PRICE DISCRIMINATION Industrial Organization B

Transcription

1 PRICE DISCRIMINATION Industrial Organization B THIBAUD VERGÉ Autorité de la Concurrence and CREST-LEI Master of Science in Economics - HEC Lausanne ( ) THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 1 / 29

2 Introduction Do firms always sell at the same price? Uniform pricing At any given date (at any given location) Same price for all consumers Reasonable approximation for a large number of products Non-uniform pricing Rebates (negotiation) Quantity rebates (decreasing average unit price) Age rebate (senior citizens, students,... ) Different prices for different stores / locations Tie-in sales THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 2 / 29

3 Introduction Price Discrimination Two necessary ingredients Identifying consumers In order to offer different prices or packages to different consumers, the firm must know few things about these consumers. Identifying types / categories of consumers (e.g. students,...) Knowing the distribution of types (e.g. business / economy class) No arbitrage If goods can easily be transferred from a consumer to another, price discrimination cannot occur. Resale Depends on the type of good (e.g electricity,...) THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 3 / 29

4 Introduction Price discrimination: A definition Definition There is discrimination when two units of the same goods are sold at different prices (possibly to the same consumer). Some problems with this definition Transportation costs Differentiated products Pigou (1920) First-, second- and third-degree price discrimination THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 4 / 29

5 Outline Introduction 1 First-degree price discrimination 2 Third-degree price discrimination 3 Second-degree price discrimination 4 Tie-in sales THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 5 / 29

6 First-degree price discrimination Unit demand First-degree price discrimination Unit demand One price for each consumer The firm knows everything about each individual consumer and charges to that consumer exactly his (her) reservation price. One unit or nothing U i = { v i p if (s)he buys 0 otherwise Individualized prices p i = v i (as long as v i c) THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 6 / 29

7 Welfare impact First-degree price discrimination Unit demand Consumer surplus Each consumer s surplus is equal to 0. Therefore S = 0 But all consumers with v i c buy. Firm s profit (v i c) = W v i c Total welfare Total welfare is maximized. THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 7 / 29

8 First-degree price discrimination Elastic demand First-degree price discrimination Elastic demand Individual demand D (p) decreasing in p, n identical consumers Can the monopolist extract the entire surplus? Yes! Using non-linear tariffs. Two-part tariff Unit price p Fixed fee (monthly fee,... ) A Tariff is thus: T (q) = A + pq THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 8 / 29

9 Optimal tariff First-degree price discrimination Elastic demand For a given quantity q... The individual consumer s surplus is S (q) = q 0 P (x) dx P (q) q (S)He is thus willing to pay: A = S (q) Therefore: T (q) = q 0 P (x) dx Firm s profit Π = n q 0 P (x) dx C (nq) thus P (q) = C (nq) Are two-part tariffs optimal? The monopolist chooses the quantity that maximizes the total welfare THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 9 / 29

10 First-degree price discrimination Elastic demand First-degree price discrimination THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 10 / 29

11 First-degree price discrimination First-degree price discrimination Heterogenous consumers Heterogenous consumers Consumers P 1 (q 1 ), P 2 (q 2 ),... Individualized fixed fee A i (q i ) = q i 0 P i (x) dx P i (q i ) q i Profit maximization = Welfare maximization thus Π = q1 0 P 1 (x) dx + q2 0 P 2 (x) dx +... C (q 1 + q ) P 1 (q 1 ) = P 2 (q 2 ) =... = C (q 1 + q ) THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 11 / 29

12 Third-degree price discrimination Third-degree price discrimination One price per consumer group Consumers Several groups of consumers (K groups) Typically: countries, regions but also age, gender, business / home,... Each group has an aggregate demand function D k (p) The monopolist offers a different price to each group No arbitrage (between groups) Impossible to discriminate within a group A linear tariff for each group (p 1, p 2,..., p K ) THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 12 / 29

13 Third-degree price discrimination The inverse elasticity rule Inverse elasticity rule Monopolist s maximization program: ( K ) Π = p 1 D 1 (p 1 ) + p 2 D 2 (p 2 ) p K D K (p K ) C D k (p k ) to be maximized with respect to p 1, p 2,..., p K. First-order conditions ( K ) p k C k=1 D k (p k ) = D k (p k ) p k p k D k (p k) = 1 ε k k=1 THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 13 / 29

14 Third-degree price discrimination Inverse elasticity rule The inverse elasticity rule (II) Higher price on markets where the price elasticity of demand is lower. Remark Special case of multi-product monopolist Inter-dependent demands (Possibly) inter-dependent costs THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 14 / 29

15 Third-degree price discrimination Inverse elasticity rule Is third-degree price discrimination legal? Third-degree price discrimination is allowed The same producer is allowed to charge different prices at different locations Or to offer different prices to senior citizens, students,... However Preventing arbitrage is prohibited Severe penalties imposed by the European Commission for restrictions of parallel imports: Nintendo (e168 million) Volkswagen, Opel, Daimler Chrysler (e90, e43, e72 million respectively) THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 15 / 29

16 Third-degree price discrimination Welfare impact Welfare impact Does imposing a uniform price increase welfare? The monopolist is always better off if it can discriminate The impact on consumer surplus is however ambiguous Two effects on consumers 1 The low-elasticity group benefits from uniform pricing 2 But the high-elasticity group doesn t Redistribution effect. THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 16 / 29

