Industrial Organization: Chapter 31 Chapter 3 Basic Monopoly Pricing and Product Strategies

Industrial Organization: Chapter 3 1

Chapter 3

Basic Monopoly Pricing

and

Product Strategies


Introduction

• A monopolist has the power to set prices

• Consider how the monopolist exercises this power– Focus in this section on a single-product monopolist

– What determines price?

– What different pricing strategies might be used?

– What product design strategies might be used?

– What constraints are there on the monopolist’s ability to extract consumer surplus?


First-Degree Price Discrimination

First-degree price discrimination occurs when the seller is able to extract the entire consumer surplus– suppose that you own five antique cars and you meet two collectors– each is willing to pay $10,000 for one car, $8,000 for a second car,

$6,000 for a third car, $4,000 for a fourth and $2,000 for a fifth – sell the first two cars at $10,000, one to each buyer– sell the second two cars at $8,000, one to each buyer– sell the fifth car to one of the buyers at $6,000– total revenue $42,000

• Highly profitable but requires– detailed information– ability to avoid arbitrage

• Leads to the efficient choice of output: since price equals marginal revenue and MR = MC


First-degree price discrimination (cont.)

• The information requirements appear to be insurmountable

• No arbitrage is less restrictive but potentially a problem

• But there are pricing schemes that will achieve the same output– non-linear prices

– two-part pricing as a particular example of non-linear prices


Two-Part Pricing

Take an example:

Demand is P = V - Q

$

Quantity

V

V

Cost is C(Q) = F + cQ

Marginal Revenue is

MR = V - 2Q

Marginal Cost is

MC = c

MR

MCc

n identical consumers

Jazz club:


Two-Part Pricing$

Quantity

V

V

MR

MCc

With a uniform price profitis maximized by settingmarginal revenue equal

to marginal cost

With a uniform price profitis maximized by settingmarginal revenue equal

to marginal cost

V - 2Q = c

So Q = (V - c)/2

(V-c)/2

P = V - Q

So P = (V + c)/2

(V+c)/2

Profit to the monopolistis

n(V - c)2/4 - F

Profit to the monopolistis

n(V - c)2/4 - F

Consumer surplus for eachconsumer is

(V - c)2/8

Consumer surplus for eachconsumer is

(V - c)2/8

What if the sellercan charge an entry

fee?

What if the sellercan charge an entry

fee?

The maximum entry fee thateach consumer will be willing

to pay is consumer surplus

The maximum entry fee thateach consumer will be willing

to pay is consumer surplus

Charging anentry fee increases

profit by(V - c)2/8

per consumer


Two-Part Pricing$

Quantity

V

V

MR

MCc

(V-c)/2

(V+c)/2

Is this the bestthe sellercan do?

Is this the bestthe sellercan do?

Lower the unit priceLower the unit price

This increases consumer surplus and so increases

the entry charge

This increases consumer surplus and so increases

the entry charge

This whole area isnow profit from each

consumer


Two-Part Pricing$

Quantity

V

V

MR

MCc

What is the bestthe sellercan do?

What is the bestthe sellercan do?

Set the unit price equalto marginal cost

Set the unit price equalto marginal cost

This gives consumer surplus of (V - c)2/2

This gives consumer surplus of (V - c)2/2

The entry chargeconverts consumersurplus into profit

V - c

Set the entry chargeto (V - c)2/2

Set the entry chargeto (V - c)2/2

Using two-part

pricing increases themonopolist’s

profit


Two-part pricing (cont.)

• First-degree price discrimination through two-part pricing– increases profit by extracting all consumer surplus

– leads to unit price equal to marginal cost

– causes the monopolist to produce the efficient level of output

• What happens if consumers are not identical?

