Help walk me through the following problem set; I'm stumped.

Department of Economics Winter 2020 University of Michigan Economics 441 Econ 441: International Trade Prof. Dominick Bartelme Winter 2020 Problem Set 3 March 17, 2020 Due on Tuesday, March 31 by midnight (11:59 pm) via Canvas. You are required to submit your answers in a single PDF file. Please write your full name and umich id on your problem set. Please pay attention to the organization of your answers. Always keep the order of the questions, write legibly, and clearly indicate what you are doing. Please staple your answer sheets together. Don't forget: the grader can only give you credit if they can read and comprehend what you have written. After derivations that need several steps, always mark your final answer clearly: put a box around it, underline it or highlight it. You should aim for brief, concise explanations. 1 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 q 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 cost u = P/c- 1 in each market. Which country has larger markups? How much larger are they (i.e. 2 times? 3 times?).Department of Economics Winter 2020 University of Michigan Economics 441 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. 2 US/Canada Free Trade, Heterogeneous Firms Let's stick with the same example, except now there are two types of firms. One type has marginal cost equal to 1 and one type has marginal cost equal to 1/2. Assume that initially, under autarky, half the firms in each country are of one type and half of the other. All other parameters are the same. 1. For each country, find the price and quantity for each type of firm, given the average price P and the number of firms N. Hint: first find the prices charged by low and high cost firms as a function of the quantities sold by each type of firm using the condition MR = c. Then solve for the quantities that each firm sells (given the average price) by plugging your solution to MR = c into the demand curve. 2. For each country, find the average firm price P charged in each country for a given number of firms N under autarky. Hint: use P = Phigh + plow 3. For each country, find the total profits of each type of firm (i.e. including fixed costs) for a given number of firms N under autarky. It's fine not to simplify your answer too much. 4. BONUS: Find the number of firms in each country under autarky, under the assumption that the high-cost firms earn zero profits (and that they make up half of all firms). Compute the ratio NUS /NCA. Hint: remember the quadratic formula, and pick the lower of the two solutions if they are both positive. Explain why you should pick the lower solution. 5. BONUS: Find the scale and markup of each type of firm in each country under autarky. 6. BONUS: Now assume the countries sign a free trade agreement. In the short run, i.e. no firms exits, compute the new scale and markups for each type of firm. Do they go up or down compared to their autarky values for each country? Does anyone have incentive to exit the market? 7. BONUS Demonstrate whether or not the long run equilibrium (in which firms are allowed to exit if the earn negative total profits but no new firms enter) will feature positive numbers of high cost firms or only low cost firms