Transcript mit.econ.au.dk

Price Discrimination
Per Baltzer Overgaard
February 2004
Adapted from the notes of
H. Peter Møllgaard (by courtesy)
Based on Carlton and Perloff
chap. 9/10
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Outline: Non-uniform pricing
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Common types of Price Discrimination
Necessary conditions for PD
1st-degree PD
3rd-degree PD
2nd-degree PD
Tying as a PD vehicle
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Common types of PD
• Student discounts on computers, software,
books, … -> 3rd degree PD
– Customers segmented into separate sub-markets
• Quantity discounts -> 2nd degree PD
– Customers self-select their discount by the size
of their order
• Individualized prices -> 1st degree PD
– Special price for you, my friend.
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Outline: Non-uniform pricing
•
•
•
•
•
•
Common types of PD
Necessary conditions for PD
1st-degree PD
3rd-degree PD
2nd-degree PD
Tying as a PD vehicle
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Necessary conditions for PD (1)
• Existence of market power
– i.e. ability to raise price above MC.
• Identification of different consumers’
willingness to pay.
– identification method differs in 1st, 2nd, and
3rd degree PD
• Firm must be able to prevent or limit resales
– arbitrage eliminates price differences
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Necessary conditions for PD (2)
Ways to prevent or limit resales
• services can often not be resold
– Want to buy my haircut?
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resale can make warranty void
transportation costs may limit resales
contractual clauses may forbid resale
vertical integration may prevent resales. ...
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Outline: Non-uniform pricing
•
•
•
•
•
•
Common types of PD
Necessary conditions for PD
1st-degree PD
3rd-degree PD
2nd-degree PD
Tying as a PD vehicle
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1st-degree or perfect PD (1)
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Each consumer needs one unit.
Their willingness to pay for a unit differs.
Firm can identify a consumer’s w.t.pay
so offers each consumer the unit at a price =
w.t.pay (- 1 cent)
• no consumer surplus is left -- firm gets it all
• but the market outcome is efficient:
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1st-degree or perfect PD (2)
willingness to
pay
price
MC
1 2 3 4 5
Firm sells as many units as
it would under perfect
competition so the market is
allocatively efficient
… but consumers
might dislike the
distributive effects
MC
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7 8
# of units
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1st-degree or perfect PD (3)
• Each consumer needs
several units.
• Individual demand
curves differ.
• Firm can identify a
consumer’s demand
• offers each an
individualized twopart tariff
w.t.p. John Smith’s demand curve
MC
Offer a two-part
pricing scheme:
Pay = FJS+pJSqJS
MC
qJS
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1st-degree or perfect PD (4)
w.t.p. John Smith’s demand curve
• What should pJS and
MC
Offer a two-part
FJS optimally be set at?
pricing scheme:
• Profit maximum is
Pay = FJS+pJSqJS
where
– pJS = MC
– FJS = “CS”
MC
qJS
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Outline: Non-uniform pricing
•
•
•
•
•
•
Common types of PD
Necessary conditions for PD
1st-degree PD
3rd-degree PD
2nd-degree PD
Tying as a PD vehicle
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3rd-degree PD (1)
• Markets may be separated
– geographically
– according to e.g. demographic characteristics:
• age (youth, elderly)
• employment status (employed, unemployed,
student)
• income level
• ...
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3rd-degree PD (2)
• Profits may be split into two separate parts
if monopolist has constant MC=m
• π = (p1(Q1)-m) Q1+ (p2(Q2)-m) Q2
• F.O.C.: pi - m + pi’ Qi = 0 ,
i = 1,2
• => pi - m = - pi’ Qi
• => (pi - m)/pi = - pi’ Qi / pi = - 1/εi
• OR p1/p2 = (1+ 1/ε2)/(1+ 1/ε1)
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3rd degree PD (3)
• So the firm acts as a monopolist on each
market segment
• Exploits differences in demand elasticities
by charging higher prices on less elastic
market segments
• If all markets are served, with a linear
demand welfare is reduced if firm is
allowed to do PD.
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3rd degree PD (4)
• But sometimes the firm would decide not to
serve small markets, if it is forced to do
uniform pricing -> blackboard drawing.
• In that case, PD may increase welfare.
• Demands in two market segments are given
by P1 = 100 - Q1 and P2 = 25 - Q2. MC = 0.
– Find the profit maximizing prices (3rd degree)
– Find the uniform monopoly price.
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Outline: Non-uniform pricing
•
•
•
•
•
•
Common types of PD
Necessary conditions for PD
1st-degree PD
3rd-degree PD
2nd-degree PD
Tying as a PD vehicle
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2nd-degree PD (1)
• What if the firm cannot sort or separate
consumers?
• Consumers willingness to pay or demand
curve is often not observable.
• The firm must make them self-select their
payments
• Consumers with high willingness to pay
could mimic low consumers
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2nd-degree PD (2)
• A single two-part tariff: Payment = T + pq
• Two types of consumers, but firm cannot
see who’s who
• At any price p, Type 2 would be willing to
pay a higher fixed fee T2 than would type 1:
• IF the firm wants to sell to both types of
consumers, the maximal T it can set is T1:
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2nd-degree PD (3)
Type 1
Type 2
T2
T1
P
MC
q1
q2
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2nd-degree PD (4)
• Firm has to leave CS for Type 2!!!
• Might try to use two different two-part
tariffs but then the customers might have
incentive to imitate another type.
• Trade-off between getting more profits and
ensuring that pricing scheme is incentive
compatible to all consumers.
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Outline: Non-uniform pricing
•
•
•
•
•
•
Common types of PD
Necessary conditions for PD
1st-degree PD
3rd-degree PD
2nd-degree PD
Tying as a PD vehicle
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Tying as a PD vehicle
• To screen customers, you may tie two
products together in service contract
• E.g. Xerox machines and Xerox paper/toner
• Heavy users will have higher willingness to
pay.
• Sell the machine at cost and reap the profits
through the paper/toner.
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What’s next?
Shapiro & Varian
Versioning and bundling, etc.
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