The Theory of Imperfect Competition
In a perfectly competitive market—a market in which there are many buyers and sellers,
none of whom represents a large part of the market—firms are price takers. That is, they
are sellers of products who believe they can sell as much as they like at the current price
but cannot influence the price they receive for their product. For example, a wheat farmer
can sell as much wheat as she likes without worrying that if she tries to sell more wheat,
she will depress the market price. The reason she need not worry about the effect of her
sales on prices is that any individual wheat grower represents only a tiny fraction of the
world market.
When only a few firms produce a good, however, the situation is different. To take perhaps
the most dramatic example, the aircraft manufacturing giant Boeing shares the market
for large jet aircraft with only one major rival, the European firm Airbus. As a result,
Boeing knows that if it produces more aircraft, it will have a significant effect on the total
supply of planes in the world and will therefore significantly drive down the price of airplanes.
Or to put it another way, Boeing knows that if it wants to sell more airplanes, it can
do so only by significantly reducing its price. In imperfect competition, then, firms are
aware that they can influence the prices of their products and that they can sell more only
by reducing their price. This situation occurs in one of two ways: when there are only a
few major producers of a particular good, or when each firm produces a good that is differentiated
(in the eyes of the consumer) from that of rival firms. As we mentioned in the
introduction, this type of competition is an inevitable outcome when there are economies
CHAPTER 8 Firms in the Global Economy 157
of scale at the level of the firm: The number of surviving firms is forced down to a small
number and/or firms must develop products that are clearly differentiated from those produced
by their rivals. Under these circumstances, each firm views itself as a price setter,
choosing the price of its product, rather than a price taker.
When firms are not price takers, it is necessary to develop additional tools to describe
how prices and outputs are determined. The simplest imperfectly competitive market
structure to examine is that of a pure monopoly, a market in which a firm faces no competition;
the tools we develop for this structure can then be used to examine more complex
market structures.
Monopoly: A Brief Review
Figure 8-1 shows the position of a single monopolistic firm. The firm faces a downwardsloping
demand curve, shown in the figure as D. The downward slope of D indicates that
the firm can sell more units of output only if the price of the output falls. As you may recall
from basic microeconomics, a marginal revenue curve corresponds to the demand curve.
Marginal revenue is the extra or marginal revenue the firm gains from selling an additional
unit. Marginal revenue for a monopolist is always less than the price because to sell an
additional unit, the firm must lower the price of all units (not just the marginal one). Thus
for a monopolist, the marginal revenue curve, MR, always lies below the demand curve.
Marginal Revenue and Price For our analysis of the monopolistic competition model
later in this section, it is important for us to determine the relationship between the price
the monopolist receives per unit and marginal revenue. Marginal revenue is always less
than the price—but how much less? The relationship between marginal revenue and price
depends on two things. First, it depends on how much output the firm is already selling:
A firm that is not selling very many units will not lose much by cutting the price it receives
on those units. Second, the gap between price and marginal revenue depends on the slope
of the demand curve, which tells us how much the monopolist has to cut his price to sell
one more unit of output. If the curve is very flat, then the monopolist can sell an additional
unit with only a small price cut. As a result, he will not have to lower the price by very
Cost, C and
Price, P
PM
AC
QM Quantity, Q
D
MC
MR
AC
Monopoly profits
Figure 8-1
Monopolistic Pricing and Production Decisions
A monopolistic firm chooses an output at which marginal
revenue, the increase in revenue from selling an
additional unit, equals marginal cost, the cost of producing
an additional unit. This profit-maximizing output
is shown as ; the price at which this output is
demanded is . The marginal revenue curve MR lies
below the demand curve D because, for a monopoly,
marginal revenue is always less than the price. The
monopoly’s profits are equal to the area of the shaded
rectangle, the difference between price and average
cost times the amount of output sold.
PM
QM
158 PART ONE International Trade Theory
much on the units he would otherwise have sold, so marginal revenue will be close to the
price per unit. On the other hand, if the demand curve is very steep, selling an additional
unit will require a large price cut, implying that marginal revenue will be much less than
the price.
We can be more specific about the relationship between price and marginal revenue if
we assume that the demand curve the firm faces is a straight line. When this is the case, the
dependence of the monopolist’s total sales on the price it charges can be represented by an
equation of the form
(8-1)
where Q is the number of units the firm sells, P the price it charges per unit, and A and B are
constants. We show in the appendix to this chapter that in this case, marginal revenue is
(8-2)
implying that
Equation (8-2) reveals that the gap between price and marginal revenue depends on the
initial sales, Q, of the firm and the slope parameter, B, of its demand curve. If sales quantity,
Q, is higher, marginal revenue is lower, because the decrease in price required to sell a
greater quantity costs the firm more. In other words, the greater is B, the more sales fall for
any given increase in price and the closer the marginal revenue is to the price of the good.
Equation (8-2) is crucial for our analysis of the monopolistic competition model of trade
in the upcoming section.
