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ECON191
Spring 2010
Outline of suggested solutions to Problem Set 3
(1)
Given, MPL = 3(K/L)
0.25
, MPK = (L/K)
0.75,
P
L
= $3/unit, P
K
= $1/unit,
P
K
K + P
L
L = 8
Cost is minimized when MPL/P
L
= MPK/P
K
(K/L)
0.25
= (L/K)
0.75
L = K
Total cost of production P
K
K + P
L
L = 8
3L + K =8
K = L = 2 units
The level of production: Y = 4K
0.25
L
0.75
Y= 4(2)
0.25
(2)
0.75
= 4(2
0.25+0.75
) = 8 units
(2)
(a)
MPL
L + MPK
K = 3(K/L)
0.25
(L) + (L/K)
0.75
(K) = 3K
0.25
L
0.75
+ L
0.75
K
0.25
= 4K
0.25
L
0.75
=Y
(b)
(MPL
L)/Y = 3K
0.25
L
0.75
/ 4K
0.25
L
0.75
=0.75
(c)
(MPK
K)/Y = L
0.75
K
0.25
/ 4K
0.25
L
0.75
= 0.25
(d)
MPL is equal to real wage rate in the competitive market. MPL
L is the total wages paid to the
workers. Similarly, MPK
K is total payment to providers of capital.
The first equation tells us that output Y is exactly exhausted by payment to workers and capitalists.
(This is true only of we have constant returns to scale, as is the case here.)
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 Spring '09
 CHAN

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