Solutions for Sample Final Questions
Fall 2008
Problem 1
Suppose that the following production function represents a firm’s ability to manufacture pencils:
f(L,K) = 3
1/2
K
1/4
L
1/4
.
a)
Show that this production function exhibits decreasing returns to scale.
(
)
( )
( )
( )
( )
(
)
(
)
K
L
f
K
L
f
L
K
L
K
K
L
f
,
,
3
3
,
2
1
4
1
4
1
2
1
2
1
4
1
4
1
2
1
λ
λ
λ
λ
λ
λ
λ
<
=
=
=
So, we have decreasing returns to scale.
b)
Assume that the wage rate is equal to 9 and the rental rate on capital is equal to 4.
In
addition assume that the firm has a fixed cost of production equal to 16. Find the
compensated factor demands for labor and capital.
Find the cost of the cost minimizing
input bundle (ie find the variable cost curve) and the total cost curve.
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c)
Find the marginal cost function and the average cost function.
Graph the marginal cost
function and the average cost function in a single diagram.
Show that the optimal size of
the firm is 2.
What is the minimum value of the average cost curve?
d)
If this firm is a price taker then what is the firm's supply curve?
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 Spring '09
 Elmes
 Microeconomics, Supply And Demand, Sheila

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