Lecture 5 Monopoly Pricing

1. ECON 4100: Industrial Organization Lecture 5 Monopoly Pricing

2. Introduction • Tim Hartford • https://www.youtube.com/watch?v=cuQUenY_dNg • Fair trade coffee • https://www.youtube.com/watch?v=V88XPEMQGjQ • Bulgaria: • https://www.youtube.com/watch?v=dJ5unKvYgcU

3. Introduction • Monopoly pricing MR = MC • uniform versus non-uniform pricing • perfect price discrimination and the appropriation of surplus • types of price discrimination and conditions to implement them • first degree price discrimination • two-part tariffs and block pricing

4. Introduction • A monopolist has the power to set prices • We assume that this power is used to maximize profits • Consider how the monopolist exercises this power • Focus first on a single-product monopolist: • MC=MR • Then charge the highest price

5. First-Degree Price Discrimination First-degree price discrimination occurs when the seller is able to extract the entire consumer surplus Highly profitable but requires: • detailed information • ability to avoid arbitrage (The rural doctor can do it, local prostitutes…and of course the personal tax consultants!) Some firms have made an art of price discrimination (real state agents, used car dealers, etc.) Leads to the efficient choice of output (P=MC): since P=MR and MR = MC

6. First-degree price discrimination (cont.) • The information requirements appear to be insurmountable • No arbitrage is less restrictive but potentially a problem • But there are pricing schemes that will achieve the same output • non-linear prices • two-part pricing as a particular example of non-linear prices

7. Two-Part Pricing $ Take an example: V Jazz club: n identical consumers Demand is P = V - Q Cost is C(Q) = F + cQ c Marginal Revenue is MC MR = V - 2Q MR Marginal Cost is V MC = c Quantity

8. Charging an entry fee increases profit by (V - c)2/8 per consumer Two-Part Pricing What if the seller can charge an entry fee? $ With a uniform price profit is maximized by setting marginal revenue equal to marginal cost V The maximum entry fee that each consumer will be willing to pay is consumer surplus (V+c)/2 V - 2Q = c c MC So Q = (V - c)/2 MR P = V - Q V So P = (V + c)/2 (V-c)/2 Quantity Profit to the monopolist is n(V - c)2/4 - F Consumer surplus for each consumer is (V - c)2/8

9. Two-Part Pricing Is this the best the seller can do? $ V This whole area is now profit from each consumer (V+c)/2 Lower the unit price c MC This increases consumer Surplus, so it increases the entry charge MR V (V-c)/2 Quantity

10. Two-Part Pricing What is the best the seller can do? $ V The entry charge converts consumer surplus into profit Using two-part pricing increases the monopolist’s profit Set the unit price equal to marginal cost c MC MR This gives consumer surplus of (V - c)2/2 V V - c Quantity Set the entry charge to (V - c)2/2

11. Two-part pricing (cont.) • First-degree price discrimination through two-part pricing • increases profit by extracting all consumer surplus • leads to unit price equal to marginal cost (or even lower than that…in fact sometimes free if exacting a price is costly) • causes the monopolist to produce the efficient level of output • What happens if consumers are not identical? • Assume that consumers differ in types and that the monopolist can identify the types • age • location • some other distinguishing and observable characteristic • We can extend our example

12. 4 4 MC MC Two-part pricing with different consumers • There is an alternative approach So the seller can charge an entry fee of $72 t o each older customer and $32 to each younger one Younger Consumers Older Consumers • Offer older customers entry plus 12 units for $120 Demand: P = 16 - Q Demand: P = 12 - Q This converts all consumer surplus into profit • and younger customers entry plus 8 units for $64 $ $ And for the younger customers consumer surplus is $32 If unit price is set at $4 older customers each buy 12 units 16 Consumer surplus for the older customers is $72 Assume that marginal cost is constant at $4 per unit And younger customers each buy 8 units 12 $72 $72 $32 $32 $48 $32 12 16 8 12 Quantity Quantity

13. 4 4 MC MC Low income consumers will not buy the ($88, 12) package since they are willing to pay only $72 for 12 drinks Second degree price discrimination 4 These packages exhibit quantity discounting: high- income pay $7.33 per unit and low-income pay $8 This is the incentive compatibility constraint High-income Low-Income So any other package offered to high-income consumers must offer at least $32 consumer surplus So will the high- income consumers: because the ($64, 8) package gives them $32 consumer surplus The low-demand consumers will be willing to buy this ($64, 8) package So they can be offered a package of ($88, 12) (since $120 - 32 = 88) and they will buy this $ High income consumers are willing to pay up to $120 for entry plus 12 drinks if no other package is available Profit from each high- income consumer is $40 ($88 – (12 x $4)) $ And profit from each low-income consumer is $32 ($64 - 8x$4) 16 Offer the low-income consumers a package of entry plus 8 drinks for $64 12 $32 8 $32 $32 $40 $32 $64 $8 $24 $16 $32 $32 $8 8 12 16 8 12 Quantity Quantity Chapter 6: Price Discrimination: Nonlinear Pricing

