This preview shows pages 1–2. Sign up to view the full content.
Rice University
Economics 370
Professor Diamond
Microeconomic Theory
PROBLEM SET 1:
INTRODUCTION AND APARTMENT SUPPLY AND DEMAND
I.
Suppose the production function for the output produced by a firm is
f
(
L
,
K
) = 40
L
3 / 4
K
1 / 4
,
where L is labor and K is capital.
1.
What is the marginal product of labor? What is the marginal product of capital?
2.
Suppose the rental rate of capital in the market is
r
=2, the wage of labor is
w
=10, the
price of output is
p
=1/3 and the amount of capital is fixed at 16 units (in the short run).
Assuming that the firm acts to maximize profit, what is the optimal level of labor?
Show
that both the first and second order conditions for a maximum are satisfied.
What is the
associated optimal output level?
II.
Suppose now that the capital stock is variable, but the firm is constrained (by its lenders) to
spend no more than a total of C=400.
Assume the firm chooses inputs to maximize
production and all prices are as indicated above, how much capital and labor will it hire?
How much will it produce and what are its profits?
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 DIAMOND
 Economics, Supply And Demand

Click to edit the document details