QUIZ 5 ANSWER KEY
Oligopoly and Collusion
Version A
I. Multiple choice [2 pt each: 10 pts total]
(1)b. (2)b. (3)c. (4)b. (5)b.
II. Problems
(1) [Game theory: 24 pts]
- Strategies are "uptown" and "downtown." See below .
- Payoffs are profits. See below.
- There are two Nash equilibria:
- Jimmy's locates uptown and John's locates downtown.
(These strategies are best replies to each other.)
- Jimmy's locates downtown and John's locates uptown.
(These strategies are best replies to each other.)
| |
John's |
| |
Uptown |
Downtown |
Jimmy's |
Uptown |
Jimmy's gets $200 thousand John's gets $200 thousand |
Jimmy's gets $400 thousand John's gets $600 thousand |
Downtown |
Jimmy's gets $600 thousand John's gets $400 thousand |
Jimmy's gets $300 thousand John's gets $300 thousand |
(2) [Oligopolist's marginal revenue: 15 pts]
- $9.50 = old price + change in quantity × slope of demand curve.
- increase.
- $2.50 = Stand A's MR - MC = $9.50 - 10 × (-$0.50) - $2.
- decrease.
- $12.50 = market MR - MC = $9.50 - 40 × (-$0.50) - $2.
(3) [Cournot duopoly: 21 pts]
- Rev_{1} = 20 q_{1} - (q_{1}^{2}/100)
- (q_{1}q_{2}/100).
- MR_{1} = 20 - (2q_{1}/100)
- (q_{2}/100).
- q_{1}* = 900 - (q_{2}/2).
- q_{1} = 600.
- Q* = 1200, P* = $8.
- L = 3/4 = 0.75.
- DWL = $1800.
(4) [Joint profit maximization: 24 pts]
- $2 because under price competition, P=MC.
- 1800 units.
- zero deadweight loss because P=MC.
- zero Lerner index because P=MC.
- 900 units, found by setting market MR = MC.
- $11.
- $4050.
- 9/11 = 0.8182.
III. Critical thinking [6 pts]
- Firm B's best reply is to choose a price slightly lower than $10, such as $9.99
(unless $10 is greater than the monopoly price, in which case Firm B's best reply is to choose the monopoly price).
- Firm A's best reply is to choose a price slightly lower than Firm A's price,
such as $9.98.
- The Nash equilibrium is for both firms to choose a price of $5 (or perhaps slightly above, such as $5.01). Once both firms are at this price, neither firm will want to raise or lower its price unilaterally. If a firm raises price, it will lose all its customers. If it lowers its price, it will gain all the customers but incur losses.
Version B
I. Multiple choice [2 pt each: 10 pts total]
(1)a. (2)c. (3)b. (4)c. (5)c.
II. Problems
(1) [Game theory: 24 pts]
- Strategies are "round" and "angular." See below .
- Payoffs are profits. See below.
- There are NO Nash equilibria in pure strategies. Whatever design Firm 1 chooses, Firm 2's best reply is to choose the same design. Whatever design Firm 2 chooses, Firm 1's best reply is to choose a different design.
| |
Firm 2 |
| |
Round |
Angular |
Firm 1 |
Round |
Firm 1 gets $10 million Firm 2 gets $5 million |
Firm 1 gets $15 million Firm 2 gets zero |
Angular |
Firm 1 gets $15 million Firm 2 gets zero |
Firm 1 gets $10 million Firm 2 gets $5 million |
(2) [Oligopolist's marginal revenue: 15 pts]
- $7.50 = old price + change in quantity × slope of demand curve.
- increase.
- $1.50 = Stand A's MR - MC = $7.50 - 10 × (-$0.50) - $1.
- decrease.
- $3.50 = market MR - MC = $7.50 - 20 × (-$0.50) - $1.
(3) [Cournot duopoly: 21 pts]
- Rev_{1} = 15 q_{1} - (q_{1}^{2}/100)
- (q_{1}q_{2}/100).
- MR_{1} = 15 - (2q_{1}/100)
- (q_{2}/100).
- q_{1}* = 600 - (q_{2}/2).
- q_{1} = 400.
- Q* = 800, P* = $7.
- L = 4/7 = 0.5714 .
- DWL = $800.
(4) [Joint profit maximization: 24 pts]
- $3 because under price competition, P=MC.
- 1200 units.
- zero deadweight loss because P=MC.
- zero Lerner index because P=MC.
- 600 units, found by setting market MR = MC.
- $9.
- $1800.
- 2/3 = 0.6667 .
III. Critical thinking [6 pts]
- Firm B's best reply is to choose a price slightly lower than $12, such as $11.99
(unless $12 is greater than the monopoly price, in which case Firm B's best reply is to choose the monopoly price).
- Firm A's best reply is to choose a price slightly lower than Firm A's price,
such as $11.98.
- The Nash equilibrium is for both firms to choose a price of $4 (or perhaps slightly above, such as $4.01). Once both firms are at this price, neither firm will want to raise or lower its price unilaterally. If a firm raises price, it will lose all its customers. If it lowers its price, it will gain all the customers but incur losses.
[end of answer key]