8a0a95feea78e48f03f701d108e60eb3.ppt
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ECON 4100: Industrial Organization Lecture 5 Monopoly Pricing 1
Introduction • Tim Hartford • https: //www. youtube. com/watch? v=cu. QUen. Y_d. Ng • Fair trade coffee • https: //www. youtube. com/watch? v=V 88 XPEMQGj. Q • Bulgaria: • https: //www. youtube. com/watch? v=d. J 5 un. Kv. Ygc. U 2
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 3
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 4
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 5
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 6
Two-Part Pricing Take an example: Jazz club: n identical consumers $ V Demand is P = V - Q Cost is C(Q) = F + c. Q Marginal Revenue is MR = V - 2 Q Marginal Cost is MC = c c MC MR V Quantity 7
Two-Part Pricing With a uniform price profit is maximized by setting Charging an marginal revenue equal entry fee increases to marginal cost profit by (V - c)2/8 V - 2 Q = c per consumer So Q = (V - c)/2 P=V-Q So P = (V + c)/2 Profit to the monopolist is n(V - c)2/4 - F $ V (V+c)/2 c What if the seller can charge an entry fee? The maximum entry fee that each consumer will be willing to pay is consumer surplus MC MR (V-c)/2 V Quantity Consumer surplus for each consumer is (V - c)2/8 8
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 This increases consumer Surplus, so it increases the entry charge MC MR (V-c)/2 V Quantity 9
Two-Part Pricing What is the best the seller can do? Set the unit price equal to marginal cost This gives consumer surplus of (V - c)2/2 $ V c The entry charge converts consumer surplus into profit MC Using two-part MR pricing increases the monopolist’s V V-c Quantity profit Set the entry charge to (V - c)2/2 10
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, SODEXO does it!) – 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 11
Two-partispricing with different consumers • There an alternative approach $ 16 4 • Offer older customers Older So the seller can charge Younger Consumers entry 12 units for o each an plus fee of $72 t Demand: P = 16 - Q $120 older customer and $32 Demand: P = 12 - Q • and to each younger one younger customers $ If unit price And for converts This the entry plus 8 is set at for $64 units $4 Assume Consumer surplus younger customers that allmarginal cost is consumer And younger for the older customers 12 consumer surplus into constant customers eachat customers is $72 each buy 12 is $32 profit buy $4 unitsunit 8 per units $72 $32 MC $48 4 MC $32 12 Quantity 16 8 12 Quantity 12
Low income Second degree price discrimination 4 consumers will not buy the ($88, 12) High-income Low-Income package since exhibit These packagesthey This is the incentive willing to pay highare discounting: So any other quantitylow-demand consumers will be packagefor 12 So will the high. The only $72 compatibility constraint pay $7. 33 per unit and income consumers: to high-income buy this ($64, 8) package offered willing low-income pay $8 So they can be offered adrinks package to because theconsumers must offer at ($64, 8) $ High income consumers= 88) And profit from Profit ($88, 12) (since $120 - 32 are of from each high- $ package gives them $32 16 willing $32 least income consumer is consumerfor each low-income and they willto pay up to $120 surplus the low-income consumer surplusbuy this 12 Offer entry plus 12 drinks if no other $40 ($88 – (12 x $4)) consumer isa package of consumers package is available $32 ($64 - 8 x$4) for $64 $32 entry plus 8 drinks 8 4 $32 $40 $64 $32 $8 $24 $32 MC $16 8 12 Quantity 4 MC $32 16 Chapter 6: Price Discrimination: Nonlinear Pricing $8 8 12 Quantity 13
• 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 14
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 15
The example again High-Demand Consumers Low-Demand Consumers Demand: P = 16 -a. Q Could the seller prevent = 12 - Q NO! If high-demand If a high-demand. Demand: P consumer pays the lower fee lowernumber consumerlimiting the this by pays the $ and gets thefee andquantity he he lower buys 12 units of units that can be bought? gets $32 of consumer($(144/2)-$32) gets $40 surplus. 12 This is still $32 better than getting of consumer surplus $0 with the 12 -drink deal! $32 $ 16 8 4 $32 $8 $32 $16 8 12 Quantity MC 4 MC $32 16 8 12 Quantity 16
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 17