• Assume that consumers differ in types and that the monopolist can identify the types– age

– location

– some other distinguishing and observable characteristic

• We can extend our example


Two-part pricing with different consumers

Older Consumers Younger Consumers

Demand: P = 16 - QDemand: P = 16 - Q Demand: P = 12 - QDemand: P = 12 - Q

$

Quantity

$

Quantity

16

16

12

12

4 MC 4 MC

Assume thatmarginal cost is

constant at$4 per unit

Assume thatmarginal cost is

constant at$4 per unit

If unit priceis set at $4

older customerseach buy 12

units

If unit priceis set at $4

older customerseach buy 12

units

12

And youngercustomers each

buy 8 units

And youngercustomers each

buy 8 units

8

Consumer surplusfor the older

customers is $72

Consumer surplusfor the older

customers is $72

$72

And for theyounger customersconsumer surplus

is $32

And for theyounger customersconsumer surplus

is $32

$32

So the seller can charge an entry fee of $72 t o each

older customer and $32to each younger one

This convertsall consumersurplus into

profit$72 $32

• There is an alternative approach

• Offer older customers entry plus 12 units for $120• and younger customers entry plus 8 units for $64

$48 $32


Second-Degree Price Discrimination

• What if the seller cannot distinguish between buyers?– perhaps they differ in income (unobservable)

• Then the type of price discrimination just discussed is impossible

• High-income buyer will pretend to be a low-income buyer – to avoid the high entry price

– to pay the smaller total charge

• Confirm from the diagram


The example again

High-DemandConsumers

Low-DemandConsumers

Demand: P = 16 - QDemand: P = 16 - Q Demand: P = 12 - QDemand: P = 12 - Q

$

Quantity Quantity

16

16

12

12

4 MC 4 MC

12 88

$32

$328

$32

$16

$32

$32

$8

$If a high-demand consumer pays the lowerfee and buys 12 units he

gets $40 of consumersurplus

If a high-demand consumer pays the lowerfee and buys 12 units he

gets $40 of consumersurplus

Could the seller prevent this by limiting the numberof units that can be bought?

Could the seller prevent this by limiting the numberof units that can be bought?

NO! If a high-demand consumer pays the lower fee and gets the lower quantity hegets $32 of consumer surplus

NO! If a high-demand consumer pays the lower fee and gets the lower quantity hegets $32 of consumer surplus


Second-Degree Price Discrimination• The seller has to compromise

• A pricing scheme must be designed that makes buyers– reveal their true types

– self-select the quantity/price package designed for them

• This is the essence of second-degree price discrimination

• It is “like” first-degree price discrimination– The seller knows that there are buyers of different types

• But– the seller is not able to identify the different types

• A two-part tariff is ineffective– allows deception by buyers

• Use quantity discounting


The example again

High-Demand Low-Demand

$

Quantity Quantity

16

16

12

12

4 MC 4 MC

12 88

$328

$16$32

$Offer the low-demand

consumers a package ofentry plus 8 drinks for $64

Offer the low-demandconsumers a package of

entry plus 8 drinks for $64

$32

$32

The low-demand consumers will bewilling to buy this ($64, 8) package

The low-demand consumers will bewilling to buy this ($64, 8) package

So will the high-demand consumers:because the ($64, 8)

package gives them $32consumer surplus

So will the high-demand consumers:because the ($64, 8)

package gives them $32consumer surplus

$64

$32

$8

So any other packageoffered to high-demandconsumers must offer at

least $32 consumer surplus

So any other packageoffered to high-demandconsumers must offer at

least $32 consumer surplus

This is the incentivecompatibility constraintHigh demand consumers are

willing to pay up to $120 forentry plus 12 drinks if no other

package is available

High demand consumers arewilling to pay up to $120 for

entry plus 12 drinks if no otherpackage is available

So they can be offered a packageof ($88, 12) (since $120 - 32 = 88)

and they will buy this

So they can be offered a packageof ($88, 12) (since $120 - 32 = 88)

and they will buy this

$24

Low demand consumers will notbuy the ($88, 12)

package since theyare willing to payonly $72 for 12

drinks

Low demand consumers will notbuy the ($88, 12)

package since theyare willing to payonly $72 for 12

drinks

$8

Profit from each high-demand consumer is$40 ($88 - 12 x $4)

Profit from each high-demand consumer is$40 ($88 - 12 x $4)

$40

And profit fromeach low-demand

consumer is$32 ($64 - 8x$4)

And profit fromeach low-demand

consumer is$32 ($64 - 8x$4)

$32

These packages exhibitquantity discounting: high-

demand pay $7.33 per unit andlow-demand pay $8


The example again

High-Demand Low-Demand

$

Quantity Quantity

16

16

12

12

4 MC 4 MC

12

$

Can the club-owner do even

better than this?

