1 Industrial Organization or Imperfect Competition Univ. Prof. dr. Maarten Janssen University of Vienna Summer semester 2011 Week 3 (March )

2 2. Price Discrimination Incentives for price discrimination D(p) MR QMQM PMPM MC Price cost Q Economic Surplus not appropriated by the seller! D(p) PMPM Price cost Q M MR QMQM D(p) PMPM Price cost Q

3 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

4 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

5 First-degree: optimal pricing rule P(x) is the inverse demand function When charging for each additional unit x price P(x) the firm’s profit equals Optimisation yields P(x) = C’(x) Which is the definition of the perfectly competitive price  Hence, efficient allocation

6 Perfect price discrimination: Two-Part Tariff Implementation 1. Set price at marginal cost. 2. Compute consumer surplus. 3. Charge a fixed-fee equal to consumer surplus. Quantity D 4 MC Fixed Fee = Profits Price Per Unit Charge

7 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*

8 Caveats with perfect price discrimination 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 won’t work if consumers can resell the good.

9 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]

10 Third Degree Price Discrimination Suppose the total demand for a product is comprised of two groups with different elasticities,  1 <  2 Notice that group 2 is more price sensitive than group 1 Profit-maximizing prices?  P 1 = [1/(1 - 1/  1 )]  MC  P 2 = [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

11 Welfare aspects of Third Degree Price Discrimination MC Da(p) Db(p) Price Cost QaQb Da+Db Q P Pb Qb Pa Qa Qb Qa - Firms are better off - Low (high) elasticity consumers are worse (better) off

12 Welfare aspects I – Analysis constant MC Without discrimination charge Pm, sell Σ i Q mi = Σ i D i (P m ). Profit π = (P m – c) Σ i Q mi With discrimination charge P i, sell Q i = D(P i ) and π = Σ i (P i - c)Q i ΔW = Σ i {(P i - c)Q i - (P m - c)Q mi } + Σ i {S i (P i ) - S i (P m )}, where ΔW change in welfare because of discrimination and S i surplus of group i Note that δS i /δp = - D i (p) and δ 2 S i /δp 2 = - δ D i (p)/δp > 0 (surplus is convex)

13 Welfare aspects: Analysis II Convexity implies that S i (P i ) - S i (P m ) ≥ S’ i (P m ){P i - P m } = - Q mi {P i - P m } So, ΔW ≥ Σ i {(P i - c)Q i - (P m - c)Q mi – Q mi (P i – P m )} = Σ i (P i - c)(Q i - Q m ). Also, S i (P m ) - S i (P i ) ≥ S’ i (P i ){P m - P i } Implying ΔW ≤ (P m - c){Σ i (Q i - Q mi )}. 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.

14 Welfare aspects: Linear Demand Analysis Q i = a i - b i P i Straightforward calculations for the discrimination case give  P i = (a i + cb i )/2b i  Q i = (a i - cb i )/2 Without discrimination (assuming all consumers are served (buy))  P m = ( Σ i a i + c Σ i b i )/2( Σ i b i )  Q m = ( Σ i a i - c Σ i b i )/2 As Σ i (Q i - Q mi ) = 0, price discrimination does not lead to welfare improvement (with linear demand), or can it?

15 Welfare aspects when some markets are not served MC Pa Pb Da(p) Db(p) Price Cost QaQb Da+Db = P Qa Qb= Q

16 Caveats with third degree price discrimination In practice, the seller needs to be able to observe the characteristics of different consumers. Price discrimination won’t 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

17 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.

18 2nd Degree Price Discrimination at work P 2 (Q) P 1 (Q) Q Price Cost MC Fixed Fee = CS 1 (c) Linear two part tariff: T=A + pq Charge p* = c Charge fixed fee A = CS 1 (c) p*=MC Q1Q1 Q2Q2

19 What is the optimal two-part tariff ? Preliminary results Two groups of consumers, with utility function θ i V(x) – T, θ 1 < θ 2 and λ (1- λ) consumers of group 1 (2) Consumers demand such that p = θ i V’(x). To make demand linear assume 2V(x) = 1-(1-x) 2 : D i (p) = 1 – p/θ i S i (p) = θ i V(D i (p)) – A - pD i (p) = (θ i -p) 2 /2θ i – A Define 1/θ = λ/θ 1 + (1- λ)/θ 2 – harmonic mean D(p) = λD 1 (p) + (1- λ)D 2 (p) = 1 – p/θ

20 What is the optimal two-part tariff ? II Participation constraints θ i V(x) – T ≥ 0  Obviously if it holds for θ 1 then also for θ 2 Highest fixed fee compatible with group 1 buying is A = (θ 1 -p) 2 /2θ 1 Thus, optimal two-part tariff when everyone buys has this A and a price p that maximizes λ[A + (p-c)D 1 (p)] + (1-λ)[A + (p-c)D 2 (p)] = A + (p-c)D(p) Yields p = c / (2 – θ/θ 1 ) > 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+ θ 2 )/2 < θ 1

21 Intuition why c < p P 2 (Q) P 1 (Q) Q Price Cost MC p*=MC Q1Q1 Q2Q2 Loss on group 1 consumers Gain on group 2 consumers

22 Math why c < p Loss on group 1: (p - c)(p/θ 1 - c/θ 1 )/2 = (p-c) 2 /2θ 1 Gain on group 2: (p - c)(p/θ 1 - p/θ 2 ) - (p-c) 2 /2θ 1 Sum is (p - c)(c/θ 1 - p/θ 2 ) Derivative wrt p is positive for p close to c and θ 2 >θ 1

23 Intuition why p < 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 D 1 (p) (first-order)

24 Is a linear tariff optimal? T x T = A + px θ 2 V(x) – T θ 1 V(x) – T Single crossing property (or sorting condition): When two indifference curves intersect, group 2’s curve is steeper

25 Incentive Compatibility It is as if monopolist constructed contract {T 1,x 1 } for group 1 and {T 2,x 2 } for group 2 Clearly, group 1 does not want to buy contract {T 2,x 2 } and vice versa, i.e., incentive compatible (IC) – contract designed for group I is bought by group I Viewed in this way, can we design better contracts? Especially, because none of the IC constraints is binding

26 Monopolist can extract more from group 2 without effecting group 1 T x T = A + px θ 2 V(x) – T θ 1 V(x) – T Monopolist’s indifference curve T – cx is constant

27 Optimal contract - graphically T x T = A + px θ 2 V(x) – T θ 1 V(x) – T x2x2 T2T2 Incentive compatibility implies that one cannot make group 2 consumers worse off than this; otherwise they switch to group 1 contract

28 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, indifference curve monopolist and high demand consumer are tangent: group 2’s consumption is socially optimal (x 2 = D 2 (c))

29 Non-linear menu- graphically T x T = A + px θ 2 V(x) – T θ 1 V(x) – T

30 2nd Degree Price Discrimination at work; Non-linear two-part tariffs: still better Q P 2 (Q) P 1 (Q) Price Cost MC p2*p2* Non-Linear two part tariffs: Offer menu {{A 1,p 1 },{A 2,p 2 }} Charge p 1 *>c; A 1 = CS 1 (p 1 *) Charge p 2 * = c; A 2 = A 1 +B+C+D Q1Q1 Q2Q2 p1*p1* A1A1 B C D

31 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