For pure exchange economies in which agents are described by a compact smooth manifold of smooth strictly monotonic and strictly concave utilities, it is shown that, at least generically, the equilibrium price set is a smooth manifold of the same dimension. Given any smooth selection from the equilibrium price manifold and any sufficiently close smooth function, the function is a selection from the equilibrium price correspondence for some manifold of economies close to the original one. In particular, the set of equilibria corresponding to any open neighborhood of an economy contains an open subset of the price simplex.
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*This paper contains some results from my Ph.D. thesis submitted to U.C. Berkeley in 1978. The members of my dissertation committee, Gerard Debreu, Andreu Mas-Colell, and Morris Hirsch, contributed helpful advice, but are, of course, exempt from responsibility. I have also benefitted from the suggestions of an anonymous referee. Financial support from the Heinrich Hertz Stiftung and an NSF Graduate Fellowship is gratefully acknowledged. Typing was provided by NSF Grant SOC76-19700, administered through the Center for Research in Management Science at U.C. Berkeley, NSF Grant SOC78-06157 to the Center for Analytic Research in Economics and the Social Sciences at Penn, and NSF Grant SOC79-07228.