Intermediate Microeconomics

MONOPOLYBEN VAN KAMMEN, PHDPURDUE UNIVERSITY

Outline of objectives1. Solve a mathematical model of an monopolist's profit

maximization problem.2. Apply simple differential calculus, to solve economic

models.3. Compare consumer utility, firm profit, tax revenue,

output, and price in equilibrium to competition.4. Classify monopoly according to net welfare improving or

net welfare detrimental.5. Modify a monopolist’s profit function to show the effect

of different forms of regulation.6. Compare consumer utility, profit, output, and price

across regulatory regimes.

Competitive firm’s demand curve

Monopolist’s demand curve

ExampleMarket demand:

𝑄𝑄 = 10 −1

20𝑃𝑃

2

𝑇𝑇𝑇𝑇 = 𝑄𝑄 200 − 20𝑄𝑄12 ⇔ 𝑇𝑇𝑇𝑇 = 200𝑄𝑄– 20𝑄𝑄

32.

𝑀𝑀𝑇𝑇 = 200 − 30𝑄𝑄12.

MR is below the price

The product rule in calculusℎ(𝑥𝑥) ≡ 𝑓𝑓(𝑥𝑥) ∗ 𝑔𝑔(𝑥𝑥)

𝜕𝜕ℎ𝜕𝜕𝑥𝑥

= 𝑔𝑔 𝑥𝑥 �𝜕𝜕𝑓𝑓𝜕𝜕𝑥𝑥

+ 𝑓𝑓 𝑥𝑥 �𝜕𝜕𝑔𝑔𝜕𝜕𝑥𝑥

The product rule in calculusIf 𝑓𝑓(𝑞𝑞) = 𝑞𝑞, and

𝑔𝑔(𝑞𝑞) = 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 𝐷𝐷𝐼𝐼𝐷𝐷𝐷𝐷𝐼𝐼𝐷𝐷 = 𝑃𝑃(𝑄𝑄),𝑇𝑇𝑇𝑇 = 𝑓𝑓 𝑞𝑞 ∗ 𝑔𝑔 𝑞𝑞 , and

𝑀𝑀𝑇𝑇 =𝜕𝜕𝑇𝑇𝑇𝑇𝜕𝜕𝑞𝑞

= 𝑔𝑔 𝑞𝑞 �𝜕𝜕𝑓𝑓𝜕𝜕𝑞𝑞

+ 𝑓𝑓 𝑞𝑞 �𝜕𝜕𝑔𝑔𝜕𝜕𝑞𝑞

.

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.

Example (continued)120 = 200 − 30𝑄𝑄

12 ⇔ 80 = 30𝑄𝑄

12

83

= 𝑄𝑄12 → 𝑄𝑄∗ =

649

= 719

.

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.

The lost welfare is called a deadweight loss.

SummaryMonopolies exist because of barriers to entry in markets.

Monopolists follow the same objective of profit maximization that competitive firms do.◦ MR < P.

Outline of objectives1. Solve a mathematical model of an monopolist's profit

maximization problem.2. Apply simple differential calculus, to solve economic

models.3. Compare consumer utility, firm profit, tax revenue,

output, and price in equilibrium to competition.4. Classify monopoly according to net welfare improving or

net welfare detrimental.5. Modify a monopolist’s profit function to show the effect

of different forms of regulation.6. Compare consumer utility, profit, output, and price

across regulatory regimes.

Why do monopolies arise?1. Net welfare improving.

2. Net welfare damaging.

Natural monopoly and legal monopoly.Barriers to entry.

A natural monopoly

Market with one seller. Monopolist maximizes profits.Q*

P*

Entry

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.

“Un” natural monopolyLegal monopoly.Legal barrier to entry consists of an enforced penalty for competing with the existing firm in a market.As bad as it sounds.Licensing for example.

Artificial monopolyThe justification for the license? ◦ Convince the public that licensure is to protect

consumers.◦ E.g., convince Congress that unlicensed hair dressers are

threaten consumer safety.

Legal barriers to entrySome licensure requirements may make goods or services safer.It’s equally sure that many are spurious.◦ Thinly veiled attempts by existing firms to keep out

competition.

Patents, copyrights, and trademarksValuable for improving welfare.

Research to develop new products.◦ Less incentive if you’re immediately exposed to

competition.

Patent system grants temporary monopolies as incentive to do research and development.◦ Increases the pace of technological advancement and

income growth in the economy.

Outline of objectives1. Solve a mathematical model of an monopolist's profit

maximization problem.2. Apply simple differential calculus, to solve economic

models.3. Compare consumer utility, firm profit, tax revenue,

output, and price in equilibrium to competition.4. Classify monopoly according to net welfare improving or

net welfare detrimental.5. Modify a monopolist’s profit function to show the effect

of different forms of regulation.6. Compare consumer utility, profit, output, and price

across regulatory regimes.

RegulationsMake price equal MC like competition?◦ MC<AC, forced to sell below AC and incur losses.

So make it up to them “gouge” at least some customers?◦ Let him charge a high price to “inelastic” demanders and

make him charge a low price to “marginal” or “elastic” demanders.

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.

Perfect price discriminationIf 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.

Summary & conclusionsIf a monopolist can identify consumers’ willingness to pay and prevent secondary transactions, it can price discriminate.Market segmentation is 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.