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3 Marginal Revenue, Marginal Cost, and Profit Maximization
CHAPTER 8 • Profit Maximization and Competitive Supply 285
(dollars per year)
F IGURE 8.1
PROFIT MAXIMIZATION IN THE
A firm chooses output q*, so that profit, the
difference AB between revenue R and cost
C, is maximized. At that output, marginal
revenue (the slope of the revenue curve) is
equal to marginal cost (the slope of the cost
Output (units per year)
For the firm illustrated in Figure 8.1, profit is negative at low levels of output because revenue is insufficient to cover fixed and variable costs. As output
increases, revenue rises more rapidly than cost, so that profit eventually becomes
positive. Profit continues to increase until output reaches the level q*. At this
point, marginal revenue and marginal cost are equal, and the vertical distance
between revenue and cost, AB, is greatest. q* is the profit-maximizing output
level. Note that at output levels above q*, cost rises more rapidly than revenue—
i.e., marginal revenue is less than marginal cost. Thus, profit declines from its
maximum when output increases above q*.
The rule that profit is maximized when marginal revenue is equal to marginal
cost holds for all firms, whether competitive or not. This important rule can also
be derived algebraically. Profit, p = R - C, is maximized at the point at which
an additional increment to output leaves profit unchanged (i.e., ⌬p/⌬q = 0):
⌬p/⌬q = ⌬R/⌬q - ⌬C/⌬q = 0
⌬R/⌬q is marginal revenue MR and ⌬C/⌬q is marginal cost MC. Thus we conclude that profit is maximized when MR - MC = 0, so that
MR(q) = MC(q)
Demand and Marginal Revenue for a Competitive Firm
Because each firm in a competitive industry sells only a small fraction of the
entire industry output, how much output the firm decides to sell will have no effect
on the market price of the product. The market price is determined by the industry
demand and supply curves. Therefore, the competitive firm is a price taker. Recall
that price taking is one of the fundamental assumptions of perfect competition.
The price-taking firm knows that its production decision will have no effect on
the price of the product. For example, when a farmer is deciding how many acres
of wheat to plant in a given year, he can take the market price of wheat—say, $4
per bushel—as given. That price will not be affected by his acreage decision.
286 PART 2 • Producers, Consumers, and Competitive Markets
Often we will want to distinguish between market demand curves and the
demand curves faced by individual firms. In this chapter we will denote market output and demand by capital letters (Q and D) and the firm’s output and
demand by lowercase letters (q and d).
Because it is a price taker, the demand curve d facing an individual competitive
firm is given by a horizontal line. In Figure 8.2(a), the farmer’s demand curve corresponds to a price of $4 per bushel of wheat. The horizontal axis measures the
amount of wheat that the farmer can sell, and the vertical axis measures the
Compare the demand curve facing the firm (in this case, the farmer) in
Figure 8.2(a) with the market demand curve D in Figure 8.2(b). The market
demand curve shows how much wheat all consumers will buy at each possible
price. It is downward sloping because consumers buy more wheat at a lower
price. The demand curve facing the firm, however, is horizontal because the
firm’s sales will have no effect on price. Suppose the firm increased its sales
from 100 to 200 bushels of wheat. This would have almost no effect on the market because industry output is 2,000 million bushels. Price is determined by the
interaction of all firms and consumers in the market, not by the output decision
of a single firm.
By the same token, when an individual firm faces a horizontal demand curve,
it can sell an additional unit of output without lowering price. As a result, when
it sells an additional unit, the firm’s total revenue increases by an amount equal to
the price: one bushel of wheat sold for $4 yields additional revenue of $4. Thus,
marginal revenue is constant at $4. At the same time, average revenue received by
In §4.1, we explain how the
demand curve relates the
quantity of a good that a
consumer will buy to the
price of that good.
F IGURE 8.2
DEMAND CURVE FACED BY A COMPETITIVE FIRM
A competitive firm supplies only a small portion of the total output of all the firms in an industry.
Therefore, the firm takes the market price of the product as given, choosing its output on the
assumption that the price will be unaffected by the output choice. In (a) the demand curve facing
the firm is perfectly elastic, even though the market demand curve in (b) is downward sloping.
CHAPTER 8 • Profit Maximization and Competitive Supply 287
the firm is also $4 because every bushel of wheat produced will be sold at $4.
The demand curve d facing an individual firm in a competitive market is
both its average revenue curve and its marginal revenue curve. Along this
demand curve, marginal revenue, average revenue, and price are all equal.
