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476 CHAPTER 11 MONOPOLY AND MONOPSONY
monopsonist desires to employ 1,000 more hours of labor per week above an initial
level of 4,000 hours per week, it will have to increase the wage from $10 per hour to
$12 per hour to do so, as shown in Figure 11.18. The firm’s total cost is the firm’s total
marginal expenditure expenditure on labor: TC wL. The firm’s marginal expenditure on labor—
on labor The rate at denoted by ME —is the rate at which the firm’s total cost goes up, per unit of labor,
L
which a firm’s total cost as it employs more labor. Figure 11.18 reveals that this additional cost has two com-
goes up, per unit of labor, ponents: areas I and II. Area I (w L) represents the extra cost that comes from em-
as it hires more labor.
ploying more workers. Area II (L w) is the extra cost that comes from having to raise
the wage for all units of labor that would have been supplied at the initial wage rate
of $10. The marginal expenditure on labor is thus:

¢TC area I area II
ME
L
¢L ¢L
w¢L L¢w

¢L
¢w
w L
¢L
Since the supply curve for labor is upward sloping, w/ L 0. The marginal expen-
diture curve therefore lies above the labor supply curve, as Figure 11.18 shows.
The coal mine’s profit-maximization problem is to choose a quantity of labor L to
maximize total profit , which is the difference between total revenue and total cost:
Pf(L) wL. The firm will maximize profit at the point at which marginal rev-
enue product of labor equals marginal expenditure on labor: MRP ME . The
L
L
profit maximum occurs in Figure 11.18 at a quantity of labor equal to 3,000 hours per
week. The wage rate needed to induce this supply of labor is $8 per hour, which is less
than the marginal expenditure on labor at L 3,000, at point T in the figure.
Why does the monopsonist fail to maximize profit if it hires more than 3,000 hours
per week? Consider what happens if it hires a 4,000th unit of labor. As Figure 11.18
shows, when L 4,000, ME MRP . The additional expenditure on that unit of
L
L
labor exceeds the additional revenues from the additional output that labor produces.
The firm would be better off not hiring that unit of labor (or any amount of labor
higher than 3,000 hours).
Similarly, the firm would not want to hire less than 3,000 hours of labor. If the
firm hired only 2,000 units, an additional unit of labor would bring in additional rev-
enues that exceed the additional expenditures (MRP ME ).
L
L

LEARNING-BY-DOING EXERCISE 11.8
S
D
E
Applying the Monopsonist’s Profit-Maximization Condition
Suppose that a monopsonist’s only input is Solution The monopsonist maximizes profit by
labor and its production function is Q 5L, where L is employing a quantity of labor corresponding to the
the quantity of labor (expressed in thousands of hours point where the marginal revenue product of labor
per week). Suppose, too, that the monopsonist can sell equals the marginal expenditure on labor.
all the output it wants at a market price of $10 per unit The marginal expenditure on labor is ME L w
and that the supply curve it faces for labor is w 2 2L. L( w/ L), where w/ L is the slope of the labor supply
curve. In this case, w/ L 2. Now we can substitute
Problem How much labor would the monopsonist this value for w/ L and the value for w given by the
hire, and what wage rate would it pay, to maximize profit?