Multiplicity of Competitive Equilibria in Semi-Algebraic Exchange Economies

Joint with: Karl Schmedders

In this paper, we examine multiplicity of equilibria in semi-algebraic exchange economies. We give examples of models that give rise to systems of polynomial equations that have few real solutions, independently of the degree of the polynomials or the number of unknown variables. We introduce computational methods to find all competitive equilibria for semi-algebraic equilibrium models. We develop a test for uniqueness of equilibria over semi-algebraic and convex set of endowments and preference parameters. The computational methods allow us to bound the maximal number of competitive equilibria for all possible profiles of individual endowments, given semi-algebraic preferences. We illustrate the method and some mathematical details in a model where all agents have constant elasticity of substitution utility.

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