Quiz 5 Version A

(1)a. (2)c. (3)d. (4)c. (5)d. (6)a. (7)c. (8)a. (9)d. (10)a.

Quiz 5 Version B

(1)a. (2)a. (3)b. (4)d. (5)c. (6)b. (7)b. (8)c. (9)a. (10)c.

Test 5 Version A

(1) [Game theory: 30 pts]

1. Strategies are "low price" and "high price." See below.
2. Payoffs are profits. See below.
3. Firm A's best reply is "low price."
4. Firm B's best reply is "high price."
5. There is only one Nash equilibrium: Firm A plays "low price" and Firm B plays "low price." This is a Nash equilibrium because these strategies are best replies to each other.

(2) [Cournot duopoly: 35 pts]

1. Rev_A = 14 q_A - (q_A²/20) - (q_Aq_B/20).
2. MR_A = 14 - (2q_A/20) - (q_B/20).
3. q_A* = 120 - (q_B/2).
4. q_A* = 80.
5. Q* = 160, P* = $6.
6. L = 2/3.
7. Social deadweight loss = $160.

(3) [Joint profit maximization: 25 pts]

1. MR = 14 - (Q/10).
2. Q = 120.
3. P = $8.
4. L = 3/4.
5. Social deadweight loss = $360.

Critical thinking [10 pts]

1. In asymmetric Cournot equilibrium, the firm with the higher marginal cost has the lower market share. So here, Firm #2 must have higher marginal cost.
2. Use the Cournot relationship: L = (P-MC_i)/P = S_i/|ε|. Here, P = $10 and ε = -2. For Firm 1, S₁ is given as 0.60, so MC₁ = $7. For Firm 2, S₂ is given as 0.40, so MC₂ = $8.

Test 5 Version B

(1) [Game theory: 30 pts]

1. Strategies are "angular" and "round." See below.
2. Payoffs are profits. See below.
3. Firm A's best reply is "angular."
4. Firm B's best reply is "amgi;ar."
5. There are no Nash equilibria (in pure strategies) in this game. There is no pair of strategies that are best replies to each other.

(2) [Cournot duopoly: 35 pts]

1. Rev_A = 10 q_A - (q_A²/100) - (q_Aq_B/100).
2. MR_A = 10 - (2q_A/100) - (q_B/100).
3. q_A* = 300 - (q_B/2).
4. q_A* = 200.
5. Q* = 400, P* = $6.
6. L = 1/3.
7. Social deadweight loss = $200.

(3) [Joint profit maximization: 25 pts]

1. MR = 10 - (Q/50).
2. Q = 300.
3. P = $7.
4. L = 3/7.
5. Social deadweight loss = $450.

Critical thinking [8 pts]

• Same as Version A.

[end of answer key]