Regulation

Monopolistic Markets

Comparison of monopolistic and competitive equilibrium output

The profits of a monopolist are maximized when MC(QM) = P(QM) + Q P’(QM)

negative

In a competitive market: MC(QC) = P

Thus: MC(QM) < MC(QC)

Competitive supply = MC with positive slope

Thus: QM < QC

MC

Q

D

MR

QC

PC

PM

QM

P

AC

A monopolist produces an output QM which is smaller then the competitive output QC

Comparison of monopolistic and competitive equilibrium output

BA

Consumers loose A+BProducer gains A - C > 0Welfare loss: B + C

C

Welfare loss caused by monopol

Q

D

MRMC

QC

PC

PM

QM

P

Regulation of a monopol

• Inefficiency of monopol: Output falls short of the competitive output.

• Regulation: Fix price P = PC • Problema: Monopolist might make negative profits

when the price is regulated. If the regulator fixes P = PC the monopolist then prefers to close down (natural monopol)

P

Price regulation

AC (QC)

In the case of a natural monopol the firm makes losses if P=PC

AC (QM)

Q

D

QC

PC MC

AC

MR

Losses when P = PC

QM

PM

Monopolistic profits

Solution 1: Price regulation based on average cost

Q

P

D

QM QC

PC MC

AC

MR

QR

PM

π = 0

QM < QR < QC

PR

Fix price P=PR equal to average cost. Advantage: the firm covers costs (π = 0) Disadvantage: output larger than QM but smaller than the efficient QC (still welfare loss)

Solution 2: Nationalization

Q

D

QC

PC MC

AC

MR

QM

Subsidy = QC (AC(QC) - PC)

Fix P = PC and subsidise the firm such that it keeps operating.

Advantage: efficient output

Disadvantage: in order to pay the subsidy the state has to impose taxes (welfare loss)

Price Discrimination

Monopolistic Markets

Price discrimination

• So far we have assumed that the monopolist charges the same price for every unit sold and that this price is the same for each customer (PM).

• We will now relax this restriction. We will see that the monopolist can increase his profits by charging different prices for different units and customers.

Q

P

D

QM QC

PC

MC

MR

PM

Extracting consumer surplusPart of the consumer surplus can be extracted by charging prices higher than PM to consumers with willingness to pay higher than PM.

Profits can also be obtained from the consumers who do not buy when the price is PM by charging lower prices.

Three degrees of price discrimination

• First degree: Each client is charged a price equal to his willingness to pay (perfect discrimination)

• Second degree: Charge different unit prices for different quantities of the same good.

• Third degree: Devide the consumers into groups of differing demands and charge a different price for each group.

Q

P

D

QM QC

PC MC

MR

PM

Variable profits when the price is PM.

Additional profits generated by first degree price discrimination.

First degree price discrimination

• Normally it is not practically feasible to charge a different price to each consumer.

• Moreover the monopolist does not know the consumers willingness to pay.

• In reality first degree price discrimination is imperfect, charging a number of different prices to groups of customers based on estimates of the groups` willingness to pay.

First degree price discrimination

• Normally the willingness to pay per unit diminishes with the total number of units purchased.

• Implementation 1: Charge P1 for the first Q1 units sold, charge P2 < P1 for the next Q2 units sold, charge P3 < P2 for .... (e.g. electricity)

• Implementation 2: Quantity discounts

Second degree price discrimination

• Suppose that two groups of consumers demand a good: 1 and 2

• Each group has its own demand curve P1(Q1) y P2(Q2)

• The monopolist can charge two different prices.

• Example: Cinema tickets for students and non-students

Third degree price discrimination

P1 P2

Q1 Q2

D1

MR1

MR2

D2

Group 1 (Students) Group 2 (Non-Students)

The demand of Group 1 is more elastic, Ed1 > Ed2.

Third degree price discrimination

The monopolist`s decision Which price to charge to each group?

Profits = Total revenue – Total cost

Total revenue = R(Q1,Q2) = R1(Q1) + R2(Q2) = P1(Q1)Q1 + P2(Q2)Q2

Total cost = C(Q1,Q2) = C(Q1+Q2)

The firm chooses Q1 y Q2 to maximize profits.

Max P1(Q1)Q1 + P2(Q2)Q2 - C(Q1+Q2)

First order conditions

2

dQ 0=

dQdC

− dR = dQdπ

dπdQ

= dRdQ

−

dCdQ

= 0

1 1 1

2

1

2

2

Max R1(Q1) + R2(Q2) - C(Q1+Q2)

MR1(Q1) = MC(Q1 +Q2) = MR2(Q2)

Q

D1

MR1

P

D2 MR2

MC

Q1

P1

Q2

P2 MR1 ( Q1 ) =MR2 ( Q2 ) = MC

Third degree price discrimination with constant MC

Q

D1

MR1

P

D2 MR2

MC

Q1

P1

QTQ2

P2 MR1 ( Q1 ) =MR2 ( Q2 ) = MC (QT)Donde QT = Q1+Q2

Third degree price discrimination with increasing MC

MR1 = MC implies:

Determination of the price ratio

MR2 = MC implies:

Thus when MR1 = MR2 =MC:

The higher price is charged to the group whose demand is less elastic (Grupo 2 = Non-Students).

Example

• A monopolist faces two markets with the following demand curves Q1=100-P1; Q2=100-2P2

• The marginal cost of the monopolist is constant MC=20.

• Calculate equilibrium quantity and price in each market when the monopolist can discriminate in price.

• Calculate the Lerner index for each market.• Which would be the monopolist`s decision if he

Example

• P1 = 100-Q1; P2 = 50 -Q2/2; D1 less elastic than D2• R1 = (100-Q1)Q1; MR1 = 100 - 2Q1• R2 = (50-Q2/2)Q2; MR2 = 50 - Q2• MR1(Q1*) = MC → Q1* = 40; P1* = 60• MR2(Q2*) = MC → Q2* = 30; P2* = 35 < P1* • L1=(P1*-MC) / P1* = 2/3 = 1/Ed1 = -(Q1*/P1*)(dP1/dQ1)• L2=(P2*-MC) / P2* = 3/7= 1/Ed2 = -(Q2*/P2*)(dP2/dQ2)• The monopoly power is larger in market 1• Q = Q1+Q2 = 200-3P; P = (200-Q)/3; MR = (200-2Q)/3• MR(Q*) = MC → Q* = 70; P* = 130/3 = 43.333