Michael Florig

Hierarchic competitive equilibria

Abstract Without an interiority or strong survival assumption, an equilibrium may not exist in the standard Arrow–Debreu model. We propose a generalized concept of competitive equilibrium, called hierarchic equilibrium. Instead of using standard prices we use hierarchic prices. Existence will be shown without a strong survival assumption and without a non-satiation condition on the preferences. Under standard assumptions this reduces to the Walras equilibrium. Hierarchic equilibria are weakly Pareto optimal and any Pareto optimum can be decentralized without a border condition. We prove the existence of a Pareto optimal hierarchic equilibrium under additional assumptions. Later, we establish a core equivalence result.

Continuity and uniqueness of equilibria for linear exchange economies

The purpose of this paper is to study the continuity and uniqueness properties of equilibria for linear exchange economies. We characterize the sets of utility vectors and initial endowments for which the equilibrium price is unique and respectively the set for which the equilibrium allocation is unique. We show that the equilibrium allocation correspondence is continuous with respect to the initial endowments and we characterize the set of full measure where the equilibrium allocation correspondence with respect to the initial endowments and utility vectors is continuous.

Differentiability of Equilibria for Linear Exchange Economies

The purpose of this paper is to study the differentiability properties of equilibrium prices and allocations in a linear exchange economy when the initial endowments and utility vectors vary. We characterize an open dense subset of full measure of the initial endowment and utility vector space on which the equilibrium price vector is a real analytic function, hence infinitely differentiable function. We provide an explicit formula to compute the equilibrium price and allocation around a point where it is known. We also show that the equilibrium price is a locally Lipschitzian mapping on the whole space. Finally, using the notion of the Clarke generalized gradient, we prove that linear exchange economies satisfy a property of gross substitution.

A note on different concepts of generalized equilibria

Abstract Without a survival assumption, equilibrium may not exist in the standard Arrow–Debreu model. Here, we study two approaches of generalized equilibrium, allowing for the relaxation of such an unrealistic assumption. Danilov and Sotskovs EV-equilibrium is characterized by a stratification of the economy into different submarkets. We show existence of such an equilibrium with a continuum of traders. This enables us to prove existence of a pseudo equilibrium [(Mertens, 1995)] for a class of preference relations containing linear utility functions. Later, we show that an iteration of pseudo equilibria (iterative pseudo equilibrium), a concept introduced in Mertens, 1995 is a particular case of an EV-equilibrium.