Can the club-owner do even

better than this?

8

Yes! Reduce the numberof units offered to eachlow-demand consumer

Yes! Reduce the numberof units offered to eachlow-demand consumer

Suppose each low-demand consumer is offered 7 drinks

7

Each consumer will pay up to $59.50 for entry and 7 drinks

$59.50

Profit from each ($59.50, 7) package is $31.50: a reduction

of $0.50 per consumer

$31.50

A high-demand consumer will pay up to $87.50 for entry and 7 drinks

7

$87.50

$28

So buying the ($59.50, 7) package gives him $28 consumer surplus

$28

So entry plus 12 drinks can be sold for $92 ($120 - 28 = $92)

$92

$28

Profit from each ($92, 12) package is $44: an increase of $4 per

consumer

$44

$48

The monopolist does better byreducing the number of units

offered to low-demand consumerssince this allows him to increase

the charge to high-demandconsumers


Second-degree price discrimination (cont.)

• Will the monopolist always want to supply both types of consumer?

• There are cases where it is better to supply only high-demand– high-class restaurants

– golf and country clubs

• Take our example again– suppose that there are Nl low-income consumers

– and Nh high-income consumers



• Suppose both types of consumer are served– two packages are offered ($57.50, 7) aimed at low-demand and

($92, 12) aimed at high-demand

– profit is $31.50xNl + $44xNh

• Now suppose only high-demand consumers are served– then a ($120, 12) package can be offered

– profit is $72xNh

• Is it profitable to serve both types?– Only if $31.50xNl + $44xNh > $72xNh 31.50Nl > 28Nh

This requires thatNh

Nl

<31.50

28= 1.125

There should not be “too high” a proportion of high-demand consumers



• Characteristics of second-degree price discrimination– extract all consumer surplus from the lowest-demand group

– leave some consumer surplus for other groups• the incentive compatibility constraint

– offer less than the socially efficient quantity to all groups other than the highest-demand group

– offer quantity-discounting

• Second-degree price discrimination converts consumer surplus into profit less effectively than first-degree

• Some consumer surplus is left “on the table” in order to induce high-demand groups to buy large quantities


Third-Degree Price Discrimination

• Consumers differ by some observable characteristic(s)

• A uniform price is charged to all consumers in a particular group

• Different uniform prices are charged to different groups– “kids are free”

– subscriptions to professional journals e.g. American Economic Review

– airlines• the number of different economy fares charged can be very large

indeed!

– early-bird specials; first-runs of movies


Third-degree price discrimination (cont.)

• Often arises when firms sell differentiated products– hard-back versus paper back books

– first-class versus economy airfare

• Price discrimination exists in these cases when:– “two varieties of a commodity are sold by the same seller to two

buyers at different net prices, the net price being the price paid by the buyer corrected for the cost associated with the product differentiation.” (Phlips)

• The seller needs an easily observable characteristic that signals willingness to pay

• The seller must be able to prevent arbitrage– e.g. require a Saturday night stay for a cheap flight



• The pricing rule is very simple:– consumers with low elasticity of demand should be charged a high

price

– consumers with high elasticity of demand should be charged a low price

• Illustrate with a simple example– monopolist has constant marginal costs of c per unit

– two types of consumers, with the type being identifiable

– all consumers of a particular type have identical demands

– two pricing rules must hold• marginal revenue must be equal on the last unit sold to each type of

consumer

• marginal revenue must equal marginal cost in each market


An example

Type 1 Demand: P = A1 - BQ1Type 1 Demand: P = A1 - BQ1 Type 2 Demand: P = A2 - BQ2

