# Pete’s Choppers Company’s cost data have been partially entered in the table

November 24, 2016

Microeconomics (Fall 2015)
Simon W. Bowmaker
Problem Set 5
Submit at lecture on Monday, October 26
Write (they don’t have to be typed) your answers on separate paper, not on this sheet of
day and time of the recitation
NB: if your recitation takes place on Monday morning, you must submit your
assignment to your teacher at the beginning of the recitation.

1. Pete’s Choppers Company’s cost data have been partially entered in the table. Following
the arrest of the company’s accountant, you are called to fill in the missing entries:

2. Kobe’s production function for mini-basketball hoops is Q = LK. The price of labor
services is w and the price of capital services is r. Suppose that w = \$4, r = \$2, and
Kobe’s total cost is \$160.
(a) What is Kobe’s MPL and MPK?
(b) What is Kobe’s optimal input combination of L and K? What is Q?
(c) Suppose the wage rate is 8 times the rental rate and Q is the same as before. What is
Kobe’s optimal input combination of L and K after the price change?

3. Suppose that each firm in a perfectly competitive industry has the short-run cost function
C 5 q 2q2, and the market price is \$45. What is the profit-maximizing output level
for each firm? What is the total revenue? What are the profits?
4. Suppose that a perfectly competitive firm’s total cost of producing output q is TC (q) =
10+10q-q2+0.25q3 and market price P*=\$10.
(a) Find the short-run supply curve of a firm in this industry.
(b) How much will the firm produce at P*=\$10?

5. Crystal skulls are produced in a perfectly competitive industry in which each firm has a
total cost function TC = 4r + wq2/4, where r is the price of a barrel of oil and w is the
price of a barrel of water. Suppose that the crystal skull industry is in long-run
equilibrium, with r = \$25 and w = \$1. What is the market price of a crystal skull? How
many skulls does each firm produce?

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