14. But… • We can check people’s ages…but sometimes age is not what matters (e.g. jazziness is what counts if we have a jazz club ) • But jazziness is not easily observable! what if there is no way for the monopolist to identify the type of customer? • The monopolist would like to design the pricing scheme in such a way that customers self-select themselves: if they identify themselves, the monopolist does not have to do it! • That is what second-degree price discrimination is about

15. Second-Degree Price Discrimination • What if the seller cannot distinguish between buyers? • perhaps they differ in income, or jazziness (unobservable) • Then the type of price discrimination just discussed is impossible • High-income buyer will pretend to be a low-income buyer • to avoid the high entry price • to pay the smaller total charge • Confirm from the diagram

16. 4 4 MC MC The example again High-Demand Consumers Low-Demand Consumers Could the seller prevent this by limiting the number of units that can be bought? Demand: P = 16 - Q Demand: P = 12 - Q If a high-demand consumer pays the lower fee and buys 12 units he gets $40 ($(144/2)-$32) of consumer surplus NO! If a high-demand consumer pays the lower fee and gets the lower quantity he gets $32 of consumer surplus. This is still $32 better than getting $0 with the 12-drink deal! $ $ 16 12 $32 8 $32 $32 $8 $16 $32 $32 8 12 16 8 12 Quantity Quantity

17. Second-Degree Price Discrimination • The seller has to compromise • A pricing scheme must be designed that makes buyers • reveal their true types • self-select the quantity/price package designed for them • This is the essence of second-degree price discrimination • It is “like” first-degree price discrimination • The seller knows that there are buyers of different types • But • the seller is not able to identify the different types • A two-part tariff is ineffective • allows deception by buyers • Use quantity discounting

18. 4 4 MC MC The example again High-Demand Low-Demand So any other package offered to high-demand consumers must offer at least $32 consumer surplus So will the high- demand consumers: because the ($64, 8) package gives them $32 consumer surplus This is the incentive compatibility constraint The low-demand consumers will be willing to buy this ($64, 8) package Low demand consumers will not buy the ($88, 12) package since they are willing to pay only $72 for 12 drinks These packages exhibit quantity discounting: high- demand pay $7.33 per unit and low-demand pay $8 So they can be offered a package of ($88, 12) (since $120 - 32 = 88) and they will buy this High demand consumers are willing to pay up to $120 for entry plus 12 drinks if no other package is available $ Profit from each high- demand consumer is $40 ($88 - 12 x $4) $ Offer the low-demand consumers a package of entry plus 8 drinks for $64 And profit from each low-demand consumer is $32 ($64 - 8x$4) 16 12 $32 8 $32 $32 $40 $32 $64 $8 $24 $16 $32 $32 $8 8 12 16 8 12 Quantity Quantity

19. 4 4 MC MC The example again The monopolist does better by reducing the number of units offered to low-demand consumers since this allows him to increase the charge to high-demand consumers Can the club- owner do even better than this? A high-demand consumer will pay up to $87.50 for entry and 7 drinks High-Demand Low-Demand So buying the ($59.50, 7) package gives him $28 consumer surplus Suppose each low-demand consumer is offered 7 drinks So entry plus 12 drinks can be sold for $92 ($120 - 28 = $92) Each consumer will pay up to $59.50 for entry and 7 drinks $ $ Profit from each ($92, 12) package is $44: an increase of $4 per consumer 16 Yes! Reduce the number of units offered to each low-demand consumer Profit from each ($59.50, 7) package is $31.50: a reduction of $0.50 per consumer 12 $28 $87.50 $31.50 $44 $92 $59.50 $28 $48 $28 7 12 16 8 12 7 Quantity Quantity

20. Second-degree price discrimination (cont.) • Will the monopolist always want to supply both types of consumer? • There are cases where it is better to supply only high-demand • high-class restaurants (try going to Raymond’s and asking for a small one of French fries with gravy • golf and country clubs • Take our example again • suppose that there are Nl low-income consumers • and Nh high-income consumers

21. Second-degree price discrimination (cont.) • This type of price discrimination is everywhere • Buy 2 litres of milk and get the 3rd one free • Buy the big pizza and we will give you a free drink • This is not generally because there are economies of scale when serving in bulk, as most people think!

