This question asks you to work throw the quantitative implications of integration between two dierent-sized countries in the monopolistic competition model. The market sizes are US = 100 and CA = 10. Firms in each country can enter the market by paying a xed cost 1 and produce with a variable cost 1 for every unit q produced, so TC(q) = 1 + Q. As in lecture, rms in each country face the demand curve Q = S (1/N (P P1)),where S is the market size, N is the number of rms, P is the price charged by the rm and P1 is the average price charged by all rms. All rms are identical. Note: don't worry about "fractions" of rms in your answer. We will interpret these quantities as millions (i.e. 2.5 rms equals 2.5 million rms), but just to keep the notation reasonable we'll use the lower numbers. Now there are two types of rms. 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 rms in each country are of one type, andhalf of the other.

Question 1: Find the number of rms in each country under autarky, under the assumption that the high-cost rms earn zero prots (and that they make up half of all rms). 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. Also find the scale and markup of each type of rm in each country under autarky.

Question 2: Now assume the countries sign a free trade agreement. In the short run, i.e. no rms exits, compute the new scale and markups for each type of rm. Do they go up or down compared to their autarky values for each country? Does anyone have incentive to exit the market? Demonstrate whether or not the long run equilibrium (in which rms are allowed to exit if the earn negative total prots but no new rms enter) will feature positive numbers of high cost rms or only low cost rms.