An Existence Theorem for Cournot-Walras Equilibria∗

We establish an existence result of Cournot-Walras equilibria in the model consists of a single consumer with constant elasty of substitution (CES) utility function and n-monopolistically competitive firms with cost functions. Instead of the traditional approach that depends on Kakutani’s fixed point theorem, we use the fact that, in our framework, the profit maximization game played by monopolistically competitive firms is, in fact, a best reply potential game, which is one of the classes of games which possess pure strat-egy Nash equilibria. This property is derived by application of the theory of monotone comparative statics employing lattice programming. It should be noted that all our as-sumptions are on the fundamental datum of the economy; in particular, quasiconcavity of best response is not required. We neither exclude cost diminishing technologies nor the existence of fixed costs. Even the existence of inseparable goods does not cause any problems for our existence theorem