Average and Marginal Costs Returning to Figure 8-1, AC represents the firm’s
average cost of production, that is, its total cost divided by its output. The downward
slope reflects our assumption that there are economies of scale, so the larger the firm’s
output, the lower its costs per unit. MC represents the firm’s marginal cost (the
amount it costs the firm to produce one extra unit). In the figure, we assumed that the
firm’s marginal cost is constant (the marginal cost curve is flat). The economies of
scale must then come from a fixed production cost. This fixed cost pushes the average
cost above the constant marginal cost of production, though the difference between the
two becomes smaller and smaller as the fixed cost is spread over an increasing number
of output units.
If we denote c as the firm’s marginal cost and F as the fixed cost, then we can write the
firm’s total cost (C) as
(8-3)
where Q is once again the firm’s output. Given this linear cost function, the firm’s average
cost is
(8-4)
As we have discussed, this average cost is always greater than the marginal cost c, and declines
with output produced Q.
If, for example, and , the average cost of producing 10 units is
, and the average cost of producing 25 units is .
These numbers may look familiar, because they were used to construct Table 7-1 in the
(5/10) + 1 = 1.5 (5/25) + 1 = 1.2
F = 5 c = 1
AC = C/Q = (F/Q) + c.
C = F + c * Q,
P - MR = Q/B.
Marginal revenue = MR = P - Q/B,
Q = A - B * P,
CHAPTER 8 Firms in the Global Economy 159
2The economic definition of profits is not the same as that used in conventional accounting, where any revenue
over and above labor and material costs is called a profit. A firm that earns a rate of return on its capital less than
what that capital could have earned in other industries is not making profits; from an economic point of view, the
normal rate of return on capital represents part of the firm’s costs, and only returns over and above that normal
rate of return represent profits.
previous chapter. (However, in this case, we assume a unit wage cost for the labor input,
and that the technology now applies to a firm instead of an industry.) The marginal
and average cost curves for this specific numeric example are plotted in Figure 8-2.
Average cost approaches infinity at zero output and approaches marginal cost at very
large output.
The profit-maximizing output of a monopolist is that at which marginal revenue (the
revenue gained from selling an extra unit) equals marginal cost (the cost of producing an
extra unit), that is, at the intersection of the MC and MR curves. In Figure 8-1 we can see
that the price at which the profit-maximizing output is demanded is , which is
greater than average cost. When , the monopolist is earning some monopoly profits,
as indicated by the shaded box.2
Monopolistic Competition
Monopoly profits rarely go uncontested. A firm making high profits normally attracts
competitors. Thus situations of pure monopoly are rare in practice. Instead, the usual market
structure in industries characterized by internal economies of scale is one of oligopoly,
in which several firms are each large enough to affect prices, but none has an uncontested
monopoly.
The general analysis of oligopoly is a complex and controversial subject because in oligopolies,
the pricing policies of firms are interdependent. Each firm in an oligopoly will,
in setting its price, consider not only the responses of consumers but also the expected
responses of competitors. These responses, however, depend in turn on the competitors’
expectations about the firm’s behavior—and we are therefore in a complex game in which
firms are trying to second-guess each other’s strategies. We will briefly discuss an example
of an oligopoly model with two firms in Chapter 12. For now, we focus on a special case
of oligopoly known as monopolistic competition. Over the last 30 years, research in
P 7 AC
QM PM
Cost per unit
Average cost
Marginal cost
6
5
4
3
2
1
0
2 4 6
Output
8 10 12 14 16 18 20 22 24
Figure 8-2
Average versus Marginal Cost
This figure illustrates the average
and marginal costs corresponding
to the total cost function
. Marginal cost is
always 1; average cost declines
as output rises.
C = 5 + x
160 PART ONE International Trade Theory
international trade has increasingly relied on models based on monopolistic competition.
This model can capture the key elements of imperfect competition based on internal
economies of scale and product differentiation at the firm level. At the same time, this
model remains relatively easy to analyze, even in a setting where economy-wide prices are
affected by international trade.
In monopolistic competition models, two key assumptions are made to get around the
problem of interdependence. First, each firm is assumed to be able to differentiate its product
from that of its rivals. That is, because a firm’s customers want to buy that particular
firm’s product, they will not rush to buy other firms’ products because of a slight price difference.
Product differentiation thus ensures that each firm has a monopoly in its particular
product within an industry and is therefore somewhat insulated from competition. Second,
each firm is assumed to take the prices charged by its rivals as given—that is, it ignores the
impact of its own price on the prices of other firms. As a result, the monopolistic competition
model assumes that even though each firm is in reality facing competition from other
firms, each firm behaves as if it were a monopolist—hence the model’s name.
