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. 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 = 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.