Question

Use the following information is answering questions 1 - 11. Assume the demand in a market is given by Q = 100 - 2P and that MC = AC = 10. Assume there are two sellers whose strategy is to choose a quantity and that seller 1 chooses first and seller 2 chooses second. Assume this game is repeated an infinite number of times.

1. The Stackelberg equilibrium in this market is for firm 1 to produce ____ and firm 2 to produce _____.

2. In the Stackelberg equilibrium, firm 1’s profit is _____ and firm 2’s profit is ______.

3. The monopoly output level in this market is ______.

4. If firm 1 promises to produce Q₁ = 28 if firm 2 will produce Q₂ = 12, firm 1 will earn profit equal to ______.

5. Firm 1’s gain in profit in this suggested collusive behavior is ______.

6. If firm 2 agrees to firm 1’s suggestion, firm 2’s profit is ______.

7. If firm 2 cheats and produces its profit maximizing level of output instead, firm 2 would produce Q₂ equal to ______.

8. If firm 2 cheats and produces its profit maximizing level of output instead, firm 2 would earn a profit equal to ______.

9. The one time gain in profit for firm 2 from cheating is equal to ______.

10. The loss in profit to firm 2 in each of the future periods because firm 2 cheats is _____.

11. Firm 2 would agree to the collusive suggestion of firm 1 as long as firm 2’s interest rate is less than ______.

Use the following information to answer questions 12 - 15.

Player 2

A B

A (3, 0) (2, -1)

Player 1

B (2, 8) (5, 3)

12. The unique Nash equilibrium in this game when it is played one time and the players choose simultaneously is ______.

13. Both players would prefer the strategy pair ______ to the Nash equilibrium.

14. When this game is repeated an infinite number of times, Player 1 would choose B when Player 2 chooses B if and only if Player 1’s rate of interest is less than _____.

15. When this game is repeated an infinite number of times, Player 2 would choose B when Player 1 chooses B if and only if Player 2’s rate of interest is less than _____.

Player 2

A B

A (3, 6) (-1, 2)

Player 1

B (6, 2) (0, 3)

Use the payoff matrix above for questions 16 - 18.

16. The unique Nash equilibrium in this game when it is played one time and the players choose simultaneously is ______.

a) (A, A)

b) (B, B)

c) (A, B)

d) (B, A)

e) there is no Nash equilibrium

17. When this game is repeated an infinite number of times, Player 1 would choose A when Player 2 chooses A if and only if Player 1’s rate of interest is less than _____.

a) 20%

b) can be any positive number

c) 50%

d) 60%

e) 30%

18. When this game is repeated an infinite number of times, Player 2 would choose A when Player 1 chooses A if and only if Player 2’s rate of interest is less than _____.

a) 20%

b) 40%

c) 60%

d) can be any positive number

e) 30%

Use the following information when answering questions 19 - 24. Assume that the reservation price for each buyer in a market is 10, and that there are 60 such buyers. Also assume that MC = AC = 6. Also assume that seller 1 and seller 2 each has a capacity of selling 50 units and that prices must be integers. Assume that if they charge the same price then they each sell half the quantity demanded. Assume the game is played one time.

19. If seller 1 chooses a price of 9, seller 2’s best response is to choose P₂ = _____.

a) 10

b) 6

c) 7

d) 8

e) 9

20. When sellers 1 and 2 each charge price equal to _____ , then we have a Bertrand/Nash equilibrium.

a) 8

b) 6

c) 9

d) 7

e) 10

21. In this Bertrand/Nash equilibrium, each seller earns a profit = _____.

a) 60

b) 40

c) 100

d) 80

e) 50

Use the following information in addition to that given above to answer questions 22 - 24. Assume the Bertrand game with capacity constraint is to be repeated an infinite number of times.

22. When each seller charges a price equal to 10, each earns a profit equal to ______.

a) 100

b) 140

c) 200

d) 120

e) 300

23. When one seller charges a price equal to 10 and the other cheats by choosing its best response, the cheating seller earns a profit equal to _____.

a) 120

b) 160

c) 150

d) 200

e) 180

24. The gain in profit from cheating rather than setting P = 10 is _____, and the loss in profit from having the Bertrand/Nash equilibrium rather than colluding and setting price equal to 10 is _____.

a) 50, 50

b) 40, 80

c) 60, 60

d) 60, 30

e) 30, 60

Answer 1