Are there any monopolistically competitive industries in the real world? The first
assumption of product differentiation across firms fits very well with the empirical evidence
in most industries. The extent of product differentiation varies widely across industries,
but consumers do perceive differences across products sold by different firms in most
sectors (even if the “actual” differences across products are very small, such as in the case
of bottled water). The second assumption—that firms ignore the consequence on rival
firms of their pricing decisions—is more of an approximation. In some sectors (such as
large jet aircraft), a small number of firms account for a very large percentage of the overall
market share. Firms in those sectors are much more likely to engage in strategic pricing
decisions with their rivals. However, these strategic effects dissipate quickly as the market
share of the largest firms drops. In any event, the main appeal of the monopolistic competition
model is not its realism but its simplicity. As we will see in the next section of this
chapter, the monopolistic competition model gives us a very clear view of how economies
of scale can give rise to mutually beneficial trade.
Before we can examine trade, however, we need to develop a basic model of monopolistic
competition. Let us therefore imagine an industry consisting of a small number of
firms. These firms produce differentiated products, that is, goods that are not exactly the
same but that could be substitutes for one another. Each firm is therefore a monopolist in
the sense that it is the only firm producing its particular good, but the demand for its good
depends on the number of other similar products available and on the prices of other firms’
products in the industry.
Assumptions of the Model We begin by describing the demand facing a typical
monopolistically competitive firm. In general, we would expect a firm to sell more the
larger the total demand for its industry’s product and the higher the prices charged by its
rivals. On the other hand, we would expect the firm to sell less the greater the number of
firms in the industry and the higher its own price. A particular equation for the demand
facing a firm that has these properties is3
Q = S * [1/n - b * (P - P)], (8-5)
3Equation (8-5) can be derived from a model in which consumers have different preferences and firms produce
varieties tailored to particular segments of the market. See Stephen Salop, “Monopolistic Competition with
Outside Goods,” Bell Journal of Economics 10 (1979), pp. 141–156, for a development of this approach.
where Q is the quantity of output demanded, S is the total output of the industry, n is the
number of firms in the industry, b is a constant term representing the responsiveness of a
firm’s sales to its price, P is the price charged by the firm itself, and is the average price
charged by its competitors. Equation (8-5) may be given the following intuitive justification:
If all firms charge the same price, each will have a market share 1/n. A firm charging
more than the average of other firms will have a smaller market share, whereas a firm
charging less will have a larger share.4
It is helpful to assume that total industry output S is unaffected by the average price
charged by firms in the industry. That is, we assume that firms can gain customers only at
each other’s expense. This is an unrealistic assumption, but it simplifies the analysis and
helps us focus on the competition among firms. In particular, it means that S is a measure
of the size of the market and that if all firms charge the same price, each sells S/n units.
Next we turn to the costs of a typical firm. Here we simply assume that total and average
costs of a typical firm are described by equations (8-3) and (8-4). Note that in this initial
model, we assume that all firms are symmetric even though they produce differentiated
products: They all face the same demand curve (8-5) and have the same cost function (8-3).
We will relax this assumption in the next section.
Market Equilibrium When the individual firms are symmetric, the state of the industry
can be described without describing any of the features of individual firms: All we really
need to know to describe the industry is how many firms there are and what price the
typical firm charges. To analyze the industry—for example, to assess the effects of
international trade—we need to determine the number of firms n and the average price
they charge . Once we have a method for determining n and , we can ask how they are
affected by international trade.
Our method for determining n and involves three steps. (1) First, we derive a relationship
between the number of firms and the average cost of a typical firm. We show
that this relationship is upward sloping; that is, the more firms there are, the lower the
output of each firm, and thus the higher each firm’s cost per unit of output. (2) We next
show the relationship between the number of firms and the price each firm charges, which
must equal in equilibrium. We show that this relationship is downward sloping: The
more firms there are, the more intense is the competition among firms, and as a result the
lower the prices they charge. (3) Finally, we introduce firm entry and exit decisions based
on the profits that each firm earns. When price exceeds average cost, firms earn positive
profits and additional firms will enter the industry; conversely, when the price is less than
average cost, profits are negative and those losses induce some firms to exit. In the long
run, this entry and exit process drives profits to zero, and the number of firms is determined
by the intersection of the curve that relates average cost to n and the curve that
relates price to n.
1. The number of firms and average cost. As a first step toward determining n and
, we ask how the average cost of a typical firm depends on the number of firms in the
industry. Since all firms are symmetric in this model, in equilibrium they all will
charge the same price. But when all firms charge the same price, so that ,
equation (8-5) tells us that ; that is, each firm’s output Q is a l/n share of the
total industry sales S. But we saw in equation (8-4) that average cost depends inversely
Q = S/n
P = P
P
P
P
P P
P
P
CHAPTER 8 Firms in the Global Economy 161
4Equation (8-5) may be rewritten as . If , this equation reduces to .
If P 7 P, Q 6 S/n, while if P 6 P, Q 7 S/n.
Q = (S/n) - S * b * (P - P) P = P Q = S/n
162 PART ONE International Trade Theory
on a firm’s output. We therefore conclude that average cost depends on the size of the
market and the number of firms in the industry:
(8-6)
Equation (8-6) tells us that other things equal, the more firms there are in the industry,
the higher is average cost. The reason is that the more firms there are, the less each
firm produces. For example, imagine an industry with total sales of 1 million widgets
annually. If there are five firms in the industry, each will sell 200,000 annually. If there
are ten firms, each will sell only 100,000, and therefore each firm will have higher
average cost. The upward-sloping relationship between n and average cost is shown as
CC in Figure 8-3.
