations of Equilibrium Economics, Cambridge University Press, Cambridge, 1983] and Hahn [Information dynamics and equilibrium, in: F. Hahn (Ed.), The Economics of Missing Markets, Information, and Games, Clarendon Press, Oxford, 1989]. We consider sellers that monopolistically compete in prices but have incomplete information about the structure of the market they face. They each entertain a simple demand conjecture in which sales are perceived to depend on the own price only, and set prices to maximize expected profits. Prior beliefs on the parameters of conjectured demand are updated into posterior beliefs upon each observation of sales at proposed prices, using Bayes’ rule. The rational learning process, thus, constructed drives the price dynamics of the model. Its properties are analysed. Moreover, a sufficient condition is provided, relating objectively possible events and subjective beliefs, under which the price process is globally stable on a conjectural equilibrium for almost all objectively possible developments of history.     

No unbounded arbitrage,weak no market arbitrage and no arbitrage price system conditions; Equivalent conditions

Page and Wooders [Page Jr., F.H., Wooders, M., 1996. A necessary and sufficient condition for compactness of individually rational and feasible outcomes and existence of an equilibrium. Economics Letters 52, 153–162] prove that the no unbounded arbitrage (NUBA), a special case of a condition in Page [Page, F.H., 1987. On equilibrium in Hart’s securities exchange model. Journal of Economic Theory 41, 392–404], is equivalent to the existence of a no arbitrage price system (NAPS) when no agent has non-null useless vectors. Allouch et al. [Allouch, N., Le Van, C., Page F.H., 2002. The geometry of arbitrage and the existence of competitive equilibrium. Journal of Mathematical Economics 38, 373–391] extend the NAPS introduced by Werner [Werner, J., 1987. Arbitrage and the existence of competitive equilibrium. Econometrica 55, 1403–1418] and show that this condition is equivalent to the weak no market arbitrage (WNMA) of Hart [Hart, O., 1974. On the existence of an equilibrium in a securities model. Journal of Economic Theory 9, 293–311]. They mention that this result implies the one given by Page and Wooders [Page Jr., F.H., Wooders, M., 1996. A necessary and sufficient condition for compactness of individually rational and feasible outcomes and existence of an equilibrium. Economics Letters 52, 153–162]. In this note, we show that all these conditions are equivalent.     

An adjustment process for nonconvex production economies

We prove the existence of a path of market conditions, i.e. combinations of market prices and production quantities, that links any arbitrarily chosen market condition with an equilibrium, in a general equilibrium model with possibly nonconvex production technologies based on Villar [Villar, A., 1994. Equilibrium with nonconvex production technologies. Economic Theory 4, 629–638] and Villar [Villar, A., 1999. Equilibrium and Efficiency in Production Economies, second ed., Springer Verlag, Berlin]. This existence theorem holds for any semi-algebraic version of the model and the adjustment of market conditions along the path can be given an economic interpretation as a tâtonnement process. Any such path can be approximated arbitrarily close by applying a simplicial algorithm. By restarting this algorithm in a different market condition, we may find more than one equilibrium.     

Unbounded exchange economies with satiation: How far can we go?

We unify and generalize the existence results in Werner [Werner, J., 1987. Arbitrage and the existence of competitive equilibrium. Econometrica 55 (6), 1403–1418], Dana et al. [Dana, R.-A., Le Van, C., Magnien, F., 1999. On the different notions of arbitrage and existence of equilibrium. Journal of Economic Theory 87 (1), 169–193], Allouch et al. [Allouch, N., Le Van, C., Page Jr., F.H., 2006. Arbitrage and equilibrium in unbounded exchange economies with satiation. Journal of Mathematical Economics 42 (6), 661–674], Allouch and Le Van [Allouch, N., Le Van, C., 2008. Erratum to “Walras and dividends equilibrium with possibly satiated consumers”. Journal of Mathematical Economics 45 (3–4), 320–328]. We also show that, in terms of weakening the set of assumptions, we cannot go too far.     

