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Chapter 9. Profit
Maximization by aMonopolist
OPEC and Output Quotas
The Organization of the Petroleum Export-
ing Countries (OPEC) regularly have meet-ings to restrict their output and allocate quo-
tas among member nations. For example, in
1982,
OPEC set an overall output limit of 18million barrels per day, down from 31 mil-
lion barrels per day in 1979.
Each member nation had an individual
production quota.
Saudi Arabia adjusted its output to main-
tain oil price at $34 per barrel.
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The average cost per barrel is about $2$4 among member nations.
The current oil price is ? . The most re-
cent production allocation can be found
on OPECs website.
Why would OPEC restrict its output? How
would the restriction in output affect oil prices?
How would OPEC choose output?
How would output restriction affect various
countries, including oil importing countries
(e.g., U.S.), and exporting countries (e.g.,
Saudi Arabia vs. Russia)?
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1. Profit Maximization by aMonopolist
Monopoly is the industry structure when thereis only one firm in the industry the oppo-site to perfect competition. We call this firmthe monopolist.
A firm in perfectly competitive markets hasa negligible impact on the market price andthus takes the price as given. By contrast,a monopolist sets the market price for itsproduct.
In doing so, the monopolist must take ac-count of the market demand. The higher itsets its price, the fewer units it will sell. Themonopolists demand curve is the market de-mand curve. See Figure 9.1.
The profit-maximizing monopolists problem
is to find the optimal trade-off between vol-ume (the number of units it sells) and margin(the difference between price and marginalcost).
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Figure 9.1 The Monopolists DemandCurve Is the Market Demand Curve
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A Monopolist Does Not Have a Sup-
ply Curve
A perfectly competitive firm takes the mar-
ket price as given and chooses a profit-maximizing
quantity. The resulting s(p) is the firms sup-
ply curve.
However, for a monopolist, there is no such
thing as given market price, since how much
output the monopoly produces will affect the
market price.
As a result, the firm can choose either price
or output. But it does not have the freedom
to choose both at the same time.
For example, if monopolist chooses price,
then consumers decide how much they are
willing to buy at this price, and the monop-
olist should supply this much.
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The Profit-Maximization Condition
Suppose a monopolist faces the demand
p = 12 Q,
where Q is measured in millions of ounces,
and p in dollar per ounce. To sell more, themonopolist has to cut its price.
Monopolists total revenue is
T R = pQ = (12Q)Q = 12Q Q2.
The monopolists cost function is
T C =1
2Q2.
Figure 9.2(a) illustrates total revenue (T R),total cost (T C) and profit graphically.
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Figure 9.2 Profit Maximization by aMonopolist
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We can find thatT C
always increases withQ, T R and profit first rises as Q increases
but then falls.
Profit is maximized at the peak of the profit
hill, which occurs at Q = 4 million.
For quantities less than Q = 4 million, in-
creasing Q increases T R more than it in-
creases T C, which moves the firm up its
profit hill.
As Figure 9.2(b) shows, when Q < 4 mil-
lion, the monopolists marginal revenue ex-
ceeds its marginal cost (M R > M C ).
For Q > 4 million, producing less output in-
creases its profit, as now M R < M C .
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A Closer Look at Marginal Revenue
In the case of perfect competition, M R = p.
However, for a monopolist, M R = p. In fact,
if Q > 0, we have M R < p. To see why,
consider the following example.
Q = 1, p = $4, T R = $4.
Q = 2, p = $3 (price reduction applies to
both units of output), T R = $6.
Marginal revenue of the second unit is
$6$4 = $2, which is less than the price
p = $3.
A comparison between perfect competition
and monopoly in terms of marginal revenue
is illustrated in Figure 9.3.
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Price
Price
CompetitiveFirm
Monopolist
Demandfacingfirm
De
mandfacingfirm
0
0P1
C A
B
A
B
Q0
Q0+1
qq+1
Firm
output
Firm
output
Figure9.3
Marginal
Revenue:Competitionvs.Monopoly
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An Example with Linear Demand
Suppose that the monopolist faces a linear
demand curve
p = 12 Q.
The cost function is
c(Q) =1
2Q2 M C = Q.
Derive the monopolists profit-maximizing out-
put, the corresponding price and profit.
Solution: We will go over it in class.
Next, we compare the demand curve with
marginal revenue curve. The demand curvehas the equation
p = 12 Q.
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It can be shown that the marginal revenuehas the equation
M R = 12 2Q.
The two curves are shown in Figure 9.4.
Comparing them, we can find that:
(1) They have the same vertical intercept.
This is because when Q = 0, p = M R = 12.
(2) The horizontal intercept of demand curveis twice that of the M R curve, or M R curve
is twice as steep as the demand curve.
0 = p = 12Q Q = 12 .
0 = M R = 12 2Q Q = 6 .
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Figure 9.4 Demand Curve and MarginalRevenue Curve
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Figure 9.5 Monopoly vs. Competition
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Monopoly Deadweight Loss
How does the difference between the monopoly
and competitive equilibria affect economic
benefits in this market?
