Industrial Organization or Imperfect Competition

1. Industrial Organization or Imperfect Competition Univ. Prof. dr. Maarten Janssen University of Vienna Summer semester 2011 Week 3 (March 24 - 25)

2. Price cost PM D(p) QM MR Q 2. Price Discrimination • Incentives for price discrimination Price cost Price cost Economic Surplus not appropriated by the seller! PM PM D(p) D(p) M MC QM MR Q 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. Price Fixed Fee = Profits Per Unit Charge 4 MC D Quantity 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.

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 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 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? • 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

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

12. Welfare aspects I – Analysis constant MC • Without discrimination charge Pm, sell ΣiQmi = ΣiDi(Pm). Profit π= (Pm – c) ΣiQmi • With discrimination charge Pi, sell Qi = D(Pi) and π= Σi(Pi - c)Qi • ΔW = Σi {(Pi - c)Qi- (Pm - c)Qmi} + Σi {Si(Pi)- Si(Pm)}, where ΔW change in welfare because of discrimination and Si surplus of group i • Note that δSi/δp = - Di(p) and δ2Si/δp2 = - δ Di(p)/δp > 0 (surplus is convex)

13. Welfare aspects: Analysis II • Convexity implies that Si(Pi)- Si(Pm) ≥ S’i(Pm){Pi - Pm} = - Qmi{Pi - Pm} • So, ΔW ≥ Σi {(Pi - c)Qi - (Pm - c)Qmi – Qmi(Pi – Pm)} = Σi(Pi - c)(Qi - Qm). • Also, Si(Pm)- Si(Pi) ≥ S’i(Pi){Pm - Pi} • Implying ΔW ≤ (Pm - c){Σi (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.

14. 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 = (Σiai + c Σibi)/2(Σibi ) • Qm = (Σiai - c Σibi)/2 • As Σi (Qi - Qmi) = 0, price discrimination does not lead to welfare improvement (with linear demand), or can it?

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

16. Caveats with third degree pricediscrimination • 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. Price Cost P2(Q) P1(Q) MC p*=MC Q Q1 Q2 2nd Degree Price Discrimination at work Linear two part tariff: T=A + pq Charge p* = c Charge fixed fee A = CS1(c) Fixed Fee = CS1(c)

19. What is the optimal two-part tariff ? Preliminary results • Two groups of consumers, with utility function θiV(x) – T, θ1 <θ2 and λ (1- λ) consumers of group 1 (2) • Consumers demand such that p = θiV’(x). To make demand linear assume 2V(x) = 1-(1-x)2: Di(p) = 1 – p/θi • Si(p) = θiV(Di(p)) – A - pDi(p) = (θi-p)2/2θi – A • Define 1/θ = λ/θ1 + (1- λ)/θ2 – harmonic mean • D(p) = λD1(p) + (1- λ)D2(p) = 1 – p/θ

20. What is the optimal two-part tariff ? II • Participation constraints θiV(x) – T ≥ 0 • Obviously if it holds for θ1 then also for θ2 • Highest fixed fee compatible with group 1 buying is A = (θ1-p)2/2θ1 • Thus, optimal two-part tariff when everyone buys has this A and a price p that maximizes λ[A + (p-c)D1(p)] + (1-λ)[A + (p-c)D2(p)] = A + (p-c)D(p) • Yields p = c / (2 – θ/θ1) > 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+ θ2)/2 < θ1

21. Price Cost P2(Q) P1(Q) MC p*=MC Q Q1 Q2 Intuition why c < p Loss on group 1 consumers Gain on group 2 consumers

22. Math why c < p • Loss on group 1: (p - c)(p/θ1 - c/θ1)/2 = (p-c)2/2θ1 • Gain on group 2: (p - c)(p/θ1 - p/θ2) - (p-c)2/2θ1 • Sum is (p - c)(c/θ1 - p/θ2) • Derivative wrt p is positive for p close to c and θ2 >θ1

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 D1(p) (first-order)

24. Is a linear tariff optimal? T T = A + px θ2V(x) – T θ1V(x) – T x 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 {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, can we design better contracts? • Especially, because none of the IC constraints is binding

26. T T = A + px θ2V(x) – T θ1V(x) – T x Monopolist can extract more from group 2 without effecting group 1 Monopolist’s indifference curve T – cx is constant

27. T T = A + px θ2V(x) – T θ1V(x) – T x Optimal contract - graphically T2 Incentive compatibility implies that one cannot make group 2 consumers worse off than this; otherwise they switch to group 1 contract x2

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 (x2 = D2(c))

29. T T = A + px θ2V(x) – T θ1V(x) – T x Non-linear menu- graphically

30. 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 *>c; A1= CS1(p1 *) Charge p2* = c; A2 = A1+B+C+D P2(Q) P1(Q) A1 p1* D B C MC p2* Q Q1 Q2

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