10. Consider a consumer that has wealth W, consumes from a set of differentiated varietiesw E n, and solves the following maximization problem: max [q (w)} J w uq(w)) da s.t. p(w)q(w) SW, Firms are monopolistic competitors, and each firm has a productivity z drawn from a country specific distribution G; (Z). Firms from country i face an iceberg trade costto sell to a destination a. Derive the first order conditions of the firm. What are the conditions on theutility function so that the problem of the firm is well defined (i.e. there existsa unique solution for the firm markup at each level of firm productivity)? b. Discuss the pricing-to-market implications of this model. How do they dependon firm market shares in a given market? c. Assume that each country has labor endowment Liand that labor marketsclear. Define a monopolistically competitive equilibrium in this setup. d. Solve for the welfare gains from trade, following Arkolakis, Costinot, Donaldson, Rodriguez-Clare (but without assuming a Pareto distribution). e. (optional)Write a program that computes the equilibrium for any level of theparameters in this model and computes the welfare. f. Compare the gains from trade in this model to the gains from Bernard, Eaton, Jensen, and Kortum model