2. The number of firms and the price. Meanwhile, the price the typical firm charges
also depends on the number of firms in the industry. In general, we would expect that
the more firms there are, the more intense will be the competition among them, and
AC = F/Q + c = (n * F/S ) + c.
Cost C, and
Price, P
P3
AC3
Number
of firms, n
n3 n2 n1
PP
CC
E
AC1
P1
P2, AC2
Figure 8-3
Equilibrium in a Monopolistically Competitive Market
The number of firms in a monopolistically competitive market, and the prices they
charge, are determined by two relationships. On one side, the more firms there are,
the more intensely they compete, and hence the lower is the industry price. This
relationship is represented by PP. On the other side, the more firms there are, the
less each firm sells and therefore the higher is the industry’s average cost. This relationship
is represented by CC. If price exceeds average cost (that is, if the PP curve
is above the CC curve), the industry will be making profits and additional firms will
enter the industry; if price is less than average cost, the industry will be incurring
losses and firms will leave the industry. The equilibrium price and number of firms
occurs when price equals average cost, at the intersection of PP and CC.
CHAPTER 8 Firms in the Global Economy 163
hence the lower the price. This turns out to be true in this model, but proving it takes a
moment. The basic trick is to show that each firm faces a straight-line demand curve of
the form we showed in equation (8-1), and then to use equation (8-2) to determine
prices.
First recall that in the monopolistic competition model, firms are assumed to take
each other’s prices as given; that is, each firm ignores the possibility that if it changes
its price, other firms will also change theirs. If each firm treats as given, we can
rewrite the demand curve (8-5) in the form
(8-7)
where b is the parameter in equation (8-5) that measured the sensitivity of each firm’s
market share to the price it charges. Now this equation is in the same form as
(8-1), with in place of the constant term A and in place of
the slope coefficient B. If we plug these values back into the formula for marginal revenue,
(8-2), we have a marginal revenue for a typical firm of
(8-8)
Profit-maximizing firms will set marginal revenue equal to their marginal cost, c, so
that
which can be rearranged to give the following equation for the price charged by a typical
firm:
(8-9)
We have already noted, however, that if all firms charge the same price, each will sell
an amount . Plugging this back into (8-9) gives us a relationship between the
number of firms and the price each firm charges:
(8-10)
Equation (8-10) says algebraically that the more firms there are in an industry, the
lower the price each firm will charge. This is because each firm’s markup over marginal
cost, , decreases with the number of competing firms.
Equation (8-10) is shown in Figure 8-3 as the downward-sloping curve PP.
3. The equilibrium number of firms. Let us now ask what Figure 8-3 means. We
have summarized an industry by two curves. The downward-sloping curve PP shows
that the more firms there are in the industry, the lower the price each firm will charge.
This makes sense: The more firms there are, the more competition each firm faces. The
upward-sloping curve CC tells us that the more firms there are in the industry, the
higher the average cost of each firm. This also makes sense: If the number of firms
increases, each firm will sell less, so firms will not be able to move as far down their
average cost curve.
The two schedules intersect at point E, corresponding to the number of firms . The
significance of is that it is the zero-profit number of firms in the industry. When there
are firms in the industry, their profit-maximizing price is , which is exactly equal to
their average cost . What we will now argue is that in the long run, the number
of firms in the industry tends to move toward , so that point E describes the industry’s
long-run equilibrium.
n2
AC2
n2 P2
n2
n2
P - c = 1/(b * n)
P = c + 1/(b * n).
Q = S/n
P = c + Q/(S * b).
MR = P - Q/(S * b) = c,
MR = P - Q/(S * b).
(S/n) + S * b * P S * b
Q = [(S/n) + S * b * P] - S * b * P,
P
164 PART ONE International Trade Theory
5This analysis slips past a slight problem: The number of firms in an industry must, of course, be a whole number
like 5 or 8. What if turns out to equal 6.37? The answer is that there will be six firms in the industry, all making
small monopoly profits and not being challenged by new entrants because everyone knows that a seven-firm
industry would lose money. In most examples of monopolistic competition, this whole-number or “integer constraint”
problem turns out not to be very important, and we ignore it here.
n2
To see why, suppose that n were less than , say . Then the price charged by firms
would be , while their average cost would be only . Thus firms would be making
monopoly profits. Conversely, suppose that n were greater than , say . Then firms
would charge only the price , while their average cost would be . Firms would be
suffering losses.
Over time, firms will enter an industry that is profitable and exit one in which they lose
money. The number of firms will rise over time if it is less than , fall if it is greater. This
means that is the equilibrium number of firms in the industry and that is the equilibrium
price.5
We have just developed a model of a monopolistically competitive industry in which
we can determine the equilibrium number of firms and the average price that firms charge.
We now use this model to derive some important conclusions about the role of economies
of scale in international trade.
