Price Discrimination - GSOM• Price discrimination exists in these cases when: – “two varieties...

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Price Discrimination

2

Introduction

• Price Discrimination describes strategies used by firms to extract surplus from customers

• Examples of price discrimination– presumably profitable– should affect market efficiency: not necessarily adversely– is price discrimination necessarily bad – even if not seen as

“fair”?

3

Mechanisms for Capturing Surplus

• Market segmentation• Non-linear pricing

– Two-part pricing– Block pricing

• Tying and bundling• Quality discrimination

4

Feasibility of price discrimination

• Market power

• Two problems confront a firm wishing to price discriminate– identification: the firm is able to identify demands of different

types of consumer or in separate markets• easier in some markets than others: e.g tax consultants, doctors

– arbitrage: prevent consumers who are charged a low price from reselling to consumers who are charged a high price

• prevent re-importation of prescription drugs to the United States

• The firm then must choose the type of price discrimination– first-degree or personalized pricing– second-degree or menu pricing– third-degree or group pricing

5

Third-degree price discrimination

• Consumers differ by some observable characteristic(s)• A uniform price is charged to all consumers in a

particular group – linear price• 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

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Third-degree price discrimination 2

• 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

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Third degree price discrimination: example

• Harry Potter volume sold in the United States and Europe• Demand:

– United States: PU = 36 – 4QU

– Europe: PE = 24 – 4QE

• Marginal cost constant in each market– MC = $4

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The example: no price discrimination

• Suppose that the same price is charged in both markets• Use the following procedure:

– calculate aggregate demand in the two markets– identify marginal revenue for that aggregate demand– equate marginal revenue with marginal cost to identify the

profit maximizing quantity– identify the market clearing price from the aggregate demand– calculate demands in the individual markets from the

individual market demand curves and the equilibrium price

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The example (cont.)

United States: PU = 36 – 4QU Invert this:

QU = 9 – P/4 for P < $36Europe: PU = 24 – 4QE InvertQE = 6 – P/4 for P < $24

Aggregate these demandsQ = QU + QE = 9 – P/4 for $36 < P < $24

At these prices only the US

market is active

Q = QU + QE = 15 – P/2 for P < $24

Now both markets are

active

10

The example (cont.)

Invert the direct demandsP = 36 – 4Q for Q < 3P = 30 – 2Q for Q > 3

$/unit

Quantity15

36

30Marginal revenue isMR = 36 – 8Q for Q < 3MR = 30 – 4Q for Q < 3

DemandMRSet MR = MC MC

Q = 6.5

P = $17

6.5

17

Price from the demand curve

11

The example (cont.)

Substitute price into the individual market demand curves:

QU = 9 – P/4 = 9 – 17/4 = 4.75 millionQE = 6 – P/4 = 6 – 17/4 = 1.75 million

Aggregate profit = (17 – 4)x6.5 = $84.5 million

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The example: price discrimination

• The firm can improve on this outcome• Check that MR is not equal to MC in both markets

– MR > MC in Europe– MR < MC in the US– the firms should transfer some books from the US to Europe

• This requires that different prices be charged in the two markets

• Procedure:– take each market separately– identify equilibrium quantity in each market by equating MR

and MC– identify the price in each market from market demand

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The example: price discrimination 2

Demand in the US: PU = 36 – 4QU

$/unit

Quantity

Demand

Marginal revenue:

MR = 36 – 8QU

36

9

MR

MC = 4 MC4

Equate MR and MCQU = 4

Price from the demand curve PU = $20

4

20

14


Demand in the Europe: PE = 24 – 4QU

$/unit

Quantity

Demand

Marginal revenue:

MR = 24 – 8QU

24

6

MR

MC = 4 MC4

Equate MR and MCQE = 2.5

Price from the demand curve PE = $14

2.5

14

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• Aggregate sales are 6.5 million books– the same as without price discrimination

• Aggregate profit is (20 – 4)x4 + (14 – 4)x2.5 = $89 million– $4.5 million greater than without price discrimination

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No price discrimination: non-constant cost

• The example assumes constant marginal cost• How is this affected if MC is non-constant?

