Price Discrimination

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

Outline: Non-uniform pricing • Common types of Price Discrimination • Necessary conditions for PD • 1st-degree PD • 3rd-degree PD • 2nd-degree PD • Tying as a PD vehicle

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.

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

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

Necessary conditions for PD (2) Ways to prevent or limit resales • services can often not be resold • Want to buy my haircut? • resale can make warranty void • transportation costs may limit resales • contractual clauses may forbid resale • vertical integration may prevent resales. ...

1st-degree or perfect PD (1) • 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:

1st-degree or perfect PD (2) willingness to pay price MC 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 # of units 1 2 3 4 5 6 7 8

1st-degree or perfect PD (3) w.t.p. MC John Smith’s demand curve • Each consumer needs several units. • Individual demand curves differ. • Firm can identify a consumer’s demand • offers each an individualized two-part tariff Offer a two-part pricing scheme: Pay = FJS+pJSqJS MC qJS

1st-degree or perfect PD (4) w.t.p. MC John Smith’s demand curve • What should pJS and FJS optimally be set at? • Profit maximum is where • pJS = MC • FJS = “CS” Offer a two-part pricing scheme: Pay = FJS+pJSqJS MC qJS

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 • ...

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)

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.

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.

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

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:

2nd-degree PD (3) Type 1 Type 2 T2 T1 P MC q1 q2

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.

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.

What’s next? Shapiro & Varian Versioning and bundling, etc.

Price Discrimination