Profit Maximization by a Competitive Firm
Because the demand curve facing a competitive firm is horizontal, so that
MR = P, the general rule for profit maximization that applies to any firm can
be simplified. A perfectly competitive firm should choose its output so that
marginal cost equals price:
MC(q) = MR = P
Note that because competitive firms take price as fixed, this is a rule for setting
output, not price.
The choice of the profit-maximizing output by a competitive firm is so important that we will devote most of the rest of this chapter to analyzing it. We begin
with the short-run output decision and then move to the long run.
8.4 Choosing Output in the Short Run
How much output should a firm produce over the short run, when its plant size
is fixed? In this section we show how a firm can use information about revenue
and cost to make a profit-maximizing output decision.
Short-Run Profit Maximization by a Competitive Firm
In the short run, a firm operates with a fixed amount of capital and must choose
the levels of its variable inputs (labor and materials) to maximize profit. Figure 8.3
shows the firm’s short-run decision. The average and marginal revenue curves are
drawn as a horizontal line at a price equal to $40. In this figure, we have drawn
the average total cost curve ATC, the average variable cost curve AVC, and the
marginal cost curve MC so that we can see the firm’s profit more easily.
Profit is maximized at point A, where output is q* ϭ 8 and the price is $40,
because marginal revenue is equal to marginal cost at this point. To see that
q* ϭ 8 is indeed the profit-maximizing output, note that at a lower output, say
q1 ϭ 7, marginal revenue is greater than marginal cost; profit could thus be
increased by increasing output. The shaded area between q1 ϭ 7 and q* shows
the lost profit associated with producing at q1. At a higher output, say q2, marginal cost is greater than marginal revenue; thus, reducing output saves a cost
that exceeds the reduction in revenue. The shaded area between q* and q2 ϭ 9
shows the lost profit associated with producing at q2. When output is q* ϭ 8,
profit is given by the area of rectangle ABCD.
The MR and MC curves cross at an output of q0 as well as q*. At q0, however,
profit is clearly not maximized. An increase in output beyond q0 increases
profit because marginal cost is well below marginal revenue. We can thus
Marginal, average, and total
cost are discussed in Đ7.1.
288 PART 2 Producers, Consumers, and Competitive Markets
Lost profit for
q1 < q*
Lost profit for
q2 > q*
AR = MR = P
F IGURE 8.3
A COMPETITIVE FIRM MAKING A POSITIVE PROFIT
In the short run, the competitive firm maximizes its profit by choosing an output q* at which its
marginal cost MC is equal to the price P (or marginal revenue MR) of its product. The profit of the
firm is measured by the rectangle ABCD. Any change in output, whether lower at q1 or higher at q2,
will lead to lower profit.
state the condition for profit maximization as follows: Marginal revenue equals
marginal cost at a point at which the marginal cost curve is rising. This conclusion
is very important because it applies to the output decisions of firms in markets that may or may not be perfectly competitive. We can restate it as follows:
Output Rule: If a firm is producing any output, it should produce at the level
at which marginal revenue equals marginal cost.
Figure 8.3 also shows the competitive firm’s short-run profit. The distance AB
is the difference between price and average cost at the output level q*, which is
the average profit per unit of output. Segment BC measures the total number of
units produced. Rectangle ABCD, therefore, is the firm’s profit.
A firm need not always earn a profit in the short run, as Figure 8.4 shows.
The major difference from Figure 8.3 is a higher fixed cost of production. This
higher fixed cost raises average total cost but does not change the average
variable cost and marginal cost curves. At the profit-maximizing output q*,
CHAPTER 8 • Profit Maximization and Competitive Supply 289
P = MR
F IGURE 8.4
A COMPETITIVE FIRM INCURRING LOSSES
A competitive firm should shut down if price is below AVC. The firm may produce in the
short run if price is greater than average variable cost.
the price P is less than average cost. Line segment AB, therefore, measures the
average loss from production. Likewise, the rectangle ABCD now measures the
firm’s total loss.
When Should the Firm Shut Down?
Suppose a firm is losing money. Should it shut down and leave the industry?
