2 Trade with Heterogeneous Firms Consider three car makers that can potentially operate under monopolistic com- petition in equilibrium. There are two completely identical countries. To start operations, a car maker i needs to pay a fixed cost of F = 1,250 and can produce at a constant marginal cost of c. To enter the foreign market, a car exporter needs to pay an additional fixed cost of Fx = 312.5. To ship an export, a car maker incurs an additional transportation cost of T = 1 (100 percent) on top of marginal production cost so that marginal costs for an export good are (1 + r). Ci In each country, the three car makers have constant marginal cost of pro- duction c = 50, C2 = 150, C3 = 300 (and i = 50, c= 150, c3 = 300). Every car maker i faces residual demand of Q = S: (1 - b.(P- P)] under monopolistic competition, where S = 5,000, b = 1/100 and P is average equilibrium price. Recall from class that, for this residual demand, optimal quantity and profits are b 1 Sb 1 Qi = P + and II = P + 2 bon 4 b.n - Ci (+b+w-c - The domestic marginal-cost ceiling at which the last (highest-cost) entrepreneur n just enters and the marginal-cost ceiling for exports at which the last (highest- cost) domestic firm nx just exports are Fx 1 n = P + bon - 2 F Sb and came = P + b.no 2V S b Use profits II, and fixed entry costs F to derive the domestic marginal-cost ceiling Cn. Use the equilibrium price-variety relationship for the average firm P = 1/b.n) + c to restate the marginal-cost ceilings in terms of the average markup 1/b.n) and market-average marginal cost c. Consider autarky (fixed export costs are prohibitively high at Fx = 350,000.) Use the marginal-cost ceiling to show that two firms will enter the domestic market, but not three. Consider free trade (fixed export cost of Fx = 312.5) and suppose that wages remain unchanged. Use the marginal-cost ceiling for exports to show that exactly one domestic firm will export and that the two foreign incumbent firms remain in operation. Also show that two exporters and two foreign incumbents cannot be an equilibrium outcome, and that one home exporter and three foreign firms cannot be an equilibrium outcome. Continue to consider free trade and unchanged wages. How does free trade affect the average markup 1/b.n) and market-average marginal cost c? How does market average price P change? 2 Trade with Heterogeneous Firms Consider three car makers that can potentially operate under monopolistic com- petition in equilibrium. There are two completely identical countries. To start operations, a car maker i needs to pay a fixed cost of F = 1,250 and can produce at a constant marginal cost of c. To enter the foreign market, a car exporter needs to pay an additional fixed cost of Fx = 312.5. To ship an export, a car maker incurs an additional transportation cost of T = 1 (100 percent) on top of marginal production cost so that marginal costs for an export good are (1 + r). Ci In each country, the three car makers have constant marginal cost of pro- duction c = 50, C2 = 150, C3 = 300 (and i = 50, c= 150, c3 = 300). Every car maker i faces residual demand of Q = S: (1 - b.(P- P)] under monopolistic competition, where S = 5,000, b = 1/100 and P is average equilibrium price. Recall from class that, for this residual demand, optimal quantity and profits are b 1 Sb 1 Qi = P + and II = P + 2 bon 4 b.n - Ci (+b+w-c - The domestic marginal-cost ceiling at which the last (highest-cost) entrepreneur n just enters and the marginal-cost ceiling for exports at which the last (highest- cost) domestic firm nx just exports are Fx 1 n = P + bon - 2 F Sb and came = P + b.no 2V S b Use profits II, and fixed entry costs F to derive the domestic marginal-cost ceiling Cn. Use the equilibrium price-variety relationship for the average firm P = 1/b.n) + c to restate the marginal-cost ceilings in terms of the average markup 1/b.n) and market-average marginal cost c. Consider autarky (fixed export costs are prohibitively high at Fx = 350,000.) Use the marginal-cost ceiling to show that two firms will enter the domestic market, but not three. Consider free trade (fixed export cost of Fx = 312.5) and suppose that wages remain unchanged. Use the marginal-cost ceiling for exports to show that exactly one domestic firm will export and that the two foreign incumbent firms remain in operation. Also show that two exporters and two foreign incumbents cannot be an equilibrium outcome, and that one home exporter and three foreign firms cannot be an equilibrium outcome. Continue to consider free trade and unchanged wages. How does free trade affect the average markup 1/b.n) and market-average marginal cost c? How does market average price P change