Welfare Analysis of a Market Model with External Increasing Returns and Differentiated Commodities

Abstract

Markets with increasing returns resulting from the positive external effects of production (hereafter external increasing returns ) have been discussed from both positive and normative points of view. We present a complete general equilibrium model in which external increasing returns prevail within industries to produce differentiated commodities which are represented by real valued functions. Firms in an industry produce the commodity characteristics which are values of each commodity function. This formulation of differentiated commodities causes the equilibrium to be characterized as the solution of a variational problem . In order to answer this mathematically formidable question, we utilize the delta function of Dirac for the calculus of variations to be done in an elementary way. To our knowledge, this is the first time the delta function appears in economic analysis.