– Suppose MC is increasing

• No price discrimination procedure– Calculate aggregate demand– Calculate the associated MR– Equate MR with MC to give aggregate output– Identify price from aggregate demand– Identify market demands from individual demand curves

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The example again

Applying this procedure assuming that MC = 0.75 + Q/2 gives:

0 5 100

10

20

30

40

DU

MRU

17

4.75

Price(a) United States

Quantity0 5 10

0

10

20

30

40

DE

MRE

1.75

17

Price(b) Europe

Quantity0 5 10 15 20

0

10

20

30

40

D

MR

MC

24

6.5

17

Price(c) Aggregate

Quantity

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Price discrimination: non-constant cost

• With price discrimination the procedure is– Identify marginal revenue in each market– Aggregate these marginal revenues to give aggregate marginal

revenue– Equate this MR with MC to give aggregate output– Identify equilibrium MR from the aggregate MR curve– Equate this MR with MC in each market to give individual

market quantities– Identify equilibrium prices from individual market demands

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The example again

Applying this procedure assuming that MC = 0.75 + Q/2 gives:

Price(a) United States

Quantity0 5 10

0

10

20

30

40

DU

MRU

4

Price(b) Europe

Quantity

4

0 5 100

10

20

30

40

DE

MRE

1.75

14

Price(c) Aggregate

Quantity0 5 10 15 20

0

10

20

30

40

MR

MC

24

6.5

17

4

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Some additional comments

• Suppose that demands are linear – price discrimination results in the same aggregate

output as no price discrimination– price discrimination increases profit

• For any demand specifications two rules apply– marginal revenue must be equalized in each market– marginal revenue must equal aggregate marginal

cost

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Third-degree price discrimination 2• 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

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Product differentiation and price discrimination

• Suppose that demand in each submarket is Pi = Ai – BiQi

• Assume that marginal cost in each submarket is MCi = ci

• Finally, suppose that consumers in submarket i do not purchase from submarket j

• Equate marginal revenue with marginal cost in each submarket

Ai – 2BiQi = ci Qi = (Ai – ci)/2Bi Pi = (Ai + ci)/2

Pi – Pj = (Ai – Aj)/2 + (ci – cj)/2

It is highly unlikely that the difference in prices will equal

the difference in marginal costs

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Other mechanisms for price discrimination

• Impose restrictions on use to control arbitrage– Saturday night stay– no changes/alterations– personal use only (academic journals)– time of purchase (movies, restaurants)

• Damaged goods• Discrimination by location

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Discrimination by location

• Suppose demand in two distinct markets is identical – Pi = A = BQi

• But suppose that there are different marginal costs in supplying the two markets– cj = ci + t

• Profit maximizing rule:– equate MR with MC in each market as before– Pi = (A + ci)/2; Pj = (A + ci + t)/2– Pj – Pi = t/2 cj – ci– difference in prices is not the same as the difference in costs

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Third-degree rice discrimination and welfare

• Does third-degree price discrimination reduce welfare?– not the same as being “fair”– relates solely to efficiency– so consider impact on total surplus

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Price discrimination and welfare

Suppose that there are two markets: “weak” and “strong”

D1

MR1

D2

MR2

MC MC

P1

P2

ΔQ1 ΔQ2

Price Price

Quantity Quantity

PU PU

The discriminatory price in the weak

market is P1

The discriminatory price in the strong

market is P2

The uniform price in bothmarket is PU

G

The maximum gain in surplus

in the weak market is G

L

The minimum loss of surplus in

the strong market is L

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Price discrimination and welfare

D1

MR1

D2

MR2

MC MC

P1

P2

ΔQ1 ΔQ2

Price Price

Quantity Quantity

PU PU

G L

It follows that ΔW < G – L = (PU – MC)ΔQ1 + (PU – MC)ΔQ2

= (PU – MC)(ΔQ1 + ΔQ2)

Price discrimination cannot increasesurplus unless it

increases aggregateoutput

Price discrimination cannot increasesurplus unless it

increases aggregateoutput

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Price discrimination and welfare 2

• Previous analysis assumes that the same markets are served with and without price discrimination

• This may not be true– uniform price is affected by demand in “weak” markets– firm may then prefer not to serve such markets without price

discrimination– price discrimination may open up weak markets

• The result can be an increase in aggregate output and an increase in welfare

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New markets: an example

Demand in “North” is PN = 100 – QN ; in “South” is PS = 100 - QS

$/unit $/unit $/unitNorth South Aggregate

Quantity Quantity Quantity

100

100

Marginal cost to supply either market is $20

MC MC MC

Demand

MR

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New Markets: the example 2

$/unitAggregate

Quantity

MC

Demand

MR

Aggregate demand is P = (1 + )50 – Q/2 provided that both markets are served

Equate MR and MC to get equilibrium output QA = (1 + )50 - 20

QA

Get equilibrium price from aggregate demand P = 35 + 25 P

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New Markets: the example 3

Now consider the impact of a reduction in

$/unitAggregate

Quantity

MC

Demand

MR

Aggregate demand changes

D'

Marginal revenue changes

MR'

It is no longer the case that both markets are served

The South market is dropped

Price in North is the monopoly price for that market

PN

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The example again

Previous illustration is too extreme

So there are potentially two equilibria with uniform pricing

MC cuts MR at two points

Quantity

$/unit

Aggregate

MC

Demand

MR

At Q1 only North is served at the monopoly price in North

Q1

PNAt Q2 both markets are served at the uniform price PU

Q2

PU

Switch from Q1 to Q2:decreases profit by the red areaincreases profit by the blue area

