Department of Economics
University of California, Irvine
210A  Microeconomic Theory I
Fall 2011
Sample Midterm Exam questions
(An exam usually consists of three questions like those below)
1.
Consider a production function
f
(
x
1
; x
2
)
, whereby output is produced
with two inputs.
a.
De°ne the
isoquant
for this production function.
b.
Find su¢ cient conditions that would guarantee the convexity of the
isoquant.
2.
a.
De°ne the
pro°t function
in the neoclassical theory of the °rm.
b.
Prove that the pro°t function is convex in prices.
3.
Consider the technology described by
f
(
x
) = 0
for all
x
°
1
and
f
(
x
) =
ln
x
for
x >
1
:
a. Derive the conditional factor demand function and the cost function
for this technology.
b. Con°rm three properties of the cost function, including Shephard±s
Lemma.
4.
a. De°ne the cost function in the neoclassical theory of the °rm.
b. Prove that the cost function is concave in prices.
c.
Show the properties of negativity and symmetry for conditional
factor demand functions.
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 Fall '08
 skaperdas
 Economics, Department of Economics

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