Answer to Practice Homework 6
7.3
At the optimum we must have
K
L
MP
MP
r
w
=
In this problem we have
200
1000
0.25
10
800
100
This implies that the firm receives more output per dollar spent on an additional machine
hour of fermentation capacity than for an additional hour spent on labor.
Therefore, the
firm could lower cost while achieving the same level of output by using fewer hours of
labor and more hours of fermentation capacity.
7.4
a)
If the price of both inputs change by the same percentage amount, the slope of the
isocost line will not change.
Since we are holding the level of output fixed, the
isocost line will be tangent to the isoquant at the same point as prior to the price
increase.
Therefore, the costminimizing quantities of the inputs will not change.
b)
If the price of capital increases by a larger percentage than the price of labor, then,
relatively speaking, the price of labor has become cheaper.
The firm will
substitute away from capital and add labor until either the tangency condition
holds or a corner solution is reached.
7.5
a)
The amount of land used in production is fixed in the shortrun. Hence, in the
shortrun the farmer chooses amount of capital and labor. It follows that cost
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 Spring '08
 Bryant
 Economics, 4 m, 1 k, 3 k, 1 3K, 3 1 3K

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