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]

1. Strategies are "uptown" and "downtown." See below .
2. Payoffs are profits. See below.
3. There are two Nash equilibria:
   1. Jimmy's locates uptown and John's locates downtown. (These strategies are best replies to each other.)
   2. Jimmy's locates downtown and John's locates uptown. (These strategies are best replies to each other.)

(2) [Oligopolist's marginal revenue: 15 pts]

1. $9.50 = old price + change in quantity × slope of demand curve.
2. increase.
3. $2.50 = Stand A's MR - MC = $9.50 - 10 × (-$0.50) - $2.
4. decrease.
5. $12.50 = market MR - MC = $9.50 - 40 × (-$0.50) - $2.

(3) [Cournot duopoly: 21 pts]

1. Rev₁ = 20 q₁ - (q₁²/100) - (q₁q₂/100).
2. MR₁ = 20 - (2q₁/100) - (q₂/100).
3. q₁* = 900 - (q₂/2).
4. q₁ = 600.
5. Q* = 1200, P* = $8.
6. L = 3/4 = 0.75.
7. DWL = $1800.

(4) [Joint profit maximization: 24 pts]

1. $2 because under price competition, P=MC.
2. 1800 units.
3. zero deadweight loss because P=MC.
4. zero Lerner index because P=MC.
5. 900 units, found by setting market MR = MC.
6. $11.
7. $4050.
8. 9/11 = 0.8182.

III. Critical thinking [6 pts]

1. 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).
2. Firm A's best reply is to choose a price slightly lower than Firm A's price, such as $9.98.
3. 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]

1. Strategies are "round" and "angular." See below .
2. Payoffs are profits. See below.
3. 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.

(2) [Oligopolist's marginal revenue: 15 pts]

1. $7.50 = old price + change in quantity × slope of demand curve.
2. increase.
3. $1.50 = Stand A's MR - MC = $7.50 - 10 × (-$0.50) - $1.
4. decrease.
5. $3.50 = market MR - MC = $7.50 - 20 × (-$0.50) - $1.

(3) [Cournot duopoly: 21 pts]

1. Rev₁ = 15 q₁ - (q₁²/100) - (q₁q₂/100).
2. MR₁ = 15 - (2q₁/100) - (q₂/100).
3. q₁* = 600 - (q₂/2).
4. q₁ = 400.
5. Q* = 800, P* = $7.
6. L = 4/7 = 0.5714 .
7. DWL = $800.

(4) [Joint profit maximization: 24 pts]

1. $3 because under price competition, P=MC.
2. 1200 units.
3. zero deadweight loss because P=MC.
4. zero Lerner index because P=MC.
5. 600 units, found by setting market MR = MC.
6. $9.
7. $1800.
8. 2/3 = 0.6667 .

III. Critical thinking [6 pts]

1. 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).
2. Firm A's best reply is to choose a price slightly lower than Firm A's price, such as $11.98.
3. 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]