In a perfectly competitive market—a market in which there are many buyers and sellers,
none of whom represents a large part of the market—firms are price takers. That is, they
are sellers of products who believe they can sell as much as they like at the current price
but cannot influence the price they receive for their product. For example, a wheat farmer
can sell as much wheat as she likes without worrying that if she tries to sell more wheat,
she will depress the market price. The reason she need not worry about the effect of her
sales on prices is that any individual wheat grower represents only a tiny fraction of the
world market.
When only a few firms produce a good, however, the situation is different. To take perhaps
the most dramatic example, the aircraft manufacturing giant Boeing shares the market
for large jet aircraft with only one major rival, the European firm Airbus. As a result,
Boeing knows that if it produces more aircraft, it will have a significant effect on the total
supply of planes in the world and will therefore significantly drive down the price of airplanes.
Or to put it another way, Boeing knows that if it wants to sell more airplanes, it can
do so only by significantly reducing its price. In imperfect competition, then, firms are
aware that they can influence the prices of their products and that they can sell more only
by reducing their price. This situation occurs in one of two ways: when there are only a
few major producers of a particular good, or when each firm produces a good that is differentiated
(in the eyes of the consumer) from that of rival firms. As we mentioned in the
introduction, this type of competition is an inevitable outcome when there are economies
CHAPTER 8 Firms in the Global Economy 157
of scale at the level of the firm: The number of surviving firms is forced down to a small
number and/or firms must develop products that are clearly differentiated from those produced
by their rivals. Under these circumstances, each firm views itself as a price setter,
choosing the price of its product, rather than a price taker.
When firms are not price takers, it is necessary to develop additional tools to describe
how prices and outputs are determined. The simplest imperfectly competitive market
structure to examine is that of a pure monopoly, a market in which a firm faces no competition;
the tools we develop for this structure can then be used to examine more complex
market structures.
Monopoly: A Brief Review
Figure 8-1 shows the position of a single monopolistic firm. The firm faces a downwardsloping
demand curve, shown in the figure as D. The downward slope of D indicates that
the firm can sell more units of output only if the price of the output falls. As you may recall
from basic microeconomics, a marginal revenue curve corresponds to the demand curve.
Marginal revenue is the extra or marginal revenue the firm gains from selling an additional
unit. Marginal revenue for a monopolist is always less than the price because to sell an
additional unit, the firm must lower the price of all units (not just the marginal one). Thus
for a monopolist, the marginal revenue curve, MR, always lies below the demand curve.
Marginal Revenue and Price For our analysis of the monopolistic competition model
later in this section, it is important for us to determine the relationship between the price
the monopolist receives per unit and marginal revenue. Marginal revenue is always less
than the price—but how much less? The relationship between marginal revenue and price
depends on two things. First, it depends on how much output the firm is already selling:
A firm that is not selling very many units will not lose much by cutting the price it receives
on those units. Second, the gap between price and marginal revenue depends on the slope
of the demand curve, which tells us how much the monopolist has to cut his price to sell
one more unit of output. If the curve is very flat, then the monopolist can sell an additional
unit with only a small price cut. As a result, he will not have to lower the price by very
Cost, C and
Price, P
PM
AC
QM Quantity, Q
D
MC
MR
AC
Monopoly profits
Figure 8-1
Monopolistic Pricing and Production Decisions
A monopolistic firm chooses an output at which marginal
revenue, the increase in revenue from selling an
additional unit, equals marginal cost, the cost of producing
an additional unit. This profit-maximizing output
is shown as ; the price at which this output is
demanded is . The marginal revenue curve MR lies
below the demand curve D because, for a monopoly,
marginal revenue is always less than the price. The
monopoly’s profits are equal to the area of the shaded
rectangle, the difference between price and average
cost times the amount of output sold.
PM
QM
158 PART ONE International Trade Theory
much on the units he would otherwise have sold, so marginal revenue will be close to the
price per unit. On the other hand, if the demand curve is very steep, selling an additional
unit will require a large price cut, implying that marginal revenue will be much less than
the price.
We can be more specific about the relationship between price and marginal revenue if
we assume that the demand curve the firm faces is a straight line. When this is the case, the
dependence of the monopolist’s total sales on the price it charges can be represented by an
equation of the form
(8-1)
where Q is the number of units the firm sells, P the price it charges per unit, and A and B are
constants. We show in the appendix to this chapter that in this case, marginal revenue is
(8-2)
implying that
Equation (8-2) reveals that the gap between price and marginal revenue depends on the
initial sales, Q, of the firm and the slope parameter, B, of its demand curve. If sales quantity,
Q, is higher, marginal revenue is lower, because the decrease in price required to sell a
greater quantity costs the firm more. In other words, the greater is B, the more sales fall for
any given increase in price and the closer the marginal revenue is to the price of the good.
Equation (8-2) is crucial for our analysis of the monopolistic competition model of trade
in the upcoming section.
