[Joseph_E._Stiglitz,_Carl_E._Walsh]_Economics(Bookos.org) (1)

Thus, in Figure 8.5, at the price p 1 , the output is Q 1 (panel A), and the labor required
to produce that output (factor demand) is L 1 (panel B).
There is another way to derive the demand for a factor. If the firm hires one
more worker, for example, the extra (or marginal) cost to the firm is her wage. The
extra benefit of the worker is the additional revenue that the firm receives from selling
the output she produces. This is equal to the price at which the good sells multiplied
by the amount of extra output she produces. The extra output produced by
the worker is the marginal product of labor—the amount of output produced by the
last worker added by the firm. Thus the marginal benefit to the firm of adding an
extra worker is the price of the firm’s good multiplied by the marginal product of
labor. If adding an extra employee at the local Jiffy Lube enables the owner to handle
an extra 50 oil changes a month, and the price of each oil change is $25, then the
marginal benefit to the owner of adding the worker is $40 times 50, or $1,250 per
month. This dollar amount is called the value of the marginal product of labor.
While the marginal product of labor is measured in units of output (e.g., 50 oil changes
per month), the value of the marginal product is measured in dollars.
As long as the value of the marginal product of labor is greater than the marginal
cost of hiring the extra worker, the firm can increase its profits by hiring an
extra worker. In the Jiffy Lube example, as long as the added wage is less than $1,250
per month, it pays the owner to hire another worker. The firm hires labor up to the
point at which the value of the marginal product (the marginal benefit to the firm)
is equal to the price of labor, the wage (the marginal cost to the firm).
Using p for the price of the good, MPL for the marginal product
of labor, and w for the wage of the worker, we can write this
equilibrium condition as
value of marginal product = p × MPL = w = wage.
From this equilibrium condition, we can derive the demand
curve for labor. Figure 8.6 plots the value of the marginal product
of labor for each level of labor. Since the marginal product of labor
decreases as labor increases, the value of the marginal product also
decreases. When the wage is w 1 , the value of the marginal product
of labor equals the wage with a level of labor at L 1 . This is the firm’s
demand for labor at a wage w 1 . Thus, the curve giving the value of
the marginal product of labor at each level of employment is the
demand curve for labor.
It is easy to use this diagram to see the effect of an increase in
the price of the good the firm produces. In Figure 8.7, the higher
price increases the value of the marginal product of labor at each
level of employment, and it immediately follows that at each wage,
the demand for labor increases. The demand curve for labor shifts
to the right.
Thus, the demand for labor depends on both the wage and
the price the firm receives for the goods it sells. In fact, the demand
for labor depends only on the ratio of the two, as we will
now see.
WAGE (w )
w 2
w 1
Old demand curve
for labor
L 2 L 3 L 1
QUANTITY OF LABOR (L )
New demand curve
for labor (value of
marginal product at
higher price)
FIGURE 8.7
EFFECT OF PRICE CHANGE ON THE DEMAND
CURVE FOR LABOR
An increase in the price received by a firm shifts the value of
the marginal product of labor curve up, so that at each wage,
the demand for labor is increased. At wage w 1 , employment
rises from L 1 to L 4 ; at wage w 2 , employment rises from L 2
to L 3 .
L 4
FIRMS AND THE DEMAND FOR LABOR ∂ 183