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, Open image in new window is a continuous function of the initial amounts of money held by the agents, Open image in new window , and their utility functions, Open image in new window . Furthermore, the correspondence Open image in new window , giving the set of equilibrium allocations for any specified Open image in new window and Open image in new window , is upper hemicontinuous, but not lower hemicontinuous. However, for a fixed Open image in new window , this correspondence is lower hemicontinuous in Open image in new window .
KeywordsEquilibrium Price Market Model Initial Endowment Unique Maximizer Column Space
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