A Generalization of Continuity and Convexity Conditions for Correspondences in Economic Equilibrium Theory

Fixed-point theorems for multi-valued mappings and economic equilibrium existence theorems are generalized from the viewpoint that the continuity and/or convexity assumptions on a mapping may be replaced by weaker local conditions on the vector field defined by the mapping. The generalization gives us natural conditions on individual (possibly non-ordered) preferences or aggregated demand behaviours so that we may obtain several extensions of recent results in social and game-theoretic equilibrium theories.
JEL Classification Numbers: C60, C62, C72, D50, D51.     

HOW LONG SHOULD WE STAY IN EDUCATION IF ABILITY IS SCREENED?

We examine how ability‐screening affects demand for education and the shape of an optimal education system. Explicitly incorporating gradual screening by education into the model, we illustrate how individuals of different abilities decide to stay in education or drop out. Gradual screening induces low‐ability individuals to receive over‐education, reducing the net benefit obtained from education by society as a whole, as well as such individuals. A mixed education system, in which public education is provided before private education, is superior to a wholly private system, in terms of both efficiency and equity, because it reduces the over‐education of low‐ability individuals.     

Indonesia After the Asian Crisis*

Indonesia was deeply affected by the 1997–1998 crisis, more so than its East Asian neighbors. Its economic contraction was deeper and more prolonged. It was the only one to experience a (temporary) loss of macroeconomic control. It also suffered “twin crises,” in the sense that its serious economic and financial problems were accompanied by regime collapse. Consequently, recovery was a slow and complex process, as new institutions had to be created, and old ones reformed under successive short‐lived administrations. But this process is largely over. The directly elected president with a strong popular mandate is in power. The new institutional framework for economic policy‐making is in place. Macroeconomic stability has been restored. Although growth has yet to return to pre‐crisis levels, by 2004 per capita income and poverty incidence had recovered to levels prevailing in the mid‐1990s, and in the circumstances economic recovery has arguably proceeded about as quickly as could reasonably have been expected.     

The spirit of capitalism, stock market bubbles and output fluctuations

This paper presents a representative agent model in which stock market bubbles cause output fluctuations. Assuming that utility depends directly on wealth, we show that stock market bubbles arise if the marginal utility of wealth does not decline to zero as wealth goes to infinity. Bubbles can affect output positively or negative depending on whether the production function exhibits increasing or decreasing returns to scale. In sunspot equilibria, the bursting of a bubble is followed by a sharp decline in output one period later. Various numerical examples are given to illustrate the behavior of stochastic bubbles and the relationship between bubbles and output.     

Böhm-Bawerk and Shibata on power or market

In 1935 the Japanese economist Shibata criticized Böhm-Bawerk's discussion to deny the role of power on market and argued that the validity of Böhm-Bawerk's conclusion depends crucially on his special assumptions on the structure of production in his theory of interest. Unfortunately, both Böhm-Bawerk and Shibata used in their discussions an untenable supposition that the value of heterogeneous capital, which depends on values of endogenous variables, can be given exogenously. Our aim is to reconsider the problem in the light of a new interpretation of Böhm-Bawerk's theory of interest, which is free from this supposition.     

A nonsmooth, nonconvex model of optimal growth

This paper analyzes the nature of economic dynamics in a one-sector optimal growth model in which the technology is generally nonconvex, nondifferentiable, and discontinuous. The model also allows for irreversible investment and unbounded growth. We develop various tools to overcome the technical difficulties posed by the generality of the model. We provide sufficient conditions for optimal paths to be bounded, to converge to zero, to be bounded away from zero, and to grow unboundedly. We also show that under certain conditions, if the discount factor is close to 1, any optimal path from a given initial capital stock converges to a small neighborhood of the golden rule capital stock, at which sustainable consumption is maximized. If it is maximized at infinity, then as the discount factor approaches 1, any optimal path either grows unboundedly or converges to an arbitrarily large capital stock.     

Lattice structure of knowledge and agreeing to disagree

This paper is a contribution to the study of the underlying mathematical structure of common-knowledge, which gives the well-known result of Aumann about the impossibility of ‘agreeing to disagree’. We present the Bayesian subjective probability model with player's belief: i.e. a triple (? %plane1D;4AF;, μ), in which i is a player. ? is a lattice in the field of sets of a state space Ω, %plane1D;4AF;, is a correspondence assigning to each state ω a filter %plane1D;4AF;(ω) in ?, and μ is a common-prior. For this model, we impose none of the important restrictions on the information structure in the Aumann-Bacharach model: axiom of knowledge K₁. axiom of transparency K₂ and axiom of wisdom K₃. We can extend both the disagreement theorem of Aumann and the agreement theorem of Geanacoplos and Polemarchakis under the assumption that each ? is an Artinian lattice.     

EQUILIBRIUM SELECTION IN THE YANO MODEL OF PRICE LEADERSHIP

Abstract. A number of studies have provided a theoretical explanation for the fact that the technologically superior firm becomes a price leader in a duopoly market for a homogeneous product. While previous studies show that the state in which the technologically superior firm becomes a price leader is a Nash equilibrium (superior leader equilibrium), they do not eliminate the possibility that the state in which the technologically inferior firm becomes a price leader is also a Nash equilibrium (inferior leader equilibrium). We demonstrate that an inferior leader equilibrium can be eliminated by the iterative elimination of weakly dominated strategies.     

Intertemporal substitution, risk aversion and ambiguity aversion

Summary. This paper axiomatizes a form of recursive utility on consumption processes that permits a role for ambiguity as well as risk. The model has two prominent special cases: (i) the recursive model of risk preference due to Kreps and Porteus [18]; and (ii) an intertemporal version of multiple-priors utility due to Epstein and Schneider [8]. The generalization presented here permits a three-way separation of intertemporal substitution, risk aversion and ambiguity aversion.Received: 5 August 2003, Revised: 12 March 2004, JEL Classification Numbers: D80, D81, D90.I am grateful to Larry Epstein for his guidance and invaluable advice, and to a referee for helpful comments and suggestions.     

A dynamic quantity adjustment process in a small open economy,and welfare effects of tariff changes

Considered an n-good small open economy where the technology is strictly convex and ad valorem tariffs are imposed. In this world it is known that the tariff-utility relationship may be perverse. The fact is known as the Vanek–Bhagwati Paradox. The source of the perversity is found in aggregate income effects. The present paper shows that D-stability of our dynamic system implies non-perverse aggregate income effects, and hence the non-perverse tariff-utility relationship.