1
Econ 191
Spring 2010
Francis Lui
Problem Set 3
Due Date:
March 22, 4:00 pm sharp.
Please submit your PS to the HW collection
cabinet outside the ECON department (Lift 1719)
(1)
Suppose that a production function is given by Y = 4K
0.25
L
0.75
. It can be shown
that MPL = 3(K/L)
0.25
and MPK = (L/K)
0.75
.
It is given that the price of K, P
K
,
is $1/unit, and the price of L, P
L
, is $3 /unit. Assuming that the total cost of
production (which is given by P
K
K + P
L
L) cannot exceed $8, what is the
highest attainable level of production? How many units of K and L will be
used?
(2)
Suppose that the production function of a firm is the same as that in Question
1.
Show that
(a)
Y = (MPL)L + (MPK)K
(b)
(MPL)L/Y = 0.75
(c)
(MPK)K/Y = 0.25.
How do you interpret these results?
(3)
Suppose that all the firms in a perfectly competitive industry have the
following identical cost function:
C = Q
3
 Q
2
+ Q.
Show that their marginal cost function is given by
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 Spring '09
 CHAN
 Economics, Supply And Demand, Francis Lui Problem, HW collection cabinet

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