A New Approach to the Uniqueness of Equilibrium in Two-Good Economies

This paper investigates the existence of unique equilibrium in two-good economies where agents have preferences with the same relative risk aversion and different utility weights. Aggregate demand behavior is characterized in terms of both macrolevel and micro-level information inherent in the economy. At the macro level, the economy makes it possible to build two representative-agent economies that provide a lower and upper bound of the price range for potential equilibrium prices. Information at the micro level is inferred by elucidating the global structure of individual demand function. When relative risk aversion is greater than 1, the price effect over the price domain is single-peaked at the inflection price that represents the maximal dominance of the income effect over the substitution effect. Based on the analysis of the first-order and second-order price effects, two sufficient conditions are presented for the uniqueness of equilibrium. The result of the paper sheds a light on the Sonnenschein-Mantel-Debreu theory that has negative implications for systematically studying the uniqueness of equilibrium.