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Industrial Organization I

Industrial Organization I. Price discrimination. Classification. Direct Discrimination. Formally : Monopolist solves : Foc’s are: After some manipulation :. Direct Discrimination: Welfare. p. p 1. p 2.

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Industrial Organization I

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  1. Industrial Organization I Price discrimination

  2. Classification

  3. Direct Discrimination • Formally: • Monopolistsolves: • Foc’s are: • Aftersomemanipulation:

  4. Direct Discrimination: Welfare p p1 p2 • In some cases, price discrimination provides goods and services to groups that would not have access under uniform pricing: • Prescription drugs: developed vs. developing countries D1 + D2 MC p*2 D2 p*1 D1 q*1 q1 q*2 q2 Q* MR Q MR1 MR2

  5. Direct Discrimination: Welfare • Firm is better off (in the worst case the firm is as well off) • Consumers in low elasticity markets are worse off • Consumers in high elasticity markets are better off

  6. Direct Discrimination: Inter-related Demands • Direct (or group) price discrimination analysis also applies to “inter-related” demands: • Electricity (off peak v. peak) • Durable goods markets • Monday night movie discounts? Wing Tuesday?

  7. Indirect Discrimination • Consumers self-select • Firm knows about two (or more) consumer types • It is unfeasible (or illegal) to use direct discrimination (arbitrage will happen) • Again, two possible kinds of “packages” • Two-part tariff: e.g. $100 for a plan, and 10c/min after 1000 min • Take it or leave it offer: buy one get one 50% off.

  8. Indirect Discrimination • Packages must comply with 2 constraints: • Incentive compatibility: we want groups to select the package designed for them • Participation: consumers must purchase (i.e. the package designed for them gives them positive utility)

  9. Graphical Illustration: Two part tariff pC Residential Commercial pR • Assumption: MC=0 • With 2 prices (6 & 12), commercial has no incentive to choose $12 • Solution: 2 plans: a)12¢/min (“12 plan”), b)6 ¢/min (“6 plan”) + fixed fee (fixed # min) • Compatibility: CSC(12 plan)>=CSC(6 plan), commercial chooses “12 plan” • “6 Plan”: fixed fee? 9 minutes? 18 minutes? • Participation: Residential must choose “6 plan” (“12 plan” is never chosen) • CSR(6)>0: 135 – 108 = 27; you can actually do better. How? 24 36 81 12 DC 12* 135 144 108 DR 108 6* qR qC 12* 18 24 6* 9 12 18

  10. Implications of ID • Low demand consumer has marginal value that exceeds marginal cost (inefficiently small amount) • High demand consumer has marginal value equal to marginal cost (efficient quantity) • We will derive this result formally below (in a simple model)

  11. A simple model (take-it-or leave it) • Assumptions: • 2 consumers • Consumer 2 is high demand, consumer 1 is low demand: • Firm is a monopolist and sells to two consumers (quantities x1 and x2)

  12. A simple model • Utility is quasi-linear: • This simplifies to: Inverse demand

  13. A simple model • Firm sets package based on inverse dd • Consumer pays and gets units (take-it-or-leave-it package):

  14. A simple model • Participation constraints: • Incentive compatibility constraints (also “self-selection” constraints):

  15. A simple model • Rearranging: • Let’s show that in each pair of constraints, only one constraint can be binding Consumer 1 Constraints (A) (B) Consumer 2 Constraints (C) (D)

  16. A simple model • Let’s see if (C) can be binding [r2=u2(x2)] : • Since • It follows that: • Which contradicts (A)

  17. A simple model • Hence, (D) must be binding: • Now, let’s consider consumer 1’s constraints: • Suppose (B) is binding: • Plugging (E) in the last expression: (E)

  18. A simple model • Last expression can also be written as: • But this violates the assumption: • Hence, (A) must be binding

  19. A simple model • Under the assumptions made: • Low demand consumer is charged his maximum willingness to pay (i.e. derives zero utility) • High demand consumer is charged highest r2 that makes him indifferent between x2 and x1 (but derives positive utility)

  20. A simple model • Profit Maximization • Rearranging (F): (F)

  21. A simple model • This implies (just as in our graphical two-part tariff illustration above): • Low demand consumer has marginal value that exceeds marginal cost (inefficiently small amount) • High demand consumer has marginal value equal to marginal cost (efficient quantity) • More on this in homework 3

  22. Indirect Discrimination: Examples • Buy 1 at $50, get one at half price ($25) Consumer Surplus 50 Elastic demand 25 1 2

  23. Indirect Discrimination: Examples • Buy one, get one half price • Incentive compatible, participation constraint satisfied Consumer surplus 50 25 Inelastic demand 1 2

  24. Important Points • Uniform (aka linear) pricing within a segment can only be used for direct price discrimination (not for indirect PD) • For indirect discrimination to work, a non-linear scheme needs to be offered: (r,q) contract or a two-part tariff contract (A,p) • Two-part tariffs and packages can be used in all three price discrimination schemes

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