Continuity Properties of Equilibrium Prices and Allocations in Linear Fisher Markets

Continuity of the mapping from initial endowments and utilities to equilibria is an essential property for a desirable model of an economy – without continuity, small errors in the observation of parameters of the economy may lead to entirely different predicted equilibria. We show that for the linear case of Fisher’s market model, the (unique) vector of equilibrium prices, p = p(m,U) is a continuous function of the initial amounts of money held by the agents, m, and their utility functions, U. Furthermore, the correspondence X(m,U), giving the set of equilibrium allocations for any specified m and U, is upper hemicontinuous, but not lower hemicontinuous. However, for a fixed U, this correspondence is lower hemicontinuous in m.