Version A

I. Multiple choice

(1)a. (2)b. (3)b. (4)c. (5)a. (6)c. (7)a. (8)c. (9)a. (10)b. (11)a. (12)b. (13)d. (14)a. (15)c.

II. Problems

(1) [Monopoly, markup formula, Lerner index: 4 pts]

1. $16, using formula P = MC / (1 + (1/ε)).
2. 1/4 = 0.25, using formula L = (P-MC)/P or for monopoly L = 1/|ε|.

(2) [Antitrust statutes: 4 pts] See Viscusi, Harrington, and Sappington textbook, appendix to chapter 3.

1. Sherman Act Section 2.
2. Federal Trade Commission Act.
3. Clayton Act Section 7.
4. Sherman Act Section 1.

(3) [Cournot duopoly: 14 pts]

1. TR_A = P q_A = 15 q_A - (q_A²/10) - (q_A q_B/10).
2. MR_A = d TR_A / d q_A = 15 - (2q_A/10) - (q_B/10).
3. q_A = 60 - (q_B/2).
4. q_A* = 40.
5. Q* = 80, P* = $7.
6. L = (P-MC)/P = 4/7.
7. Deadweight loss = $80. (Note that competitive supply curve is horizontal at $3, and intersects demand at Q=120.)

(4) [Joint profit maximization: 10 pts]

1. MR = 15 - (2Q/10).
2. Q* = 60.
3. P* = $9.
4. L = (P-MC)/P = 2/3.
5. Deadweight loss = $180.

(5) [Price-setting (Bertrand) duopoly with differentiated products: 15 pts]

1. TR_A = 300 P_A - 20 P_A² + 10 P_A P_B.
2. Set 0 = dTR_A/dP_A = 300 - 40 P_A + 10 P_B, and solve for P_A to get
   P_A = (30 + P_B) / 4.
3. Substitute P_A for P_B in the best reply function and solve to get
   P_A* = $10 = P_B*.
4. Subsitute $10 for P_A and P_B in Firm A's demand function to get
   Q_A* = 200 = Q_B*.
5. TR_A* = P_A* × Q_A* = $2000 = TR_B*.

(6) [Measures of concentration: 6 pts]

1. 59 percent.
2. 88 percent.
3. 1126.

(7) [Entry barriers and contestable markets: 26 pts]

1. Min AC = $2.
2. Min efficient scale = 8 million.
3. L = (P-MC)/P = 3/5 = 0.6 .
4. P = $3.
5. AC = $4.
6. Loss, because P < AC.
7. $4 million.
8. Q = 12 million.
9. AC = $2.
10. Profit, because entrant's P > AC.
11. $24 million.
12. $2, to prevent profitable entry.
13. L = (P-MC)/P = 0, since P=AC=MC.

III. Critical thinking [4 pts]

(1) Collusion with differentiated products

1. TR = TR_A + TR_B = (300 P_A - 20 P_A² + 10 P_A P_B) + (300 P_B - 20 P_B² + 10 P_A P_B).
   To maximize combined profit, set
   0 = dTR/dP_A = 300 - 40 P_A + 20 P_B, and 0 = dTR/dP_B = 300 - 40 P_B + 20 P_A.
   Assuming symmetry (P_A = P_B) we can use just the first equation and substitute to get
   0 = 300 - 40 P_A + 20 P_A. Solve to get P_A* = $15 = P_B*.
2. Substitute these prices into either demand equation to get Q_A* = 150 = Q_B*.
3. TR* = TR_A* + TR_B* = (P_A* × Q_A*) + (P_B* × Q_B*).
   = $4500, which is higher than combined revenue in problem (5).

(2) Credible threat

1. A credible threat is action that a player will actually have an incentive to carry out when provoked.
2. In the scenario of the question, Firm A threatens to lower its price below its average cost if Firm B enters the market. Since firm A would thereby make losses, its threat is not credible.

Version B

I. Multiple choice

(1)c. (2)a. (3)e. (4)a. (5)c. (6)d. (7)b. (8)b. (9)c. (10)c. (11)b. (12)a. (13)c. (14)b. (15)d.

II. Problems

(1) [Monopoly, markup formula, Lerner index: 4 pts]

1. $10, using formula P = MC / (1 + (1/ε)).
2. 1/5 = 0.2, using formula L = (P-MC)/P or for monopoly L = 1/|ε|.

(2) [Antitrust statutes: 4 pts] See Viscusi, Harrington, and Sappington textbook, appendix to chapter 3.

1. Clayton Act Section 7.
2. Sherman Act Section 1.
3. Sherman Act Section 2.
4. Federal Trade Commission Act.

(3) [Cournot duopoly: 14 pts]

1. TR_A = P_A = 10 q_A - (q_A²/100) - (q_A q_B/100).
2. MR_A = d TR_A / d q_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 = (P-MC)/P = 1/3.
7. Deadweight loss = $200. (Note that competitive supply curve is horizontal at $4, and intersects demand at Q=600.)

(4) [Joint profit maximization: 10 pts]

1. MR = 10 - (2Q/100).
2. Q* = 300.
3. P* = $7.
4. L = (P-MC)/P = 3/7.
5. Deadweight loss = $450.

(5) [Price-setting (Bertrand) duopoly with differentiated products: 15 pts]

1. TR_A = 200 P_A - 30 P_A² + 10 P_A P_B.
2. Set 0 = dTR_A/dP_A = 200 - 60 P_A + 10 P_B, and solve for P_A to get
   P_A = (20 + P_B) / 6.
3. Substitute P_A for P_B in the best reply function and solve to get
   P_A* = $4 = P_B*.
4. Subsitute $4 for P_A and P_B in Firm A's demand function to get
   Q_A* = 120 = Q_B*.
5. TR_A* = P_A* × Q_A* = $480 = TR_B*.

(6) [Measures of concentration: 6 pts]

1. 31 percent.
2. 51 percent.
3. 404.

(7) [Entry barriers and contestable markets: 26 pts]

1. Min AC = $4.
2. Min efficient scale = 5 million.
3. L = (P-MC)/P = 1/3 .
4. P = $4.
5. AC = $5.
6. Loss, because P < AC.
7. $4 million.
8. Q = 10 million.
9. AC = $4.
10. Profit, because entrant's P > AC.
11. $10 million.
12. $4, to prevent profitable entry.
13. L = (P-MC)/P = 0, since P=AC=MC.

III. Critical thinking [4 pts]

(1) Collusion with differentiated products

1. TR = TR_A + TR_B = (200 P q_A - 30 P_A² + 10 P_A P_B) + (200 P q_B - 30 P_B² + 10 P_A P_B).
   To maximize combined profit, set
   0 = dTR/dP_A = 200 - 60 P_A + 20 P_B, and 0 = dTR/dP_B = 200 - 60 P_B + 20 P_A.
   Assuming symmetry (P_A = P_B) we can use just the first equation and substitute to get
   0 = 200 - 30 P_A + 20 P_A. Solve to get P_A* = $5 = P_B*.
2. Substitute these prices into either demand equation to get Q_A* = 100 = Q_B*.
3. TR* = TR_A* + TR_B* = (P_A* × Q_A*) + (P_B* × Q_B*).
   = $1000, which is higher than combined revenue in problem (5).

(2) Credible threat--same as Version A.

[end of answer key]