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ADD-ON 9B
PROFIT MAXIMIZATION BY A PRICE-TAKING FIRM WHEN
THE MARGINAL COST CURVE IS NOT UPWARD SLOPING
In Figures 9.6 and 9.7, as well as all of the other examples in Chapter 9, the firm’s marginal cost curve was upward sloping. This meant that there was only one positive sales
quantity at which price equaled marginal cost. In some cases, however, marginal cost may
fall over some ranges of output and rise over others. If so, then when applying the twostep procedure for finding a price-taking firm’s profit-maximizing output, there may be
more than one output level at which the price equals marginal cost.
Figure 9B.1 provides an example. In Figure 9B.1(a), the marginal cost curve first falls
and then rises as output increases. At price P⬘ which is above ACmin, there are two quantities
at which the price equals marginal cost, Q1 and Q2. Step 1 of the two-step procedure then
requires that we compare the profits at these two quantities. This is simple, though. If the
firm produces Q1, its average cost is above P⬘, so it earns a negative profit. In contrast, it
Figure 9B.1
An Example of Profit Maximization when the MC Curve Is Not Upward Sloping. In Figure (a), at price P# , marginal cost
equals price at two sales quantities, Q1 and Q2. At Q1, average cost is above marginal cost (and hence, P# ), so profit is negative.
At Q2, profit is positive, so that is the firm’s best positive sales quantity. Figure (b) shows the firm’s supply curve in green.
(a)
(b)
MC
AC
MC
Price ($)
$
P⬘
ACmin
ACmin
S(P)
Q1
Qe
Q2
Quantity
Qe
Quantity
Microeconomia
Douglas Bernheim, Michael Whinston Copyright © 2009 – The McGraw-Hill Companies srl
ber00279_add_09b_001-003.indd 1
10/29/07 12:48:56 PM
Chapter 9 Profit Maximization
makes a positive profit if it produces Q2 units. Thus, Q2 must be its most profitable positive
sales quantity when the price is P⬘. More generally, only sales quantities at which the marginal cost curve is above the average cost curve can yield a positive profit. As a result, the
firm’s supply curve, shown in Figure 9B.1(b), looks just like those we saw in Chapter 9.
Sometimes there can be several output levels at which the price equals marginal cost,
all of which occur where the marginal cost curve is above the average cost curve (so all
yield a positive profit). Figure 9B.2(a) shows such a case. For prices between P⬘ and P⬙,
there are three sales quantities at which P ⫽ MC. At P# , for example, these are Q1, Q2, and
Q3. Which is the most profitable? Consider an increase in the firm’s sales from Q1 to Q2.
At every quantity between those two, marginal cost is above P# . So, each sale in this range
adds less in revenue than it adds in cost. Now consider increasing the firm’s sales from Q2
to Q3. At every quantity between those two, the price P# is above marginal cost. So, each
sale in this range adds more in revenue than it adds in cost. This means that Q2 is less
profitable than either Q1 or Q3.
How do the profits at Q1 and Q3 compare? To answer this question, consider the
cumulative additions to revenues and costs as the sales quantity increases from Q1 to Q3.
The red-shaded area equals the total profit lost in moving from Q1 to Q2, while the greenshaded area equals the total profit gained in moving from Q2 to Q3. (This also equals the
change in producer surplus; see Section 9.5.) If the green-shaded region is bigger than the
red-shaded one, then profit is larger at Q3, while it is larger at Q1 if the reverse is true. In
Figure 9B.2
Another Example of Profit Maximization when the MC Curve Is Not Upward Sloping. In Figure (a), for prices between P⬘
and P ⬙, marginal cost equals price at more than one sales quantity. Because the red- and green-shaded areas are equal, at price
P# , the profits from selling Q1 units and Q3 units are equal, and exceed the profit from selling Q2 units. At prices between P⬘ and
P# , selling less than Q1 is best, while at prices between P# and P ⬙, selling more than Q3 is best. Figure (b) shows the firm’s supply
curve in green.
(a)
(b)
MC
MC
AC
P⬙
$
Price ($)
P
P⬘
Q1
Q2
P
Q3
Quantity
S(P)
Q1
Q3
Quantity
Microeconomia
Douglas Bernheim, Michael Whinston Copyright © 2009 – The McGraw-Hill Companies srl
ber00279_add_09b_001-003.indd 2
10/29/07 12:48:58 PM
Chapter 9 Profit Maximization
the figure, the two regions are equal, so the profits of these two quantities at price P# are
the same.
However, if the price falls below P# , the red-shaded area grows and the green-shaded
region shrinks. So at all prices between P# and P⬘, profits are maximized selling less than
Q1. Similarly, if the price rises above P# , the red-shaded area shrinks and the green-shaded
region grows. So at all prices between P# and P⬙, profits are maximized selling more than
Q3. Figure 9B.2(b) shows the resulting supply curve, which has a jump at price P# .
Microeconomia
Douglas Bernheim, Michael Whinston Copyright © 2009 – The McGraw-Hill Companies srl
ber00279_add_09b_001-003.indd 3
10/16/07 3:02:31 PM