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Generic Properties of the Core and Equilibria of Pure Exchange Economies

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  • Ashvin Varada Rajan

Abstract

We present a unified mathematical framework within which pure exchange economies with a finite set of agents as well as those with a continuum of traders as mathematically modelled by Aumann (1964) can be analyzed simultaneously We prove that the number of equilibrium price vectors of our economies are generically finite Hence for markets with a continuum of traders the equilibrium allocations (which by the celebrated theorem of Aumann (1964) coincide with the core allocations) are finite for an open dense set of such markets This presents a limiting case result that complements similar asymptotic theorems about cores of large economies that have been proved by Bewley (1973) and Dierker (1975) If we assume that the measure on the space of agents is one with a finite number of atoms of equal weight our reasoning recovers the classical theorems proved about equilibria by Debreu (1970) for economies with a finite number of agents

Suggested Citation

  • Ashvin Varada Rajan, 1996. "Generic Properties of the Core and Equilibria of Pure Exchange Economies," Economics Working Paper Archive 363, The Johns Hopkins University,Department of Economics.
    • Handle: RePEc:jhu:papers:363
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