Dixit-Stiglitz with Firm Heterogeneity: (s22q1) Consider the Dixit-Stiglitz model of monopolistic competition with the following modifications. Retail firms operate in a perfectly competitive market according to following production technology: y=(01yi1/edi), where >1 is a measure of elasticity of substitution between the goods lying in the unit interval. Each good i is produced by a monopolistically competitive wholesale producer described below. Retail firms do not use any factor of production: they simply combine wholesale products into an aggregate good and sell it to the consumers at a price of P. Assume throughout the question that P=1. Wholesale producers, on the other hand, operate on a constant returns to scale production technology which uses only labor. More specifically, the production function is given by: yi=ini, where i is a measure of productivity. Let pi denote the price of the wholesale good i and w be the real wage rate in a perfectly competitive market for capital and labor. (a) Write down the profit maximization problem of retails firms and obtain demand for good j,yj, in terms of ,pj, and y. (b) Solve for the profit maximizing price of a wholesale firm j. Note that your answer will depend on j. (c) Assume for the rest of the question that i=0.5 for firms indexed between 0 and 0.5, and i=1.5 for firms indexed between 0.5 and 1 . What is the market clearing wage rate in terms of ? (d) If =2 and labor is inelastically supplied at ns=1, what is the total production of retail sector, y