Smooth preferences and the regularity of equilibria

To study equilibria we describe an economy by its distribution of consumers' preferences and endowments. All preferences are smooth and weakly convex. Demand of an economy need not be single valued, but there is an open dense set of economies for which demand is a C¹-function in a neighborhood of the equilibrium prices. We call an economy regular if its excess demand is transversal to zero. A regular economy has locally unique equilibria. It is shown that regular economies form an open dense set on which the equilibrium price correspondence varies continuously and the number of equilibria is locally constant.     

Equilibria with coordination failures

This paper extends the literature on equilibria with coordination failures to arbitrary convex sets of admissible prices. This makes it possible to address coordination failures for cases with price indexation or more general price linkages between commodities. We introduce a new equilibrium concept, called quantity constrained equilibrium (QCE), giving a unified treatment to all cases considered in the literature so far. At a QCE the expected trade opportunities on supply and demand are completely determined by a rationing vector satisfying that the prevailing price system maximizes the value of the rationing vector within the set of admissible prices. When the set of admissible prices is compact, we show the existence of a connected set of QCEs. This set connects two trivial no-trade equilibria, one with completely pessimistic expectations concerning supply opportunities and one with completely pessimistic expectations concerning demand opportunities. Moreover, the set contains for every commodity a generalized Drèze equilibrium, being a QCE at which for that commodity no binding trade opportunities on both supply and demand are expected, and also a generalized supply-constrained equilibrium at which no binding constraints on demand opportunities are expected and for at least one commodity also not on supply. We apply this main result to several special cases, and also discuss the case of an unbounded set of admissible prices.     

Utility perturbations and the equilibrium price set

For pure exchange economies in which agents are described by a compact smooth manifold of smooth strictly monotonic and strictly concave utilities, it is shown that, at least generically, the equilibrium price set is a smooth manifold of the same dimension. Given any smooth selection from the equilibrium price manifold and any sufficiently close smooth function, the function is a selection from the equilibrium price correspondence for some manifold of economies close to the original one. In particular, the set of equilibria corresponding to any open neighborhood of an economy contains an open subset of the price simplex.     

Analysis of a dynamic, decentralized exchange economy

A model of a dynamic exchange economy is presented. Similarly to the Walrasian equilibrium problem, each consumer is characterized by a feasible set and by an instantaneous demand function, that depends on the price vector, time, and the commodity holding. The commodity holding of each consumer varies, at each moment, according to this instantaneous demand function. We show that the market can choose prices that keep the commodity holding of each consumer within his consumption set, while ensuring that the aggregate commodity holding satisfies the scarcity constraints of the market.     

On the structure of the set of fixed price equilibria

Working in the framework suggested by Drèze, this paper studies the number of fixed price equilibria and their continuity with respect to the price system. In an exchange economy, the concept of a rationing scheme is introduced, which specifies how shortages are shared among agents. For given utility functions and a given rationing scheme, under standard assumptions, an existence theorem is recalled, and it is shown that the graph of the equilibrium correspondence, when prices and initial endowments vary, is a piecewise continuously differentiable manifold. Moreover, generically, the number of equilibria for an economy, at given prices, is finite and the set of equilibria varies continuously with the price system and the initial endowments.     

Indivisible commodities and an equivalence theorem on the strong core

We consider a pure exchange economy with finitely many indivisible commodities that are available only in integer quantities. We prove that in such an economy with a sufficiently large number of agents, but finitely many agents, the strong core coincides with the set of expenditure-minimizing Walrasian allocations. Because of the indivisibility, the preference maximization does not imply the expenditure minimization. An expenditure-minimizing Walrasian equilibrium is a state where, under some price vector, all agents satisfy both the preference maximization and the expenditure minimization.     

