Basic Monopoly Pricing and Product Strategies

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1 Chapter 3 Basic Monopoly Pricing and Product Strategies Industrial 1

2 Introduction A monopolist has the power to set prices Consider how the monopolist exercises this power Focus in this section on a single-product monopolist What determines price? What different pricing strategies might be used? What product design strategies might be used? What constraints are there on the monopolist s ability to extract consumer surplus? Industrial 2

3 First-Degree Price Discrimination First-degree price discrimination occurs when the seller is able to extract the entire consumer surplus suppose that you own five antique cars and you meet two collectors each is willing to pay \$10,000 for one car, \$8,000 for a second car, \$6,000 for a third car, \$4,000 for a fourth and \$2,000 for a fifth sell the first two cars at \$10,000, one to each buyer sell the second two cars at \$8,000, one to each buyer sell the fifth car to one of the buyers at \$6,000 total revenue \$42,000 Highly profitable but requires detailed information ability to avoid arbitrage Leads to the efficient choice of output: since price equals marginal revenue and MR = MC Industrial 3

4 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 Industrial 4

5 Take an example: Jazz club: n identical consumers Demand is P = V - Q Cost is C(Q) = F + cq Marginal Revenue is MR = V - 2Q Marginal Cost is MC = c Two-Part Pricing \$ V c MR V MC Industrial 5

6 With With a uniform price price profit is is maximized by by setting Charging an marginal revenue equal entry to to marginal fee increases cost cost profit by (V - c) 2 /8 per consumer V - 2Q = c So Q = (V - c)/2 P = V - Q So P = (V + c)/2 Two-Part Pricing \$ V (V+c)/2 c (V-c)/2 What if if the seller can charge an an entry fee? The The maximum entry entry fee fee that that each each consumer will will be be willing to to pay pay is is consumer surplus MC MR V Profit to to the the monopolist is is n(v n(v -- c) c) 2 /4 2 /4-- F Consumer surplus for for each each consumer is is (V (V-- c) c) 2 /8 2 /8 Industrial 6

7 Is Is this the best the seller can do? Two-Part Pricing \$ V (V+c)/2 This whole area is now profit from each consumer Lower the the unit unit price price This This increases consumer surplus and and so so increases the the entry entry charge c (V-c)/2 MR V MC Industrial 7

8 What is is the best the seller can do? Two-Part Pricing \$ V The entry charge converts consumer surplus into profit Set Set the the unit unit price price equal to to marginal cost cost This This gives consumer surplus of of (V (V-- c) c) 2 /2 2 /2 c Using two-part pricing increases MR the monopolist s profit V - c V MC Set Set the the entry entry charge to to (V (V-- c) c) 2 /2 2 /2 Industrial 8

9 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 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 Industrial 9

10 \$ 16 Two-part pricing with different consumers There is an alternative approach Older Offer So Consumers the older seller customers can charge Younger Consumers entry an entry plus 12 fee units of \$72 for t o each Demand: \$120older P = 16 customer Q and \$32 Demand: P = Q and to younger each \$ If younger customers If unit unit price one price And And This for for converts the the entry plus Consumer 8 is units is set set at surplus at for \$4 \$64 \$4 younger customers older for 12 older for the the customers older all older consumer And consumer And surplus younger customers each each buy buy is is \$72 12 \$72 12 customers is surplus is \$32 \$32 constant each into eachat units units buy buy profit \$4 8 units units per unit \$72 \$32 Assume that that marginal cost cost is is constant at \$4 per unit 4 MC 4 MC \$48 \$ Industrial 10

11 Second-Degree Price Discrimination What if the seller cannot distinguish between buyers? perhaps they differ in income (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 Industrial 11

12 The example again High-Demand Consumers Low-Demand Consumers Demand: NO! P = Q Demand: P = Q NO! If If a high-demand Could the seller prevent \$ consumer pays pays this If the If the a by by lower high-demand limiting fee fee the \$ number 16 and and gets gets the the consumer lower of pays pays the the lower fee of units quantity fee and that and buys can buys units be 12 units he be bought? gets gets \$32 \$32 of of consumer surplus he gets gets \$40 \$40 of of consumer \$32 surplus 8 \$32 \$32 4 \$8 MC 4 MC \$32 \$16 \$ Industrial 12

