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Please write all answers in the spaces provided. Please show your work in order to receive any partial credit on this exam.

1. (16 points) Suppose a firm has a production function given by Q = L1/2K1/2. Therefore,

MPL = , and MPK =

The firm can purchase labor, L at a price w = 9, and capital, K at a price of r = 16.

What is the firm’s total cost function?

TC = 24Q

2. (18 total points) Suppose a monopolist faces a demand curve P = 134 – 2Q. The monopolist’s marginal cost is constant and equal to $14.

a) (6 points) How much output should the firm produce in order to maximize profit?

QM = 30

b) (6 points) What is the deadweight loss associated with this monopoly?

DWL = 900

c) (6 points) What is the value of the Lerner Index?

LI = 60/74 = 30/37 = .81

3. (11 total points) Suppose in the short run a perfectly competitive firm has variable cost = 2q2, and MC = 4q where q is the quantity of output produced. Also, the firm has fixed cost F = 200.

a) (4 points) If the market price of the product is $48, how much output should the firm produce in order to maximize profit?

q = 12

b) (4 points) How much profit will this firm make?

TR = P*q = 48*12 = 576

TC = 200 + 2*122 = 488

Profit = 88

c) (3 points) Given your answer to b), what will happen to the market price as we move from the short run to the long run?

Price will decrease

4. (20 total points) (Cournot Duopoly) Note: The following formulas will be