# 微观经济学辅导 | Econ 101 Summer Session C Midterm Version 10

### 2 Test Questions: 60 Total Points

1. Monopoly. A monopolist sells to a population of consumers with willingness to pay that is uniform
between 5 and 10. That is:
f(w) =
8
<
:
1=5 if 5  x  10
0 else

You can assume the amount of consumers is normalized to 1 like in class. The monopolist has constant
marginal cost c.

a. Given willingness to pay, show how to derive demand and inverse demand. Hint: you should nd
that inverse demand is p(q) = 10 5q. (4 pts)

b. Solve for the monopolist price, quantity and total surplus.(8 pts)

c. Suppose that instead of a monopolist, there is perfect competition. Derive the price, quantity and
total surplus under perfect competition. (4 pts)

d. Suppose the government wants to maximize total surplus and institutes a price ceiling on the
monopolist. Which price ceiling should they choose if c = 2? (4 pts)

### 2. Static Game Theory. Consider the following game.

Player 2
A B C
Player 1
A (2; 2) ( 1; 2) ( 1; 2)
B ( 1; 1) (1; 1) ( 1; 2)
C ( 1; 1) ( 1; 2) (1; 1)

a. Are there any dominant strategies? Are there any dominated strategies? (2 pts)

b. Find all pure strategy Nash equilibrium. Write down the strategy pairs for each. (5 pts)

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