GENERIC PROPERTIES OF THE CORE AND EQUILIBRIA OF PURE EXCHANGE ECONOMIES

We show that for an open dense set of markets with a continuum of trad ers the number of equilibrium allocations [which by the celebrated the orem of Aumann (Econometrica, 1964, 32, 39-50) coincide with the core allocations for such markets] are finite. This presents a limiting cas e result that complements similar asymptotic theorems for cores of lar ge economies proved by Bewley (Econometrica, 1973, 41, 425-454), and D ierker (Journal of Mathematical Economics, 1975, 2, 155-169). If we re quire that the measure on the space of agents be one with a finite num ber of atoms of equal weight, our reasoning recovers the classical res ults obtained by Debreu (Econometrica, 1970, 38, 387-392) for economie s with a finite number of agents.