Economics 151a
Spring 2008
Homework 2  Solutions
41. Suppose there are two inputs in the production function, labor and capital, and these
two inputs are perfect substitutes. The existing technology permits 1 machine to do the
work of 3 workers. The firm wants to produce 100 units of output. Suppose the price of
capital is $750 per machine per week. What combination of inputs will the firm use if the
weekly salary of each worker is $300? What combination of inputs will the firm use if the
weekly salary of each worker is $225? What is the elasticity of labor demand as the wage
falls from $300 to $225?
Because labor and capital are perfect substitutes, the isoquants (in bold) are linear and the firm
will use only labor or only capital, depending on which is cheaper in producing 100 units of
output.
The (absolute value of the) slope of the isoquant (
MP
E
/
MP
K
) is 1/3 because 1 machine does the
work of 3 workers. When the wage is $300 (left panel), the slope of the isocost is 300/750. The
isocost curve, therefore, is steeper than the isoquant, and the firm only hires capital (at point
A
).
When the weekly wage is $225 (right panel), the isoquant is steeper than the isocost and the firm
hires only labor (at point
B
).
Weekly Salary = $300
Weekly Salary = $225
The elasticity of labor demand is defined as the percentage change in labor divided by the
percentage change in the wage. Because the demand for labor goes from 0 to a positive quantity
when the wage dropped to $225, the (absolute value of the) elasticity of labor demand is infinity.
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View Full Document44. Consider a firm for which production depends on two normal inputs, labor and capital,
with prices
w
and
r
,
respectively. Initially the firm faces market prices of
w
= 6 and
r
= 4.
These prices then shift to
w
= 4 and
r
= 2.
(a) In which direction will the substitution effect change the firm’s employment and capital
stock?
Prior to the price shift, the absolute value of the slope of the isocost line (
w/r
) was 1.5. After the
price shift, the slope is 2. In other words, labor has become relatively more expensive than
capital. As a result, there will be a substitution away from labor and towards capital (the
substitution effect).
(b) In which direction will the scale effect change the firm’s employment and capital stock?
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 Spring '06
 Miller
 Economics, Supply And Demand, Ann, Chicken Hut

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