Intermediate Microeconomics
MONOPOLY
BEN VAN KAMMEN, PHD
PURDUE UNIVERSITY
Price making
A monopoly seller in a goods market is the
conceptual opposite from perfectly competitive
firms.
◦ The monopolist does not face competition from other
firms because he is the only seller.
◦ He is still constrained in his behavior, however, by
consumers’ willingness to pay for his output, i.e., by the
demand curve.
A monopolist faces the entire market demand for
his good, though, so when he chooses an output
level, he implicitly determines the price.
◦ Thus the term “price maker”.
Competitive firm’s demand curve
Monopolist’s demand curve
Total revenue
Competitive firms get the same price for all units sold, so:
𝑇𝑇𝑇𝑇 = 𝑞𝑞𝑃𝑃∗ .
If a monopolist wants to sell more, he has to cut the price
on all units sold.
TR is still equal to 𝑄𝑄𝑃𝑃∗ , but P* is now a function of Q.
◦ Note: Q as market quantity as distinct from q for firm’s quantity.
Specifically the demand curve tells you P* as a function of
Q.
Example
Say that market demand is given by:
2
1
𝑃𝑃
𝑄𝑄 = 10 −
20
. . . and the inverse demand you see on Marshall’s diagram: 𝑃𝑃 =
1
200– 20𝑄𝑄2 .
𝑇𝑇𝑇𝑇 = 𝑄𝑄𝑄𝑄, where P is given by the inverse demand function.
1
𝑇𝑇𝑇𝑇 = 𝑄𝑄 200 − 20𝑄𝑄2
3
𝑇𝑇𝑇𝑇 = 200𝑄𝑄– 20𝑄𝑄2 .
Taking the partial derivative to get MR:
𝑀𝑀𝑀𝑀 =
1
200 − 30𝑄𝑄2 .
.
MR is below the price
q*
The product rule in calculus
The basic reason that 𝑀𝑀𝑀𝑀 < 𝑃𝑃 for a firm facing downwardsloping demand has to do with the product rule in calculus.
The product rule is as follows: when you multiply two
functions of the same variable together, the differential of
the product is:
ℎ(𝑥𝑥) ≡ 𝑓𝑓(𝑥𝑥) ∗ 𝑔𝑔(𝑥𝑥)
𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
= 𝑔𝑔 𝑥𝑥 �
+ 𝑓𝑓 𝑥𝑥 �
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
The product rule in calculus
So if 𝑓𝑓(𝑞𝑞) = 𝑞𝑞, and 𝑔𝑔(𝑞𝑞) = [𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷] = 𝑃𝑃(𝑄𝑄),
𝑇𝑇𝑇𝑇 = 𝑓𝑓 𝑞𝑞 ∗ 𝑔𝑔 𝑞𝑞 , and
𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
= 𝑔𝑔 𝑞𝑞 �
+ 𝑓𝑓 𝑞𝑞 �
.
𝑀𝑀𝑀𝑀 =
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
The first term in MR is the quantity effect that comes from
selling an additional unit. The second term is the price
effect that comes from cutting the price in order to sell the
extra unit.
𝜕𝜕𝜕𝜕
◦ Since Demand curves slope downward,
is negative, so the price
𝜕𝜕𝜕𝜕
effect has to be negative.
The difference between monopoly
and competition
Perfect Competition is like having a price effect that
equals zero. If ∂g/∂q = 0 (no price effect), the 2nd term
in the MR drops out, and you have only a quantity
effect:
MR = (∂f/∂q)g(q) + 0 = 1*g(q).
Since g(q) is the inverse demand curve, g(q) gives the
market price, so MR = 1*P . . . MR = P.
In almost any other scenario, however, there is a
negative price effect from increasing output.
◦ This is particularly true of monopolies.
MC Intersects MR at Q*
A monopolist chooses optimal output the same, though, finding where MC=MR.
Monopoly price exceeds MC
P*
MC = MR dictates the optimal Q, but the monopolist would be foolish not to
“mark up” its output by charging consumers the price from the demand curve.
Monopoly profits
The result of the monopolist’s profit maximizing Q is that its
output gets “marked up” beyond its marginal cost.
