Abstract
We provide a mathematical formulation of the idea of perfect competition for an economy with infinitely many agents and commodities. We conclude that in the presence of infinitely many commodities the Aumann (1964, 1966) measure space of agents, i.e., the interval [0,1] endowed with Lebesgue measure, is not appropriate to model the idea of perfect competition and we provide a characterization of the “appropriate” measure space of agents in an infinite dimensional commodity space setting. The latter is achieved by modeling precisely the idea of an economy with “many more” agents than commodities. For such an economy the existence of a competitive equilibrium is proved. The convexity assumption on preferences is not needed in the existence proof. We wish to thank Tom Armstrong for useful comments. As always we are responsible for any remaining errors.
We wish to thank Tom Armstrong for useful comments. As always we are responsible for any remaining errors.
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Rustichini, A., Yannelis, N.C. (1991). What is Perfect Competition?. In: Khan, M.A., Yannelis, N.C. (eds) Equilibrium Theory in Infinite Dimensional Spaces. Studies in Economic Theory, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-07071-0_11
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DOI: https://doi.org/10.1007/978-3-662-07071-0_11
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