Lecture 5 - Price Discrimination

8/4/2019 Lecture 5 - Price Discrimination

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Simon Cowan

Department of Economics and WorcesterCollege

Thursday 27th May, 2010

MFE Course on Industrial Organization

Price Discrimination


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outline What 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 prices

Microsoft sets different prices for the Office suite

Airlines charge different amounts for similar tickets

More generally price discrimination is present

when two or more similar goods are sold at pricesthat are in different ratios to marginal costs

(Varian, 1989, p 598)

So a uniform delivered price, e.g. for letters, isdiscriminatory if costs differ

If price differences reflect cost differences thenthere is no discrimination

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

Especially for services

Firm has market power

Can raise price above marginal cost

Market 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 knowledgeof customers

2. 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 discrimination

2. Durable-goods monopoly5


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Types of discrimination Pigous 1920 three-fold classification, applied here tomonopoly

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

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

competition Menus of tariffs; Nonlinear tariffs Airline 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 toclassify customers Partial information, linear pricing, no competition

Educational discounts for software Consultants paying more for conferences thanacademics

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Simple monopoly pricing

Price

Quantity

MarginalCost

Monopolyprice

Monopoly volume

Demand

MR

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Monopoly pricing and the priceelasticity

The monopoly mark-up, at the profit-maximizingprice, 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 surplus

If they could be identified then they could becharged more (as long as there is no resale)

Customers who value the good below the priceset by the monopolist dont buy at all

Can they be persuaded to buy, without at the sametime 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 dontbuy at all this is the loss to society from

monopoly: the deadweight loss

Monopoly

profit

Monopolyprice

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First-degree price discrimination The firm knows the maximum amount that each

customer is willing to pay, and charges each customerthis 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 firm

Requires too much information to be feasible in most11


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

E.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 ingeneral 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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discrimination good for socialwelfare? In general the effect is ambiguous

The firm gains from extra flexibility

Customers offered higher prices lose

Customers offered lower prices gain

Discrimination may open a new market

anti-retroviral drugs are now available in Africa at

prices much lower than in North America andEurope

this gives a weak Pareto improvement if (but notonly if) only one market was served withoutdiscrimination, and marginal cost is not increasingin output13


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Price discrimination opens a newmarket

Price

Quantity

MarginalCost

Price inMarket 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 notbother to sell in Market 2Demand in 1

Aggregatedemand

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What about when new marketsare not opened?

Schmalensee (AER, 1981): a necessarycondition fordiscrimination to raise welfare is that total output rises

Misallocation effect: Inefficient distribution of the givenoutput across markets with discrimination

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

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output is constant, so welfarefalls Suppose q1 = 1p1 and q2 = 2p2; c= 0 Discriminatory prices and quantities:

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

Profit in 2, p2(2p2), is maximized with p2 = 1, q2 = 1

With non-discriminatory pricing, the profit function isp(1p+ 2p) = p(3 2p) for p 1 and

p(2p) 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 generalization Define the curvature(or convexity) of demand as pq(p)/q(p) The non-discriminatory price is pN Call the low-price market L and the high-price market H For a very large set of demand functions a sufficient

conditionfor social welfare to fall with discrimination isH(pN) L(pN)

The linear example is a special case So a necessary conditionfor discrimination to raise welfare

is thatL(pN) > H(pN)

Aguirre, Cowan and Vickers (AER, forthcoming) giveadditional conditions

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Second-degree: two-part tariffs Conventional pricing is known as linear pricing

Price per unit = p, total payment for qunits = pq

The total payment is proportionalto the quantity

Tariffs need not be linear

A two-part tariffis the simplest form of nonlinearpricing

Total payment = fixed fee + price

quantity; T(q) =A + pq

E.g. utility tariffs, gym membership, warehouseclubs, railcards to obtain discounts, mobile phone

tariffs

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Individual two-part tariffs Suppose (i) the firm knows each customers

demand function (and therefore their consumersurplus) and (ii) it can use individual two-parttariffs {Ai, pi}

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

The lump-sum fees are individual, Ai

, and are setto extract each consumers surplus

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

This is first-degree discrimination again19


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its total payment-quantitypackage

Price

Quantity

pi=c

Ai

20 qi(c)

cqi(c)


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second-degree: nonlinear pricing Now assume the firm cannot identify each

customers type

Large customers are willing to pay more thansmall customers, and want to buy more

First-degree discrimination is not incentive-compatible

The firm offers alternative packages that specify

the quantity and total payment. Customers canchoose.

