Simon CowanDepartment of Economics and

Worcester College

Thursday 27th May, 2010MFE Course on Industrial

Organization

Price Discrimination

outlineWhat is price discrimination, when is it

feasible, why do firms do it?

What types of price discrimination are there?

What are the welfare effects?

Price discrimination and oligopoly

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What is price discrimination?Simple definition: discrimination means selling

the same good at different pricesMicrosoft sets different prices for the Office suiteAirlines charge different amounts for similar tickets

More generally “price discrimination is present when two or more similar goods are sold at prices that are in different ratios to marginal costs” (Varian, 1989, p 598)So a uniform delivered price, e.g. for letters, is

discriminatory if costs differIf price differences reflect cost differences then

there is no discrimination

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When is discrimination feasible?No arbitrage (i.e. no resale)

Especially for services

Firm has market powerCan raise price above marginal costMarket power need not be complete

Ability to sort or classify customers

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Why do firms discriminate?

The firm aims to convert consumer surplus into profit full conversion requires

1. complete knowledge of customers2. sufficient pricing instruments3. no competition

Often the firm is better off with the ability to discriminate

But discrimination does not always raise profits:1. Oligopolistic discrimination2. Durable-goods monopoly

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Types of discriminationPigou’s 1920 three-fold classification, applied here to

monopoly

First-degree: complete information, take-it-or-leave-it offers by the firm, no competition

Second-degree: customer self-selection Partial information, full set of pricing instruments, no

competitionMenus of tariffs; Nonlinear tariffsAirline customers can choose when to travel and whether

to stay a Saturday night or not, phone customers can choose their tariffs

Third-degree: exogenous signal that the firm uses to classify customersPartial information, linear pricing, no competition

Educational discounts for softwareConsultants paying more for conferences than academics

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Simple monopoly pricing

Price

Quantity

MarginalCost

Monopoly price

Monopoly volume

Demand

MR

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Monopoly pricing and the price elasticity

The monopoly mark-up, at the profit-maximizing price, is

Percentage change in quantity demandedPrice Elasticity of Demand =

Percentage change in price

Price Marginal Cost 1

Price Price Elasticity

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Can the firm do better?Customers with valuations above the

monopoly price obtain a surplusIf they could be identified then they could be

charged more (as long as there is no resale)Customers who value the good below the

price set by the monopolist don’t buy at allCan they be persuaded to buy, without at the

same time cutting the price(s) that existing customers pay?

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The lost surpluses

Price

Quantity

MarginalCost

Monopoly volume

Surplus of consumers who buy at the monopoly price

Surplus lost because these customers don’tbuy at all – this is the loss to society from

monopoly: the deadweight lossMonopoly

profit

Monopoly price

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First-degree price discriminationThe firm knows the maximum amount that each

customer is willing to pay, and charges each customer this amount

Marginal revenue now becomes the (inverse) demand function (no need to drop the price on other units)

De Beers’ sales of rough diamonds: Diamonds sorted into 12,000 categories based on size,

shape, quality, colour. Offered on a “take-it-or-never buy from us again” basis.

With linear demand profits double: the firm grabs both the triangles as well as the rectangle

Social welfare is maximized, but it all goes to the firmRequires too much information to be feasible in most

cases

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Third-degree price discrimination The firm sorts customers into separate markets using an

exogenous signalE.g. students, seniors, families, income bracket, business

v. domestic Instruments: “linear” pricing in each separate market So standard monopoly pricing in each market Price is higher in less elastic markets (remember the

elasticity in general is endogenous)Microsoft Office

UK price of Office Standard was £329 in 2008 USA price was $399.95 (=£200.98 at the exchange rate of $1.99:

£1)The American Economic Association charges according to

income for membership Annual income < $50,000: $64 $50,000 Annual Income $66,000: $77 $66,000 < Annual income: $90 Student member (written verification required): $32

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Is third-degree price discrimination good for social welfare?In general the effect is ambiguous

The firm gains from extra flexibilityCustomers offered higher prices loseCustomers offered lower prices gain

Discrimination may open a new marketanti-retroviral drugs are now available in Africa at

prices much lower than in North America and Europe

this gives a weak Pareto improvement if (but not only if) only one market was served without discrimination, and marginal cost is not increasing in output

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Price discrimination opens a new market

Price

Quantity

MarginalCost

Price in Market 1

Monopoly volume

Market 2

If required to sell at the same pricein both markets, the firm will just setthe best price for Market 1 and not bother to sell in Market 2Demand in 1

Aggregatedemand

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What about when new markets are not opened?

