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Unformatted text preview: First and Last Name: Section: Net ID: College of Human Ecology
Cornell University, Ithaca, New York
Department of Policy Analysis and Management
PAM 2000 Intermediate Microeconomics
A. Sinan Un¨ r – Spring 2009 Homework 3
Due February 25, 2009 Instructions
This homework is due by 12:20 pm on February 25th. You may turn in your homework any
time before the deadline but no late submissions will be accepted.
Write your answers on separate sheets and staple them securely to this cover sheet before you
turn them in. Questions
Consider a ﬁrm which produces burgers using the production function
Q = F(L, K) = 2 KL.
Suppose the wage rate is w = $8/hour and the rental rate on capital rate is r = $2/hour.
1) Initially, suppose the ﬁrm is operating with ﬁxed capital K = 1.
(i) Derive the ﬁrm’s short run demand for labor.
(ii) Derive the ﬁrm’s short run total cost function.
(iii) Derive the ﬁrm’s short run average total cost function.
(iv) Derive the ﬁrm’s short run average ﬁxed cost function.
(v) Derive the ﬁrm’s short run average variable cost function. 1 2) Now, suppose that the ﬁrm has the option of choosing K as well as L. Given the production
function above, the ﬁrm will use both inputs at positive levels to produce any given output level.
The marginal products of labor and capital are
MPL = K
and MPK =
L so that
MRT SL,K = L
L What is the cost-minimizing K-L ratio given the input prices?
(i) Derive the ﬁrm’s demand for a labor as function of its output level.
(ii) Derive the ﬁrm’s demand for capital as a function of its output level.
(iii) What is the ﬁrm’s long run total cost function?
(iv) What is the ﬁrm’s long run average cost?
(v) What is the ﬁrm’s long run marginal cost? 2 ...
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