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]
 $16, using formula P = MC / (1 + (1/ε)).
 1/4 = 0.25, using formula L = (PMC)/P or for monopoly L = 1/ε.
(2) [Antitrust statutes: 4 pts] See Viscusi, Harrington, and Sappington textbook, appendix to chapter 3.
 Sherman Act Section 2.
 Federal Trade Commission Act.
 Clayton Act Section 7.
 Sherman Act Section 1.
(3) [Cournot duopoly: 14 pts]
 TR_{A} = P q_{A}
= 15 q_{A}  (q_{A}^{2}/10)
 (q_{A} q_{B}/10).
 MR_{A} = d TR_{A} / d q_{A}
= 15  (2q_{A}/10)  (q_{B}/10).
 q_{A} = 60  (q_{B}/2).
 q_{A}* = 40.
 Q* = 80, P* = $7.
 L = (PMC)/P = 4/7.
 Deadweight loss = $80. (Note that competitive supply curve is horizontal at $3, and intersects demand at Q=120.)
(4) [Joint profit maximization: 10 pts]
 MR = 15  (2Q/10).
 Q* = 60.
 P* = $9.
 L = (PMC)/P = 2/3.
 Deadweight loss = $180.
(5) [Pricesetting (Bertrand) duopoly with differentiated products: 15 pts]
 TR_{A} = 300 P_{A}  20 P_{A}^{2}
+ 10 P_{A} P_{B}.
 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.
 Substitute P_{A} for P_{B}
in the best reply function and solve to get
P_{A}* = $10 = P_{B}*.
 Subsitute $10 for P_{A} and P_{B} in
Firm A's demand function to get
Q_{A}* = 200 = Q_{B}*.
 TR_{A}* = P_{A}* × Q_{A}*
= $2000 = TR_{B}*.
(6) [Measures of concentration: 6 pts]
 59 percent.
 88 percent.
 1126.
(7) [Entry barriers and contestable markets: 26 pts]
 Min AC = $2.
 Min efficient scale = 8 million.
 L = (PMC)/P = 3/5 = 0.6 .
 P = $3.
 AC = $4.
 Loss, because P < AC.
 $4 million.
 Q = 12 million.
 AC = $2.
 Profit, because entrant's P > AC.
 $24 million.
 $2, to prevent profitable entry.
 L = (PMC)/P = 0, since P=AC=MC.
III. Critical thinking [4 pts]
(1) Collusion with differentiated products
 TR = TR_{A} + TR_{B}
= (300 P_{A}  20 P_{A}^{2}
+ 10 P_{A} P_{B})
+ (300 P_{B}  20 P_{B}^{2}
+ 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}*.
 Substitute these prices into either demand equation to get
Q_{A}* = 150 = Q_{B}*.
 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
 A credible threat is action that a player will actually have an incentive to carry out when provoked.
 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]
 $10, using formula P = MC / (1 + (1/ε)).
 1/5 = 0.2, using formula L = (PMC)/P or for monopoly L = 1/ε.
(2) [Antitrust statutes: 4 pts] See Viscusi, Harrington, and Sappington textbook, appendix to chapter 3.
 Clayton Act Section 7.
 Sherman Act Section 1.
 Sherman Act Section 2.
 Federal Trade Commission Act.
(3) [Cournot duopoly: 14 pts]
 TR_{A} = P_{A}
= 10 q_{A}  (q_{A}^{2}/100)
 (q_{A} q_{B}/100).
 MR_{A} = d TR_{A} / d q_{A}
= 10  (2q_{A}/100)  (q_{B}/100).
 q_{A} = 300  (q_{B}/2).
 q_{A}* = 200.
 Q* = 400, P* = $6.
 L = (PMC)/P = 1/3.
 Deadweight loss = $200. (Note that competitive supply curve is horizontal at $4, and intersects demand at Q=600.)
(4) [Joint profit maximization: 10 pts]
 MR = 10  (2Q/100).
 Q* = 300.
 P* = $7.
 L = (PMC)/P = 3/7.
 Deadweight loss = $450.
(5) [Pricesetting (Bertrand) duopoly with differentiated products: 15 pts]
 TR_{A} = 200 P_{A}  30 P_{A}^{2}
+ 10 P_{A} P_{B}.
 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.
 Substitute P_{A} for P_{B}
in the best reply function and solve to get
P_{A}* = $4 = P_{B}*.
 Subsitute $4 for P_{A} and P_{B} in
Firm A's demand function to get
Q_{A}* = 120 = Q_{B}*.
 TR_{A}* = P_{A}* × Q_{A}*
= $480 = TR_{B}*.
(6) [Measures of concentration: 6 pts]
 31 percent.
 51 percent.
 404.
(7) [Entry barriers and contestable markets: 26 pts]
 Min AC = $4.
 Min efficient scale = 5 million.
 L = (PMC)/P = 1/3 .
 P = $4.
 AC = $5.
 Loss, because P < AC.
 $4 million.
 Q = 10 million.
 AC = $4.
 Profit, because entrant's P > AC.
 $10 million.
 $4, to prevent profitable entry.
 L = (PMC)/P = 0, since P=AC=MC.
III. Critical thinking [4 pts]
(1) Collusion with differentiated products
 TR = TR_{A} + TR_{B}
= (200 P q_{A}  30 P_{A}^{2}
+ 10 P_{A} P_{B})
+ (200 P q_{B}  30 P_{B}^{2}
+ 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}*.
 Substitute these prices into either demand equation to get
Q_{A}* = 100 = Q_{B}*.
 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 threatsame as Version A.
[end of answer key]