Thus far we have analyzed monopoly profit maximization in terms of the output decision. As was the case for competition, the manager can also maximize profit by choosing the optimal level of input usage. Choosing the optimal level of input
Now try Technical Problem 10.
D 50
350
Price and cost (dollars)
0 D
Quantity MR SMC1
55 A LAC
C B
LMC
ATC1
F I G U R E 12.5 Long-Run Profit Maximization under Monopoly
usage results in exactly the same output, price, and profit level as choosing the op- timal level of output would. We now discuss the monopoly firm’s input decision assuming that there is only one variable input.
The analytical principles underlying the input decision for the manager of a monopoly are the same as those for managers of perfectly competitive firms.
But since price does not equal marginal revenue for a monopoly, P × MP is not the correct measure of the marginal revenue product (MRP)—the increase in revenue attributable to hiring an additional unit of the variable input. Sup- pose a monopolist employs an additional unit of labor, which causes output to increase by the amount of the marginal product of labor. To sell this larger output, the manager must reduce the price of the good. Each additional unit adds marginal revenue (MR) to total revenue. Thus the additional unit of labor adds to total revenue an amount equal to marginal revenue times the marginal product of labor
MRP = ∆TR/∆L = MR × MP
For example, suppose hiring the 10th unit of labor increases output by 20 units (MP = 20). To sell these 20 additional units of output, the monopolist must lower price. Further suppose that marginal revenue is $5 per additional unit. Thus the additional revenue attributable to hiring the 10th unit of labor is the $5 additional revenue received on each of the 20 additional units of output produced and sold, or $100 (= $5 × 20). The marginal revenue product of the 10th unit of labor is $100.
Recall that in the case of perfect competition, marginal revenue product is mea- sured by multiplying price (= MR) by the marginal product of labor. Also recall that MRP for a perfect competitor declines because marginal product declines. For a monopolist, marginal revenue product declines with increases in input usage not only because marginal product declines but also because marginal revenue declines as output is increased.
Figure 12.6 shows the positive portion of MRP below ARP, which is the rele- vant portion of the MRP curve for a monopolist employing labor as its only vari- able input. Just as for a perfectly competitive firm, a monopolist shuts down and hires no labor when the wage rate exceeds average revenue product (w > ARP) at the level of input usage where MRP = w. Suppose the wage rate is $45. To maximize profit, the manager should hire 400 units of labor at a wage rate of $45.
To see why this is the optimal level of labor usage, suppose the manager hires only 300 units of labor. Hiring the 301st unit of labor adds slightly less than $58 to total revenue while adding only $45 to total cost. Clearly, hiring the 301st unit increases profit, in this case, $13 (= $58 − $45). The manager should continue to hire additional units of labor until MRP = w1 = $45 at point A in Figure 12.6. If the manager mistakenly hired more than 400 units, say, 500 units of labor, the additional revenue from hiring the last unit of labor ($30 for the 500th unit) is less than the additional cost, $45, and profit falls if the 500th worker is hired.
Getting rid of the 500th worker lowers cost by $45 but revenue falls by only $30;
marginal revenue product (MRP) The additional revenue attributable to hiring one additional unit of the input, which is also equal to the product of marginal revenue times marginal product, MRP = MR × MP.
thus, reducing labor by 1 unit increases profit by $15. And each additional 1 unit reduction in labor similarly increases profit until labor usage is reduced down to the 400th worker.
If the wage rate falls to $30 per unit (shown by the horizontal line w2), the man- ager should hire 500 units of labor (point B) to maximize monopoly profit. Simi- larly, at a wage of $58, the manager would hire 300 workers (point C). Thus you can see that, over the relevant range, the MRP curve is the monopolist’s demand curve for a single variable input.
We now show that a monopolist would never choose a level of variable input usage at which the average revenue product is less than the marginal revenue product (ARP < MRP). If, at the level of input usage where MRP = w,
MRP > ARP then
w > PQ/L and
wL > PQ
which implies that total variable cost exceeds total revenue, and the profit- maximizing monopolist would hire 0 units of the variable input and shut down.
F I G U R E 12.6 A Monopoly Firm’s D emand for Labor
300
Marginal revenue product and wage (dollars)
0
Units of labor
58 C
A
B
w1
w2 ARP5 P3AP 45
30
400 500
MRP5 MR 3MP
Principle When producing with a single variable input, a monopolist will maximize profit by employing that amount of the input for which marginal revenue product (MRP ) equals the price of the input when input price is given. Consequently, the MRP curve, over the relevant range, is the monopolist’s demand curve for the variable input when only one variable input is employed. The relevant range of the MRP curve is the downward-sloping, positive portion of MRP for which ARP > MRP.
Now try Technical Problems 11–12.
As for the case of a competitive firm, the manager of a firm with market power that employs two or more variable inputs maximizes profits by choosing input levels so that the marginal revenue product equals the input price for all inputs simultaneously.
Recall that, for a price-taking firm, the profit-maximizing condition that the marginal revenue product of labor equals the wage rate (MRP = w) is equiva- lent to the profit-maximizing condition that product price equals marginal cost (P = SMC). By “equivalent” we mean that regardless of whether the manager chooses Q or L to maximize profit, the resulting levels of output, labor usage, and profit are identical. We will now demonstrate that, for a monopolist, the profit-maximizing condition MRP = w is equivalent to the profit-maximizing condition MR = SMC.
Suppose the manager of a monopoly firm chooses the level of output to maxi- mize profit. The optimal output for the monopolist is where
MR = MC Recall from Chapter 8 that
SMC = ____MP w
where MP is the marginal product of labor and w is its price. Substituting this equation for marginal cost, the profit-maximizing condition MR = SMC can be expressed as
MR = ____MP w or
MR × MP = w MRP = w
Thus you can see that the two profit-maximizing rules are equivalent: MR = MC implies MRP = w, and vice versa.
Relation For a monopolist, the profit-maximizing condition that the marginal revenue product of the variable input must equal the price of the input (MRP = w ) is equivalent to the profit-maximizing condition that marginal revenue must equal marginal cost (MR = MC ). Thus, regardless of whether the manager chooses Q or L to maximize profit, the resulting levels of input usage, output, price, and profit are the same in either case.