13 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 Industrial 13

14 The example again High-Demand Low-Demand So The The low-demand consumers will will be So will will the the So So high- any other package be willing to to buy buy this this (\$64, Low demand (\$64, 8) 8) package consumers: Low demand offered to to high-demand \$ because So So they This is the incentive High they can the (\$64, (\$64, 8) High consumers 8) \$ 16 package Offer the the low-demand gives demand can be be offered a gives them compatibility consumers package consumers will will not These packages exhibit not Profit must them \$32 offer constraint are at (\$88, are at willing (\$88, 12) 12) (since \$32 least consumer \$32 to \$120 consumers 12 a package of surplus to pay pay consumer up \$120 - up to to \$ = \$120 surplus for 88) buy 88) buy the the (\$88, (\$88, 12) from quantity each each discounting: high- highdemand consumer pay \$7.33 is is per unit they And 12) for And profit entry they of entry they will plus drinks will buy buy this package from demand if if no this since they no other and each other each low-demand \$40 entry entry plus are plus are 8 willing drinks for to for to pay \$40 (\$88 (\$88-- \$64 pay package low-demand x \$4) \$4) \$64 \$32 is is available pay \$8 consumer is only only \$72 is \$72 for for 12 \$32 12 \$32 (\$64 (\$64-- 8x\$4) drinks 8 \$32 \$64 \$40 \$32 \$8 4 \$24 MC 4 MC \$32 \$16 \$32 \$ Industrial 14

15 The example again A high-demand consumer will pay High-Demand up to \$87.50 for The Can entry monopolist the and clubowner reducing 7 drinks does Low-Demand better by So buying the (\$59.50, do 7) package do even the gives him \$28 consumer surplus number of units offered better than to low-demand this? So entry plus 12 drinks can be consumers sold for \$92 since (\$120 - this 28 = allows \$92) him to increase \$ Profit from each the (\$92, charge 12) package to high-demand is \$44: an increase of \$4 consumers per Suppose each low-demand consumer is offered 7 drinks Each consumer will pay up to \$ \$59.50 for entry and 7 drinks 16 Yes! Profit 12 Yes! Reduce from each the (\$59.50, the number7) consumer package of of units is units offered \$31.50: to a reduction to each each \$28 of \$0.50 per consumer low-demand consumer \$87.50 \$44\$92 \$59.50 \$ MC 4 MC \$28\$48 \$ Industrial 15

16 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 golf and country clubs Take our example again suppose that there are N l low-income consumers and N h high-income consumers Industrial 16

17 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 \$31.50xN l + \$44xN h Now suppose only high-demand consumers are served then a (\$120, 12) package can be offered profit is \$72xN h Is it profitable to serve both types? Only if \$31.50xN l + \$44xN h > \$72xN h 31.50N l > 28N h This requires that N h < N l 28 = There should not be too high a proportion of high-demand consumers Industrial 17

18 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 Industrial 18

19 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 Industrial 19

20 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 Industrial 20

21 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 Illustrate with a simple example monopolist has constant marginal costs of c per unit two types of consumers, with the type being identifiable 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 Industrial 21

22 An example Type Type 1 Demand: P = A BQ BQ 1 Type 1 Type 2 Demand: P = A BQ BQ 2 2 \$ A 1 (A 1 +c)/2 MR 1 = A 1-2BQ 1 MC = c Q 1 = (A 1 - c)/2b Since A 1 > A 2 Type 1 consumers are charged a P 1 = (A 1 + c)/2 higher price than \$ Type 2 consumers A 2 (A 2 +c)/2 MR 2 = A 2-2BQ 2 MC = c Q 2 = (A 2 - c)/2b P 2 = (A 2 + c)/2 c MC c MC MR 1 MR 2 (A 1 -c)/2b A 1 /B (A 2 -c)/2b A 2 /B Industrial 22

23 Third-degree price discrimination (cont.) What happens if marginal costs are not constant? The same principles apply marginal revenue equalized across consumer types marginal revenue equal to marginal cost where marginal cost is measured at aggregate output Consider an example Industrial 23

24 Two markets Market 1: P = 20 - Q 1 Market 2: P = 16-2Q 2 MR 1 = 20-2Q 1 The example Now Now calculate aggregate marginal revenue MR 2 = 16-4Q 2 Note Note that that this this applies applies Invert these to give Q as a function only only for for of prices prices MR: less less than than Q 1 = 10 - MR/2 \$16 \$16 MC = 2Q Q 2 = 4 - MR/4 The MC = MR 2Q = 56/3-4Q/3 The consumers with with So aggregate less marginal revenue is less elastic demand are are Q = 5.6 Q = Q 1 + Q 2 = charged 14-3MR/4 higher prices MR = \$11.20 Invert this to give marginal revenue: Q 1 = 4.4 and Q 2 = 1.2 MR = 56/3-4Q/3 for MR < \$16 P 1 = \$15.60 and P 2 = \$13.60 MR = 20-2Q for MR > \$16 Industrial 24

