Consumer's Surplus in Monopolistic Competition a la Dixit and Stiglitz
Sinha, Deepak K., Atlantic Economic Journal
Dixit and Stiglitz's ["Monopolistic Competition and Optimum Product Diversity," AER, 1977] model of monopolistic competition has been used by a number of economists in recent years to gain insight into phenomena ranging from monetary policy to intra-industry trade. In this model, there are n (i = 1,...n) monopolistically competitive (MC) firms facing demand given by [q.sub.i] = [k.sub.i] [([P.sub.i]/P).sup.[epsilon]] where [k.sub.i] is a firm specific constant, [P.sub.i] is firm i's nominal price, and n is large so that a small change in [P.sub.i] has little impact on the industry price index, P. The elasticity of demand for firms in the industry, [epsilon], is therefore constant. A lower value of [epsilon] indicates greater product differentiation and (assuming constant returns to technology) a higher price-cost margin ( = 1 / [epsilon]). Conversely, a higher value of [epsilon] indicates greater product homogeneity and a lower margin. As [epsilon] [arrow right] [infinity], the structure of an industry approaches that of perfect competition.
This paper reports an interesting property of constant elasticity demand. It appears to be singularly partial to consumers in the division of gross surplus.
Proposition 1: Assume that the production technology exhibits constant returns and the reservation prices are sufficiently high. Then consumer's surplus, due to a MC firm facing constant elasticity demand, will be at least as large as the firm's gross profit.
Proof: At any instant, consumer's surplus due to firm i is:
(1) [Mathematical Expression Omitted]
where [P.sub.i] is the reservation price, which is assumed to be high. …