Perfect competition in the continuous assignment model

This paper provides a rigorous formalization, in the context of the transfe rable utility assignment model, of perfect competition as the inability of individuals to (favorably) influence prices. The central tool for the analy sis is the social gains function; the central issue is differentiability of the gains function with respect to the population. Seven conditions are sh own to be equivalent to perfect competition. Perfect competition and imperf ect competition are possible for both finite and continuum assignment econo mies, but most finite economics are imperfectly competitive, while most con tinuum economies are perfectly competitive. However, most large finite assi gnment economies are approximately perfectly competitive. Classification Nu mbers: CGI. C62, C78. (C) 1999 Academic Press.