Schmalensee (AER, 1981): a necessary condition for discrimination to raise welfare is that total output rises

Misallocation effect: Inefficient distribution of the given output across markets with discrimination

Output effect: An output increase is good for welfare when prices exceed marginal cost

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With linear demand functionsoutput is constant, so welfare fallsSuppose q1 = 1 – p1 and q2 = 2 – p2; c = 0Discriminatory prices and quantities:

Profit in 1, p1(1 – p1), is maximized with p1 = 0.5, q1 = 0.5

Profit in 2, p2(2 – p2), is maximized with p2 = 1, q2 = 1With non-discriminatory pricing, the profit function

isp(1 – p + 2 – p) = p(3 – 2p) for p ≤ 1 andp(2 – p) for p > 1

Best non-discriminatory price is p = 0.75 and q1 + q2 = 3 – 20.75 = 1.5

Total output is the same with and without discrimination when demand functions are linear

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A generalizationDefine the curvature (or convexity) of demand as –

pq(p)/q(p) The non-discriminatory price is pNCall the low-price market L and the high-price market HFor a very large set of demand functions a sufficient

condition for social welfare to fall with discrimination is H(pN) L(pN)

The linear example is a special caseSo a necessary condition for discrimination to raise

welfare is that L(pN) > H(pN)

Aguirre, Cowan and Vickers (AER, forthcoming) give additional conditions

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Second-degree: two-part tariffsConventional pricing is known as “linear pricing”

Price per unit = p, total payment for q units = pqThe total payment is proportional to the quantity

Tariffs need not be linearA two-part tariff is the simplest form of nonlinear pricingTotal payment = fixed fee + price quantity; T(q) = A +

pqE.g. utility tariffs, gym membership, warehouse clubs,

railcards to obtain discounts, mobile phone tariffsSuch tariffs are used to extract additional consumer

surplus

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Individual two-part tariffsSuppose (i) the firm knows each customer’s

demand function (and therefore their consumer surplus) and (ii) it can use individual two-part tariffs {Ai, pi}

The profit-maximizing strategy is to set the same marginal price, equal to marginal cost, for all i: pi = c

The lump-sum fees are individual, Ai, and are set to extract each consumer’s surplus

Equivalently the firm sets total payment-quantity bundles: {Ti, qi}={Ai + cqi(c), qi(c)}

This is first-degree discrimination again19

An individual two-part tariff, and its total payment-quantity package

Price

Quantity

pi =c

Ai

20 qi(c)

cqi(c)

second-degree: nonlinear pricingNow assume the firm cannot identify each customer’s

“type”Large customers are willing to pay more than small

customers, and want to buy moreFirst-degree discrimination is not incentive-compatibleThe firm offers alternative packages that specify the

quantity and total payment. Customers can choose.The key is to extract as much profit as possible from

the large customers, while still selling to the small customers

This is done by making the package for the small customers sufficiently unattractive for large customers

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First-degree discrimination is not incentive-compatible

Price

Quantity22c

B

D

E

With first-degree discrimination the largecustomer pays B + D + E for qH while the smallcustomer pays B for qL. When given a choice the large customer will pay B for qL, giving a surplus of D.Profit = 2B.More profitable: offer a choice between:{B, qL} and {B + E, qH}Profit = 2B + E

qL qH

Dupuit and incentive compatibilityOn railway tariffs and classes (1849)“It is not because of the few thousand francs which

would have to be spent to put a roof over the third-class carriages or to upholster the third-class seats that some company or other has open carriages with wooden benches...What the company is trying to do is prevent the passengers who pay the second-class fare from travelling third-class; it hits the poor, not because it wants to hurt them, but to frighten the rich...And it is again for the same reason that the companies, having proved almost cruel to third-class passengers and mean to second-class ones, becomes lavish in dealing with first-class passengers. Having refused the poor what is necessary, they give the rich what is superfluous.”