◦ The monopolist makes a profit of (𝑃𝑃 − 𝐴𝐴𝐴𝐴) per unit, and a total
profit: Π = 𝑄𝑄(𝑃𝑃 − 𝐴𝐴𝐴𝐴).
◦ If the monopolist has constant marginal cost, as in the previous
graph, AC = MC, so Π = 𝑄𝑄(𝑃𝑃 − 𝑀𝑀𝑀𝑀).
Since no firms enter the market to compete them away, the
monopoly profits persist even in the long run.
Example (continued)
The previous graph contains the MR and Demand curves from
the example.
◦ In the graph I have set the MC to a constant ($120).
To solve for optimal Q, set 𝑀𝑀𝑀𝑀 = 120 and solve for Q:
1
30𝑄𝑄 2
120 = 200 −
⇔ 80 =
1
8
64
1
= 𝑄𝑄 2 → 𝑄𝑄 ∗ =
=7 .
3
9
9
1
30𝑄𝑄 2
To solve for the Price, substitute Q* into the inverse Demand:
64
𝑃𝑃 = 200 − 20
9
1
2
→ 𝑃𝑃∗ = $146.67.
64
= $189.63.
Π = 𝑄𝑄 𝑃𝑃– 𝐴𝐴𝐴𝐴 = (146.67 − 120) ∗
9
Efficiency loss from monopoly
Monopolies create an efficiency loss because they charge a
price greater than the marginal cost.
◦ This is good for the monopolist because they get profits, and it’s bad
for consumers because they pay higher prices and do not get to
enjoy as much of the good.
◦ But the welfare loss to consumers is larger than the gain to
monopolist, so the net effect is negative for welfare.
The lost welfare is called a deadweight loss.
Why do monopolies arise?
There are several reasons monopolies arise, but they can be
grouped into two categories:
1.
2.
Net welfare improving.
Net welfare damaging.
Both can be broken down further into two sub categories:
natural monopoly and legal monopoly.
In any case the general explanation for a monopoly is a
barrier to entry. Any market can be monopolized if an
effective barrier to prevent competition is erected.
Natural barriers to entry
New firms could be prevented from entering a market
because the cost would be prohibitive.
Some cost functions prohibit more than one firm from
operating profitably in a market.
◦ Specifically when there are very large sunk costs and low marginal
cost, natural monopolies are common.
A natural monopoly
P*
Q*
Market with one seller. Monopolist maximizes profits.
If a 2nd seller enters, demand is split
between them
Pink Curves are the firms’ individual demand curves.
Losses after entry
𝐴𝐴𝐴𝐴 > 𝑃𝑃 at 𝑄𝑄 ∗
Q*
If the market is split between 2 firms, neither can make a profit.
Reasoning: natural monopoly
Since both firms incur the large fixed costs and face a lower
price than the monopoly did, neither can make a profit.
◦ So eventually at least one will go out of business.
◦ Then the market will go back to being a monopoly, hence, its natural
state is monopoly.
“Un” natural monopoly
Every firm would love to eliminate its competitors, increase
its market power, and earn monopoly profits.
Consequently we often see attempts to create artificial
barriers to entry that raise competitors’ costs and keep
them out of a market.
The most conspicuous example of this is the creation of a
legal monopoly.
◦ A legal barrier to entry consists of an enforced penalty for competing
with the existing firm in a market.
But the idea of government granting monopoly powers by
punishing competitors sounds like unfair favoritism to most
people.
◦ So the firms seeking such legal protection have to create a
justification for their greed.
Artificial monopoly
A common device for creating a legal monopoly is a
licensure requirement.
Combine it with a penalty for operating without a license
and you have a legal monopoly for the license holder.
The justification for the license? That’s where they have to
get a little creative.
◦ If they can convince the public that the licensure scheme is to
protect consumers, that will usually appease them.
◦ E.g., convince Congress that unlicensed hair dressers are the biggest
threat to consumer safety since the Corvair, and they might support a
licensure regulation that “protects” consumers from this peril.
Legal barriers to entry
Many licensure requirements may genuinely make goods or
services safer by excluding scammers and quacks (think
about Doctor Nick Riviera on The Simpsons, for example)
from the market.
◦ But it is equally sure that many such requirements and regulations
are spurious. Instead many are thinly veiled attempts by existing
firms to keep out competition and make monopoly profits.
