Trade and the Gains from Variety Consider the monopolistic competition model of trade studied in class. Suppose that there are M2 countries, and all countries are identical. In each country, demand for each firm's product is given by: Q=S[N1r(PP)] where S denotes the size of the market in each country, N denotes the number of firms producing, and P denotes the average price charged by firms in the market. All firms produce with the same technology, which features a constant marginal cost c and a fixed cost of production f, such that the total cost for a firm producing Q units of output is: TC=cQ+f In what follows, assume that the parameter values are: Srcf=10=0.01=1=0.1 First, suppose that each country is in autarky, and take the number of firms N as given. (a) Write down the profit-maximization problem for each firm (assume that firms choose output Q ). (b) What output level does each firm choose? What is the corresponding price? 1 (c) What are operating profits (revenue net of total costs) for each firm? Now suppose that there is free entry, so that in equilibrium, all firms earn zero operating profits. (d) What must the number of firms N be given free entry? Now suppose that the M countries sign a trade agreement that allows each country to trade freely with all the other countries. The size of the market for firms in any one country is hence MS instead of S. (e) What must the total number of firms N be given free entry under trade? (f) How does the total number of firms N vary with the number of countries M ? Explain why N varies with M in this way. (g) How do prices P and output per firm Q vary with the number of countries M ? Explain why P and Q vary with M in this way. (h) How does the number of firms per country N/M vary with the number of counrtries M ? Explain why N/M varies with M in this way. Trade and the Gains from Variety Consider the monopolistic competition model of trade studied in class. Suppose that there are M2 countries, and all countries are identical. In each country, demand for each firm's product is given by: Q=S[N1r(PP)] where S denotes the size of the market in each country, N denotes the number of firms producing, and P denotes the average price charged by firms in the market. All firms produce with the same technology, which features a constant marginal cost c and a fixed cost of production f, such that the total cost for a firm producing Q units of output is: TC=cQ+f In what follows, assume that the parameter values are: Srcf=10=0.01=1=0.1 First, suppose that each country is in autarky, and take the number of firms N as given. (a) Write down the profit-maximization problem for each firm (assume that firms choose output Q ). (b) What output level does each firm choose? What is the corresponding price? 1 (c) What are operating profits (revenue net of total costs) for each firm? Now suppose that there is free entry, so that in equilibrium, all firms earn zero operating profits. (d) What must the number of firms N be given free entry? Now suppose that the M countries sign a trade agreement that allows each country to trade freely with all the other countries. The size of the market for firms in any one country is hence MS instead of S. (e) What must the total number of firms N be given free entry under trade? (f) How does the total number of firms N vary with the number of countries M ? Explain why N varies with M in this way. (g) How do prices P and output per firm Q vary with the number of countries M ? Explain why P and Q vary with M in this way. (h) How does the number of firms per country N/M vary with the number of counrtries M ? Explain why N/M varies with M in this way