If South demand is “low enough” or MC “high enough” serve only North

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Price discrimination and welfare Again

Quantity

$/unit Aggregate

MC

Demand

MR

Q1

PN

In this case only North is served with uniform pricingBut MC is less than the reservation price PR in South

PR

So price discrimination will lead to South being supplied

Price discrimination leaves surplus unchanged in North

But price discrimination generates profit and consumer surplus in South

So price discrimination increases welfare

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Introduction to Nonlinear Pricing

• Annual subscriptions generally cost less in total than one-off purchases

• Buying in bulk usually offers a price discount– these are price discrimination reflecting quantity discounts– prices are nonlinear, with the unit price dependent upon the quantity

bought– allows pricing nearer to willingness to pay– so should be more profitable than third-degree price discrimination

• How to design such pricing schemes?– depends upon the information available to the seller about buyers– distinguish first-degree (personalized) and second-degree (menu)

pricing

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First-degree price discrimination 2

• Monopolist can charge maximum price that each consumer is willing to pay

• Extracts all consumer surplus• Since profit is now total surplus, find that first-degree

price discrimination is efficient

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• First-degree price discrimination is 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– no value-creating exchanges are missed

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• The information requirements appear to be insurmountable– but not in particular cases

• tax accountants, doctors, students applying to private universities

• But there are pricing schemes that will achieve the same outcome– non-linear prices– two-part pricing as a particular example of non-linear prices

• charge a quantity-independent fee (membership?) plus a per unit usage charge

– block pricing is another• bundle total charge and quantity in a package

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Two-part pricing

• Jazz club serves two types of customer– Old: demand for entry plus Qo drinks is P = Vo – Qo– Young: demand for entry plus Qy drinks is P = Vy –

Qy– Equal numbers of each type– Assume that Vo > Vy: Old are willing to pay more

than Young– Cost of operating the jazz club C(Q) = F + cQ

• Demand and costs are all in daily units

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Two-part pricing 2

• Suppose that the jazz club owner applies “traditional”linear pricing: free entry and a set price for drinks– aggregate demand is Q = Qo + Qy = (Vo + Vy) – 2P– invert to give: P = (Vo + Vy)/2 – Q/2– MR is then MR = (Vo + Vy)/2 – Q– equate MR and MC, where MC = c and solve for Q to give– QU = (Vo + Vy)/2 – c– substitute into aggregate demand to give the equilibrium price– PU = (Vo + Vy)/4 + c/2– each Old consumer buys Qo = (3Vo – Vy)/4 – c/2 drinks– each Young consumer buys Qy = (3Vy – Vo)/4 – c/2 drinks– profit from each pair of Old and Young is U = (Vo + Vy – 2c)2

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Two part pricing 3

This example can be illustrated as follows:

Price

Quantity

Vo

Vo

Price

Quantity

Vy

Vy

Price

Quantity

Vo

Vo + Vy

MC

MR

(a) Old Customers (b) Young Customers (c) Old/Young Pair of Customers

Vo+Vy

2 - c

c

Vo+Vy4 + c

2h i

jk

a

bd

e

fg

Linear pricing leaves each type of consumer with consumer surplus

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Two part pricing 4

• Jazz club owner can do better than this• Consumer surplus at the uniform linear price is:

– Old: CSo = (Vo – PU).Qo/2 = (Qo)2/2– Young: CSy = (Vy – PU).Qy/2 = (Qy)2/2

• So charge an entry fee (just less than):– Eo = CSo to each Old customer and Ey = CSy to each Young

customer• check IDs to implement this policy

– each type will still be willing to frequent the club and buy theequilibrium number of drinks

• So this increases profit by Eo for each Old and Ey for each Young customer

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Two part pricing 5

• The jazz club can do even better– reduce the price per drink– this increases consumer surplus– but the additional consumer surplus can be extracted through

a higher entry fee

• Consider the best that the jazz club owner can do with respect to each type of consumer

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Two-Part Pricing

$/unit

Quantity

Vi

Vi

MRMCc

Set the unit price equalto marginal cost

Set the unit price equalto marginal cost

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

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

The entry chargeconverts consumersurplus into profit

Vi - cSet the entry charge

to (Vi - c)2/2Set the entry charge

to (Vi - c)2/2

Profit from each pair of Old and Young now d = [(Vo – c)2 + (Vy – c)2]/2

Using two-partpricing increases themonopolist’s

profit

Using two-partpricing increases themonopolist’s

profit

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Block pricing

• There is another pricing method that the club owner can apply– offer a package of “Entry plus X drinks for $Y”

• To maximize profit apply two rules– set the quantity offered to each consumer type equal to the

amount that type would buy at price equal to marginal cost– set the total charge for each consumer type to the total

willingness to pay for the relevant quantity

• Return to the example:

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Block pricing 2

Old$

Quantity

Vo

Vo

Young$

Quantity

Vy

Vy

MC MCc c

Quantity supplied to each Old customer

Quantity supplied to each Young

customer

Qo Qy

Willingness to pay of each

Old customerWillingness to

pay of each Young customer

WTPo = (Vo – c)2/2 + (Vo – c)c = (Vo2 – c2)/2

WTPy = (Vy – c)2/2 + (Vy – c)c = (Vy2 – c2)/2

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Block pricing 3

• How to implement this policy?