In contrast there is another class of legal monopolies that
includes some of the most efficient monopolies in
existence: the patent system.
Patents, copyrights, and trademarks
This system of legal barriers is considered one of the most
valuable for improving welfare.
Inventors engage in expensive and time-consuming research to develop
new products.
◦ They would be much less inclined to do so if, upon discovery,
everyone could simply copy their technology and compete their
profits away.
As an incentive for research and development, the patent system grants
temporary monopolies to the discoverers of new inventions as a
reward.
This increases the overall pace of technological advancement and
income growth in the economy.
Regulating natural monopolies
For legal monopolies, the critical question for economic
efficiency is: whether to grant them or not?
For a natural monopoly, the monopolist’s incentives still
create a deadweight loss that regulations could mitigate.
The basic problem is that monopolists charge too high a
price and produce too little output.
Regulations
If the price were restricted to the marginal cost, consumers
would be happy, but for a natural monopoly this would
drive them out of business.
◦ Since MC<AC for the natural monopolist, this would force him to sell
below AC and incur losses.
A common solution for this is to allow the monopolist to
mark up the output he sells to some consumers but make
him sell to other consumers at a low price.
◦ Particularly they let him charge a high price to “inelastic” demanders
and make him charge a low price to “marginal” or “elastic”
demanders. This enables the monopolist to stay in business and
produce a more efficient level of output.
Market segmentation
𝑃𝑃2 > 𝑀𝑀𝑀𝑀
𝑃𝑃1 = 𝑀𝑀𝑀𝑀
If inelastic consumers can be segregated from inelastic ones, the monopolist
can offset losses from elastic consumers with profits from inelastic consumers.
Price discrimination
The regulation policy in which the monopolist charges
different groups of consumers different prices is an example
of price discrimination.
So far we have confined ourselves to talking about firms
that charge the same price to all consumers.
If a firm with market power (like a monopolist) can tell
consumers apart on the basis of their willingness to pay, it
has an incentive to price discriminate.
Perfect price discrimination
The demand curve reveals each consumers’ willingness to
pay for a good.
◦ But not which consumers have high willingness and which have low
willingness to pay.
◦ If the seller is confident that side transactions will not be made
between consumers with different valuations, he will attempt to
charge the high-valuing consumer a higher price and the low-valuing
consumer a lower price (as long as it’s above MC).
If the seller knew every consumer’s willingness to pay, he
could charge each of them that full amount
◦ Thereby getting all the consumer surplus for himself as
monopoly profit.
No DWL for perfect price
discrimination
Ironically if a monopolist could perfectly price discriminate,
he would not create a deadweight loss.
◦ Instead of excluding consumers that would pay more than the
marginal cost, he can now sell to them and make a profit. This gets
rid of the deadweight loss from a single-price monopolist.
◦ Even if perfect price discrimination may be more efficient in an
overall sense, there may be objections because all the “surplus” is in
the hands of the monopolist.
Summary
Monopolies exist because there is are barriers to entry in
some markets.
◦ Since competition is prevented either by law or by production
characteristics, there is only one seller in a monopoly market.
Monopolists follow the same objective of profit
maximization that competitive firms do.
◦ The primary difference is that a monopolist’s demand curve is the
whole market demand—and is consequently downward sloping.
◦ MR < P.
Summary
Monopolies earn profits that do not get competed away in
the long run.
They create a deadweight loss (and efficiency loss) by
raising the price above MC and restricting output.
Competitive firms have an incentive to try to establish
spurious barriers to entry to protect their own profits.
Some legal barriers to entry are welfare improving because
they encourage research and development.
Summary
If a monopolist can identify consumers’ willingness to pay
and prevent secondary transactions, it can price
discriminate.
◦ Charge each consumer a different price based on his willingness to
pay.
Market segmentation is an example of price discrimination
in which the monopolist charges different prices to elastic
and inelastic demanders.
◦ Deliberate market segmentation is a method for regulating natural
monopolies to get their markets to be more efficient.
Conclusion
Monopoly and perfect competition are two extreme market
structures.
Most real markets are neither monopolized nor perfectly
competitive and have features of both.
The last market structure we will examine is imperfect
competition
◦ A case in which a small number of firms interact strategically
by influencing (and being influenced by) the others’ decisions.