Page 471 - Microeconomics, Fourth Edition

c11monopolyandmonopsony.qxd 7/14/10 7:58 PM Page 445

11.1 PROFIT MAXIMIZATION BY A MONOPOLIST 445

revenue sacrificed on the inframarginal units: TR area III area I $21 million
$6 million $15 million. Or, put another way, the monopolist’s total revenues go up
at a rate of $15 million/3 million ounces $5 per ounce.
To derive a general expression for marginal revenue, note that in Figure 11.3: 3

Area III price change in quantity P Q
Area I quantity change in price Q P

Thus, the change in the monopolist’s total revenue is: TR area III area I
P Q Q P.
If we divide this change in total revenue by the change in quantity, we get the rate
of change in total revenue with respect to quantity, or marginal revenue:

¢TR P¢Q Q¢P ¢P
MR P Q (11.2)
¢Q ¢Q ¢Q

Equation (11.2) indicates that marginal revenue consists of two parts. The first
part, P, corresponds to the increase in revenue due to higher volume—the marginal
units. The second part, Q( P/ Q) (which is negative, since P is negative), corre-
sponds to the decrease in revenue due to the reduced price of the inframarginal
units. Since Q( P/ Q) 0, then MR P. That is, the marginal revenue is less than
the price the monopolist can charge to sell that quantity, for any quantity greater
than 0.
When Q 0, equation (11.2) implies that marginal revenue and price are equal.
This makes sense in light of Figure 11.3. Suppose the monopolist charges a price of
$12 per ounce and thus sells zero output. To increase its output, the monopolist has
to lower its price, but starting at Q 0, it has no inframarginal units. That is, per
equation (11.2), marginal revenue equals price plus Q( P/ Q), but when Q 0,
Q( P/ Q) 0, and marginal revenue equals price.
Note that marginal revenue can either be positive or negative. It is negative if the
increased revenue the firm gets from selling additional volume is more than offset by
the decrease in revenue caused by the reduction in price on units that it could have
sold at a higher price. In fact, the greater the quantity, the more likely it is that mar-
ginal revenue will be negative because the reduced price (needed to sell more output)
affects more inframarginal units.

AVERAGE REVENUE AND MARGINAL REVENUE

In previous chapters, we usually contrasted the average of something with the mar-
ginal of the same thing (e.g., average product versus marginal product, average cost
versus marginal cost). For a monopolist, it is important to contrast average revenue
with marginal revenue because this will help explain why the monopolist’s marginal
revenue curve MR is not the same as its demand curve D, as shown in Figure 11.4(b)
[and first illustrated in Figure 11.2(b)].

3 We put a minus sign in front of this expression for area I because if price goes down, as in Figure 11.2,
the change in price will be negative. The minus sign ensures that the calculated area is a positive number.