From Figure 9.5, the consumer surplus (CS)in monopoly is area A. The monopolists
producer surplus is the accumulation of the
difference between the monopolists price and
its marginal cost. This corresponds to area
B + E + H. Thus the net economic ben-
efit (or social surplus SS) in the monopoly
equilibrium is A + B + E + H.
In the perfectly competitive equilibrium, con-
sumer suplus is area A + B + F. Producer
surplus is area E + G + H. Social surplus isA + B + E + F + G + H.
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The table in Figure 9.5 compares the con-
sumer surplus, producer surplus (profit) and
net economic benefit (social surplus) under
monopoly and perfect competition. It shows
that consumers surplus and social surplus is
higher under perfect competition than monopoly.
The difference is area F + G. This differ-
ence is the deadweight loss (DW L) due to
monopoly.
The DWL arises because the monopolist does
not produce the socially optimal output level.
When 600 < Q < 1000, consumers willing-
ness to pay (social benefit) exceeds firms
marginal cost (social cost), but the monopo-
list chooses not to produce because marginal
revenue (firms benefit) is less than marginalcost (firms cost).
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Example
Consider a market where demand is charac-
terized by p = 2Q. The monopolists cost
function is c(Q) = 12Q2. Then M C = Q.
We want to compare two cases. Case 1
is monopoly. In case 2, the monopolist is
forced to behave competitively (i.e., p =
M C). The two cases are shown in Figure
9.6 and 9.7 respectively. The following ta-
ble summarizes the results. We will go over
the details in class.
Variable Competition Monopoly
Price 1 43Quantity 1 23
Profit 12 1Consumer surplus 12
29
Social surplus 1 89
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Figure 9.6 Monopoly
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Figure 9.7 Monopolist Forced to Behave
Competitively
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Rent-Seeking Activities
Question: Is the DWL listed in Figure 9.5
the true monopoly DWL loss?
Because a monopolist often earns above nor-
mal economic profits, you might expect that
firms would have an incentive to acquire monopoly
power.
For example, during the 1990s, cable televi-
sion companies spent millions lobbying Congressto preserve regulations that limit the ability
of satellite broadcasters to compete with tra-
ditional cable service.
Activities aimed at creating or preserving monopoly
power are called rent-seeking activities.
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Expenditures on rent-seeking activities can
represent an important social cost of monopoly
that the table in Figure 9.5 does not reflect.
What is the maximum amount that a firm is
willing to spend to become such a monopo-list as in Figure 9.5?
Suppose that a competitive firm earns zero
profit, than a firm would be willing to spend
up to B + E+ H to become the monopolist.
The upper bound of social waste of monopoly
is (B+E+H)+(F+G), if all the rent-seeking
activities does not generate any net benefit
to the society.
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3. Why Do Monopoly MarketsExist?
Now we have seen that monopoly equilibrium
can create a deadweight loss. But how do
monopolies arise in the first place?
Natural Monopoly
A market is a natural monopoly if, for rel-
evant output levels, a single firm can sup-
ply the market more efficiently than multiple
firms.
Figure 9.8 shows a natural monopoly market.Suppose that the industry is to supply Q =
9000. If supplied by a single firm, AC = $1.
If supplied equally by two firms, AC = $1.2.
If one firm can serve a market at lower cost
than two or more firms, we would expectthat, without government interference, the
market would eventually become monopo-
lized.
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Figure 9.8 Natural Monopoly Market
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Barriers to Entry
A natural monopoly is an example of a more
general phenomenon known as barriers to entry.
Barriers to entry are factors that allow an in-
cumbent firm to earn positive economic prof-
its, while at the same time making it unprof-
itable for newcomers to enter the industry.
Barriers to entry are essential for a firm to
remain a monopolist. Barriers to entry can
be structural, legal, or strategic.
Structural barriers to entry exist when incum-
bent firms have cost or marketing advan-
tage that would make it unattractive for a
new firm to enter the industry and compete
against them.
We will look at two of such factors.
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(1) Economies of scale.
When new firm enters, each firm (incumbent
and entrant) both have to produce fewer
outputs, and AC would be higher due to
economies of scale, and the market becomesless profitable.
(2) Network externality.
The auction site Ebay is attractive to both
buyers and sellers because of its volume. The
more buyers there are, the more attractive
Ebay is to sellers. More sellers will do busi-
ness on Ebay, making Ebay more attractive
to buyers, in turn luring more buyers there.
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Legal barriers to entry exist when an incum-
bent firm is legally protected against compe-
tition. Patents are an important legal barrier
to entry. Government regulation can also
create legal barriers to entry.
Strategic barriers to entry result when an in-
cumbent firm takes explicit steps to deter
entry.
An example would be the development of
a reputation over time as a firm that will
aggressively defend its market against en-
croachment by new entrants (e.g., by start-
ing a price war if a new firm chooses to come
into the market).
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Summary
In this chapter, we have
Analyzed production and pricing decisionsin a market with a monopolist.
Compared market equilibrium in monopoly
markets and perfectly competitive mar-
kets.
Seen why monopoly markets arise and
explored the notion of barriers to entry.