Simon Cowan

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Price Discrimination

• Simon Cowan
• Department of Economics and Worcester College
• Thursday 4th June, 2009
• MFE Course on Industrial Organization

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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
• Tying and bundling

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

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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?

• To capture more consumer surplus
• Usually, at least with monopoly, the firm is
  better off with the ability to discriminate
• But discrimination does not always raise profits
• Durable-goods monopoly the firm would like to
  commit to keep prices high, but once the
  high-value customers have purchased the firm
  cannot resist cutting price to the remaining
  lower-value customers. Anticipating this, some
  high-value customers delay purchasing.
• Discrimination with oligopoly the firm may have
  a unilateral incentive to discriminate, but all
  firms can be worse off if all discriminate as
  competition for particular customers is intense

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Types of discrimination

• Pigous 1920 three-fold classification
• First-degree complete information,
  take-it-or-leave-it offers by the firm
• Second-degree customer self-selection
• Menus of tariffs
• Nonlinear tariffs
• airline customers can choose when to travel and
  whether to stay a Saturday night or not
• Third-degree exogenous signal that the firm uses
  to classify customers
• Educational discounts for software
• Consultants paying more for conferences than
  academics

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Simple monopoly pricing
Price
Demand
Monopoly price
Marginal Cost
MR
Quantity
Monopoly volume
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Monopoly pricing and the price elasticity

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

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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 be
  charged more (as long as there is no resale)
• Customers who value the good below the price set
  by the monopolist dont buy at all
• Can 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
Surplus of consumers who buy at the monopoly price
Monopoly price
Monopoly profit
Surplus lost because these customers dont buy at
all this is the loss to society from
monopoly the deadweight loss
Marginal Cost
Quantity
Monopoly volume
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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
• Monopoly pricing in each separate 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 lt 50,000 64
• 50,000 ? Annual Income ? 66,000 77
• 66,000 lt 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
• Sometime discrimination opens a new market, which
  has an unambiguously good effect (a weak Pareto
  improvement)
• anti-retroviral drugs are now available in Africa
  at prices much lower than in North America and
  Europe

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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
Marginal Cost
Quantity
Monopoly volume
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

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With linear demand functionsoutput 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 gt 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) gt ? H(pN)
• Cowan (2008) gives additional conditions

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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

• If the firm knows each customers demand function
  (and therefore their consumer surplus) then
  individual two-part tariffs Ai, pi can be used
• 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 consumers surplus
• Equivalently the firm sets total payment-quantity
  bundles Ti, qiAi cqi(c), qi(c)
• This is first-degree discrimination again

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second-degree nonlinear pricing

• Now assume the firm cannot identify each
  customers 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 bundles 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
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
Quantity
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 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
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
y
E
x
c
Quantity
qL
qH
q
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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 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-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 can offer individual prices
• Consider a consumer located near A with x lt 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) gt 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)

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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 gt 0.5
• pB(x) c for x lt 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
1
0.5
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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 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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Tying

• If you buy my machine you must also buy spare
  parts from me (even though spare parts could be
  supplied by a competitive market)
• Printers and cartridges
• Enables the firm to make more profit from large
  users (spare parts priced above marginal cost)
• Effectively a two-part tariff price for the
  good and a price for the spare parts

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Bundling

• Selling two goods in fixed proportions
• Selling both channels separately
• p(Sport) 8 Profit 16
• p(Doc) 10 Profit 20
• Total profit 36
• Bundle price is 20 profit 40
• Negative correlation of valuations makes bundling
  profitable
• Moving closer to first-degree discrimination
  (with which profit would be 45)

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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

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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), 7.3.2.2 (tying) 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.
• S. Cowan (2008) When does third-degree price
  discrimination reduce social welfare, and when
  does it raise it?, Department of Economics
  Discussion Paper No. 410, http//www.economics.ox.
  ac.uk/index.php/papers/details/when_does_third_deg
  ree_410/ new results on the welfare effects of
  third-degree discrimination