Yves Balasko

The Structure of Financial Equilibrium with Exogenous Yields: The Case of Incomplete Markets

This paper presents an analysis of the structure of competitive equilibrium in a smooth, exchange economy where there are incomplete markets in financial instruments whose overall payoffs (both prices and yields) are fixed in units of account. The main result establishes that such market incompleteness generates a comparable degree of allocation indeterminateness. It is also shown how this real indeterminacy may increase when prices and yields are treated as variables rather than parameters. Copyright 1989 by The Econometric Society.

Existence of competitive equilibrium in a general overlapping-generations model

In the companion paper [2], Balasko and Shell establish existence of competitive equilibrium for a pure-distribution, overlapping-generations economy without money (see, especially, Propositions (3.10) and (3.11) in Section 3). That argument is remarkably simple, but depends critically on some strong hypotheses concerning individual tastes and endowments. In particular, it is assumed that, in any given period, every living consumer has a utility function which is strictly increasing in every available commodity, as well as an endowment which is strictly positive in every available commodity. These two assumptions are especially difficult to rationalize in an intergenerational context. How many teen-agers do you know who are eager viewers of Lawrence Welk? How many “middle-agers” who are likely users of Clearasil? So much for increasing (much less strictly increasing) utility functions! Regarding strictly positive endowments, we invite the reader to dream up his/her own counterexamples. (Another hint: How do you respond to the commonly heard lament, “What I wouldn’t give to be young again!“?) In the present paper, we do away with such unrealistically severe hypotheses. And we do more. Following the Arrow-Debreu tradition, we postulate fairly mild conditions on individual tastes and endowments. Of course, in line with the same tradition, we must then impose some further conditions on the potential economic interrelationships among consumers. This additional structure is an application to the overlapping-generations model of McKenzie’s basic concept of irreducibility.

The structure of financial equilibrium with exogenous yields : The case of restricted participation

Abstract We analyze the competitive equilibria in a model in which there are two periods, with uncertainty in the second, and households exchange both physical commodities and financial instruments - or current and future credit - on the spot market in the first period. Future returns from the financial instruments are fixed in terms of units of account (exogenous yields), and households face linear homogeneous constraints on their opportunities for transacting in financial instruments (restricted participation). Our main result establishes that if enough households are subject to the same constraints on exchanging credit, then restricted participation leads to a degree of real indeterminacy comparable to that obtaining in a model where there are simply too few available financial instruments (incomplete markets).

Budget-constrained Pareto-efficient allocations

Abstract This paper is concerned with a study of budget-constrained Pareto-efficient (BCPE) allocations, i.e., allocations which given a price system satisfy a given income distribution. We prove existence, show structural stability, and establish a sufficient condition for uniqueness of BCPE allocations. These properties of the BCPE allocations are deduced from similar properties of Walrasian equilibria by a duality theory which is of independent interest.

Market Participation and Sunspot Equilibria

We investigate the structure of competitive equilibria in an exchange economy parametrized by (i) endowments and (ii) restrictions on market participation. For arbitrary regular endowments, if few consumers are restricted, there are no sunspot equilibria. If endowments are allowed to vary, while restrictions on market participation are fixed, there is a generic set of preferences such that sunspot equilibria exist for a non-empty subset of endowments. Our analysis extends to the general case of an arbitrary number of restricted consumers the results of Cass and Shell for the polar cases in which either (i) no consumers are restricted or (ii) all consumers are restricted.

A geometric approach to equilibrium analysis

This article represents an attempt to deal with singular economies and related subjects. We use a geometric approach based on intersecting suitable manifolds and affine spaces embedded in some Euclidean space. This purely geometric theory is in fact in duality with Walrasian equilibrium theory. This approach provides a deeper insight in several subjects such as the structure of the set of critical equilibria, the characterization of economies with a unique equilibrium, the global properties of economies with several equilibria.

The set of regular equilibria

Abstract Debreu has shown that the set of regular economies is open dense. This paper investigates the closely related issue of the size of the set of regular equilibria. It is shown that this set is an open dense subset of the equilibrium manifold. The proof exploits the real algebraic nature of the set of critical equilibria belonging to any given fiber of the equilibrium manifold. This proof yields as by-product an alternative proof of Debreus theorem, a proof that does not hinge on Sards theorem.

Equilibrium Analysis of the Infinite Horizon Model with Smooth Discounted Utility Functions

Abstract The equilibrium set and the natural projection are studied within the setup of the pure exchange infinite-horizon model with a finite number of infinitely lived agents, utility functions belonging to the smooth discounted variety, and individual endowments being variable. We show that the equilibrium set has convex fibers, which implies arc-connectedness and, more generally, contractibility. We also show that the sets of regular equilibria and of regular economies are open and dense for the product topology. Therefore, it is generically true that the equilibria of infinite-horizon economies with smooth discounted utility functions can be approximated by those of finite-horizon truncated economies.

The natural projection approach to the infinite-horizon model

Abstract We extend the approach through the natural projection to the infinite-horizon general equilibrium model with smooth, discounted utility functions. We show that the natural projection is a smooth, proper Fredholm map of index zero. This enables us to define its Brouwer degree. We then show that this degree is equal to one, which yields an alternative proof of the existence of equilibria. A variant of Smales infinite dimensional extension of Sards theorem implies that the set of regular economies is open and dense.

Regular Demand with Several, General Budget Constraints

The past several years have witnessed burgeoning interest in models of competitive equilibrium with incomplete financial markets. Unlike the earlier development of the now standard Walrasian theory, this later development has passed very quickly from concern with the fundamental properties of existence and optimality to more general concern with the structure of the equilibrium set from the differentiable viewpoint.1 There are a number of plausible explanations for this rapid shift of emphasis. The presence of a large literature on smooth Walrasian models (see, for instance, the extensive references in Balasko, 1988) is surely by itself quite important. However, two substantive considerations stand out: first, in some formulations of the model with incomplete markets (e.g., where nominal yields on financial instruments are taken to depend linearly on spot prices for physical commodities), perhaps the most basic question about equilibrium — existence — is best answered in generic terms. Second, in other formulations of the model (e.g., where nominal yields are taken to be exogenous to the markets under consideration), perhaps the most critical property of equilibrium, multiplicity (or indeterminacy), is best characterised in dimensional terms.