Quantity Adjustment in an Arrow-Debreu-Mckenzie Type Model

Abstract

Our purpose is to examine long run entry/exit dynamics in a limit economy with infinitesimal firms and in Cournot economies (where firms recognize their influence on price) which are “close” to the limit economy. In the short run certain factors are immobile, and short run equilibrium prices reflect only the relative scarcity of factors that are instantaneously variable. The returns to immobile factors are not necessarily equalized. In the long run all factors are free to vary, and the factors that are immobile in the short run “flow towards that branch of production” in which there are profits to be realized. We formalize this in a long run entry/exit dynamics for a limit economy with infinitesimal firms. We also examine the long run dynamics in Cournot economies, with non-infinitesimal firms, because we view perfect competition as an idealization which should be interpreted as a limit of imperfect competition. With this view, the properties of the dynamics (and the equilibria) of the Cournot economies are the true objects of interest, and the dynamics (and the equilibria) of the limit economy are of interest only insofar as they represent limits of the results for a sequence of Cournot economies which converge to the limit economy. See Novshek and Sonnenschein [1983] for an extensive discussion of this point of view and the basic framework of the analysis. Here we amplify and extend the discussion of dynamics in that paper by explicitly treating decreasing returns to scale in the aggregate and also discussing the dynamics in the Cournot economies.

We gratefully acknowledge the support of the National Science Foundation and our universities.