Homework 7 ECO 3101 This is due Monday, June 20. 1. Two firms, A and B each produce the same type of good, x. Demand for x is x = 600 – 3P, where P is the price of x. Both firms have a total cost function of 15x. If the firms successfully collude, to generate a monopoly like outcome, what level of x should each firm produce? (a.) 138.75 (b.) 122.5 (c.) 112.5 (d.) 101.1 2. If the firms in problem 1 collude, what is the profit each firm makes? (a.) $20,940.4 (b.) $17,775 (c.) $19,251 (d.) $12,834 3. Consider the two firms, A and B from problem 1. If firm A produces the “colluding” output you solved for in problem 1, but firm B finds a way to cheat and produce whatever he wants, then firm B will produce an x of ____ . (a.) 125 (b.) 177.55 (c.) 208.13 (d.) 244.44 4. Suppose two Cournot competitors, called A & B, each have total cost of 20 + 10x, where x is a firm’s output choice. Say demand is X = 1400 – P, where P is price. If firm B produces 200 units of output, what is firm A’s optimal output amount? (a.) 450 (b.) 350 (c.) 595 (d.) 120 (e.) None of the above 5. Consider the two firms in problem 4 again. If firm B produces the 200 units of output and A produces the output you solved for in question 4, then what will the market price be? (a.) $605 (b.) $588 (c.) $495 (d.) $423 6. There are two Cournot competitors, A & B. Each has total cost of 12x, where x is a firm’s output, and demand is X = 600 – P, where P is market price. The Nash equilibrium for this game is (a.) Both firms produce 230 units (b.) Both firms produce 299 units (c.) Both firms produce 196 units (d.) Both firms produce 88 units 7. Consider the Cournot game in problem 6. What will market price be in equilibrium? (a.) $288 (b.) $265 (c.) $224 (d.) $208 8. Firm A and B are Bertrand competitors, and each has a total cost function 25xi, where xi is firm i’s output. Demand for x is x = 400 – P, where P is the price of x. In the equilibrium, firm A charges a price of ___ and firm B charges a price of ____. (a.) $40; $20 (b.) $20; $20 (c.) $25; $25 (d.) $20; $25 9. Consider the Bertrand game described in question 8. Exactly how much x will trade in the market when the two firms are both charging the optimal price? (a.) 380 (b.) 155 (c.) 125 (d.) 375 10. In the Bertrand game in question 8, when the two firms charge their optimal profit, what is firm A’s profit amount? (a.) $0 (b.) $12 (c.) $44 (d.) $64