Question 3: US/Canada Free Trade Agreement This question asks you to work throw the quantitative implications of integration between two different-sized countries in the monopolistic competition model. The market sizes are SUS = 100 and SCA = 10. Firms in each country can enter the market by paying a fixed cost 1 and produce with a variable cost 1 for every unit g produced, so TC(q) = 1+Q. As in lecture, firms in each country face the demand curve Q = S. (1/N -(P-P)) where S is the market size, N is the number of firms, P is the price charged by the firm and P is the average price charged by all firms. All firms are identical. Note: don't worry about "fractions of firms in your answer. We will interpret these quantities as millions (i.e. 2.5 firms equals 2.5 million firms), but just to keep the notation reasonable we'll use the lower numbers. 1. Find the marginal revenue curve for each country under autarky. 2. Assume that, under autarky, free entry drives profits to zero. Derive the long run equilibrium number of firms in each market, and compute the ratio of U.S. firms to Canadian firms. 3. Derive the scale of firms in each country, i.e. the quantity Q produced by each firm. Which country has larger firms? How much larger are they (i.e. 2 times? 3 times?). 4. Derive the markup of price over marginal costu = P/c-1 in each market. Which country has larger markups? How much larger are they (i.e. 2 times? 3 times?). 5. Now lets assume that the two countries sign a free trade agreement. Effectively, firms in each country now share the same market. In the short run, i.e. no firms exits, compute the new scale of each firm (now common across countries) and the new markups (also common across countries). Do they go up or down compared to their autarky values for each country? 6. Describe the two sources of gains from trade for consumers in each economy. Which country do you think gains more from trade in the short run? 7. Compute the total profits per firm under free trade, in the short run. Explain the logic behind your answer 8. Compute the long-run equilibrium number of firms using the zero profit condition under free trade. Is it larger or smaller than the short-run number of firms? 9. Compute the long-run scale Q and markup under free trade. Compare them to their short-run values and provide intuition for the difference. Question 3: US/Canada Free Trade Agreement This question asks you to work throw the quantitative implications of integration between two different-sized countries in the monopolistic competition model. The market sizes are SUS = 100 and SCA = 10. Firms in each country can enter the market by paying a fixed cost 1 and produce with a variable cost 1 for every unit g produced, so TC(q) = 1+Q. As in lecture, firms in each country face the demand curve Q = S. (1/N -(P-P)) where S is the market size, N is the number of firms, P is the price charged by the firm and P is the average price charged by all firms. All firms are identical. Note: don't worry about "fractions of firms in your answer. We will interpret these quantities as millions (i.e. 2.5 firms equals 2.5 million firms), but just to keep the notation reasonable we'll use the lower numbers. 1. Find the marginal revenue curve for each country under autarky. 2. Assume that, under autarky, free entry drives profits to zero. Derive the long run equilibrium number of firms in each market, and compute the ratio of U.S. firms to Canadian firms. 3. Derive the scale of firms in each country, i.e. the quantity Q produced by each firm. Which country has larger firms? How much larger are they (i.e. 2 times? 3 times?). 4. Derive the markup of price over marginal costu = P/c-1 in each market. Which country has larger markups? How much larger are they (i.e. 2 times? 3 times?). 5. Now lets assume that the two countries sign a free trade agreement. Effectively, firms in each country now share the same market. In the short run, i.e. no firms exits, compute the new scale of each firm (now common across countries) and the new markups (also common across countries). Do they go up or down compared to their autarky values for each country? 6. Describe the two sources of gains from trade for consumers in each economy. Which country do you think gains more from trade in the short run? 7. Compute the total profits per firm under free trade, in the short run. Explain the logic behind your answer 8. Compute the long-run equilibrium number of firms using the zero profit condition under free trade. Is it larger or smaller than the short-run number of firms? 9. Compute the long-run scale Q and markup under free trade. Compare them to their short-run values and provide intuition for the difference