17 Third-degree price discrimination Welfare impact Welfare impact (II) An example of welfare-enhancing discrimination Two groups, demands D 1 < D 2 With price discrimination, both groups consume Under uniform pricing, group 1 does not buy Why is price discrimination good? p 2 doesn t change if price discrimination is banned! Linear demand case: prohibiting discrimination increases total welfare 1 Linear demands: D k = a k b k p 2 Constant marginal cost: C (q) = cq 3 Then total welfare is greater under uniform pricing. THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 17 / 29

18 Third-degree price discrimination Welfare impact Overall: ambiguous impact Positive impact of price discrimination On markets where consumers are highly price sensitive Negative impact of price discrimination On markets where price elasticity of demand is low Globally, banning price discrimination 1 Does not necessarily increase total welfare. 2 Is never Pareto-improving. THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 18 / 29

19 Second-degree price discrimination Second-degree price discrimination Impossible to distinguish consumers, but price discrimination is still feasible. The monopolist knows how consumers differ (i.e. the distribution of types) But cannot identify individual types. It offers different packages (e.g. (price, quantity) or (price, quality)) Consumers select their preferred package Therefore additional self-selection constraints are required (consumers need to prefer the package that has been designed for them) THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 19 / 29

20 Second-degree price discrimination Two types Two types = Two tariffs Example Two groups of consumers Proportion λ of consumers with U 1 = θ 1 V (q) T (q) Proportion 1 λ of consumers with U 2 = θ 2 V (q) T (q) θ 1 < θ 2 The monopolist offers the choice between two tariffs: ((q 1, T 1 ), (q 2, T 2 )) Monopolist s profit: λ (T 1 cq 1 ) + (1 λ) (T 2 cq 2 ) Chooses q 1, q 2, T 1 and T 2 But has to satisfy the self-selection (and participation ) constraints... THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 20 / 29

21 Second-degree price discrimination Two types Self-selection and participation constraints The constraints Participation θ 1 V (q 1 ) T 1 0 (CP 1) θ 2 V (q 2 ) T 2 0 (CP 2) Self-selection θ 1 V (q 1 ) T 1 θ 1 V (q 2 ) T 2 (CI 1) θ 2 V (q 2 ) T 2 θ 2 V (q 1 ) T 1 (CI 2) Remark: (CP 1) and (CI 2) imply (CP 2) THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 21 / 29

22 Second-degree price discrimination Two types The maximization program The firm maximizes λ (T 1 cq 1 ) + (1 λ) (T 2 cq 2 ) θ 1 V (q 1 ) T 1 0 (CP 1) θ 2 V (q 2 ) T 2 θ 2 V (q 1 ) T 1 (CI 2) Remark: at this stage, we ignore (CI 1) Constraints are binding T 1 = θ 1 V (q 1 ) (CP 1)(no surplus) Replacing T 1 by its value in (CI 2) yields T 2 = θ 2 V (q 2 ) (θ 2 θ 1 ) V (q 1 ) (CI 2)(surplus) THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 22 / 29

23 Second-degree price discrimination Rewriting the program Two types The firm maximizes λ (θ 1 V (q 1 ) cq 1 ) + (1 λ) (θ 2 V (q 2 ) (θ 2 θ 1 ) V (q 1 ) cq 2 ) First-order conditions ( θ 1 V (q 1 ) = c/ 1 1 λ θ 2 θ 1 λ θ 1 )and θ 2 V (q 2 ) = c Interpretation 1 The high demand group buys the socially optimal quantity (marginal utility = marginal cost) 2 The low demand group buys less than the socially optimal quantity THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 23 / 29

24 Second-degree price discrimination The socially optimal tariffs Two types T T 2 V q c T 1 V q q 1 S q 2 S q THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 24 / 29

25 Second-degree price discrimination Two types Packages offered by the monopolist T Sub-optimal quantity for type 1 Rent for type 2 q 1 q 1 S q 1 S q 2 q 2 S q THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 25 / 29

26 Second-degree price discrimination Menu of two-part tariffs Two types T T 2 q A 2 p 2 q T 1 q A 1 p 1 q p 2 p 1 A 2 A 1 q 1 q 1 S q 1 S q 2 q 2 S q THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 26 / 29

27 Non-linear tariff Second-degree price discrimination Two types T q 1 q 1 S q 1 S q 2 q 2 S q THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 27 / 29

28 Tie-in sales Tie-in sales Selling (as a bundle) two different goods or two units of the same good Examples Return ticket (vs. two singles) TV programs + adverts DVD + bonus, CD (vs. singles) Almost any packaged grocery product Monthly or annual contracts (e.g. mobile phone contract,... ) Product + Insurance / Warranty Microsoft Office THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 28 / 29

29 Tie-in sales Tie-in sales as a way to discriminate Simple example Two goods, zero production cost Heterogenous consumers, θ [0, 1] (uniform distribution) U (θ, p 1, p 2 ) = (θ p 1 ) } {{ } + ((1 θ) p 2 ) } {{ } if buys good 1 if buys good 2 Separate sales D 1 (p 1 ) = (1 p 1 ) and D 2 (p 2 ) = (1 p 2 ) p 1 = p 2 = 1 2, π 1 = π 2 = 1 4, Π = 1 2 Tie-in sales D (p) = 1 (because θ + 1 θ = 1) p = 1 and thus Π = 1 THIBAUD VERGÉ (AdlC, CREST-LEI) Price Discrimination IO B (Ch.2) 29 / 29