大學MBA中級微觀講義Chapter

Twenty-FiveMonopoly

Behavior壟斷行為How

Should

a

Monopoly

Price?u

So

far

a

monopoly

has

been

thoughtof

as

a

firm

which

has

to

sell

itsproduct

at

the

same

price

to

everycustomer.

This

is

uniform

pricing.u

Can

price-discrimination

（差別定價）earn

a

monopoly

higher

profits?Structureu

First-degree

price

discrimination

u

Second-degree

price

discriminationu

Third-degree

price

discrimination

u

Bundlingu

Two-part

tariffTypes

of

Price

Discriminationu

1st-degree:

Each

output

unit

is

soldat

a

different

price.

Pricesmay

differacross

buyers.u

2nd-degree:

The

price

paid

by

abuyer

can

vary

with

the

quantitydemanded

by

the

buyer.

But

allcustomers

face

the

same

priceschedule.

E.g.

bulk-buyingdiscounts.Types

of

Price

Discriminationu

3rd-degree:

Price

paid

by

buyers

in

agiven

group

is

the

same

for

all

unitspurchased.

But

price

may

differacross

buyer

groups.E.g.,

senior

citizen

and

studentdiscounts

vs.

no

discounts

formiddle-aged

persons.First-degree

Price

Discriminationu

Each

output

unit

is

sold

at

a

differentprice.

Pricemay

differ

across

buyers.u

It

requires

that

the

monopolist

candiscover

the

buyer

with

the

highestvaluation

of

its

product,

the

buyer

withthe

next

highest

valuation,

and

so

on.First-degree

Price

DiscriminationMC(y)p(y)y$/output

unitSell

theth

unit

for

$First-degree

Price

DiscriminationMC(y)p(y)y$/output

unitSell

thesell

theth

unit

for

$th

unit

for

$Later

onFirst-degree

Price

Discriminationp(y)yMC(y)Later

on$/output

unitSell

thesell

theth

unit

for

$th

unit

for

$Finallysell

theth

unit

for

marginalcost,

$First-degree

Price

Discrimination$/output

unitThe

gains

to

the

monopoliston

these

trades

are:and

zero.MC(y)p(y)yThe

consumers’

gains

are

zero.First-degree

Price

Discriminationp(y)y$/output

unitMC(y)So

the

sum

of

the

gains

tothe

monopolist

on

alltrades

is

the

maximumpossible

total

gains-to-tradPSFirst-degree

Price

Discrimination$/output

unitMC(y)The

monopolist

getsthe

maximum

possiblegains

from

trade.PSp(y)yFirst-degree

price

discriminationis

Pareto-efficient.First-degree

Price

Discriminationu

First-degree

price

discriminationgives

a

monopolist

all

of

the

possiblegains-to-trade,

leaves

the

buyerswith

zero

surplus,

and

supplies

theefficient

amount

of

output.Exles

of

1st-degree

PriceDiscriminationu

Auction

of

antiqueu

Carsalesu

Financial

aid

in

universitiesu

May

not

be

practicaldo

notknow

willingness

to

paytoo

costlyu

Non-linear

pricingUnit

price

depends

on

quantitypurchased–

Bulk

discountu

SettingA

seller

does

not

know

the

willingnessto

pay

by

each

individualbuyerConsumer’s

marginal

willingness

to

paydeclines

withquantitySecond-degree

Price

Discriminationu

Setting

a

uniform

price

is

not

optimalu

Too

high

a

price

would

lose

high

volumeconsumer.u

Too

low

a

price

would

lost

revenue

fromlow

volume

consumer.u

Coke

exle.u

Mechanism：

Set

price

for

differentvolumes

to

let

consumers

identifythemselvesSecond-degree

Price

Discriminationu

Two

consumersPerson

1

has

low

willingness-to-pay–

Person

1

has

high

willingness-to-payu

Assume

0

MCAn

ExleAquantity$/outputunitx10x20CBCharge

A

for

x1

hoping

to

get

person

10Charge

A+B+C

for

x2

hoping

to

get

person

201But

person

2

is

better

off

buying

x

0

andreceiving

a

cs=BFail

to

let

consumers

self-select

themselvesProfit=2A2Can

alternatively

charge

A+C

for

x

0to

identify

person

2profit=2A+CSecond-degree

Price

DiscriminationAquantity$/output

unitx10x20CBReduce

x

0

so

A

is

reduced

by

a

little

but1C

can

be

increased

by

a

lot。Persons

1and

2

are

still

identifiedProfit

is

higherSecond-degree

Price

DiscriminationAquantity$/output

unitMC(y)x1mx20CB1Profit

is

maximized

at

x

mSecond-degree

Price

Discriminationu

2nd-degree

discriminationcan

alsooccur

inthedimensionof

qualityu

Different

prices

for

different

seats

ina

theateru

Different

prices

for

economy

classvs.

business

class

seats

in

airplanesSecond-degree

Price

DiscriminationThird-degree

Price

Discriminationu

Price

paid

by

buyers

ina

given

groupis

the

same

for

all

units

purchased.But

price

may

differ

across

buyergroups.u

Quality

of

goods

is

the

same

acrossgroups.u

Can

identify

groups

but

no

furtheridentification

within

that

group.Third-degree

Price

Discriminationu

A

monopolist

manipulates

marketprice

by

altering

the

quantity

ofproduct

supplied

to

that

market.u

So

the

question

“What

discriminatoryprices

will

the

monopolist

set,

oneforeach

group?”

