I. Multiple choice

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

II. Problems

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

1. $6, using formula P = MC / (1 + (1/ε)).
2. 1/3 = 0.667, using formula L = (P-MC)/P or for monopoly L = 1/|ε|.

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

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

(3) [Cournot duopoly: 14 pts]

1. TR_A = P q_A = 21 q_A - (q_A²/10) - (q_A q_B/10).
2. MR_A = d TR_A / d q_A = 21 - (2q_A/10) - (q_B/10).
3. q_A = 90 - (q_B/2).
4. q_A* = 60.
5. Q* = 120, P* = $9.
6. L = (P-MC)/P = 2/3.
7. Deadweight loss = $180.

(4) [Joint profit maximization: 10 pts]

1. MR = 21 - (2Q/10).
2. Q* = 90.
3. P* = $12.
4. L = (P-MC)/P = 3/4.
5. Deadweight loss = $405.

(5) [Measures of concentration: 6 pts]

1. 68 percent.
2. 85 percent.
3. 1254.

(6) [Equilibrium entry: 19 pts]

1. Equilibrium market price = $13, $9, $7, $5.80, $5.
2. Annual profit per firm = $1440, $640, $360, $230.40, $160.
3. PDF profit per firm = $14400, $6400, $3600, $2304, $1600.
4. 2 firms.
5. 4 firms.

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

1. Min AC = $3.
2. Min efficient scale = 8 million.
3. L = (P-MC)/P = 1/2 .
4. P = $4.
5. AC = $6.
6. Loss, because P < AC.
7. $8 million.
8. Q = 10 million.
9. AC = $3.
10. Profit, because entrant's P > AC.
11. $20 million.
12. $3, to prevent profitable entry.
13. L = (P-MC)/P = 0, since P=AC=MC.

III. Critical thinking [4 pts]

(1) Willingness to pay for cartel

• The maximum amount of money the two firms would pay Congress for the right to form a cartel is the difference in their profits with and without a cartel. Assuming the market would be competitive without a cartel, profit would be zero because under competition P=MC=AC. A cartel would maximize profit by setting a price of $12 and a quantity of 90, as shown in problem (4). Since AC=$3, the cartel would enjoy a profit of $810. So the maximum amount of money the two firms would pay is $810.
  (If you assumed that without a cartel the market would be a Cournot duopoly, as in problem (3), then the maximum amount of money the two firms would pay would be the difference between cartel profit ($810) and total Cournot profits ($720), or $90.)

(2) Price competition in the pizza market

1. If Amy has chosen a price of $10, Barney's best reply is $9.99. Barney will then have all the buyers in the market at the highest possible price. If Barney merely matches Amy's price, he will have only half the buyers. If Barney sets a price lower than $9.99, he will have slightly more customers, but his profit will be less. (This answer assumes that Amy's price is less than or equal to the monopoly price, so that every further price reduction lowers total profit.)
2. If Barney has chosen a price of $9.99, Amy's best reply is $9.98. The reasoning is the same as part (a).
3. The Nash equilibrium is for both players to set a price equal to their marginal and average cost, $5, because at that price no player wants to change unilaterally, even though neither player enjoys any profit. If one player raises price, even by one cent, that player will lose all customers and will still have zero profit. If one player lowers price, even by one cent, that player will gain all the customers, but will make a loss equal to one cent times the quantity demanded.

[end of answer key]