The key is to extract as much profit as possiblefrom the large customers, while still selling to the

small customers21


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First-degree discrimination is notincentive-compatible

Price

Quantity22

c

B

D

E

With first-degree discrimination the largecustomer pays B + D + Efor qH while the smallcustomer pays Bfor qL.When given a choice the large customerwill pay Bfor 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


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Dupuit and incentive compatibility

On 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 seatsthat some company or other has open carriages withwooden benches...What the company is trying to do isprevent the passengers who pay the second-classfare from travelling third-class; it hits the poor, notbecause it wants to hurt them, but to frighten the

rich...And it is again for the same reason that thecompanies, having proved almost cruel to third-classpassengers 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 15023


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Nonlinear pricing: distorting thequantity to capture more surplus

Price

Quantity24

c

B

D

E

qL

qHq*

Now the firm offers q*at B x, andqHat B + E + y .Profits rise by y x.

Optimal q* balances marginal yagainstmarginal x.The large customer consumes the efficientquantity, but the quantity for the smallcustomer is distorted below qL.

y

x


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Optional two-part tariffs: a simpleform of nonlinear pricing

total payment

volume of calls

tariff designed for households

tariff designed for businesscustomers

Household chooses here

Business customer chooses here

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Damaging goods Another way to encourage customers to self-

select is to damage ones good, in order artificially

to provide a range of qualities

The Intel 486 chip came in two versions

The main version had the math-coprocessorworking

The secondary version had the math-coprocessorswitched off

IBM sold a printer which came in two versions

The main version worked at 12 pages per minute

The other version included an instruction to slowdown the rate of printing, so that it printed 8 pages

per minute26


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Oligopoly: no discrimination Hotelling model, consumers uniformly distributed

along [0, 1]

Firm A located at 0, price pA; firm B at 1, pB Consumer at xpays pA+ txwhen buying from A,pB+

t(1x) from B. t =unit transport cost When pA+ tx = pB+ t(1x) the consumer at xis

indifferent:

qA = x = + (pB pA)/2t

qB

= 1x = + (pA

pB

)/2t

A = (pAc)[ + (pB pA)/2t]

B= (pBc)[ + (pA pB)/2t]

Bertrand-Nash equilibrium in prices: pA = pB= c +t

Profit per firm is t/227


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Oligopoly Discrimination I Now both firms know the location of each consumer,

i.e. x, and can offer individual prices

Consider a consumer located near A with x<

Given the price that Boffers, 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. p

B

(x) = c

At this point A can win by pricing a penny lower thanthe price implied by the equally good deal equation: tofind this set pB(x) = cin the equation, giving pA(x) = c+ t(12x)

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Oligopoly Discrimination II

The 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< 0.5pB(x) = c + t(2x 1) for x 0.5

Apart from the consumers at 0 and 1, every

consumer pays less when there is pricediscrimination

Profits per firm drop from t/2 to t/4 withdiscrimination

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Prices and profits

0 1

c+ t c+ t

0.5c

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Oligopoly discrimination III The model has assumed best-response

asymmetry, so the firms do not share the same

view about which market will have the higherprice once discrimination is allowed

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

Alternatively there may be best-responsesymmetry: e.g. when the demand functions foreach firm in a large market are both higher thanthose in a small market

In this case price rises in the large market andfalls in the small market

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Summary Price discrimination is very common, and takes

many forms

The main aim of the discrimination analyzed hereis to extract more surplus from consumers

This usually has ambiguous welfare effects

Discrimination is of antitrust concern, particularlyin intermediate goods markets, when it is a sign

of something else: excessive market power

predatory pricing

market foreclosure and exclusion

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Reading, with annotations

J. Tirole, Theory of Industrial Organization, 1988, Ch 3

excellent textbooksurvey

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

M. Motta, Competition Policy, CUP, 2004, Ch 7.4 (discrimination) emphasis oncompetition 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 athttp://econpapers.repec.org/bookchap/eeeindchp/3-34.htm verycomprehensive on discrimination and competition.

Iaki Aguirre, Simon Cowan and John Vickers, "Monopoly Price Discriminationand Demand Curvature", American Economic Review, forthcoming, available atthe AER website and athttp://www.economics.ox.ac.uk/members/simon.cowan/PapersandFiles/WelfareEffects10Sep.pdf new results on the welfare effects of third-degreediscrimination

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http://econpapers.repec.org/bookchap/eeeindchp/3-34.htmhttp://www.economics.ox.ac.uk/members/simon.cowan/PapersandFiles/WelfareEffects10Sep.pdfhttp://www.economics.ox.ac.uk/members/simon.cowan/PapersandFiles/WelfareEffects10Sep.pdfhttp://www.economics.ox.ac.uk/members/simon.cowan/PapersandFiles/WelfareEffects10Sep.pdfhttp://www.economics.ox.ac.uk/members/simon.cowan/PapersandFiles/WelfareEffects10Sep.pdfhttp://econpapers.repec.org/bookchap/eeeindchp/3-34.htmhttp://econpapers.repec.org/bookchap/eeeindchp/3-34.htmhttp://econpapers.repec.org/bookchap/eeeindchp/3-34.htm

Lecture 5 - Price Discrimination

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