Average and Marginal Costs Returning to Figure 8-1, AC represents the firm’s
average cost of production, that is, its total cost divided by its output. The downward
slope reflects our assumption that there are economies of scale, so the larger the firm’s
output, the lower its costs per unit. MC represents the firm’s marginal cost (the
amount it costs the firm to produce one extra unit). In the figure, we assumed that the
firm’s marginal cost is constant (the marginal cost curve is flat). The economies of
scale must then come from a fixed production cost. This fixed cost pushes the average
cost above the constant marginal cost of production, though the difference between the
two becomes smaller and smaller as the fixed cost is spread over an increasing number
of output units.
If we denote c as the firm’s marginal cost and F as the fixed cost, then we can write the
firm’s total cost (C) as
(8-3)
where Q is once again the firm’s output. Given this linear cost function, the firm’s average
cost is
(8-4)
As we have discussed, this average cost is always greater than the marginal cost c, and declines
with output produced Q.
If, for example, and , the average cost of producing 10 units is
, and the average cost of producing 25 units is .
These numbers may look familiar, because they were used to construct Table 7-1 in the
(5/10) + 1 = 1.5 (5/25) + 1 = 1.2
F = 5 c = 1
AC = C/Q = (F/Q) + c.
C = F + c * Q,
P - MR = Q/B.
Marginal revenue = MR = P - Q/B,
Q = A - B * P,
CHAPTER 8 Firms in the Global Economy 159
2The economic definition of profits is not the same as that used in conventional accounting, where any revenue
over and above labor and material costs is called a profit. A firm that earns a rate of return on its capital less than
what that capital could have earned in other industries is not making profits; from an economic point of view, the
normal rate of return on capital represents part of the firm’s costs, and only returns over and above that normal
rate of return represent profits.
previous chapter. (However, in this case, we assume a unit wage cost for the labor input,
and that the technology now applies to a firm instead of an industry.) The marginal
and average cost curves for this specific numeric example are plotted in Figure 8-2.
Average cost approaches infinity at zero output and approaches marginal cost at very
large output.
The profit-maximizing output of a monopolist is that at which marginal revenue (the
revenue gained from selling an extra unit) equals marginal cost (the cost of producing an
extra unit), that is, at the intersection of the MC and MR curves. In Figure 8-1 we can see
that the price at which the profit-maximizing output is demanded is , which is
greater than average cost. When , the monopolist is earning some monopoly profits,
as indicated by the shaded box.2
Monopolistic Competition
Monopoly profits rarely go uncontested. A firm making high profits normally attracts
competitors. Thus situations of pure monopoly are rare in practice. Instead, the usual market
structure in industries characterized by internal economies of scale is one of oligopoly,
in which several firms are each large enough to affect prices, but none has an uncontested
monopoly.
The general analysis of oligopoly is a complex and controversial subject because in oligopolies,
the pricing policies of firms are interdependent. Each firm in an oligopoly will,
in setting its price, consider not only the responses of consumers but also the expected
responses of competitors. These responses, however, depend in turn on the competitors’
expectations about the firm’s behavior—and we are therefore in a complex game in which
firms are trying to second-guess each other’s strategies. We will briefly discuss an example
of an oligopoly model with two firms in Chapter 12. For now, we focus on a special case
of oligopoly known as monopolistic competition. Over the last 30 years, research in
P 7 AC
QM PM
Cost per unit
Average cost
Marginal cost
6
5
4
3
2
1
0
2 4 6
Output
8 10 12 14 16 18 20 22 24
Figure 8-2
Average versus Marginal Cost
This figure illustrates the average
and marginal costs corresponding
to the total cost function
. Marginal cost is
always 1; average cost declines
as output rises.
C = 5 + x
160 PART ONE International Trade Theory
international trade has increasingly relied on models based on monopolistic competition.
This model can capture the key elements of imperfect competition based on internal
economies of scale and product differentiation at the firm level. At the same time, this
model remains relatively easy to analyze, even in a setting where economy-wide prices are
affected by international trade.
In monopolistic competition models, two key assumptions are made to get around the
problem of interdependence. First, each firm is assumed to be able to differentiate its product
from that of its rivals. That is, because a firm’s customers want to buy that particular
firm’s product, they will not rush to buy other firms’ products because of a slight price difference.
Product differentiation thus ensures that each firm has a monopoly in its particular
product within an industry and is therefore somewhat insulated from competition. Second,
each firm is assumed to take the prices charged by its rivals as given—that is, it ignores the
impact of its own price on the prices of other firms. As a result, the monopolistic competition
model assumes that even though each firm is in reality facing competition from other
firms, each firm behaves as if it were a monopolist—hence the model’s name.
