Suppose a firm has a production function given

1. Quantity FC VC TC AFC AVC ATC MC
0 120 0 — — — —
1 150
2 40
3 10
2.
(16 total points) Suppose a firm has a production function given by Q = L1/2K1/2. Therefore,

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The firm can purchase labor, L at a price w = 15, and capital, K at a price of r = 60.

a) What is the firm’s Total Cost function, TC(Q)?

b) What is the firm’s marginal cost of production?

3.
(10 points) Suppose that a perfectly competitive firm has Fixed Cost = 30 and Variable Cost = 3q2, so that MC = 6q. What is the maximum profit this firm could make if the market price of the good is $72?

4.

3. (25 total points) Suppose a monopolist faces the following demand curve:

P = 90 – 4Q.

The long run marginal cost of production is constant and equal to $10, and there are no fixed costs.

A) What is the monopolist’s profit maximizing level of output?

B) What price will the profit maximizing monopolist produce?

C) How much profit will the monopolist make if she maximizes her profit?

D) What would be the value of consumer surplus if the market were perfectly competitive?

E) What is the value of the deadweight loss when the market is a monopoly?

5.
(25 total points) Suppose there are two firms in a market who each simultaneously choose a quantity. Firm 1’s quantity is q1, and firm 2’s quantity is q2. Therefore the market quantity is Q = q1 + q2. The market demand curve is given by P = 160 – 2Q. Also, each firm has constant marginal cost equal to 10. There are no fixed costs.

The marginal revenue of the two firms are given by:

MR1 = 160 – 4q1 – 2q2
MR2 = 160 – 2q1 – 4q2.
A) How much output will each firm produce in the Cournot equilibrium?

B) What will be the market price of the good?

C) What is the deadweight loss that results from this duopoly?

D) How much profit does each firm make?

E) Suppose Firm 2 produced 30 units of output. How much output should Firm 1 produce in order to maximize profit?

6.
(14 total points) Suppose that two players are playing the following game. Player 1 can choose either Top or Bottom, and Player 2 can choose either Left or Right. The payoffs are given in the following table:

Player 1 Player 2
Left Right
Top 9 5 2 3
Bottom 7 4 5 6
where the number on the left is the payoff to Player A, and the number on the right is the payoff to Player B.

A) (2 points) Does player 1 have a dominant strategy, and if so what is it?

B) (2 points) Does player 2 have a dominant strategy and if so what is it?

C) (1 point each) For each of the following strategy combinations, write TRUE if it is a Nash Equilibrium, and FALSE if it is not:

i) Top/Left
ii) Top/Right
iii) Bottom/Left
iv) Bottom Right
D) (2 points) What is Player 1’s maximin strategy?

E) (2 points) What is player 2’s maximin strategy?

F) (2 points) If the game were played with Player 1 moving first and player 2 moving second, using the backward induction method we went over in class, what strategy will each player choose?

7.
(4 points) Suppose the price of a good is $25. Also suppose the price elasticity of demand is equal to -5. What is the firm’s marginal revenue?