4. Trade under Monopolistic Competition Consider the model presented in class, where a firm's demand is...

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4. Trade under Monopolistic Competition Consider the model presented in class, where a firm's demand is given by the following q(P) = S|=== (P = 1)], and the firm's cost function be given by 1 1 N b C(q) = c * q + F. Suppose the economy is characterized by the following S=50, b=4, F=2, c=1/2. a. Assume that initially there are 5 firms (N=5), find the price charged and quantity sold by each firm, as well as the average price level and profits (if any) made by each firm. Be sure you show the entire derivation. b. Show your solution to (a) graphically. c. Now assume there is free entry of firms into this market. Will firms choose to enter or exit the market, why? Firms will enter the market until the profits for each firm are zero d. Find the equilibrium number of firms in the long run and show (analytically and graphically) how the optimal price and quantity changes for all firms. e. From the long run autarky equilibrium, show what would happen if this country could trade with an identical country (analytically and graphically, show what happens to prices, sales, firms). f. Fill in the following table: Autarky Trade Number total varieties Number of firms in each country Quantity produced per variety Price g. Describe the gains form trade. 4. Trade under Monopolistic Competition Consider the model presented in class, where a firm's demand is given by the following q(P) = S|=== (P = 1)], and the firm's cost function be given by 1 1 N b C(q) = c * q + F. Suppose the economy is characterized by the following S=50, b=4, F=2, c=1/2. a. Assume that initially there are 5 firms (N=5), find the price charged and quantity sold by each firm, as well as the average price level and profits (if any) made by each firm. Be sure you show the entire derivation. b. Show your solution to (a) graphically. c. Now assume there is free entry of firms into this market. Will firms choose to enter or exit the market, why? Firms will enter the market until the profits for each firm are zero d. Find the equilibrium number of firms in the long run and show (analytically and graphically) how the optimal price and quantity changes for all firms. e. From the long run autarky equilibrium, show what would happen if this country could trade with an identical country (analytically and graphically, show what happens to prices, sales, firms). f. Fill in the following table: Autarky Trade Number total varieties Number of firms in each country Quantity produced per variety Price g. Describe the gains form trade.