1 Price Discrimination Per Baltzer Overgaard February, 2003 Adapted from the notes of H. Peter Møllgaard (by courtesy) Based on Carlton and Perloff chap

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Price Discrimination

Per Baltzer Overgaard

February, 2003

Adapted from the notes of

H. Peter Møllgaard (by courtesy)

Based on Carlton and Perloff

chap. 9/10

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Outline: Non-uniform pricing

• Common types of Price Discrimination

• Necessary conditions for PD

• 1st-degree PD

• 3rd-degree PD

• 2nd-degree PD

• Tying as a PD vehicle

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Common types of PD

• Student discounts on computers, software, books, … -> 3rd degree PD– Customers segmented into separate sub-markets

• Quantity discounts -> 2nd degree PD– Customers self-select their discount by the size

of their order

• Individualized prices -> 1st degree PD– Special price for you, my friend.

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• Common types of PD


• 1st-degree PD

• 3rd-degree PD

• 2nd-degree PD


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Necessary conditions for PD (1)

• Existence of market power– i.e. ability to raise price above MC.

• Identification of different consumers’ willingness to pay.– identification method differs in 1st, 2nd, and

3rd degree PD

• Firm must be able to prevent or limit resales– arbitrage eliminates price differences

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Necessary conditions for PD (2)

Ways to prevent or limit resales

• services can often not be resold– Want to buy my haircut?

• resale can make warranty void

• transportation costs may limit resales

• contractual clauses may forbid resale

• vertical integration may prevent resales. ...

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• 1st-degree PD

• 3rd-degree PD

• 2nd-degree PD


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1st-degree or perfect PD (1)

• Each consumer needs one unit.

• Their willingness to pay for a unit differs.

• Firm can identify a consumer’s w.t.pay

• so offers each consumer the unit at a price = w.t.pay (-)

• no consumer surplus is left -- firm gets it all

• but the market outcome is efficient:

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1 2 3 4 5 6 7 81 2 3 4 5 6 7 8 # of units# of units

willingness towillingness topay pricepay priceMCMC

MCMC

Firm sells as many units as Firm sells as many units as it would under perfect it would under perfect competition so the market is competition so the market is allocatively efficient allocatively efficient

… … but consumersbut consumersmight dislike themight dislike thedistributive effectsdistributive effects

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• Each consumer needs several units.

• Individual demand curves differ.

• Firm can identify a consumer’s demand

• offers each an individualized two-part tariff

w.t.p.w.t.p.MCMC

qqJSJS

MCMC

John Smith’s demand curveJohn Smith’s demand curve

Offer a two-partOffer a two-partpricing scheme:pricing scheme:Pay = FPay = FJSJS+p+pJSJSqqJSJS

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• What should pJS and FJS optimally be set at?

• Profit maximum is where – pJS = MC

– FJS = “CS”

w.t.p.w.t.p.MCMC

qqJSJS

MCMC

John Smith’s demand curveJohn Smith’s demand curve

Offer a two-partOffer a two-partpricing scheme:pricing scheme:Pay = FPay = FJSJS+p+pJSJSqqJSJS

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• 1st-degree PD

• 3rd-degree PD

• 2nd-degree PD


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3rd-degree PD (1)

• Markets may be separated– geographically– according to e.g. demographic characteristics:

• age (youth, elderly)

• employment status (employed, unemployed, student)

• income level

• ...

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3rd-degree PD (2)

• Profits may be split into two separate parts if monopolist has constant MC=m

• π = (p1(Q1)-m) Q1+ (p2(Q2)-m) Q2

• F.O.C.: pi - m + pi’ Qi = 0 , i = 1,2

• => pi - m = - pi’ Qi

• => (pi - m)/pi = - pi’ Qi / pi = - 1/εi

• OR p1/p2 = (1+ 1/ε2)/(1+ 1/ε1)

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3rd degree PD (3)

• So the firm acts as a monopolist on each market segment

• Exploits differences in demand elasticities by charging higher prices on less elastic market segments

• If all markets are served, with a linear demand welfare is reduced if firm is allowed to do PD.

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3rd degree PD (4)

• But sometimes the firm would decide not to serve small markets, if it is forced to do uniform pricing -> blackboard drawing.

• In that case, PD may increase welfare.

• Demands in two market segments are given by P1 = 100 - Q1 and P2 = 25 - Q2. MC = 0.

– Find the profit maximizing prices (3rd degree)– Find the uniform monopoly price.

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• 1st-degree PD

• 3rd-degree PD

• 2nd-degree PD


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2nd-degree PD (1)

• What if the firm cannot sort or separate consumers?

• Consumers willingness to pay or demand curve is often not observable.

• The firm must make them self-select their payments

• Consumers with high willingness to pay could mimic low consumers

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2nd-degree PD (2)

• A single two-part tariff: Payment = T + pq

• Two types of consumers, but firm cannot see who’s who

• At any price p, Type 2 would be willing to pay a higher fixed fee T2 than would type 1:

• IF the firm wants to sell to both types of consumers, the maximal T it can set is T1:

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2nd-degree PD (3)

Type 1Type 1 Type 2Type 2

qq11 qq22

PP MCMC

TT11

TT22

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2nd-degree PD (4)

• Firm has to leave CS for Type 2!!!

• Might try to use two different two-part tariffs but then the customers might have incentive to imitate another type.

• Trade-off between getting more profits and ensuring that pricing scheme is incentive compatible to all consumers.

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• 1st-degree PD

• 3rd-degree PD

• 2nd-degree PD


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Tying as a PD vehicle

• To screen customers, you may tie two products together in service contract

• E.g. Xerox machines and Xerox paper/toner

• Heavy users will have higher willingness to pay.

• Sell the machine at cost and reap the profits through the paper/toner.

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What’s next?

Shapiro & Varian

Versioning and bundling, etc.

Documents

1 Price Discrimination Per Baltzer Overgaard February, 2003 Adapted from the notes of H. Peter Møllgaard (by courtesy) Based on Carlton and Perloff chap