exercise after Mid (new)

1. 1. a. 7 units. b. $28. c. $224, since $32 × 7 = $224. d. $98, since $14 × 7 = $98. e. $126 (the difference between total cost and variable cost). f. It is earning a loss of $28, since ($28 -$32) × 7 = - $28. g. - $126, since its loss will equal its fixed costs. h. Shut down. 2. A firm sells its product in a perfectly competitive market where other firms charge a price of $90 per unit. The firm’s total costs are C(Q) = 50 + 10Q + 2Q2. (LO3) a. How much output should the firm produce in the short run? b. What price should the firm charge in the short run? c. What are the firm’s short-run profits? d. What adjustments should be anticipated in the long run? Entry will occur, the market price will fall, and the firm should plan to reduce its output. In the long-run, economic profits will shrink to zero. d b c

2. The inverse market demand in a homogeneous-product Cournot duopoly is P = 200 − 3(Q1 + Q2) and costs are C1(Q1) = 26Q1 and C2(Q2) = 32Q2. a. Determine the reaction function for each firm. b. Calculate each firm’s equilibrium output. c. Calculate the equilibrium market price. d. Calculate the profit each firm earns in equilibrium. b) a) C2(Q2) = 32Q2 C1(Q1) = 26Q1 d) c) P = 200 − 3(Q1 + Q2) P = 200 − 3(20+ 18) P = 200 − 114 P = $86

3. The inverse demand for a homogeneous-product Stackelberg duopoly is P = 16,000 − 4Q. The cost structures for the leader and the follower, respectively, are CL(QL) = 4,000QL and CF(QF) = 6,000QF a. What is the follower’s reaction function? b. Determine the equilibrium output level for both the leader and the follower. c. Determine the equilibrium market price. d. Determine the profits of the leader and the follower.

4. 2. In a two-player, one-shot, simultaneous-move game, each player can choose strategy A or strategy B. If both players choose strategy A, each earns a payoff of $400. If both players choose strategy B, each earns a payoff of $200. If player 1 chooses strategy A and player 2 chooses strategy B, then player 1 earns $100 and player 2 earns $600. If player 1 chooses strategy B and player 2 chooses strategy A, then player 1 earns $600 and player 2 earns $100. a. Write this game in normal form. b. Find each player’s dominant strategy, if it exists. c. Find the Nash equilibrium (or equilibria) of this game. d. Rank strategy pairs by aggregate payoff (highest to lowest). e. Can the outcome with the highest aggregate payoff be sustained in equilibrium? Why or why not? a) b. B is dominant for each player. c. (B, B). d. Joint payoffs from (A, A) > joint payoffs from (A, B) = joint payoffs from (B, A) > joint payoffs from (B, B). e. No; each firm’s dominant strategy is B. Therefore, since this is a one-shot game, each player would have an incentive to cheat on any collusive arrangement

5. Suppose Toyota and Honda must decide whether to make a new breed of side-impact airbags standard equipment on all models. Side-impact airbags raise the price of each automobile by $1,000. If both firms make side-impact airbags standard equipment, each company will earn profits of $2.5 billion. If neither company adopts the side-impact airbag technology, each company will earn $1 billion (due to lost sales to other automakers). If one company adopts the technology as standard equipment and the other does not, the adopting company will earn a profit of $3 billion and the other company will lose $1.5 billion. If you were a decision maker at Honda, would you make side-impact airbags standard equipment? Explain.

6. a. Determine the expected value of each option. b. Determine the variance and standard deviation of each option. c. Which option is most risky? a) b) b) c) Option 2 is riskier since both have the same mean but option 2 has greater variance