25 Third-degree price discrimination (cont.) A general rule characterizes third-degree price discrimination Recall the formula for marginal revenue in market i: MR i = P i (1-1/η i ) where η 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 so MR 1 = MR 2 are always higher P 1 (1-1/ η 1 ) = P 2 (1-1/ η 2 ) in in markets where P (1-1/ η ) demand is is inelastic 1 2 = P 2 (1-1/ η 1 ) Industrial 25

26 Price Discrimination and Welfare Does price discrimination reduce welfare? First- and second- degree: not necessarily because output is at or near to the efficient level Third-degree is less clear monopolist restricts output in the markets supplied but markets may be served that would otherwise be left unsupplied A necessary condition for third-degree price discrimination not to reduce welfare is that it leads to an increase in output Industrial 26

27 Public Policy Uneven Robinson-Patman makes price discrimination illegal if it is intended to create a monopoly One defense is if discriminatory prices are intended to meet the competition Enforcement has been spotty weak in recent years but note the pharmaceutical case private actions are possible: see International restrictions also exist anti-dumping regulations these are currently pursued very actively Industrial 27

28 Monopoly and Product Quality Firms can, and do, produce goods of different qualities Quality then is an important strategic variable The choice of product quality by a monopolist is determined by its ability to generate profit Focus for the moment on a monopolist producing a single good what quality should it have? determined by consumer attitudes to quality prefer high to low quality willing to pay more for high quality but this requires that the consumer recognizes quality also some are willing to pay more than others for quality Industrial 28

29 Demand and Quality We might think of individual demand as being of the form Q i = 1 if P i < R i (Z) and = 0 otherwise for each consumer i Each consumer buys exactly one unit so long as price is less than her reservation price the reservation price is affected by product quality Z Assume that consumers vary in their reservation prices Then aggregate demand is of the form P = P(Q, Z) An increase in product quality increases demand Industrial 29

30 Demand and quality (cont.) Begin with with a particular demand curve for for a good good of of quality Z 1 Price 1 Then Then an an increase in in product R 1 (Z 2 ) P(Q, Z Suppose that quality that an an increase from from Z 1 to in in quality If If the the price price is is P 1 and increases 1 and the the product the 1 to Z 2 rotates 2 ) 2 the the demand quality the curve around willingness is is Z 1 then 1 then all all consumers the to with to pay with reservation pay of the quantity axis of axis as as follows P 2 inframarginal consumers more R prices greater P 1 will 1 will buy buy the the good 1 (Z 1 ) than than that that of of the the marginal good P These 1 are This are This the is the is the consumer the Q 1 can 1 can now now be be inframarginal marginal sold sold for for the the higher consumers consumer price price P 2 2 P(Q, Z 1 ) Q 1 Industrial 30

31 Demand and quality (cont.) Price R 1 (Z 1 ) P 2 P 1 P(Q, Z 1 ) Suppose instead that that an an increase Then Then an an increase in in product quality quality increases from from the the Z 1 to 1 to Z 2 rotates 2 willingness to the to the pay pay demand of of marginal curve around consumers the the price price more axis axis as as follows than than that that of of the the inframarginal consumers Once again quantity Q 1 1 can can now now be be sold sold for for a higher price price P 2 2 P(Q, Z 2 ) Q 1 Industrial 31

32 Demand and quality (cont.) The monopolist must choose both price (or quantity) quality Two profit-maximizing rules marginal revenue equals marginal cost on the last unit sold for a given quality marginal revenue from increased quality equals marginal cost of increased quality for a given quantity This can be illustrated with a simple example: P = Z(θ - Q) where Z is an index of quality Industrial 32

33 P = Z(θ - Q) Demand and quality: an example Assume that marginal cost of output is zero: MC(Q) = 0 Cost of quality is D(Z) = αz 2 Marginal cost of quality = dd(z)/d(z) This This means that that quality is = 2αZ is costly and and becomes The firm s profit is: increasingly costly π(q, Z) =P.Q - D(Z) = Z(θ - Q)Q - αz 2 The firm chooses Q and Z to maximize profit. Take the choice of quantity first: this is easiest. Marginal revenue = MR = Zθ - 2ZQ MR = MC Zθ - 2ZQ = 0 Q* = θ/2 P* = Zθ/2 Industrial 33