Type 2 Demand: P = A2 - BQ2

$

Quantity Quantity

A1

A1/B

A2

A2/B

c MC c MC

$

MR1MR2

MR1 = A1 - 2BQ1

MC = c Q1 = (A1 - c)/2B

(A1-c)/2B

P1 = (A1 + c)/2

(A1+c)/2

MR2 = A2 - 2BQ2

MC = c Q2 = (A2 - c)/2B

P2 = (A2 + c)/2

(A2-c)/2B

(A2+c)/2

Since A1 > A2 Type 1consumers are charged a

higher price thanType 2 consumers



• What happens if marginal costs are not constant?

• The same principles apply– marginal revenue equalized across consumer types

– marginal revenue equal to marginal cost where marginal cost is measured at aggregate output

• Consider an example


The example• Two markets

– Market 1: P = 20 - Q1

– Market 2: P = 16 - 2Q2

MR1 = 20 - 2Q1

MR2 = 16 - 4Q2

Now calculateaggregate marginal

revenue

Now calculateaggregate marginal

revenue

Invert these to give Q as a function of MR:

Q1 = 10 - MR/2

Q2 = 4 - MR/4

Note that this appliesonly for prices less than

$16

Note that this appliesonly for prices less than

$16

So aggregate marginal revenue is

Q = Q1 + Q2 = 14 - 3MR/4

Invert this to give marginal revenue:

MR = 56/3 - 4Q/3 for MR < $16

MR = 20 - 2Q for MR > $16

MC = 2Q

MC = MR 2Q = 56/3 - 4Q/3

Q = 5.6

MR = $11.20

Q1 = 4.4 and Q2 = 1.2

P1 = $15.60 and P2 = $13.60

The consumers withless elastic demand arecharged higher prices

The consumers withless elastic demand arecharged higher prices



• A general rule characterizes third-degree price discrimination

• Recall the formula for marginal revenue in market i:– MRi = Pi(1 - 1/i) where i is the price elasticity of demand

• Recall also that when serving two markets profit maximization requires that MR is equalized in each market– so MR1 = MR2

P1(1 - 1/ 1) = P2(1 - 1/ 2)

P1

P2

=(1 - 1/ 2)

(1 - 1/ 1)

Prices are alwayshigher in markets where

demand is inelastic

Prices are alwayshigher in markets where

demand is inelastic


Price Discrimination and Welfare

• Does price discrimination reduce welfare?

• First- and second- degree: “not necessarily”– because output is at or near to the efficient level

• Third-degree is less clear– monopolist restricts output in the markets supplied

– but markets may be served that would otherwise be left unsupplied

• A necessary condition for third-degree price discrimination not to reduce welfare is that it leads to an increase in output


Public Policy

• Uneven– Robinson-Patman makes price discrimination illegal if it is

intended to create a monopoly

– One defense is if discriminatory prices are intended to “meet the competition”

• Enforcement has been spotty– weak in recent years

– but note the pharmaceutical case

– private actions are possible: see http://lawmall.com

• International restrictions also exist– anti-dumping regulations

– these are currently pursued very actively


Monopoly and Product Quality

• Firms can, and do, produce goods of different qualities

• Quality then is an important strategic variable

• The choice of product quality by a monopolist is determined by its ability to generate profit

• Focus for the moment on a monopolist producing a single good– what quality should it have?

– determined by consumer attitudes to quality• prefer high to low quality

• willing to pay more for high quality

• but this requires that the consumer recognizes quality

• also some are willing to pay more than others for quality


Demand and Quality

• We might think of individual demand as being of the form– Qi = 1 if Pi < Ri(Z) and = 0 otherwise for each consumer i

– Each consumer buys exactly one unit so long as price is less than her reservation price

– the reservation price is affected by product quality Z

• Assume that consumers vary in their reservation prices

• Then aggregate demand is of the form P = P(Q, Z)

• An increase in product quality increases demand


Demand and quality (cont.)

