Economics 11 – Fall 2009
Professor Mazzocco
Problem Set 6
Due by November 12 before 9:00am in the box located outside room 2221E
1)
Suppose that a firm’s production function is given by: Q=
K
L
where
is a given parameter.
a)
Find the marginal product of capital and labor.
b) Find the average product of capital and labor.
c) Does this production function have increasing, constant or decreasing returns to
scale? Explain.
d)
Find the Ratio of Technical Substitution
e)
Use your result in (d) to find the elasticity of substitution.
Answer
a)
MP
L
=
[K
1/2
+L
1/2
]
1
(1/2)L
1/2
MP
K
=
[K
1/2
+L
1/2
]
1
(1/2)K
1/2
b)
AP
L
=[K
1/2
+L
1/2
]
/L
AP
K
=[K
1/2
+L
1/2
]
/K
c) Suppose that we increase K and L by a factor of t, then we have:
Q* =
tK
tL
=
t
/ 2
K
L
t
/ 2
Q
Then:
i)
MP
K
= (K/L)
1/2
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 Fall '07
 McDevitt
 Economics, Microeconomics, Economics of production

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