Inverse of the Berge maximum theorem

Summary We consider an inverse of the Berge maximum theorem. We also give an application of our result to fixed point theory.     

A general-equilibrium re-appraisal of the Stolper-Samuelson theorem

This paper conducts a general-equilibrium analysis of the Heckscher-Ohlin model in which product price is endogenized. It applies both marginal and infra-marginal comparative-static analyses to examine the co-movement of factor and product prices. It shows that the Stolper-Samuelson theorem's prediction does not always hold, in particular, it does not always hold inside the diversification cone when changes in production parameters lead to changes in prices; or when the general equilibrium jumps from one structure to another. The result of this paper supports the everything-possible theorem and casts doubt on the general applicability of other core trade theorems derived from the same framework as the Stolper-Samuelson theorem.     

A refinement of the core equivalence theorem

It is known that if blocking coalitions are restricted to be small relative to the size of the economy then the approximation of core allocations by competitive allocations can still be assured. This paper proves that the same type of approximation result is valid if the absolute size of the blocking coalition is bounded. The methods of Anderson (1978) are applied.     

A new proof of the maximum principle

Summary. We offer a new proof of the maximum principle, by using the envelope theorem that is frequently used in the standard microeconomic theory. Received: April 11, 2002; revised version: June 26, 2002 Correspondence to: K. Shimomura     

A unifying impossibility theorem

This paper identifies and illuminates a common impossibility principle underlying a number of impossibility theorems in social choice. We consider social choice correspondences assigning a choice set to each non-empty subset of social alternatives. Three simple axioms are imposed as follows: unanimity, independence of preferences over infeasible alternatives, and choice consistency with respect to choices out of all possible alternatives. With more than three social alternatives and the universal preference domain, any social choice correspondence that satisfies our axioms is serially dictatorial. A number of known impossibility theorems—including Arrow’s Impossibility Theorem, the Muller–Satterthwaite Theorem, and the impossibility theorem under strategic candidacy—follow as corollaries.     

A clarification of the interest rate parity theorem

Recognition of the role of market-makers in the euro-deposit and exchange markets, makes it necessary to re-formulate the interest rate parity theorem's predicted equilibrium relationship between forward exchange rates and interest rates in terms of a set of inequalities, rather than an equation. A euro-bank quotes typically for two-way business in euro-currency deposits swaps, outright forward exchange and spot exchange. It must decide whether to quote for each directly or indirectly, by combining quotes from two or more of the other markets. Where indirect (satellite) quotation prevails the inequalities collapse into continuous identities. Market conditions which favour direct compared to indirect quotation are assessed.     

A wide range no-regret theorem

In a sequential decision problem at any stage a decision maker, based on the history, takes a decision and receives a payoff which depends also on the realized state of nature. A strategy, f, is said to be as good as an alternative strategy g at a sequence of states, if in the long run f does, on average, at least as well as g does. It is shown that for any distribution, μ, over the alternative strategies there is a strategy f which is, at any sequence of states, as good as μ-almost any alternative g.     

A simple proof of K-K-M-S theorem

Summary We give a simple proof of the K-K-M-S theorem based on the Kakutani fixed point theorem, the separation theorem for convex sets and the Berge maximum theorem.The author is grateful to Gerard Debreu for his advice and to Tatsuro Ichiishi, Michael Todd, Rajiv Vohra, Nicholas Yannelis, Lin Zhou and two anonymous referees for their comments. The original version of this note was written in the fall 1992 while the author was visiting the Department of Economics, University of California at Berkeley.     

A theorem on open coverings of a simplex and Scarf's core existence theorem through Brouwer's fixed point theorem

Summary This paper provides simple proofs of a theorem on open coverings of a simplex and Scarf's core existence theorem through Brouwer's fixed point theorem.I want to thank Daniel Abrams, Yakar Kannai, Herbert Scarf, Nicholas Yannelis, Jingang Zhao, and an anonymous referee for their helpful comments. I also gratefully acknowledge the financial support from the Alfred P. Sloan Foundation.     

A constructive proof of the ordinal efficiency welfare theorem

We provide a non-geometric constructive short proof of the ordinal efficiency welfare theorem.     

A note on the fundamental theorem of exact aggregation

If individual i's demands for a commodity are a function of prices, p, income M_i and a vector of attributes A_i, then aggregate demand is

This paper derives the necessary and sufficient conditions of f_i, F and a system of functions g_k(M₁,…,M_N,A₁,…,A_N) symmetric in the M's and A's such that F can be written in the form F(p, g, (M₁,…,M_n,A₁,…,A_N),…, g_n(M₁,…,M_n,A₁,… ,A_n)) for all values of its arguments.     

A counterexample to the folk theorem with discounting

The ‘folk theorem’ formalizes the theme that ‘repetition leads to cooperation’. We present an example showing that, even with perfect monitoring, the set of Nash equilibria of the discounted games does not have to converge to the feasible, individually rational set, i.e., this version of the ‘folk theorem’ can break down.     

A generalized hazard rate

We present a general class of probability functions in which the hazard rate depends on both time and a shift parameter. It is used, for example, to generalize a model of innovation due to Loury and Dasgupta and Stiglitz.     

A generalized specification test

In a non-linear parametric setting, a class of specification tests developed by Hausman (1978) is extended to accomodate a singular covariance matrix. An application to limited information tests for the exogeneity of instrumental variables is presented.     

A short proof of Harsanyi''s purification theorem

A short proof of more general version of Harsanyi's purification theorem is provided through an application of a powerful, yet intuitive, result from algebraic topology.