The answer depends in part on the firm’s expectations about its future business conditions. If it believes that conditions will improve and the business
will be profitable in the future, it might make sense to operate at a loss in the
short run. But let’s assume for the moment that the firm expects the price of
its product to remain the same for the foreseeable future. What, then, should
Note that the firm is losing money when its price is less than average total
cost at the profit-maximizing output q*. In that case, if there is little chance that
conditions will improve, it should shut down and leave the industry. This decision is appropriate even if price is greater than average variable cost, as shown
in Figure 8.4. If the firm continues to produce, the firm minimizes its losses at
output q*, but it will still have losses rather than profits because price is less
than average total cost. Note also that in Figure 8.4, because of the presence of
fixed costs, average total cost exceeds average variable cost, and average total
cost also exceeds price, so that the firm is indeed losing money. Recall that
290 PART 2 Producers, Consumers, and Competitive Markets
Remember from Đ7.1 that
a fixed cost is an ongoing
cost that does not change
with the level of output but
is eliminated if the firm shuts
fixed costs do not change with the level of output, but they can be eliminated
if the firm shuts down. (Examples of fixed costs include the salaries of plant
managers and security personnel, and the electricity to keep the lights and
Will shutting down always be the sensible strategy? Not necessarily. The
firm might operate at a loss in the short run because it expects to become profitable again in the future, when the price of its product increases or the cost of
production falls. Operating at a loss might be painful, but it will keep open
the prospect of better times in the future. Moreover, by staying in business,
the firm retains the flexibility to change the amount of capital that it uses
and thereby reduce its average total cost. This alternative seems particularly
appealing if the price of the product is greater than the average variable cost
of production, since operating at q* will allow the firm to cover a portion of its
Our example of a pizzeria in Chapter 7 (Example 7.2) provides a useful illustration. Recall that pizzerias have high fixed costs (the rent that must be paid,
the pizza ovens, and so on) and low variable costs (the ingredients and perhaps
some employee wages). Suppose the price that the pizzeria is charging its customers is below the average total cost of production.Then the pizzeria is losing
money by continuing to sell pizzas and it should shut down if it expects business conditions to remain unchanged in the future. But, should the owner sell
the store and go out of business? Not necessarily; that decision depends on the
owner’s expectation as to how the pizza business will fare in the future. Perhaps
adding jalapeno peppers, raising the price, and advertising the new spicy pizzas
will do the trick.
E XA MPLE 8.2 THE SHORT-RUN OUTPUT DECISION OF AN ALUMINUM
How should the manager of an
aluminum smelting plant determine the plant’s profit-maximizing
output? Recall from Example 7.3
(page 240) that the smelting plant’s
short-run marginal cost of production depends on whether it is running two or three shifts per day. As
shown in Figure 8.5, marginal cost
is $1140 per ton for output levels
up to 600 tons per day and $1300
per ton for output levels between
600 and 900 tons per day.
Suppose that the price of aluminum is initially P1 ϭ $1250 per
ton. In that case, the profit-maximizing output is 600 tons; the firm
can make a profit above its variable cost of $110
per ton by employing workers for two shifts a
day. Running a third shift would
involve overtime, and the price
of the aluminum is insufficient
to make the added production
profitable. Suppose, however,
that the price of aluminum were
to increase to P 2 ϭ $1360 per
ton. This price is greater than
the $1300 marginal cost of the
third shift, making it profitable
to increase output to 900 tons
Finally, suppose the price drops
to only $1100 per ton. In this case,
the firm should stop producing,
but it should probably stay in business. By taking this step, it could
resume producing in the future should the price
CHAPTER 8 • Profit Maximization and Competitive Supply 291
(dollars per ton)
Output (tons per day)
F IGURE 8.5
THE SHORT-RUN OUTPUT OF AN ALUMINUM SMELTING PLANT
In the short run, the plant should produce 600 tons per day if price is above
$1140 per ton but less than $1300 per ton. If price is greater than $1300 per
ton, it should run an overtime shift and produce 900 tons per day. If price drops
below $1140 per ton, the firm should stop producing, but it should probably
stay in business because the price may rise in the future.
EX AMPLE 8. 3 SOME COST CONSIDERATIONS FOR MANAGERS
The application of the rule that marginal revenue
should equal marginal cost depends on a manager’s ability to estimate marginal cost.3 To obtain
useful measures of cost, managers should keep
three guidelines in mind.
First, except under limited circumstances, average variable cost should not be used as a substitute
for marginal cost. When marginal and average variable cost are nearly constant, there is little difference
between them. However, if both marginal and average cost are increasing sharply, the use of average
variable cost can be misleading in deciding how much
to produce. Suppose for example, that a company
has the following cost information:
100 units per day, 80 of which are produced during the regular shift and
20 of which are produced during overtime
$8 per unit for all output
$30 per unit for the regular shift; $50 per unit for the overtime shift
This example draws on the discussion of costs and managerial decision making in Thomas Nagle and
Reed Holden, The Strategy and Tactics of Pricing, 5th ed. (Upper Saddle River, NJ: Prentice Hall, 2010), ch. 2.