Begin with a particular demand curvefor a good of quality Z1

Begin with a particular demand curvefor a good of quality Z1

Price

Quantity

P(Q, Z1)

P1

Q1

If the price is P1 and the product qualityis Z1 then all consumers with reservationprices greater than P1 will buy the good

If the price is P1 and the product qualityis Z1 then all consumers with reservationprices greater than P1 will buy the goodR1(Z1)

These are theinframarginal

consumers

These are theinframarginal

consumers

This is themarginalconsumer

This is themarginalconsumer

Suppose that an increase inquality increases thewillingness to pay of

inframarginal consumers morethan that of the marginal

consumer

Suppose that an increase inquality increases thewillingness to pay of

inframarginal consumers morethan that of the marginal

consumer

Then an increase in productquality from Z1 to Z2 rotates

the demand curve aroundthe quantity axis as follows


the demand curve aroundthe quantity axis as follows

R1(Z2)

P2

Quantity Q1 can now besold for the higher

price P2

Quantity Q1 can now besold for the higher

price P2

P(Q, Z2)



Price

Quantity

P(Q, Z1)

P1

Q1

R1(Z1)

Suppose instead that an increase in

quality increases thewillingness to pay of marginal

consumers morethan that of the inframarginal

consumers

Suppose instead that an increase in

quality increases thewillingness to pay of marginal

consumers morethan that of the inframarginal

consumers


the demand curve aroundthe price axis as follows


the demand curve aroundthe price axis as follows

P(Q, Z2)

Once again quantity Q1 can now be sold for a

higher price P2

Once again quantity Q1 can now be sold for a

higher price P2

P2



• The monopolist must choose both– price (or quantity)

– quality

• Two profit-maximizing rules– marginal revenue equals marginal cost on the last unit sold for a

given quality

– marginal revenue from increased quality equals marginal cost of increased quality for a given quantity

• This can be illustrated with a simple example:

P = Z( - Q) where Z is an index of quality


Demand and quality: an example

P = Z( - Q)

Assume that marginal cost of output is zero: MC(Q) = 0

Cost of quality is D(Z) = Z2

This means that quality iscostly and becomesincreasingly costly

This means that quality iscostly and becomesincreasingly costly

Marginal cost of quality = dD(Z)/d(Z)

= 2Z

The firm’s profit is:

(Q, Z) =P.Q - D(Z) = Z( - Q)Q - Z2

The firm chooses Q and Z to maximize profit.

Take the choice of quantity first: this is easiest.

Marginal revenue = MR = Z - 2ZQ

MR = MC Z - 2ZQ = 0 Q* = /2

P* = Z/2


The example continued

Total revenue = P*Q* = (Z/2)x(/2) = Z2/4

So marginal revenue from increased quality is MR(Z) = 2/4

Marginal cost of quality is MC(Z) = 2Z

Equating MR(Z) = MC(Z) then gives Z* = 2/8

Does the monopolist produce too high or too low quality?

Is it possible that quality is too high?

Only in particular constrained circumstances.


The Multiplant Monopolist

• A monopolist rarely produces all output in one plant– how should production be allocated across plants?

– this is especially important if different plants have different costs

• To maximize profit set MR = MC on the last unit produced

• But with several plants what is MC?

• First case:– marginal costs constant within a plant but varying across plants

– each plant has a capacity constraint


The multiplant monopolist (cont.)Price

Quantity

MR

q1

MC1

q1 + q2

MC2

MC3

Produce output Q* using plant1 and plant 2. Plant 3 is not

operated (or introduced)

Produce output Q* using plant1 and plant 2. Plant 3 is not

operated (or introduced)

Q*

Suppose that there are three possible plants.

Arrange them in orderof their marginal costs

Suppose that there are three possible plants.

Arrange them in orderof their marginal costs

Plant 1 has marginalcost MC1 and

capacity q1


capacity q1


capacity q2


capacity q2


capacity q3


capacity q3

Maximize profit byequating marginal costand marginal revenue

Maximize profit byequating marginal costand marginal revenue


The multiplant monopolist (cont.)