Are there any monopolistically competitive industries in the real world? The first
assumption of product differentiation across firms fits very well with the empirical evidence
in most industries. The extent of product differentiation varies widely across industries,
but consumers do perceive differences across products sold by different firms in most
sectors (even if the “actual” differences across products are very small, such as in the case
of bottled water). The second assumption—that firms ignore the consequence on rival
firms of their pricing decisions—is more of an approximation. In some sectors (such as
large jet aircraft), a small number of firms account for a very large percentage of the overall
market share. Firms in those sectors are much more likely to engage in strategic pricing
decisions with their rivals. However, these strategic effects dissipate quickly as the market
share of the largest firms drops. In any event, the main appeal of the monopolistic competition
model is not its realism but its simplicity. As we will see in the next section of this
chapter, the monopolistic competition model gives us a very clear view of how economies
of scale can give rise to mutually beneficial trade.
Before we can examine trade, however, we need to develop a basic model of monopolistic
competition. Let us therefore imagine an industry consisting of a small number of
firms. These firms produce differentiated products, that is, goods that are not exactly the
same but that could be substitutes for one another. Each firm is therefore a monopolist in
the sense that it is the only firm producing its particular good, but the demand for its good
depends on the number of other similar products available and on the prices of other firms’
products in the industry.
Assumptions of the Model We begin by describing the demand facing a typical
monopolistically competitive firm. In general, we would expect a firm to sell more the
larger the total demand for its industry’s product and the higher the prices charged by its
rivals. On the other hand, we would expect the firm to sell less the greater the number of
firms in the industry and the higher its own price. A particular equation for the demand
facing a firm that has these properties is3
Q = S * [1/n - b * (P - P)], (8-5)
3Equation (8-5) can be derived from a model in which consumers have different preferences and firms produce
varieties tailored to particular segments of the market. See Stephen Salop, “Monopolistic Competition with
Outside Goods,” Bell Journal of Economics 10 (1979), pp. 141–156, for a development of this approach.
where Q is the quantity of output demanded, S is the total output of the industry, n is the
number of firms in the industry, b is a constant term representing the responsiveness of a
firm’s sales to its price, P is the price charged by the firm itself, and is the average price
charged by its competitors. Equation (8-5) may be given the following intuitive justification:
If all firms charge the same price, each will have a market share 1/n. A firm charging
more than the average of other firms will have a smaller market share, whereas a firm
charging less will have a larger share.4
It is helpful to assume that total industry output S is unaffected by the average price
charged by firms in the industry. That is, we assume that firms can gain customers only at
each other’s expense. This is an unrealistic assumption, but it simplifies the analysis and
helps us focus on the competition among firms. In particular, it means that S is a measure
of the size of the market and that if all firms charge the same price, each sells S/n units.
Next we turn to the costs of a typical firm. Here we simply assume that total and average
costs of a typical firm are described by equations (8-3) and (8-4). Note that in this initial
model, we assume that all firms are symmetric even though they produce differentiated
products: They all face the same demand curve (8-5) and have the same cost function (8-3).
We will relax this assumption in the next section.
Market Equilibrium When the individual firms are symmetric, the state of the industry
can be described without describing any of the features of individual firms: All we really
need to know to describe the industry is how many firms there are and what price the
typical firm charges. To analyze the industry—for example, to assess the effects of
international trade—we need to determine the number of firms n and the average price
they charge . Once we have a method for determining n and , we can ask how they are
affected by international trade.
Our method for determining n and involves three steps. (1) First, we derive a relationship
between the number of firms and the average cost of a typical firm. We show
that this relationship is upward sloping; that is, the more firms there are, the lower the
output of each firm, and thus the higher each firm’s cost per unit of output. (2) We next
show the relationship between the number of firms and the price each firm charges, which
must equal in equilibrium. We show that this relationship is downward sloping: The
more firms there are, the more intense is the competition among firms, and as a result the
lower the prices they charge. (3) Finally, we introduce firm entry and exit decisions based
on the profits that each firm earns. When price exceeds average cost, firms earn positive
profits and additional firms will enter the industry; conversely, when the price is less than
average cost, profits are negative and those losses induce some firms to exit. In the long
run, this entry and exit process drives profits to zero, and the number of firms is determined
by the intersection of the curve that relates average cost to n and the curve that
relates price to n.
1. The number of firms and average cost. As a first step toward determining n and
, we ask how the average cost of a typical firm depends on the number of firms in the
industry. Since all firms are symmetric in this model, in equilibrium they all will
charge the same price. But when all firms charge the same price, so that ,
equation (8-5) tells us that ; that is, each firm’s output Q is a l/n share of the
total industry sales S. But we saw in equation (8-4) that average cost depends inversely
Q = S/n
P = P
P
P
P
P P
P
P
CHAPTER 8 Firms in the Global Economy 161
4Equation (8-5) may be rewritten as . If , this equation reduces to .
If P 7 P, Q 6 S/n, while if P 6 P, Q 7 S/n.
Q = (S/n) - S * b * (P - P) P = P Q = S/n
162 PART ONE International Trade Theory
on a firm’s output. We therefore conclude that average cost depends on the size of the
market and the number of firms in the industry:
(8-6)
Equation (8-6) tells us that other things equal, the more firms there are in the industry,
the higher is average cost. The reason is that the more firms there are, the less each
firm produces. For example, imagine an industry with total sales of 1 million widgets
annually. If there are five firms in the industry, each will sell 200,000 annually. If there
are ten firms, each will sell only 100,000, and therefore each firm will have higher
average cost. The upward-sloping relationship between n and average cost is shown as
CC in Figure 8-3.
