Intermediate Microeconomics

MONOPOLYBEN VAN KAMMEN, PHDPURDUE UNIVERSITY

Price makingA 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 revenueCompetitive 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.

ExampleSay that market demand is given by:

𝑄𝑄 = 10 −1

20𝑃𝑃

2

. . . and the inverse demand you see on Marshall’s diagram: 𝑃𝑃 =200– 20𝑄𝑄

12.

𝑇𝑇𝑇𝑇 = 𝑄𝑄𝑃𝑃, where P is given by the inverse demand function.

𝑇𝑇𝑇𝑇 = 𝑄𝑄 200 − 20𝑄𝑄12 .

𝑇𝑇𝑇𝑇 = 200𝑄𝑄– 20𝑄𝑄32.

Taking the partial derivative to get MR:

𝑀𝑀𝑇𝑇 = 200 − 30𝑄𝑄12.

MR is below the price

q*

The product rule in calculusThe basic reason that 𝑀𝑀𝑇𝑇 < 𝑃𝑃 for a firm facing downward-sloping 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)𝜕𝜕ℎ𝜕𝜕𝑥𝑥

= 𝑔𝑔 𝑥𝑥 �𝜕𝜕𝑓𝑓𝜕𝜕𝑥𝑥

+ 𝑓𝑓 𝑥𝑥 �𝜕𝜕𝑔𝑔𝜕𝜕𝑥𝑥

The product rule in calculusSo if 𝑓𝑓(𝑞𝑞) = 𝑞𝑞, and 𝑔𝑔(𝑞𝑞) = [𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 𝐷𝐷𝐼𝐼𝐷𝐷𝐷𝐷𝐼𝐼𝐷𝐷] = 𝑃𝑃(𝑄𝑄),

𝑇𝑇𝑇𝑇 = 𝑓𝑓 𝑞𝑞 ∗ 𝑔𝑔 𝑞𝑞 , and

𝑀𝑀𝑇𝑇 =𝜕𝜕ℎ𝜕𝜕𝑞𝑞

= 𝑔𝑔 𝑞𝑞 �𝜕𝜕𝑓𝑓𝜕𝜕𝑞𝑞

+ 𝑓𝑓 𝑞𝑞 �𝜕𝜕𝑔𝑔𝜕𝜕𝑞𝑞

.

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 profitsThe 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 −𝑀𝑀𝐴𝐴).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 𝑀𝑀𝑇𝑇 = 120 and solve for Q: 120 = 200 − 30𝑄𝑄

12 ⇔ 80 = 30𝑄𝑄

12

83

= 𝑄𝑄12 → 𝑄𝑄∗ =

649

= 719

.

To solve for the Price, substitute Q* into the inverse Demand:

𝑃𝑃 = 200 − 20649

12→ 𝑃𝑃∗ = $146.67.

Π = 𝑄𝑄 𝑃𝑃–𝐴𝐴𝐴𝐴 = (146.67 − 120) ∗649

= $189.63.

Efficiency loss from monopolyMonopolies 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. Net welfare improving.2. 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 entryNew 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

Market with one seller. Monopolist maximizes profits.Q*

P*

If a 2nd seller enters, demand is split between them

Pink Curves are the firms’ individual demand curves.

Losses after entry

Q*

𝐴𝐴𝐴𝐴 > 𝑃𝑃 at 𝑄𝑄∗

If the market is split between 2 firms, neither can make a profit.

Reasoning: natural monopolySince 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 monopolyEvery 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 monopolyA 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 entryMany 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 trademarksThis 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 monopoliesFor 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.

RegulationsIf 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 andproduce a more efficient level of output.

Market segmentation

𝑃𝑃1 = 𝑀𝑀𝐴𝐴

𝑃𝑃2 > 𝑀𝑀𝐴𝐴

If inelastic consumers can be segregated from inelastic ones, the monopolist can offset losses from elastic consumers with profits from inelastic consumers.

Price discriminationThe 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 discriminationThe 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 discriminationIronically 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.

SummaryMonopolies 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.

SummaryMonopolies 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.

SummaryIf 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.

ConclusionMonopoly 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.