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

### 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.
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 - (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) [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.

(3) [Cournot duopoly: 14 pts]

1. TRA = P qA = 10 qA - (qA2/100) - (qA qB/100).
2. MRA = d TRA / d qA = 10 - (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) [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.