2. The number of firms and the price. Meanwhile, the price the typical firm charges
also depends on the number of firms in the industry. In general, we would expect that
the more firms there are, the more intense will be the competition among them, and
AC = F/Q + c = (n * F/S ) + c.
Cost C, and
Price, P
P3
AC3
Number
of firms, n
n3 n2 n1
PP
CC
E
AC1
P1
P2, AC2
Figure 8-3
Equilibrium in a Monopolistically Competitive Market
The number of firms in a monopolistically competitive market, and the prices they
charge, are determined by two relationships. On one side, the more firms there are,
the more intensely they compete, and hence the lower is the industry price. This
relationship is represented by PP. On the other side, the more firms there are, the
less each firm sells and therefore the higher is the industry’s average cost. This relationship
is represented by CC. If price exceeds average cost (that is, if the PP curve
is above the CC curve), the industry will be making profits and additional firms will
enter the industry; if price is less than average cost, the industry will be incurring
losses and firms will leave the industry. The equilibrium price and number of firms
occurs when price equals average cost, at the intersection of PP and CC.
CHAPTER 8 Firms in the Global Economy 163
hence the lower the price. This turns out to be true in this model, but proving it takes a
moment. The basic trick is to show that each firm faces a straight-line demand curve of
the form we showed in equation (8-1), and then to use equation (8-2) to determine
prices.
First recall that in the monopolistic competition model, firms are assumed to take
each other’s prices as given; that is, each firm ignores the possibility that if it changes
its price, other firms will also change theirs. If each firm treats as given, we can
rewrite the demand curve (8-5) in the form
(8-7)
where b is the parameter in equation (8-5) that measured the sensitivity of each firm’s
market share to the price it charges. Now this equation is in the same form as
(8-1), with in place of the constant term A and in place of
the slope coefficient B. If we plug these values back into the formula for marginal revenue,
(8-2), we have a marginal revenue for a typical firm of
(8-8)
Profit-maximizing firms will set marginal revenue equal to their marginal cost, c, so
that
which can be rearranged to give the following equation for the price charged by a typical
firm:
(8-9)
We have already noted, however, that if all firms charge the same price, each will sell
an amount . Plugging this back into (8-9) gives us a relationship between the
number of firms and the price each firm charges:
(8-10)
Equation (8-10) says algebraically that the more firms there are in an industry, the
lower the price each firm will charge. This is because each firm’s markup over marginal
cost, , decreases with the number of competing firms.
Equation (8-10) is shown in Figure 8-3 as the downward-sloping curve PP.
3. The equilibrium number of firms. Let us now ask what Figure 8-3 means. We
have summarized an industry by two curves. The downward-sloping curve PP shows
that the more firms there are in the industry, the lower the price each firm will charge.
This makes sense: The more firms there are, the more competition each firm faces. The
upward-sloping curve CC tells us that the more firms there are in the industry, the
higher the average cost of each firm. This also makes sense: If the number of firms
increases, each firm will sell less, so firms will not be able to move as far down their
average cost curve.
The two schedules intersect at point E, corresponding to the number of firms . The
significance of is that it is the zero-profit number of firms in the industry. When there
are firms in the industry, their profit-maximizing price is , which is exactly equal to
their average cost . What we will now argue is that in the long run, the number
of firms in the industry tends to move toward , so that point E describes the industry’s
long-run equilibrium.
n2
AC2
n2 P2
n2
n2
P - c = 1/(b * n)
P = c + 1/(b * n).
Q = S/n
P = c + Q/(S * b).
MR = P - Q/(S * b) = c,
MR = P - Q/(S * b).
(S/n) + S * b * P S * b
Q = [(S/n) + S * b * P] - S * b * P,
P
164 PART ONE International Trade Theory
5This analysis slips past a slight problem: The number of firms in an industry must, of course, be a whole number
like 5 or 8. What if turns out to equal 6.37? The answer is that there will be six firms in the industry, all making
small monopoly profits and not being challenged by new entrants because everyone knows that a seven-firm
industry would lose money. In most examples of monopolistic competition, this whole-number or “integer constraint”
problem turns out not to be very important, and we ignore it here.
n2
To see why, suppose that n were less than , say . Then the price charged by firms
would be , while their average cost would be only . Thus firms would be making
monopoly profits. Conversely, suppose that n were greater than , say . Then firms
would charge only the price , while their average cost would be . Firms would be
suffering losses.
Over time, firms will enter an industry that is profitable and exit one in which they lose
money. The number of firms will rise over time if it is less than , fall if it is greater. This
means that is the equilibrium number of firms in the industry and that is the equilibrium
price.5
We have just developed a model of a monopolistically competitive industry in which
we can determine the equilibrium number of firms and the average price that firms charge.
We now use this model to derive some important conclusions about the role of economies
of scale in international trade.
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