Wage gradients,rent gradients,and the price elasticity of demand for housing: An empirical investigation

As developed in Muth's “Cities and Housing,” attainment of locational equilibrium within an urban area implies a necessary functional correspondence between wage and price gradients and the compensated price elasticity of demand for housing. In this paper estimates of the rent and wage gradients are utilized to generate price-elasticity estimates via this equilibrium correspondence. The Box-Cox transformation technique is used with data from the metropolitan Chicago area to test for the functional forms of the wage and rent gradients. The optimal maximum-likelihood functional forms for both gradients yield a price-elasticity estimate of ?0.40.     

Characterization of the Walrasian equilibria of the assignment model

We study the assignment model where a collection of indivisible goods are sold to a set of buyers who want to buy at most one good. We characterize the extreme and interior points of the set of Walrasian equilibrium price vectors for this model. Our characterizations are in terms of demand sets of buyers. Using these characterizations, we also give a unique characterization of the minimum and the maximum Walrasian equilibrium price vectors. Also, necessary and sufficient conditions are given under which the interior of the set of Walrasian equilibrium price vectors is non-empty. Several of the results are derived by interpreting Walrasian equilibrium price vectors as potential functions of an appropriate directed graph.     

First price package auction with many traders

This paper studies a first price package auction in which multiple sellers participate in addition to multiple buyers. We generalize the notion of the profit-target strategy which is first introduced as a truthful strategy in a first price package auction with a single seller by Bernheim and Whinston (1986b). We then show that the set of equilibrium payoffs in profit-target strategies is equal to the bidder-optimal core, and is also equal to the set of coalition-proof Nash equilibria. Using this result, we find that any equilibrium payoff vector is weakly Pareto-dominated by the VCG payoff vector for buyers, and that the Walrasian competitive equilibrium payoff vector is weakly Pareto-dominated by some equilibrium payoff vector for buyers, even if goods are substitutes. This contrasts with the first price package auction with a single seller, in which it is shown that if goods are substitutes, then those three outcomes are payoff-equivalent.     

A Theoretical Analysis of Liner Shipping Conferences and Strategic Alliances

We analyze the economic impacts of industrial organizational struggles on the international liner shipping market. Operating ratios of different markets are discussed by incorporating rate, service level, and other variables into a standard microeconomic model. If two different carriers agree on a shipping conference price and/or share a strategic alliance service level, and maximize consolidated profit, a member carrier finds it easier to make its operation profitable than the individual profit optimization case; other carriers are worse off in becoming profitable. If the carriers face inelastic demand, the price continues rising until demand becomes elastic enough for the equilibrium to be relevant. The conference is expected to play a coordination role so that the market does not become unsustainable in the adjustment process to reach equilibrium.     

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.     

Global analysis and economics IV : Finiteness and stability of equilibria with general consumption sets and production

Among other things a global version of the fundamental theorem of welfare economics is proved. One starts with a pure exchange economy with fixed total resources where hypotheses of differentiability, convexity, and monotonicity are made on the utility functions. Let be the set of price equilibria where the initial allocation coincides with the final one. Then the map which assigns to such a price equilibrium, the corresponding allocation is a diffeomorphism (a complete correspondence) between and the set of Pareto Optima.     

Global analysis and economics III: Pareto Optima and price equilibria

Among other things a global version of the fundamental theorem of welfare economics is proved. One starts with a pure exchange economy with fixed total resources where hypotheses of differentiability, convexity, and monotonicity are made on the utility functions. Let ? be the set of price equilibria where the initial allocation coincides with the final one. Then the map which assigns to such a price equilibrium, the corresponding allocation is a diffeomorphism (a complete correspondence) between ? and the set of Pareto Optima.     

Equilibrium selection in games: the mollifier method

This paper introduces an embedding of a Nash equilibrium into a sequence of perturbed games, which achieves continuous differentiability of best responses by mollifying them over a continuously differentiable density with compact support (window size). Along any sequence with shrinking window size, the equilibria are single-valued whenever the function has a regular Jacobian and the set of equilibria where it is singular has measure zero. We achieve a further reduction of the equilibrium set by inserting within the embedding a procedure that eliminates the strict interior of equilibrium sets. The mollifier can be approximated consistently using kernel density regression, and we sketch a non-stationary stochastic optimization algorithm that uses this approximation and converges with probability one to an equilibrium of the original game.     

