Lectures_1-2_monopoly

Marginal revenue, linear demand

I What is MR in case of linear (inverse) demand

P = a bq

I let’s calculate

MR = P(q) + qP0(q) = a 2bq

I How does it look on a graph?

I MR(q) is exactly halfway from P(q) towards the vertical axis!

p

p(q)

MR(q)

q

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Marginal revenue, isoelastic demand

I What is MR in case of isoelastic (inverse) demand

P = aq 1/#

Icheck it is isoelastic

Ilet’s calculate

MR = aq 1/# + q ( 1/#) aq 1/# 1 = (1 1/#)aq 1/#

I MR(q) is lower than P(q) exactly by the factor (1 1/#) p

p(q)

MR(q)

q

I

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Monopolist problem (cont.)

I Back to the monopolist’ problem

P(q) + qP0(q) = C 0(q)

Imonopolist only operates on the elastic part of the demand curve # > 1

IIf elasticity is below 1 then MR is negative!

Iprice " 1% ) demand # by less than 1% ) revenue increases + cost falls (!)

IMonopoly wants to raise prices as high as possible and produce as little as possible, cannot be pro…t-maximizing

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Monopolist problem (cont.)

IIntroduce mark-up= by how much the price is above the competitive one

IMonopolistic FOC can be rewritten as

Ithe more elastic is the demand, the lower is the monopolistic mark-up!

I Alternatively, we can write

P(q) C 0(q) = 1

P(q) #

I LHS - Lerner Index= measure of market power

ILerner Index for perfectly competitive situation?

I=0!

IPositive ( 1) for monopoly

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Solution of the monopoly

P

MR(qmon)=MC(qmon)

pmon

MC=c

Q

qmon

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Comparative statics: tax incidence under monopoly

IWhat happens to the perfectly competitive market with constant MC, when the government introduces a tax on this market’s product?

IPrice goes up.

IBy how much?

I by exactly the tax size t!

I Consumers take all the tax burden!

I And under monopoly?

Iprice usually goes up as well

Ibut may go up by a more or less than t

I depends on the shape of the demand curve

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Taxation of monopoly, linear demand

The change in price is less than the tax increase

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Taxation of monopoly, isoelastic demand

IWhat is the e¤ect of a tax increase by $1/unit ?

IThe price may go up by more or by less than $1!

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Ine¢ ciency of monopoly

I Is monopoly e¢ cient?

Ithere are people who are willing to buy the good at the price above the marginal cost, but below the monopoly price

Iserving them - Pareto improvement

IBut monopoly does not do so = Dead-weight loss (DWL)

IMonopoly is ine¢ cient!

p

Competitive equilibrium

q

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Regulation of monopoly

IMonopolistic price is too high!

IShall the government tax monopoly to restore e¢ ciency?

I

I No, subsidize!

I how much?

I Alternatively, the government can use price caps

Iwe will see later, that social e¢ ciency may be di¢ cult to restore

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