34 The example continued Total revenue = P*Q* = (Zθ/2)x(θ/2) = Zθ 2 /4 So marginal revenue from increased quality is MR(Z) = θ 2 /4 Marginal cost of quality is MC(Z) = 2αZ Equating MR(Z) = MC(Z) then gives Z* = θ 2 /8α Does the monopolist produce too high or too low quality? Is it possible that quality is too high? Only in particular constrained circumstances. Industrial 34

35 The Multiplant Monopolist A monopolist rarely produces all output in one plant how should production be allocated across plants? this is especially important if different plants have different costs To maximize profit set MR = MC on the last unit produced But with several plants what is MC? First case: marginal costs constant within a plant but varying across plants each plant has a capacity constraint Industrial 35

36 Price The multiplant monopolist (cont.) MC 1 Plant Plant 3 has has marginal cost Suppose cost MC MC 3 that and that there there are 3 and are Plant three three possible plants. Plant 2 has has marginal capacity q 3 MCcost 3 Maximize Arrange them 3 them in in order cost MC MC 2 and profit 2 and by by Plant of of their their marginal costs Plant 1 has has marginal equating capacity marginal costs q cost 2 cost cost MC cost 2 MC MC 1 and and 2 1 and and marginal revenue Produce output Q* Q* using plant capacity plant q and and plant plant Plant Plant 3 is is not not operated (or (or introduced) MR q 1 Q* q 1 + q 2 Industrial 36

37 The multiplant monopolist (cont.) What happens if marginal costs are not constant? Output allocation operate plants such that marginal cost is equal on the last unit produced in each plant Why? If not, then cost can be reduced by reallocating output between plants For example: suppose MC 1 = \$10 and MC 2 = \$15 Reducing output of plant 2 by one unit and increasing output of plant 1 by one unit reduces total costs Industrial 37

38 Suppose MC MC 1 = 1 αq αq 1 and 1 and MC MC 2 = 2 βq βq 2 2 An Example q 1 = 1 MC/α ;; q 2 = 2 MC/β \$ Allocate output to to the the two two plants to to equate marginal costs costs MC 2 = βq 2 MC 1 = αq 1 \$ Q =q =q q 2 = 2 MC(α + β)/αβ Maximize profit MC MC by by = setting Qαβ/ (α (α marginal + β) β) revenue equal to to marginal cost cost MC 1 + MC 2 MR q 2 * q 1 * Q* Industrial 38

39 Industrial 39

40 Demand and quality (cont.) Price Z 2 θ Z 1 θ P 2 = Z 2 θ/2 P 1 = Z 1 θ/2 P(Q, Z 2 ) MR(Z 2 ) MR(Z 1 ) When quality is is Z 2 2 price price is is When Z quality 2 θ/2 2 θ/2 How How is does is does Z 1 1 increased quality price price is is affect demand? Z 1 θ/2 1 θ/2 P(Q,Z 1 ) θ/2 Q* θ Industrial 40

41 Demand and quality (cont.) Price Z 2 θ Z 1 θ P 2 = Z 2 θ/2 P 1 = Z 1 θ/2 So So an an increase is is quality from from Social Z 1 to 1 to Zsurplus 2 increases 2 at at quality surplus Z 2 2 is by is this by this this this area area area area minus minus quality the the increase in costs in quality costs costs costs An An increase in in quality from from Z 1 to 1 to Z 2 increases 2 Social revenue surplus by by this this at at area quality area Z 1 1 is is this this area area minus quality costs costs The increase is total surplus is greater than the increase in profit. The monopolist produces too little quality θ/2 Q* θ Industrial 41

42 Demand and quality: an alternative The The increase in in Price social surplus The The increase in is in Assume that that an an increase quality is this this area increases area The increase quality in from total minus from Z 1 to the 1 to profit the cost by cost of by this this area of increased area Z 2 rotates 2 the the demand quality surplus is less than minus the the cost cost of of the increase function in profit. as as follows increased quality The monopolist produces Further assume that too much quality that the the firm firm is is constrained to to produce output Q P(Q,Z 2 ) Exporters subject to to quotas P(Q,Z This 1 ) This may may arise arise as as a result tend tend to to export high high quality Q of of an an export quota or or goods other restriction on on output Industrial 42

43 Demand and quality Derivation of aggregate demand Order consumers by their reservation prices Aggregate individual demand horizontally Price Industrial 43

44 Market Market 1 Market Market 2 Aggregate \$ \$ \$ \$20 \$20 MC \$15.60 \$16 \$13.60 \$16 \$11.20 D 1 MR D MR 1 +MR 2 1 MR Industrial 44

45 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 piece rates in factories have to be accompanied by strict quality inspection encouragement to buy in bulk must offer a price discount Industrial 45

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