• What happens if marginal costs are not constant?

• Output allocation– operate plants such that marginal cost is equal on the last unit

produced in each plant

• Why?– If not, then cost can be reduced by reallocating output between

plants

– For example: suppose MC1 = $10 and MC2 = $15

– Reducing output of plant 2 by one unit and increasing output of plant 1 by one unit reduces total costs


An Example

Suppose MC1 = q1 and MC2 = q2Suppose MC1 = q1 and MC2 = q2

Quantity

$

MC1 = q1

MC2 = q2

q1 = MC/ ; q2 = MC/q1 = MC/ ; q2 = MC/

Q =q1 + q2 = MC()/ Q =q1 + q2 = MC()/

MC = Q() MC = Q()

$

Quantity

MC1 + MC2

MR

Maximize profitby setting marginal

revenue equalto marginal cost

Maximize profitby setting marginal

revenue equalto marginal cost

Q*q2* q1*

Allocate output to the two plants

to equatemarginal costs

Allocate output to the two plants

to equatemarginal costs




Price

Quantity

Z1

P(Q,Z1)

How does increased quality affect demand?

How does increased quality affect demand?

Z2P(Q, Z2)

MR(Z1)

MR(Z2)

/2

Q*

P1 = Z1/2

P2 = Z2/2

When quality is Z1

price isZ1/2

When quality is Z1

price isZ1/2

When quality is Z2

price isZ2/2

When quality is Z2

price isZ2/2



Price

Quantity

Z1

Z2

/2

Q*

P1 = Z1/2

P2 = Z2/2

An increase in quality fromZ1 to Z2 increases

revenue by this area

An increase in quality fromZ1 to Z2 increases

revenue by this areaSocial surplus at quality Z1

is this area minus qualitycosts

Social surplus at quality Z1






So an increase is quality fromZ1 to Z2 increases surplus

by this area minus theincrease in quality costs

So an increase is quality fromZ1 to Z2 increases surplus

by this area minus theincrease in quality costs

The increase is total surplus is greater than the increase in profit.

The monopolist produces too little quality


Demand and quality: an alternative

Price

Quantity

P(Q,Z1)

Assume that an increasein quality from Z1 to

Z2 rotates the demand function as follows

Assume that an increasein quality from Z1 to

Z2 rotates the demand function as follows

P(Q,Z2)

Further assume thatthe firm is constrainedto produce output Q

Further assume thatthe firm is constrainedto produce output Q

Q

The increase inquality increasesprofit by this areaminus the cost ofincreased quality

The increase inquality increasesprofit by this areaminus the cost ofincreased quality

The increase insocial surplus

is this areaminus the cost ofincreased quality

The increase insocial surplus

is this areaminus the cost ofincreased quality

The increase in total surplus is less than

the increase in profit. The monopolist produces

too much quality

This may arise as a resultof an export quota or

other restriction on output

This may arise as a resultof an export quota or

other restriction on output

Exporters subject to quotastend to export high quality

goods

Exporters subject to quotastend to export high quality

goods


Demand and quality

Derivation of aggregate demand

Order consumers by their reservation prices

Aggregate individual demand horizontally

Price

Quantity1 2 3 4 5 6 7 8


Market 1Market 1

$

Quantity

$16

8

$

Quantity

$20

2010 4

D1D2

MR1 MR2

MR1+MR2

Quantity

$

Market 2Market 2 AggregateAggregate

$20

$16

14

MC

5.6

$11.20

4.4 1.2

$15.60$13.60


The incentive compatibility constraint

• Any offer made to high demand consumers must offer them as much consumer surplus as they would get from an offer designed for low-demand consumers.

• This is a common phenomenon– performance bonuses must encourage effort

– insurance policies need large deductibles to deter cheating

– piece rates in factories have to be accompanied by strict quality inspection

– encouragement to buy in bulk must offer a price discount

Documents

Industrial Organization: Chapter 31 Chapter 3 Basic Monopoly Pricing and Product Strategies