22. Second-degree price discrimination (cont.) • Suppose both types of consumer are served • two packages are offered ($57.50, 7) aimed at low-demand and ($92, 12) aimed at high-demand • profit is $31.50xNl + $44xNh • Now suppose only high-demand consumers are served • then a ($120, 12) package can be offered • profit is $72xNh • Is it profitable to serve both types? • Only if $31.50xNl + $44xNh > $72xNh 31.50Nl > 28Nh Nh 31.50 This requires that < = 1.125 Nl 28 There should not be “too high” a proportion of high-demand consumers

23. Second-degree price discrimination (cont.) • Characteristics of second-degree price discrimination • extract all consumer surplus from the lowest-demand group • leave some consumer surplus for other groups • the incentive compatibility constraint • offer less than the socially efficient quantity to all groups other than the highest-demand group • offer quantity-discounting • Second-degree price discrimination converts consumer surplus into profit less effectively than first-degree • Some consumer surplus is left “on the table” in order to induce high-demand groups to buy large quantities

24. Third-Degree Price Discrimination • Consumers differ by some observable characteristic(s) • A uniform price is charged to all consumers in a particular group • Different uniform prices are charged to different groups • “kids are free” • subscriptions to professional journals e.g. American Economic Review • airlines • the number of different economy fares charged can be very large indeed! • early-bird specials; first-runs of movies versus rented ones

25. Third-degree price discrimination (cont.) • Often arises when firms sell differentiated products • hard-back versus paper back books • first-class versus economy airfare • Price discrimination exists in these cases when: • “two varieties of a commodity are sold by the same seller to two buyers at different net prices, the net price being the price paid by the buyer corrected for the cost associated with the product differentiation.” (Phlips) • The seller needs an easily observable characteristic that signals willingness to pay • The seller must be able to prevent arbitrage • e.g. require a Saturday night stay for a cheap flight

26. Third-degree price discrimination (cont.) • The pricing rule is very simple: • consumers with low elasticity of demand should be charged a high price • consumers with high elasticity of demand should be charged a low price • We can illustrate with a simple example on the board • monopolist has constant marginal costs of c per unit • two identifiable types of consumers • all consumers of a particular type have identical demands • two pricing rules must hold • marginal revenue must be equal on the last unit sold to each type of consumer • marginal revenue must equal marginal cost in each market

27. Third-degree price discrimination (cont.) • https://www.youtube.com/watch?v=A3RP46aKvDI

28. Third-degree price discrimination with varying MC • Now consider an increasing MC (MC=2Q) • two identifiable types of consumers • all consumers of a particular type have identical demands • two pricing rules must hold • marginal revenue must be equal on the last unit sold to each type of consumer • marginal revenue must equal marginal cost in each market

29. The example • Two markets • Market 1: P = 20 - Q1 • Market 2: P = 16 - 2Q2 Now calculate aggregate marginal revenue MR1 = 20 - 2Q1 MR2 = 16 - 4Q2 Note that this applies only for prices less than $16 (there is a KINK) Invert these to give Q as a function of MR: Q1 = 10 - MR/2 MC = 2Q Q2 = 4 - MR/4 The consumers with less elastic demand are charged higher prices MC = MR  2Q = 56/3 - 4Q/3 So aggregate marginal revenue is  Q = 5.6 Q = Q1 + Q2 = 14 - 3MR/4  MR = $11.20 Invert this to give marginal revenue:  Q1 = 4.4 and Q2 = 1.2 MR = 56/3 - 4Q/3 for MR < $16  P1 = $15.60 and P2 = $13.60 MR = 20 - 2Q for MR > $16

30. Third-degree price discrimination (cont.) • A general rule characterizes third-degree price discrimination • Recall the formula for marginal revenue in market i: • MRi = Pi(1 - 1/i) where i is the price elasticity of demand • Recall also that when serving two markets profit maximization requires that MR is equalized in each market • so MR1 = MR2 •  P1(1 - 1/ 1) = P2(1 - 1/ 2) Prices are always higher in markets where demand is inelastic P1 (1 - 1/ 2)  = P2 (1 - 1/ 1)

31. Next • Price discrimination and welfare • Public Policy • The multiplant monopolist

32. Market 1 Market 2 Aggregate $ $ $ $20 $20 MC $16 $16 $15.60 $13.60 $11.20 D1 MR1+MR2 MR1 D2 MR2 4.4 10 20 1.2 4 8 5.6 14 Quantity Quantity Quantity

33. The incentive compatibility constraint • Any offer made to high demand consumers must offer them as much consumer surplus as they would get from an offer designed for low-demand consumers. • This is a common phenomenon • performance bonuses must encourage effort • insurance policies need large deductibles to deter cheating • encouragement to buy in bulk must offer a price discount