Equilibria without the survival assumption

It is well known that an equilibrium in the Arrow–Debreu model may fail to exist if a very restrictive condition called the survival assumption is not satisfied. We study two approaches that allow for the relaxation of this condition. Danilov and Sotskov [Danilov, V.I., Sotskov, A.I., 1990. A generalized economic equilibrium. Journal of Mathematical Economics 19, 341–356], and Florig [Florig, M., 2001. Hierarchic competitive equilibria. Journal of Mathematical Economics 35, 515–546] developed a concept of a generalized equilibrium based on a notion of hierarchic prices. Marakulin [Marakulin, V., 1988. An equilibrium with nonstandard prices and its properties in mathematical models of economy. Discussion Paper No. 18. Institute of Mathematics, Siberian Branch of the USSR Academy of Sciences, Novosibirsk, 51 pp. (in Russian); Marakulin, V., 1990. Equilibrium with nonstandard prices in exchange economies. In: Quandt, R., Triska, D. (Eds.), Optimal Decisions in Market and Planned Economies. Westview Press, London, pp. 268–282] proposed a concept of an equilibrium with non-standard prices. In this paper, we establish the equivalence between non-standard and hierarchic equilibria. Furthermore, we show that for any specified system of dividends the set of such equilibria is generically finite. As a consequence, we have generic finiteness of Mas-Colell’s equilibria with slack, uniform dividend equilibria, and other special cases of our concept.     

Growth and fluctuations: The role of public dividends and public spending

In this paper, we consider a discrete-time version of the endogenous growth model developed by Barro [Barro, R.J., 1990. Government spending in a simple model of endogenous growth. Journal of Political Economy 98, 103–125], but augmented in order to envisage a public participation in the production of private goods. Public dividends are invested in order to provide a public good; in turn, the public good plays a role of indispensable production externality and, eventually, of growth engine.For what concerns the production of private goods, we find that an optimal policy is always based on a positive participation of the government as shareholder; also, when growth is slow, a public intervention or large substitution effects stabilize the economy.A right mix of short-run services and long-run infrastructures is suggested in slow economies to rule out expectation-driven fluctuations. Infrastructures are mainly recommended in presence of moderate income effects, while services are recommended in presence of strong income effects.     

Generalized weak transfer continuity and the Nash equilibrium

This paper introduces the notion of generalized weak transfer continuity and establishes that a bounded, compact locally convex metric quasiconcave and generalized weak transfer continuous game has a Nash equilibrium. Our equilibrium existence result neither implies nor is implied by the existing results in the literature such as those in [Carmona, G., 2011. Understanding some recent existence results for discontinuous games. Economic Theory 48, 31–45], [Prokopovych, P., 2011. On equilibrium existence in payoff secure games. Economic Theory 48, 5–16], [Carmona, G., 2009. An existence result for discontinuous games. Journal of Economic Theory 144, 1333–1340], and [Reny, P.J., 1999. On the existence of pure and mixed strategy Nash equilibria in discontinuous games, Econometrica 67, 1029–1056].     

Inconsequential arbitrage

We introduce the concept of inconsequential arbitrage and, in the context of a model allowing short-sales and half-lines in indifference surfaces, prove that inconsequential arbitrage is sufficient for existence of equilibrium. Moreover, with a slightly stronger condition of nonsatiation than that required for existence of equilibrium and with a mild uniformity condition on arbitrage opportunities, we show that inconsequential arbitrage, the existence of a Pareto optimal allocation, and compactness of the set of utility possibilities are equivalent. Thus, when all equilibria are Pareto optimal — for example, when local nonsatiation holds — inconsequential arbitrage is necessary and sufficient for existence of an equilibrium. By further strengthening our nonsatiation condition, we obtain a second welfare theorem for exchange economies allowing short sales.Finally, we compare inconsequential arbitrage to the conditions limiting arbitrage of Hart [Hart, O.D., 1974. J. Econ. Theory 9, 293–311], Werner [Werner, J., 1987. Econometrica 55, abs1403–1418], Dana et al. [Dana, R.A., Le Van, C., Magnien, F., 1999. J. Econ. Theory 87, 169–193] and Allouch [Allouch, N., 1999. Equilibrium and no market arbitrage. CERMSEM, Universite de Paris I]. For example, we show that the condition of Hart (translated to a general equilibrium setting) and the condition of werner are equivalent. We then show that the Hart/Werner conditions imply inconsequential arbitrage. To highlight the extent to which we extend Hart and Werner, we construct an example of an exchange economy in which inconsequential arbitrage holds (and is necessary and sufficient for existence), while the Hart/Werner conditions do not hold.     