The example again High-Demand $ 16 8 4 Low-Demand The low-demand consumers will be So any So will the high- other package Low 8) package willing to buy this ($64, demand consumers: high-demand offered to consumers will not So they can. This is the incentive be offered a These packages exhibit because consumers must package the demand consumers are at ($64, 8) High compatibility constraint buy the ($88, $ Profit from each(since $120 - offer And profit from 12) of ($88, 12) discounting: 32 = 88) Offer the low-demand highquantity $32 highpackage willing to pay up to $120 for gives them package since of least pay is demand consumer surplus low-demand they a package demand$32 will per no and each consumer plus 12$7. 33 buy thisother consumerswilling to pay surplus drinks if unit entry 12 x $4) 12 are $40 ($88 - low-demand pay $8 entry plus 8 drinks for $64 consumer is package is available only $72 for 12 $32 ($64 - 8 x$4) $32 drinks $32 $40 $64 $32 $8 $24 $32 MC $16 8 12 Quantity 4 MC $32 16 $8 8 12 Quantity 18
The example again A high-demand consumer will pay up to $87. 50 for monopolist High-Demand entry andclub- does better by The the 7 drinks Low-Demand Can So buying the ($59. 50, 7) package reducing the number of Suppose each low-demand units owner do even gives him $28 consumer surplus offered than this? better to low-demand consumers offered 7 drinks consumer is So entry plus 12 drinks can be sold Each consumer will pay up to for $92 since -this allows him to increase ($120 28 = $92) $ $59. 50 the charge to high-demand for entry and 7 drinks Profit from each ($92, 12) package Profit from each number is $44: an increase of $4 per consumers Yes! Reduce the($59. 50, 7) 12 package isoffered toreduction consumer of units $31. 50: a each of $0. 50 per consumer $28 low-demand consumer $ 16 4 $87. 50 $44$92 MC $28 $48 4 $31. 50 $59. 50 MC $28 7 12 Quantity 16 7 8 12 Quantity 19
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 highdemand – 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 20
Second-degree price discrimination (cont. ) • • This type of price discrimination is everywhere Buy 2 litres of milk and get the 3 rd 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! 21
Second-degree price discrimination (cont. ) • Suppose both types of consumer are served – two packages are offered ($57. 50, 7) aimed at low-demand ($92, 12) aimed at high-demand – profit is $31. 50 x. Nl + $44 x. Nh • Now suppose only high-demand consumers are served – then a ($120, 12) package can be offered – profit is $72 x. Nh • Is it profitable to serve both types? – Only if $31. 50 x. Nl + $44 x. Nh > $72 x. Nh 31. 50 Nl > 28 Nh This requires that Nh Nl 31. 50 < 28 = 1. 125 There should not be “too high” a proportion of high-demand consumers 22
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 23
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 24
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 25
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 26
Third-degree price discrimination (cont. ) • https: //www. youtube. com/watch? v=A 3 RP 46 a. Kv. DI 27
Third-degree price discrimination with varying MC • Now consider an increasing MC (MC=2 Q) – 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 28
The example • Two markets – Market 1: P = 20 - Q 1 – Market 2: P = 16 - 2 Q 2 Now calculate aggregate marginal revenue MR 1 = 20 - 2 Q 1 MR 2 = 16 - 4 Q 2 Note that this applies only for prices less Invert these to give Q as a function of MR: than Q 1 = 10 - MR/2 $16 (there is a KINK) MC = 2 Q Q 2 = 4 - MR/4 The consumers with So aggregate marginal demand are less elastic revenue is Q = Q 1 + Q 2 charged higher prices = 14 - 3 MR/4 Invert this to give marginal revenue: MR = 56/3 - 4 Q/3 for MR < $16 MC = MR 2 Q = 56/3 - 4 Q/3 Q = 5. 6 MR = $11. 20 Q 1 = 4. 4 and Q 2 = 1. 2 P 1 = $15. 60 and P 2 = $13. 60 MR = 20 - 2 Q for MR > $16 29
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 Prices are always – so MR 1 = MR 2 – P 1(1 - 1/ 1) = P 2(1 - 1/ 2) higher in markets where demand is inelastic P 1 (1 - 1/ 2) = P 2 (1 - 1/ 1) 30
Next – Price discrimination and welfare – Public Policy – The multiplant monopolist 31
Market 1 Market 2 $ $ Aggregate $ $20 $16 $13. 60 $15. 60 MR 1 4. 4 10 Quantity $16 $11. 20 D 1 MR 2 20 MC D 2 1. 2 4 8 Quantity MR 1+MR 2 5. 6 14 Quantity 32
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 33