is

really

the

question“How

manyunits

of

product

will

themonopolist

supply

to

each

group?”Third-degree

Price

Discriminationu

Two

markets,

1

and

2.u

y1

is

the

quantity

supplied

to

market

1.Market

1’s

inverse

demand

function

isp1(y1).u

y2

is

the

quantity

supplied

to

market

2.Market

2’s

inverse

demand

function

isp2(y2).Third-degree

Price

Discriminationu

For

given

supply

levels

y1

and

y2

thefirm’s

profit

isu

What

values

of

y1

and

y2

maximizeprofit?Third-degree

Price

DiscriminationThe

profit-maximization

conditions

areThird-degree

Price

Discriminationand

sothe

profit-maximization

conditions

areandThird-degree

Price

Discriminationt

y

üMR1(y1)

=

MR2(y2)

says

that

the

allocationy1,

y2

maximizes

the

revenue

from

sellingy1

+

y2

output

units.E.g.

if

MR1(y1)

>

MR2(y2)

then

an

output

unitshould

be

moved

from

market

2

to

market

1to

increase

total

revenue.Third-degree

Price

Discriminationüt

yThe

marginal

revenue

common

to

bothmarkets

equals

the

marginal

productioncost

if

profit

is

to

be

maximized.Third-degree

Price

Discriminationp1(y1*)p2(y2*)MCMCMarket

1

Market

2p1(y1)p2(y2)y1*

y1MR1(y1)MR1(y1*)

=

MR2(y2*)

=

MCy2*

y2MR2(y2)and

p1(y1*)

1

p2(y2*).Third-degree

Price

DiscriminationuIn

which

market

will

the

monopolistset

the

higher

price?u

Recall

thatanduBut,Third-degree

Price

DiscriminationSoTherefore, only

ifThe

monopolist

sets

the

higher

price

inthe

market

where

demand

is

leastown-price

elastic.Exles

of

3rd-degree

PriceDiscriminationu

Discounts

tostudents,

senior

citizensu

Business

travelers

and

vacationersu

Government

and

private-sectorpurchasersu

Coupons

and

rebatesu

First-run

movies

and

dollar

movieu

Hardcover

books

and

paperback

booksBundlingTypes

ofconsumersWordprocessorSpreadsheetType

A120100Type

B100120Willingness

to

pay

for

software

componentsTwo

Marketing

Policiesu

Sell

separately:Word

processor:

p=100,revenue=200Speadsheet;

p=100,

revenue=200u

BundlingSetp=220

for

the

bundleRevenue=440Two-Part

Tariffsu

A

two-part

tariff

is

a

lump-sum

fee,p1,

plus

a

price

p2

for

each

unit

ofproduct

purchased.u

Thus

the

cost

of

buying

x

units

ofproduct

isp1

+

p2x.Two-Part

Tariffsu

Should

a

monopolist

prefer

a

two-part

tariff

to

uniform

pricing,

or

toany

of

the

price-discriminationschemes

discussed

so

far?u

If

so,

how

should

the

monopolistdesign

its

two-part

tariff?Two-Part

Tariffsup1

+

p2xu

Q:

What

is

the

largest

that

p1

can

be?u

A:

p1

is

the

“entrance

fee”so

thelargest

it

can

be

is

the

surplus

thebuyer

gains

from

entering

themarket.u

Set

p1

=

CS

and

now

ask

whatshould

be

p2?Two-Part

Tariffsp(y)$/output

unitMC(y)yShould

the

monopolistset

p2

above

MC?Two-Part

Tariffsp(y)$/output

unitCSShould

the

monopolistset

p2

above

MC?p1

=

CS.MC(y)yTwo-Part

Tariffsp(y)y$/output

unitCSShould

the

monopolistset

p2

above

MC?p1

=

CS.PS

is

profit

from

sales.MC(y)PSTwo-Part

Tariffsp(y)y$/output

unitCSPSShould

the

monopolistset

p2

above

MC?p1

=

CS.PS

is

profit

from

sales.MC(y)Total

profitTwo-Part

Tariffsp(y)$/output

unitShould

the

monopolistset

p2

=

MC?MC(y)yTwo-Part

Tariffsp(y)y$/output

unitShould

the

monopolistset

p2

=

MC?p1

=

CS.CSMC(y)Two-Part

Tariffsp(y)y$/output

unitShould

the

monopolistset

p2

=

MC?p1

=

CS.PS

is

profit

from

sales.MC(y)CSPSTwo-Part

Tariffsp(y)y$/output

unitShould

the

monopolistset

p2

=

MC?p1

=

CS.PS

is

profit

from

sales.MC(y)Total

profitCSPSTwo-Part

Tariffsp(y)y$/output

unitShould

the

monopolistset

p2

=

MC?p1

=

CS.PS

is

profit

from

sales.MC(y)CSPSTwo-Part

Tariffsp(y)$/output

unitShould

the

monopolistset

p2

=

MC?p1

=

CS.PS

is

profit

from

sales.MC(y)yAdditional

profit

from

setting

p2

=

MC.CSPSTwo-Part

Tariffsu

The

monopolist

maximizes

its

profitwhen

using

a

two-part

tariff

bysetting

its

per

unit

price

p2

atmarginal

cost

and

setting

its

lump-sum

fee

p1

equal

to

Consumers’Surplus.Two-Part

TariffsuA

profit-maximizing

tw