Abstract
This paper investigates the uniqueness of equilibrium in the economy where agents have preferences with possibly distinct levels of relative risk aversion. Equilibrium prices exist in a price range determined by micro and macroeconomic information. Macroeconomic information is inferred from two representative-agent economies, which provide lower and upper bounds on aggregate demand, respectively. Analysis of the first and second-order price effects shows that individual demand has a unique inflection point at which the income effect maximally dominates the substitution effect. In contrast, aggregate demand may have multiple inflection points, which creates multiple equilibria. Sufficient conditions for the uniqueness of equilibrium are characterized by the local behavior of individual demand at the inflection point. They require that aggregate demand must have no more than two inflection points in the equilibrium price range. The result of this paper sheds light on the Sonnenschein-Mantel-Debreu theory that has negative implications for the uniqueness of equilibrium.
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