292 PART 2 • Producers, Consumers, and Competitive Markets
Let’s calculate average variable cost and marginal cost
for the first 80 units of output and then see how both
cost measures change when we include the additional
20 units produced with overtime labor. For the first 80
units, average variable cost is simply the labor cost
($2400 ϭ $30 per unit ϫ 80 units) plus the materials
cost ($640 ϭ $8 per unit ϫ 80 units) divided by the
80 units—($2400 ϩ $640)/80 ϭ $38 per unit. Because
average variable cost is the same for each unit of output, marginal cost is also equal to $38 per unit.
When output increases to 100 units per day, both
average variable cost and marginal cost change.
The variable cost has now increased; it includes
the additional materials cost of $160 (20 units ϫ
$8 per unit) and the additional labor cost of $1000
(20 units ϫ $50 per unit). Average variable cost is
therefore the total labor cost plus the materials cost
($2400 ϩ $1000 ϩ $640 ϩ $160) divided by the
100 units of output, or $42 per unit.
What about marginal cost? While the materials cost
per unit has remained unchanged at $8 per unit, the
marginal cost of labor has now increased to $50 per
unit, so that the marginal cost of each unit of overtime
output is $58 per day. Because marginal cost is higher
than average variable cost, a manager who relies on
average variable cost will produce too much.
Second, a single item on a firm’s accounting ledger may have two components, only one of which
involves marginal cost. Suppose that a manager
is trying to cut back production. She reduces the
number of hours that some employees work and
lays off others. But the salary of an employee who
is laid off may not be an accurate measure of the
marginal cost of production when cuts are made.
Union contracts, for example, often require the firm
to pay laid-off employees part of their salaries. In
this case, the marginal cost of increasing production is not the same as the savings in marginal cost
when production is decreased. The savings is the
labor cost after the required layoff salary has been
Third, all opportunity costs should be included in
determining marginal cost. Suppose a department
store wants to sell children’s furniture. Instead of
building a new selling area, the manager decides
to use part of the third floor, which had been used
for appliances, for the furniture. The marginal cost
of this space is the $90 per square foot per day in
profit that would have been earned had the store
continued to sell appliances there. This opportunity
cost measure may be much greater than what the
store actually paid for that part of the building.
These three guidelines can help a manager to
measure marginal cost correctly. Failure to do so
can cause production to be too high or too low and
thereby reduce profit.
8.5 The Competitive Firm’s Short-Run
A supply curve for a firm tells us how much output it will produce at every possible price. We have seen that competitive firms will increase output to the point
at which price is equal to marginal cost, but will shut down if price is below
average variable cost. Therefore, the firm’s supply curve is the portion of the marginal cost curve for which marginal cost is greater than average variable cost.
Figure 8.6 illustrates the short-run supply curve. Note that for any P greater
than minimum AVC, the profit-maximizing output can be read directly from
the graph. At a price P1, for example, the quantity supplied will be q1; and at P2,
it will be q2. For P less than (or equal to) minimum AVC, the profit-maximizing
output is equal to zero. In Figure 8.6 the entire short-run supply curve consists
of the crosshatched portion of the vertical axis plus the marginal cost curve
above the point of minimum average variable cost.
Short-run supply curves for competitive firms slope upward for the same reason that marginal cost increases—the presence of diminishing marginal returns to
one or more factors of production. As a result, an increase in the market price will
induce those firms already in the market to increase the quantities they produce.
CHAPTER 8 • Profit Maximization and Competitive Supply 293
F IGURE 8.6
SUPPLY CURVE FOR
A COMPETITIVE FIRM
In the short run, the firm
chooses its output so that
marginal cost MC is equal to
price as long as the firm covers its average variable cost.
The short-run supply curve
is given by the crosshatched
portion of the marginal cost
P = AVC
The higher price not only makes the additional production profitable, but also
increases the firm’s total profit because it applies to all units that the firm produces.
The Firm’s Response to an Input Price Change
When the price of its product changes, the firm changes its output level to
ensure that marginal cost of production remains equal to price. Often, however,
the product price changes at the same time that the prices of inputs change. In
this section we show how the firm’s output decision changes in response to a
change in the price of one of its inputs.
Figure 8.7 shows a firm’s marginal cost curve that is initially given by MC1 when
the firm faces a price of $5 for its product. The firm maximizes profit by producing
(dollars per unit)
In §6.2, we explain that
diminishing marginal returns
occurs when each additional
increase in an input results
in a smaller and smaller
increase in output.
F IGURE 8.7
THE RESPONSE OF A FIRM TO A CHANGE
IN INPUT PRICE
When the marginal cost of production for a firm
increases (from MC1 to MC2), the level of output that
maximizes profit falls (from q1 to q2).