ECON 120 - Regulation and Antitrust Policy Drake University, Spring 2019 William M. Boal

EXAM 2 ANSWER KEY

### 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. TRA = P qA = 15 qA - (qA2/10) - (qA qB/10).
2. MRA = d TRA / d qA = 15 qA - (2qA/10) - (qB/10).
3. qA = 60 - (qB/2).
4. qA* = 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. TRA = 300 P qA - 20 PA2 + 10 PA PB.
2. Set 0 = dTRA/dPA = 300 - 40 PA + 10 PB, and solve for PA to get
PA = (30 + PB) / 4.
3. Substitute PA for PB in the best reply function and solve to get
PA* = \$10 = PB*.
4. Subsitute \$10 for PA and PB in Firm A's demand function to get
QA* = 200 = QB*.
5. TRA* = PA* × QA* = \$2000 = TRB*.

(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 = TRA + TRB = (300 P qA - 20 PA2 + 10 PA PB) + (300 P qB - 20 PB2 + 10 PA PB).
To maximize combined profit, set
0 = dTR/dPA = 300 - 40 PA + 20 PB, and 0 = dTR/dPB = 300 - 40 PB + 20 PA.
Assuming symmetry (PA = PB) we can use just the first equation and substitute to get
0 = 300 - 40 PA + 20 PA. Solve to get PA* = \$15 = PB*.
2. Substitute these prices into either demand equation to get QA* = 150 = QB*.
3. TR* = TRA* + TRB* = (PA* × QA*) + (PB* × QB*).
= \$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. TRA = P qA = 10 qA - (qA2/100) - (qA qB/100).
2. MRA = d TRA / d qA = 10 qA - (2qA/100) - (qB/100).
3. qA = 300 - (qB/2).
4. qA* = 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. TRA = 200 P qA - 30 PA2 + 10 PA PB.
2. Set 0 = dTRA/dPA = 200 - 60 PA + 10 PB, and solve for PA to get
PA = (20 + PB) / 6.
3. Substitute PA for PB in the best reply function and solve to get
PA* = \$4 = PB*.
4. Subsitute \$4 for PA and PB in Firm A's demand function to get
QA* = 120 = QB*.
5. TRA* = PA* × QA* = \$480 = TRB*.

(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 = TRA + TRB = (200 P qA - 30 PA2 + 10 PA PB) + (200 P qB - 30 PB2 + 10 PA PB).
To maximize combined profit, set
0 = dTR/dPA = 200 - 60 PA + 20 PB, and 0 = dTR/dPB = 200 - 60 PB + 20 PA.
Assuming symmetry (PA = PB) we can use just the first equation and substitute to get
0 = 200 - 30 PA + 20 PA. Solve to get PA* = \$5 = PB*.
2. Substitute these prices into either demand equation to get QA* = 100 = QB*.
3. TR* = TRA* + TRB* = (PA* × QA*) + (PB* × QB*).
= \$1000, which is higher than combined revenue in problem (5).

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

[end of answer key]