Industrial Organization or Imperfect Competition

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Industrial Organization or Imperfect Competition

• Univ. Prof. dr. Maarten Janssen
• University of Vienna
• Summer semester 2008
• Week 3 (March 31- April 1)

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2. Price Discrimination

• Incentives for price discrimination

Price cost
Price cost
Economic Surplus not appropriated by the seller!
PM
PM
D(p)
D(p)
MC
M
QM
MR
Q
Q
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Price Discrimination

• First Degree (or perfect)
• Personalised pricing
• Third Degree (group pricing)
• Observe a group signal and charge different
  prices to different groups
• Second degree (menu of contracts, versioning)
• Offer a menu of price-quantity (quality,)
  bundles and let consumers choose

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First-Degree or Perfect Price Discrimination

• Practice of charging each consumer the maximum
  amount he or she will pay for each incremental
  unit
• Permits a firm to extract all surplus from
  consumers

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First-degree optimal pricing rule

• P(x) is the inverse demand function
• When charging for each additional unit x price
  P(x) the firms profit equals
• Optimisation yields P(x) C(x)
• Which is the definition of the perfectly
  competitive price
• Hence, efficient allocation

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Perfect price discriminationTwo-Part Tariff
Implementation
1. Set price at marginal cost. 2. Compute
consumer surplus. 3. Charge a fixed-fee equal to
consumer surplus.
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Two-Part Tariff optimal pricing rule

• Total price for x units T(x) A px, where A is
  fixed fee and p price per unit
• When consumer buys x units, net utility equals
  U(x) A px.
• Given T(x), consumer buys x units, where U(x)
  p
• Participation constraint U(x) A px 0
• Max A (p-c)x by choosing A and p given
  participation constraint and optimal consumer
  choice
• Obviously, in the optimum PC binds and we should
  have U(x) p c. Moreover, A U(x) cx

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Caveats with perfect pricediscrimination

• Even though it leads to an efficient outcome, is
  it a fair distribution of wealth in the society?
• In practice, transactions costs and information
  constraints make it difficult to implement (but
  car dealers and some professionals try to come
  close).
• Arbitrage Price discrimination wont work if
  consumers can resell the good.

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Third Degree Price Discrimination

• The practice of charging different groups of
  consumers different prices for the same product
• Examples
• Journals, software institutions, individuals,
  students
• International pricing
• Physicians rich and poor patients

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Third Degree Price Discrimination

• Suppose the total demand for a product is
  comprised of two groups with different
  elasticities, ? 1 lt ? 2
• Notice that group 2 is more price sensitive than
  group 1
• Profit-maximizing prices?
• P1 1/(1 - 1/?1) ? MC
• P2 1/(1 - 1/?2) ? MC
• More price sensitive consumers pay lower prices
• Usually, people with lower incomes (students)
• Even if firms have no redistribution intention

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Welfare aspects ofThird Degree Price
Discrimination
- Firms are better off - Low (high) elasticity
consumers are worse (better) off
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Welfare aspects I Analysis constant MC

• Without discrimination charge Pm, sell Si Qmi
  Si Di(Pm). Profit p (Pm c) Si Qmi
• With discrimination charge Pi, sell Qi D(Pi)
  and p Si (Pi - c)Qi
• ?W Si (Pi - c)Qi - (Pm - c)Qmi
  Si Si(Pi) - Si(Pm),
  where ?W change in welfare because of
  discrimination and Si surplus of group i
• Note that dSi/dp - Di(p) and d2Si/dp2 - d
  Di(p)/dp gt 0 (surplus is convex)

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Welfare aspects Analysis II

• Convexity implies that Si(Pi) - Si(Pm)
  Si(Pm)Pi - Pm - QmiPi - Pm
• So, ?W Si (Pi - c)Qi - (Pm - c)Qmi Qmi(Pi
  Pm) Si (Pi - c)(Qi - Qm).
• Also, Si(Pm) - Si(Pi) Si(Pi)Pm - Pi
• Implying ?W (Pm - c)Si (Qi - Qmi).
• So, if price discrimination does not result in
  more output being sold, then welfare declines
• No surprise discrimination leads to marginal
  rates of substitution being different among
  different consumers. Generally, inefficient from
  distributional perspective.

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Welfare aspects Linear Demand Analysis

• Qi ai - biPi
• Straightforward calculations for the
  discrimination case give
• Pi (ai cbi)/2bi
• Qi (ai - cbi)/2
• Without discrimination (assuming all consumers
  are served (buy))
• Pm (Si ai c Sibi)/2(Sibi )
• Qm (Si ai - c Sibi)/2
• As Si (Qi - Qmi) 0, price discrimination does
  not lead to welfare improvement (with linear
  demand), or can it?