On intermediate utility functions

Intermediate utility functions have been recently introduced by Persson and Tabellini (2000, Political Economics: Explaining Economics Policy, MIT Press, Cambridge) and ensure the existence of a majority voting equilibrium at multi-dimensional voting. Here, we show that monotone transforms of these utility functions also are sufficient for the existence of a Condorcet winner.     

Applicability of a spatial computable general equilibrium model to assess the short-term economic impact of natural disasters

Computable general equilibrium (CGE) models have been widely used to assess the economic impact of natural disasters, but the models have not been fully validated by applying them to real disasters. This study focuses on validating a model for use in a short-run case in which the functional recovery of infrastructure and businesses occurred on a time scale of a few months. A special attempt is made to determine the parameter values of elasticity of substitutions, which play an important role in the effect on supply chains. In this study, a spatial CGE model, in which Japan is divided into nine regions, is constructed and applied to the case of the 2011 Great East Japan Earthquake and Tsunami. Through this application, the best estimates of the elasticity parameters generated relatively consistent estimates of production change compared with the observed change, both in severely affected regions and in other regions.     

The relationship between carbon dioxide emissions and economic growth: quantile panel-type analysis

This paper samples the data of 138 countries during the 1971–2007 period, and performs an empirical test to validate the relationship between carbon dioxide emissions and economic growth. It first performs panel data analysis and quantile regression analysis to estimate the long-run elasticity relationships, and then analyzes the short-run error correction model to verify the causal relationship between the two. The empirical results indicate the following. (1) The long-run relationship between global carbon dioxide emissions and GDP is stable, with 32.6% of the sampled countries showing cross-coupling of the two (with an elasticity value of greater than 1), 47.1% reporting relative-decoupling (with an elasticity value between 0 and 1), and 20.3% seeing absolute-decoupling (with an elasticity value of smaller than 0). (2) The quantile regression shows that long-run elasticity declines along with the rise of carbon dioxide emission quantiles. In other words, cross-coupling turns into relative-decoupling. (3) The analysis of short-run panel data and quantile regressions mostly support the feedback relationship between carbon dioxide emissions growth and economic growth. This is consistent with the hypothesis developed by Kuznets. (4) According to the results of the quantile regression, the higher the quantiles, the faster and more stable of the short-run error-correction mechanism of the adjustments from short-run disequilibrium to long-run equilibrium. (5) Under the low-quantile carbon dioxide emissions growth and economic growth, the relationship between these two is not stable of the short-run disequilibrium adjustments in the error-correction adjustment process. However, the relationship between these two is steady and feedback in the case of high quantiles. Therefore, the first priority to combat global warming is to focus on the countries with high economic growth and high carbon dioxide emissions growth.     

R&D policy in a volatile economy

The literature on R&D-based growth establishes that market equilibrium is inefficient and derives optimal R&D policy. Normative analyses of this type use the assumption of steady state, largely motivated by analytical convenience. This paper questions this steady-state approach by introducing endogenous cycles as long-run equilibria. We show that the government fails to maximize welfare if policy which is optimal in steady state is myopically applied in cyclical equilibria. More specifically, we demonstrate that (i) cycles arise in the (very) standard R&D-based model of Grossman and Helpman [1991. Innovation and Growth in the Global Economy. MIT Press, Cambridge, MA (Chapter 3)] once the model is framed in discrete time, (ii) these cycles are inefficient in the sense that they prevent welfare maximization, (iii) optimal steady-state R&D policy fails to eliminate cycles, and can even create inefficient cycles, (iv) the application of R&D subsidies leads to a trade-off between growth and macroeconomic stability, and (v) optimal R&D policy in a fluctuating economy is state-dependent, which generalizes optimal steady-state R&D policy.     

Uniqueness conditions for strongly point-rationalizable solutions to games with metrizable strategy sets

