Minimaximin results with applications to economic equilibrium

Abstract theorems are proved that can be used to establish the existence of a free disposal equilibrium in some infinite dimensional models of the economy. The results generalize those previously proved in that they apply to concave–convex functions rather than bilinear functions and excess demand correspondence dedicated to Professor Heinz König rather than excess demand functions.     

Satiation and existence of competitive equilibrium

In this paper, we introduce a new assumption concerning the (non)satiation property of preferences and establish the existence of a competitive equilibrium under it. The assumption is weaker than the standard nonsatiation assumption and “weak nonsatiation” introduced by Allouch and Le Van (2008). In particular, it allows preferences to be satiated only inside the set of individually rational feasible consumptions, while the two nonsatiation assumptions do not. It is also worth noting that just like the two nonsatiation assumptions, our new assumption depends solely on the characteristics of consumers.     

Some general results for moments in bivariate distributions

The purpose of this paper is to present a closed formula to compute the moments of a general function from the knowledge of its bivariate survival function. The result is derived by utilizing an integration by parts formula for two variables, which is not readily available in the literature. Many of the existing results are obtained as special cases. Finally, two examples are presented to illustrate the results. In both the examples, mixed moments as well as moments for the series system and parallel system are obtained. The integration by parts formula in two variables, derived here, is of interest in its own right and we hope that it will be useful in other investigations. The integration by parts formula in two variables is derived as a special case of a general formula in n variables.     

Some results about averaging in stochastic approximation

The paper presents some results concerning the averaging approach in a general linear regression model in one dimension under suitable conditions about the martingale structure of errors. At first asymptotics of the primary and averaged estimators are discussed. Then it is shown that variances of estimators can be consistently estimated by appropriate integrated squared deviations functionals. Finally applications to the construction of confidence regions are considered.     

On the existence of walrasian equilibrium in large-square economies

An existence theorem for Walrasian equilibrium is demonstrated for an economy with a continuum of consumers and an infinite-dimensional commodity space, such as l₁ or c₀, having an ‘order-compatible’ basis.     

深化经济责任审计的几点意见

经济责任审计是广大审计干部在实践中创造,并受到党中央、国务院充分肯定的,具有中国特色的一项审计工作.自从1999年中办、国办两个通知下发以后,这项工作进展很快,全国各地在经济责任审计方面取得了可喜的成绩.这里我就如何深入开展这项工作讲几点具体意见.     

On existence of optimal programs: The RSS model without concavity assumptions on felicities

In the context of a model due to Robinson, Solow and Srinivasan (the RSS model) with time-dependent felicity functions that are not necessarily concave, we report a theorem on the existence of optimal programs. An extended introduction places our theorem in the context of previous work on the existence question.     

Macroeconomic scenarios for the south Mediterranean countries: Evidence from general equilibrium model simulation results

The “Arab spring” aftermath calls for a closer look at the developments in the south Mediterranean countries. This paper develops and assesses alternative scenarios for the region up to the year 2030 with the employment of GEM-E3, a computable general equilibrium model. The scenarios quantify three alternative visions of the regional future which assume: (i) south Mediterranean-EU cooperation, (ii) south Mediterranean global opening and (iii) escalation of regional conflicts and failure to cooperate. The scenarios are compared to the baseline scenario, which assumes a continuation of the regional policies observed in the recent past. Assumptions on trade integration, infrastructure, population and governance developments are adopted in each scenario. Infrastructure upgrades and governance improvements within an EU cooperation context are found to benefit the region most. The findings have important policy implications indicating alternatives to be implemented.     

On the existence of equilibrium in social systems with coordination

Social systems with coordination were introduced by Vind (1983) as a general model of economic institutions. The present paper gives a general existence theorem for equilibria in social systems with coordination extending Vind's result.     

The existence of equilibrium when excess demand obeys the weak axiom

This paper gives a non-fixed point theoretic proof of equilibrium existence when the excess demand function of an exchange economy obeys the weak axiom of revealed preference.     

Existence of equilibrium actions and of equilibrium : A note on the ‘new’ existence theorems

A lemma by Ky Fan, which asserts the existence of a maximal element relative to some ordering (an equilibrium action) in a compact choice set, is extended to a larger class of orderings. This extension allows one to generalize slightly several existence theorems and seems to be useful for the applications. Kakutani's fixed-point theorem and the existence of an equilibrium in a generalized game are used to exemplify this. In the last case the method of proof may be of some independent interest involving, as it does, the reduction of an n-person game to a corresponding 1-person game.     

The core-periphery model: A note on the existence and uniqueness of short-run equilibrium

We consider the core-periphery model [P. Krugman, Increasing returns and economic geography, Journal of Political Economy 199 (1) (1991) 483–499]. The nature and stability of the possible steady states of the model have been made progressively precise; [M. Fujita, P. Krugman, A. Venables, The Spatial Economy. Cities, Regions and International Trade, MIT Press, Cambridge, 1999; R. Baldwin, R. Forslid, Ph. Martin, G. Ottaviano, F. Robert-Nicoud, Economic Geography and Public Policy, Princeton Univ. Press, 2003]. In that model as well as in all the new economic geography models that have been derived from it, the short-run (instantaneous) equilibrium is implicitly determined by the current labor distribution across regions. The numerical computations used so far to determine the short-run equilibrium, tend to suggest its existence. In this paper, an existence and uniqueness proof of short-run equilibrium is provided.     

Limited arbitrage is necessary and sufficient for the existence of an equilibrium

In Chichilnisky (Working Paper No. 586, 1991), Chichilnisky (Working Paper No. 650, 1992) and Chichilnisky (Economic Theory, 1995, 5, 79–108), I introduced the concept of a global cone and used it to define a condition on endowments and preferences, ‘limited arbitrage’, which I showed to be necessary and sufficient for the existence of a competitive equilibrium. In response to a comment (Monteiro et al., Journal of Mathematical Economics, 1997, 26, 000-000), I show here that the authors misunderstood my results by focussing on brief announcements which cover other areas, social choice (Chichilnisky, American Economic Review, 1994, 427–434 and algebraic topology (Chichilnisky, Bulletin of the American Mathematical Society, 1993, 29, 189–207), rather than on the publication which contains may proofs on equilibrium. The comment's example is irrelevant to my results in Chichilnisky (Economic Theory, 1995, 5, 79–108) because it starts from different conditions. Limited arbitrae is always necessary and sufficient for the existence of a competitive equilibrium, with or without short sales, with the global cones as I defined them, and exactly as proved in Chichilnisky (Economic Theory, 1995, 5, 79–108).     

The current non-status of general equilibrium theory

This paper argues that the abandonment of general equilibrium theory by microeconomists was a mistake. It provides counter arguments to two of the reasons for that abandonment—lack of both generality and consistency with methodological individualism in uniqueness and stability analysis of equilibria—and urges microeconomists to refocus some of their attention on it.     

The general equilibrium effects of congestion externalities

This is the second in a series of three articles on the topic of congestion externalities. We use an urban general-equilibrium model to compute two types of cities: the market-equilibrium city, in which congestion externalities occur, and the optimum city. The optimum city has a more dispersed distribution of employment, and a more concentrated distribution of residence. If the population of the city is fixed, the optimum pricing of transportation generates a per capita welfare gain of $3.78 per week. If the population of the city is endogenous, the internalization of congestion externalities causes the city to grow.     

A simple proof of the existence of an equilibrium when the weak axiom holds

An elementary proof of the existence of a competitive equilibrium is given for economies where the weak axiom holds. It is shown by an induction argument on the number of goods that the problem is reduced to the question of the existence of an equilibrium in a two-good economy.