Price Discrimination

Simon Cowan Department of Economics and Worcester College Thursday 27

th

May, 2010 MFE Course on Industrial Organization

2

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

3

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 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 differ  If price differences reflect cost differences then there is no discrimination

4

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

5

Why do firms discriminate?

  The firm aims to convert consumer surplus into profit full conversion requires 1.

2.

3.

complete knowledge of customers sufficient pricing instruments

no competition

 Often the firm is better off with the ability to discriminate  But discrimination does not always raise profits: 1.

2.

Oligopolistic discrimination Durable-goods monopoly

6 

Types of discrimination

Pigou’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 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 to classify customers  Partial information, linear pricing, no competition  Educational discounts for software  Consultants paying more for conferences than academics

Simple monopoly pricing

Price Demand Monopoly price 7 Marginal Cost MR Monopoly volume Quantity

8

Monopoly pricing and the price elasticity

Price Elasticity of Demand =  Percentage change in quantity demanded Percentage change in price  The monopoly mark-up, at the profit-maximizing price, is Price  Marginal Cost Price  1 Price Elasticity

9

Can the firm do better?

  Customers with valuations above the monopoly price obtain a surplus  If 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 all  Can they be persuaded to buy, without at the same time cutting the price(s) that existing customers pay?

The lost surpluses

Price Surplus of consumers who buy at the monopoly price 10 Monopoly price Monopoly profit Marginal Cost Surplus lost because these customers don’t buy at all Monopoly volume – this is the loss to society from monopoly: the deadweight loss Quantity

11

First-degree price discrimination

      The 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 firm Requires 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 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 in general is endogenous)  Microsoft Office  UK price of Office Standard was £329 in 2008   The American Economic Association charges according to income for membership  Annual income < $50,000: $64  $50,000  Annual Income  $66,000: $77  USA price was $399.95 (=£200.98 at the exchange rate of $1.99: £1) $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 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 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

Price discrimination opens a new market

Price If required to sell at the same price in both markets, the firm will just set the best price for Market 1 and not bother to sell in Market 2 Demand in 1 Market 2 Price in Market 1 Aggregate demand 14 Marginal Cost Monopoly volume Quantity

15

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

16

With linear demand functions output is constant, so welfare falls

     Suppose q 1 = 1 – p 1 and q 2 = 2 – p 2 ; c = 0 Discriminatory prices and quantities:   Profit in 1, p 1 (1 – p 1 ), is maximized with p 1 Profit in 2, p 2 (2 – p 2 ), is maximized with p 2 = 0.5, q 1 = 1, q 2 = 0.5

= 1 With non-discriminatory pricing, the profit function is p(1 – p + 2 – p) = p(3 – 2p) for p ≤ 1 and p(2 – p) for p > 1 Best non-discriminatory price is p = 0.75 and

q

1 + q 2 = 3 – 2  0.75 = 1.5

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

17    

A generalization

Define the curvature (or convexity) of demand as   – pq  (p)/q  (p) The non-discriminatory price is p

N

Call the low-price market L and the high-price market H For a very large set of demand functions a sufficient condition for social welfare to fall with discrimination is 

H

(p

N

)  

L

(p

N

)   The linear example is a special case So a necessary condition for discrimination to raise welfare is that 

L

(p

N

) > 

H

(p

N

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

18

Second-degree: two-part tariffs

 Conventional pricing is known as “linear pricing”   Price per unit = p, total payment for q units = pq The total payment is proportional to the quantity    Tariffs need not be linear   A two-part tariff is the simplest form of nonlinear pricing Total payment = fixed fee + price  quantity; T(q) = A + pq E.g. utility tariffs, gym membership, warehouse clubs, railcards to obtain discounts, mobile phone tariffs Such tariffs are used to extract additional consumer surplus

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Individual two-part tariffs

     Suppose (i) the firm knows each customer’s demand function (and therefore their consumer surplus) and (ii) it can use individual two-part tariffs {A

i

, p

i

} The profit-maximizing strategy is to set the same marginal price, equal to marginal cost, for all i: p

i = c

The lump-sum fees are individual, A

i

, and are set to extract each consumer’s surplus Equivalently the firm sets total payment-quantity bundles: {T

i

, q

i

}={A

i + cq i

(c), q

i

(c)} This is first-degree discrimination again

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

Price 20

p i =c A i cq i

(

c

)

q i

(

c

) Quantity

21

second-degree: nonlinear pricing

      Now assume the firm cannot identify each customer’s “type” Large customers are willing to pay more than small 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 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 With first-degree discrimination the large customer pays B + D + E for q

H

while the small customer pays B for q will pay B for q

L L

. When given a choice the large customer , giving a surplus of D.

Profit = 2B.

More profitable: offer a choice between: {B, q

L

} and {B + E, q

H

} Profit = 2B + E

D B c q L E q H

Quantity

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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 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

D

Now the firm offers q* at B – x, and

q H

at B + E + y . Profits rise by y – x. Optimal q* balances marginal y against marginal x.

The large customer consumes the efficient quantity, but the quantity for the small customer is distorted below q

L .

B c y q* x q L E q H

Quantity

25

Optional two-part tariffs: a simple form of nonlinear pricing

total payment tariff designed for households tariff designed for business customers Business customer chooses here Household chooses here volume of calls

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Damaging goods

   Another 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 versions   The main version had the math-coprocessor working The secondary version had the math-coprocessor switched 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 slow down the rate of printing, so that it printed 8 pages per minute Otherwise the printers were identical

27

Oligopoly: no discrimination

      Hotelling model, consumers uniformly distributed along [0, 1] Firm A located at 0, price p

A

; firm B at 1, p

B

Consumer at x pays p

A

+ tx when buying from A, p

B

B. t = unit transport cost + t(1 – x) from When p

A

+ tx = p

B q A

= x = ½ + (p

B

+ t(1 – x) the consumer at x is indifferent: – p

A

)/2t

q B

= 1 – x = ½ + (p

A



A

= (p

A

– c)[½ + (p

B



B

= (p

B

– c)[½ + (p

A

– p

B

)/2t – p – p

A B

)/2t] )/2t] Bertrand-Nash equilibrium in prices: p

A = p B

= c + t Profit per firm is t/2

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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 < ½ Given the price that B offers, p

B

(x), A could offer a price that gives just as good a deal defined by

p A

(x) + tx = p

B

(x) + t(1 – x) So p

A

(x) = p

B

(x) + t(1 – 2x) > p

B

(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 than the price implied by the equally good deal equation: to find this set p

B

(x) = c in the equation, giving p

A

(x) = c + t(1 – 2x)

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Oligopoly Discrimination II

The discriminatory price schedules are:

p A

(x) = c + t(1 – 2x) for x ≤ 0.5

p A

(x) = c for x > 0.5

p B

(x) = c for x < 0.5

p B

(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

Prices and profits

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c

+

t c

0 0.5

1

c

+

t

31

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 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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Summary

    Price discrimination is very common, and takes many forms The main aim of the discrimination analyzed here is to extract more surplus from consumers This usually has ambiguous welfare effects Discrimination is of antitrust concern, particularly in intermediate goods markets, when it is a sign of something else:    excessive market power predatory pricing market foreclosure and exclusion

33 

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.p

df – new results on the welfare effects of third-degree discrimination