Middle East Technical University
Spring 2011
Department of Economics
ECON 201
Erol Çakmak
TA: Osman Değer
PROBLEM SET 7
1)
A firm has a production function Q(K,L)= 4K
1/3
L
1/3
, where the unit prices of labor
and capital are both equal to 1. P is the price of the product in a perfectly competitive
market.
a. Determine the long run supply function of this firm.
b. What is the profit maximizing output level when P=3?
c. Derive the short run supply function for K
0
=9.
2)
Suppose the inverse demand function for cab rides in Chicago is given by
P(Y)= 40000/Y
where Y is the total number of cab rides in a given year. Assume that there are 100
identical cabs in this market, and that the cost function for each cab is given by
C(y)= 200 + y
2
/2
where
y
is the number of rides per year produced by a typical cab and 200 represents
the annual cost of a taxi license that is issued by the city (for simplicity, we assume
away the cost of buying or renting a cab).
a. Find the equilibrium price, if all cabs behave as if they operate in a perfectly
competitive market.
b. Is this equilibrium the industry
’
s long
‐
run equilibrium, i.e. will cabs have an
incentive to enter or exit at the equilibrium price derived in part (a) ?
c. Now assume that, in an effort to raise revenue, the city raises the price of taxi
licenses to $250 per year.
i. How many cabs will be buying a license at the new price and offering rides in the
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 Fall '10
 çAKMAK
 Economics

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