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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

• Take a specific example– Ph = 16 – Qh– Pl = 12 – Ql– MC = 4

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Second-degree price discrimination 2

• First-degree price discrimination requires:– High Income: entry fee $72 and $4 per drink or entry plus 12

drinks for a total charge of $120– Low Income: entry fee $32 and $4 per drink or entry plus 8

drinks for total charge of $64• This will not work

– high income types get no consumer surplus from the package designed for them but get consumer surplus from the other package

– so they will pretend to be low income even if this limits the number of drinks they can buy

• Need to design a “menu” of offerings targeted at the two types

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• The seller has to compromise• Design a pricing scheme that makes buyers

– reveal their true types– self-select the quantity/price package designed for them

• 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

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Second degree price discrimination 4

High-income Low-Income

$

Quantity Quantity

16

16

12

12

4 MC 4 MC

12 88

$328

$16$32

$

Offer the low-incomeconsumers a package of

entry plus 8 drinks for $64

Offer the low-incomeconsumers 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-income consumers:because the ($64, 8)

package gives them $32consumer surplus

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

package gives them $32consumer surplus

$64

$32

$8

So any other packageoffered to high-income

consumers must offer atleast $32 consumer surplus

So any other packageoffered to high-income

consumers must offer atleast $32 consumer surplus

This is the incentivecompatibility constraint

High income consumers arewilling to pay up to $120 for

entry plus 12 drinks if no otherpackage is available

High income 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 income consumers will notbuy the ($88, 12)

package since theyare willing to payonly $72 for 12

drinks

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

package since theyare willing to payonly $72 for 12

drinks

$8

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

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

$40

And profit fromeach low-income

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

And profit fromeach low-income

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

$32

These packages exhibitquantity discounting: high-

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

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Second degree price discrimination 5

High-Income

Low-Income$

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?

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

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

Suppose each low-income 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-income 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-income consumerssince this allows him to increase

the charge to high-incomeconsumers

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

• There are cases where it is better to supply only high-demand types– high-class restaurants– golf and country clubs

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

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

($92, 12) aimed at high-income– profit is $31.50xNl + $44xNh

• Now suppose only high-income 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 that NhNl

< 31.5028

= 1.125

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

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• 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

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Non-linear pricing and welfare 1

• Pricing policy affects– distribution of surplus– output of the firm

• First is welfare neutral• Second affects welfare• Does it increase social welfare?• Price discrimination increases

social welfare of group i if it increases quantity supplied to group i

Price

Quantity

Demand

c MC

Qi Qi(c)

TotalSurplus

Q’i

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• First-degree price discrimination always increases social welfare– extracts all consumer surplus– but generates socially

optimal output– output to group i is Qi(c)– this exceeds output with

uniform (non-discriminatory) pricing

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• Menu pricing is less straightforward– suppose that there are two markets

• low demand• high demand

• Uniform price is PU

• Menu pricing gives quantities Q1s, Q2

s

• Welfare loss is greater than L• Welfare gain is less than G

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Price

QuantityPrice

Quantity

MC

MC

PU

PU

QlU

QhU

Qls

Qhs

L

G

= (PU – MC)ΔQ1 + (PU – MC)ΔQ2

= (PU – MC)(ΔQ1 + ΔQ2)

ΔW < G – L

• A necessary condition for second-degree price discrimination to increase social welfare is that it increases total output

• It follows that

• “Like” third-degree price discrimination• But second-degree price discrimination

is more likely to increase output

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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– encouragement to buy in bulk must offer a price discount

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Tying

• Tying is a seller’s conditioning the purchase of one product on the purchase of another – Technological ties

• Printer cartridges

– Contractual ties• Car dealer and car parts

• Why tying?

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Quality Discrimination

• Why is Quality Discrimination a form of Price Discrimination?– First / business class airfare vs economy class

• Reduction in quality of the lower-quality good to reduce the incentive of people with high willingness to pay to switch from the high-quality good when the firm increases its price– “Damaged goods”

Price Discrimination - GSOM• Price discrimination exists in these cases when: – “two varieties...

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