Price Discrimination
Simon Cowan
Department of Economics and Worcester College
Thursday 27th May, 2010
MFE Course on Industrial Organization
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
2
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
3
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
4
Why do firms discriminate?
 The firm aims to convert consumer surplus into profit
 full conversion requires
1. complete knowledge of customers
2. sufficient pricing instruments
3. 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 monopoly
5
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
6
Simple monopoly pricing
Price
Demand
Monopoly
price
Marginal
Cost
7
MR
Monopoly volume
Quantity
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
1

Price
Price Elasticity
8
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?
9
The lost surpluses
Price
Surplus of consumers who buy at the monopoly price
Monopoly
price
Monopoly profit
Surplus lost because these customers don’t
buy at all – this is the loss to society from
monopoly: the deadweight loss
Marginal
Cost
10
Monopoly volume
Quantity
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
11
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
 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




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Annual income < $50,000: $64
$50,000  Annual Income  $66,000: $77
$66,000 < Annual income: $90
Student member (written verification required): $32
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
13
Price discrimination opens a new
market
Price
Demand in 1
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
Market 2
Price in
Market 1
Aggregate
demand
Marginal
Cost
14
Monopoly volume
Quantity
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
15
With linear demand functions
output is constant, so welfare falls
 Suppose q1 = 1 – p1 and q2 = 2 – p2; c = 0
 Discriminatory 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 = 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
q1 + q2 = 3 – 20.75 = 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 condition for social
welfare to fall with discrimination is
 H(pN)   L(pN)
 The linear example is a special case
 So a necessary condition for discrimination to raise welfare is that
 L(pN) >  H(pN)
 Aguirre, Cowan and Vickers (AER, forthcoming) give additional
conditions
17
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
18
Individual two-part tariffs
 Suppose (i) the firm knows each customer’s demand function




19
(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 again
An individual two-part tariff, and its
total payment-quantity package
Price
Ai
pi =c
cqi(c)
20
qi(c)
Quantity
second-degree: nonlinear pricing
 Now assume the firm cannot identify each customer’s “type”
 Large customers are willing to pay more than small




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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
First-degree discrimination is not
incentive-compatible
With first-degree discrimination the large
customer pays B + D + E for qH while the small
customer 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
Price
D
B
E
c
22
qL
qH Quantity
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
23
Nonlinear pricing: distorting the
quantity to capture more surplus
Price
Now the firm offers q* at B – x, and
qH 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 qL.
D
B
c
24
y
E
x
q*
qL
qH Quantity
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
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volume of calls
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
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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 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 + 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





28
can offer individual prices
Consider a consumer located near A with x < ½
Given the price that B offers, pB(x), A could offer a price that gives
just as good a deal defined by
pA(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) = 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 pB(x) = c
in the equation, giving pA(x) = c + t(1 – 2x)
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 < 0.5
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
c+t
c+t
c
0
30
0.5
1
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
31
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
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Reading, with annotations
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
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/334.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