This paper introduces the iterative solution concept of strong point-rationalizability as a strengthening of standard point-rationalizability by stipulating that any two players have identical beliefs about the strategy choices of their common opponents. By adopting and generalizing the contraction-property approach of Moulin [Moulin, H., 1984. Dominance solvability and cournot stability. Mathematical Social Sciences 7, 83–102] and Bernheim [Bernheim, B.D., 1984. Rationalizable strategic behavior. Econometrica 52, 1007–1028] we derive sufficient conditions for the existence of unique strongly point-rationalizable strategies in strategic games with best response functions. These uniqueness results are derived under fairly general assumptions and are especially useful for complete and bounded, as well as finite strategy sets. For games with monotonic individual best response functions, equivalence between a unique strongly point-rationalizable and a unique point-rationalizable solution in the standard sense is established. Furthermore, the existence of unique fixed points is proven under conditions that generalize for bounded metric spaces an established fixed point theorem by Bonsall [Bonsall, F.F., 1962. Lectures on Some Fixed Point Theorems of Functional Analysis. Tata Institute of Fundamental Research, Bombay] and Smart [Smart, D.R., 1974. Fixed Point Theorems. Cambridge University Press, Cambridge, London]. Possible extensions of our findings to games with multi-valued best response correspondences are discussed.     

New Economic Geography: An appraisal on the occasion of Paul Krugman's 2008 Nobel Prize in Economic Sciences

Paul Krugman has clarified the microeconomic underpinnings of both spatial economic agglomerations and regional imbalances at national and international levels. He has achieved this with a series of remarkably original papers and books that succeed in combining imperfect competition, increasing returns, and transportation costs in new and powerful ways. Yet, not everything was brand new in New Economic Geography. To be precise, several disparate pieces of high-quality work were available in urban economics and location theory. Our purpose in this paper is to shed new light on economic geography through the lenses of these two fields of economics and regional science.     

Trade and Geography: Paul Krugman and the 2008 Nobel Prize for Economics

Abstract

The 2008 Nobel Prize for economics was awarded to Paul Krugman for three papers—Krugman (1979, 1980, 1991). In this paper we illustrate that, indeed, these three papers are closely connected. We present a summary of the papers using a unified framework. Central in the discussion is the so-called home market effect that was already alluded to in Krugman (1979). We evaluate his work and conclude that these three papers changed and improved the way in which economists think about trade and geography.

Commerce et Géographie: Paul Krugman et le Prix Nobel 2008 en Économie

Résumé Dans la présent communication, nous illustrons la façon dont ces trois communications sont en rapport étroit. Nous présentons un récapitulatif sur ces communications, en suivant un cadre unifié. Au c?ur même de ces discussions se trouve ce que l'on appelle l'effet du marché intérieur, déjà évoqué dans Krugman (1979). Nous évaluons cet ouvrage, en concluant que ces communications ont changé et optimisé la façon dont les économistes conçoivent le commerce et la géographie.

Comercio y Geografía: Paul Krugman y el Premio Nobel 2008 en Economía

Résumén En este documento ilustramos que, de hecho, estos tres ensayos están estrechamente relacionados. Presentamos un resumen de los ensayos utilizando un marco unificado. Un factor fundamental del debate es el denominado efecto del mercado nacional, al que ya se había hecho alusión en Krugman (1979). Evaluamos este trabajo y concluimos que estos tres ensayos cambiaron y mejoraron la forma de pensar de los economistas sobre el comercio y la geografía.     

were the green belts wasted effort?

What have been the effects of development planning? Professor Donald Denman, Emeritus Professor of Land Economy at Cambridge University, argues that they have been self-defeating, at least in the case of the Green Belts. Professor Denman's autobiography, A Half and Half Affair: Chronicles of a Hybrid Don, will shortly be published by the Churchill Press.     

Existence of an equilibrium for infinite horizon economies with and without complete information

This work proves the existence of an equilibrium for an infinite horizon economy where trade takes place sequentially over time. There exist two types of agents: the first correctly anticipates all future contingent endogenous variables with complete information as in Radner [Radner, R. (1972). Existence of equilibrium of plans, prices and price expectations in a sequence of markets. Econometrica, 289–303] and the second has exogenous expectations about the future environment as in Grandmont [Grandmont, J. M. (1977). Temporary general equilibrium theory. Econometrica, 535–572] and information based on the current and past aggregate variables including those which are private knowledge. Agents with exogenous expectations may have inconsistent optimal plans but have predictive beliefs in the context of Blackwell and Dubbins [Blackwell, D., Dubins, L. (1962). Merging of opinions with increasing information. The Annals of Mathematical Statistics, 882–886] with probability transition rules based on all observed variables. We provide examples of this framework applied to models of differential information and environments exhibiting results of market selection and convergence of an equilibrium. The existence result can be used to conclude that, by adding the continuity assumption on the probability transition rules, we obtain the existence of an equilibrium for some models of differential information and incomplete markets.