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Welfare aspects when some markets are not served
Price Cost
Pb
P
Db(p)
Pa
DaDb
MC
Da(p)
Qa
Qb
Qb
Q
Qa
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Caveats with third degree pricediscrimination

• In practice, the seller needs to be able to
  observe the characteristics of different
  consumers.
• Price discrimination wont work if consumers can
  resell the good (arbitrage) or (successfully)
  pretend to be of a different group
• Interesting angle to discuss economic aspects
  around the issue of privacy (cf., Google
  internet) price discrimination can only work if
  firms have some information about consumers

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Second Degree Price Discrimination

• The practice of offering a menu of contracts
  intended to sort out (screen) consumers of
  different types
• For example, by setting a two-part tariff T(x)
  A px, where consumers can choose any quantity
  they want
• Examples
• Insurance companies, airlines, utilities (water,
  electricity, telephony), etc.

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Exercise on Price Discrimination in class

• Consider the model of second degree price
  discrimination with 2V(x) 1-(1-x)2. Show that
  for any linear tariff with T px (with p gt c),
  there is a two-part-tariff T A px such that
  if consumers are offered the choice, then both
  types of consumers and the firm prefer T to T.

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2nd Degree Price Discrimination at work
Linear two part tariff TA pq Charge p
c Charge fixed fee A CS1(c)
Fixed Fee CS1(c)
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What is the optimal two-part tariff ?
Preliminary results

• Two groups of consumers, with utility function
  ?iV(x) T, ?1 lt ?2 and ? (1- ?) consumers of
  group 1 (2)
• Consumers demand such that p ?iV(x). To make
  demand linear assume 2V(x) 1-(1-x)2 Di(p) 1
  p/?i
• Si(p) ?iV(Di(p)) A - pDi(p) (?i-p)2/2?i A
• Define 1/? ?/?1 (1- ?)/?2 harmonic mean
• D(p) ?D1(p) (1- ?)D2(p) 1 p/?

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What is the optimal two-part tariff ? II

• Participation constraints ?iV(x) T 0
• Obviously if it holds for ?1 then also for ?2
• Highest fixed fee compatible with group 1 buying
  is A (?1-p)2/2?1
• Thus, optimal two-part tariff when everyone buys
  has this A and a price p that maximizes ?A
  (p-c)D1(p) (1-?)A (p-c)D2(p) A
  (p-c)D(p)
• Yields p c / (2 ?/?1) gt c
• Thus, optimal price per unit is larger than
  marginal cost!
• and smaller than the monopoly price provided all
  both groups buy at this price, i.e., (c ?2)/2 lt
  ?1

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Intuition why c lt p
Loss on group 1 consumers
Gain on group 2 consumers
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Math why c lt p

• Loss on group 1 (p - c)(p/?1 - c/?1)/2
  (p-c)2/2?1
• Gain on group 2 (p - c)(p/?1 - p/?2) -
  (p-c)2/2?1
• Sum is (p - c)(c/?1 - p/?2)
• Derivative wrt p is positive for p close to c and
  ?2 gt?1

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Intuition why p lt Pm

• By reducing p a little bit (starting from Pm)
  reduction on variable profits (p-c)D(p) is only
  of second-order by definition
• However, increase in consumer surplus (which can
  be extracted) is in order of D1(p) (first-order)

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Is a linear tariff optimal?
T
T A px
?2V(x) T
?1V(x) T
x
Single crossing property (or sorting condition)
When two indifference curves intersect, group 2s
curve is steeper
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Incentive Compatibility

• It is as if monopolist constructed contract
  T1,x1 for group 1 and T2,x2 for group 2
• Clearly, group 1 does not want to buy contract
  T2,x2 and vice versa, i.e., incentive
  compatible (IC) contract designed for group I
  is bought by group I
• Viewed in this way, van we design better
  contracts?
• Especially, because none of the IC constraints is
  binding

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Monopolist can extract more from group 2 worse
off without effecting group 1
Monopolists indifference curve T cx is constant
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Optimal contract - graphically
T2
Incentive compatbility implies that one cannot
make group 2 consumers worse off than this
otherwise they switch to group 1 contract
x2
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Remarks

• How to get this either just set menu of two
  contracts, or non-linear set of contracts
• In optimal contract incentive compatibility
  constraint must be binding
• That is why linear contract is not optimal
• In optimal contract, indiffernec curve monopolist
  and high demand consumer are tangent group 2s
  consumption is socially optimal (x2 D2(c))

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Non-linear menu- graphically
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2nd Degree Price Discrimination at work
Non-linear two-part tariffs still better
Price Cost
Non-Linear two part tariffs Offer menu
A1,p1,A2,p2 Charge p1 gtc A1 CS1(p1
) Charge p2 c A2 A1BCD
P2(Q)
P1(Q)
A1
p1
D
B
C
MC
p2
Q
Q1
Q2
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Conclusion

• First degree price discrimination
• Efficient from TS perspective, but extreme
  distribution of welfare
• Third degree price discrimination
• Yields higher profits than single pricing
• Ambiguous welfare results vis-à-vis monopoly
  pricing (depending on whether or not total output
  increases)
• Second degree price discrimination
• Yields higher profits than single pricing
• Better for all consumers than single pricing
• Two part-tariffs are also better for all