The comparative statics of cumulative distribution function changes for the class of risk averse agents

We examine the connection between Walrasian equilibria of a limit economy (with infinitesimal firms) and the noncooperative (Cournot) equilibria of approximating finite economies (with significant firms). Following earlier work of Novshek and Sonnenschein we allow for set-up cost and permit a minimal form of mixed strategies. We depart from them by requiring that the aggregate production set exhibits some degree (however small) of decreasing returns. Contrasting with their results, it is shown that a (regular) Walrasian equilibrium of a limit economy can always be approximated by a sequence of noncooperative equilibria for the tail of the approximating (finite) economies. Thus, there is a surprising qualitative discontinuity when one passes from the Novshek-Sonnenschein case of aggregate constant returns to scale of the decreasing returns case of this paper.