Source: Tirole, p 150

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Nonlinear pricing: distorting the quantity to capture more surplus

Price

Quantity24c

B

D

E

qL qHq*

Now the firm offers q* at B – x, and qH at B + E + y .Profits rise by y – x. Optimal q* balances marginal y againstmarginal x.The large customer consumes the efficientquantity, but the quantity for the smallcustomer is distorted below qL.

y

x

Optional two-part tariffs: a simple form of nonlinear pricingtotal payment

volume of calls

tariff designed for households

tariff designed for businesscustomers

Household chooses here

Business customer chooses here

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Damaging goodsAnother way to encourage customers to self-select

is to damage one’s good, in order artificially to provide a range of qualities

The Intel 486 chip came in two versionsThe main version had the math-coprocessor workingThe secondary version had the math-coprocessor

switched offIBM sold a printer which came in two versions

The main version worked at 12 pages per minuteThe other version included an instruction to slow

down the rate of printing, so that it printed 8 pages per minute

Otherwise the printers were identical

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Oligopoly: no discriminationHotelling model, consumers uniformly distributed

along [0, 1]Firm A located at 0, price pA; firm B at 1, pB

Consumer at x pays pA+ tx when buying from A, pB + t(1 – x) from B. t = unit transport cost

When pA+ tx = pB + t(1 – x) the consumer at x is indifferent: qA = x = ½ + (pB – pA)/2t

qB = 1 – x = ½ + (pA – pB)/2t

A = (pA – c)[½ + (pB – pA)/2t]

B = (pB – c)[½ + (pA – pB)/2t]Bertrand-Nash equilibrium in prices: pA = pB = c + tProfit per firm is t/2

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Oligopoly Discrimination INow both firms know the location of each consumer,

i.e. x, and can offer individual pricesConsider a consumer located near A with x < ½Given the price that B offers, pB(x), A could offer a

price that gives just as good a deal defined bypA(x) + tx = pB(x) + t(1 – x)

So pA(x) = pB(x) + t(1 – 2x) > pB(x)The firms compete for this customer until the less-

favoured firm, B, just makes zero profit, i.e. pB(x) = cAt this point A can win by pricing a penny lower than

the price implied by the equally good deal equation: to find this set pB(x) = c in the equation, giving pA(x) = c + t(1 – 2x)

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Oligopoly Discrimination IIThe discriminatory price schedules are:pA(x) = c + t(1 – 2x) for x ≤ 0.5

pA(x) = c for x > 0.5

pB(x) = c for x < 0.5

pB(x) = c + t(2x – 1) for x 0.5

Apart from the consumers at 0 and 1, every consumer pays less when there is price discrimination

Profits per firm drop from t/2 to t/4 with discrimination

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Prices and profits

0 1

c + t c + t

0.5c

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Oligopoly discrimination IIIThe model has assumed “best-response

asymmetry”, so the firms do not share the same view about which market will have the higher price once discrimination is allowed

I want to price high in my back-yard, while you want to price low in my back-yard

Alternatively there may be best-response symmetry: e.g. when the demand functions for each firm in a large market are both higher than those in a small market

In this case price rises in the large market and falls in the small market

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SummaryPrice discrimination is very common, and takes

many formsThe main aim of the discrimination analyzed

here is to extract more surplus from consumersThis usually has ambiguous welfare effectsDiscrimination is of antitrust concern,

particularly in intermediate goods markets, when it is a sign of something else: excessive market powerpredatory pricingmarket foreclosure and exclusion

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Reading, with annotations J. Tirole, Theory of Industrial Organization, 1988, Ch 3 – excellent

textbook survey

H. Varian, Ch 10 in Handbook of Industrial Organization, Vol 1, edited by R. Schmalensee and R. Willig, 1989 – the main survey of monopolistic discrimination

M. Motta, Competition Policy, CUP, 2004, Ch 7.4 (discrimination) – emphasis on competition policy implications

L. Stole, Ch 34 in Handbook of Industrial Organization, Vol 3, edited by M. Armstrong and R. Porter, 2007, especially Section 3.4, available at http://econpapers.repec.org/bookchap/eeeindchp/3-34.htm – very comprehensive on discrimination and competition.

Iñaki Aguirre, Simon Cowan and John Vickers, "Monopoly Price Discrimination and Demand Curvature", American Economic Review, forthcoming, available at the AER website and at http://www.economics.ox.ac.uk/members/simon.cowan/PapersandFiles/WelfareEffects10Sep.pdf – new results on the welfare effects of third-degree discrimination

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