A remark on the fiscal theory of price determination

The fiscal theory of price determination asserts that the price level is determined by the ratio of nominal public debt to the present value of real primary surpluses. To show its fragility, we describe a simple monetary economy with an infinitely lived real productive asset. Under the hypotheses of the fiscal theory, speculative bubbles occur at equilibrium, thus leading to an indeterminate price level.     

A remark on the fiscal theory of price determination

The fiscal theory of price determination asserts that the price level is determined by the ratio of nominal public debt to the present value of real primary surpluses. To show its fragility, we describe a simple monetary economy with an infinitely lived real productive asset. Under the hypotheses of the fiscal theory, speculative bubbles occur at equilibrium, thus leading to an indeterminate price level.     

Evolution in a General Equilibrium framework

In this paper, we consider a general equilibrium model in which the economies are characterized by the distribution of firms on a set of branches of production; we will show that based on the decisions of the managers of the firms, it is possible to build a dynamic system whose solutions reproduce the possible trajectories of the economy. Once the initial state of an economy is known, that is, the initial distribution of firms, we will have a unique solution for this dynamic system, which will coincide with the evolution of the economy, that is, the evolution of prices and equilibrium allocations.The investment decisions of the administrators of the companies will change the distribution over the set of existing productive branches, which in turn will produce changes in the wealth of consumers who are also shareholders of the companies and then as a consequence, their demand will change, and therefore the equilibrium allocations and prices will too.In most cases, these decisions lead to an improvement in the efficiency of the productive side of the economy and an increase in the welfare of the economy as a whole, but, as we will show, under some particular circumstances, even when it comes to rational decisions from the point of view of administrators, this can lead to undesirable repercussions on the welfare of consumers. Besides, in a neighborhood of a critical economy, even when these decisions may involve small changes in the distribution of companies, they can cause abrupt and unexpected changes in the behavior of the economy, or in other words, they can cause an economic crisis. These are characterized by large changes in the prices, in the demand, and in the supply of goods. In contrast, in a sufficiently small neighborhood of a regular economy, small changes in the distribution of firms produced by the investment decisions of managers do not lead to large changes in the subsequent behavior of the economy. We will exemplify these statements with several numerical examples.     

Existence of a competitive equilibrium when all goods are indivisible

This paper investigates an economy where all consumption goods are indivisible at the individual level, but perfectly divisible at the overall level of the economy. In order to facilitate trading of goods, we introduce a perfectly divisible parameter that does not enter into consumer preferences — fiat money. When consumption goods are indivisible, a Walras equilibrium does not necessarily exist. We introduce the rationing equilibrium concept and prove its existence. Unlike the standard Arrow–Debreu model, fiat money can always have a strictly positive price at the rationing equilibrium. In our set up, if the initial endowment of fiat money is dispersed, then a rationing equilibrium is a Walras equilibrium. This result implies the existence of a dividend equilibrium or a Walras equilibrium with slack.     

甘肃省电力需求的协整与误差修正分析

以甘肃省1978-2012年数据为例,采用协整与误差修正模型技术研究了甘肃省电力需求的决定因素,建立了甘肃电力需求函数,检验了电力需求与国内生产总值、电力价格、经济结构、电力使用效率之间的长期均衡关系及短期波动关系。     

Productivity dispersion: facts,theory, and implications

This paper discusses the stylized facts, the theory, and the remaining problems of productivity dispersion, which is essentially related to the concept of equilibrium in the neoclassical theory. Empirical study of data relating to Japanese firms shows that they all obey the Pareto law, and also that the Pareto index decreases with the level of aggregation. In order to explain these two stylized facts we propose a theoretical framework built on the basic principle of statistical physics and on the concept of superstatistics, an approach that accommodates fluctuations of aggregate demand. We show that the allocation of production factors depends crucially on the level of aggregate demand, and that the higher the level of aggregate demand, the closer the economy is to the frontier of the production possibility set.