2. Assume that each firm produces a different variety w and draws a productivity level from a cumulative distribution function G() in each sector with support [,", ">p>0. Manufacturing 1 unit of output costs, where c, is the cost of a cost-minimizing bundle of inputs specific to each country j. Since c, captures differences in aggregate productivity, factor prices, and factor intensities across countries. Exporters also incur iceberg trade costs so that Tij > 1 units of a product need to be shipped for 1 unit to arrive. Firms in country j can export to i by paying a fixed cost cifi, each period, where f>0 for i j and f, 0. Firms from country j choose their export price and quantity in country i to maximize profits. (a) Write the profit maximization function of exporters (5 points). (b) Show firms' optimal export price is (5 points) TijCj P4 (c) Calculate firms' optimal export quantity (5 points). (d) Calculate firms' optimal export revenue (5 points). 1