Uniqueness and stability of equilibrium in economies with two goods

We offer new sufficient conditions ensuring demand is downward sloping local to equilibrium. It follows that equilibrium is unique and stable in the sense that rising supply implies falling prices. In our setting, there are two goods, which we interpret as consumption in different time periods, and many impatience types. Agents have the same Bernoulli utility function, but the types differ arbitrarily in time preference. Our main result is that if endowments are identical and utility displays nonincreasing absolute risk aversion, then market demand is strictly downward sloping local to equilibrium. We discuss implications for the literature surrounding Diamond and Dybvig (1983).