1 Price Discrimination

2 Introduction Price Discrimination describes strategies used by firms to extract surplus from customers

3 Mechanisms for Capturing Surplus Market segmentation Non-linear pricing –Two-part pricing –Block pricing Tying and bundling Quality discrimination

4 Feasibility of price discrimination Market power Two problems confront a firm wishing to price discriminate –identification: the firm is able to identify demands of different types of consumer or in separate markets –arbitrage: prevent consumers who are charged a low price from reselling to consumers who are charged a high price The firm then must choose the type of price discrimination –first-degree or personalized pricing –second-degree or menu pricing –third-degree or group pricing

5 Third-degree price discrimination Consumers differ by some observable characteristic(s) A uniform price is charged to all consumers in a particular group – linear price Different uniform prices are charged to different groups –“kids are free” –subscriptions to professional journals e.g. American Economic Review –Airlines –early-bird specials

6 Third-degree price discrimination 2 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

7 Third degree price discrimination: example Harry Potter volume sold in the United States and Europe Demand: –United States: P U = 36 – 4Q U –Europe: P E = 24 – 4Q E Marginal cost constant in each market –MC = $4

8 The example: no price discrimination Suppose that the same price is charged in both markets Use the following procedure: –calculate aggregate demand in the two markets –identify marginal revenue for that aggregate demand –equate marginal revenue with marginal cost to identify the profit maximizing quantity –identify the market clearing price from the aggregate demand –calculate demands in the individual markets from the individual market demand curves and the equilibrium price

9 The example (cont.) United States: P U = 36 – 4Q U Invert this: Q U = 9 – P/4 for P < $36 Europe: P U = 24 – 4Q E Invert Q E = 6 – P/4 for P < $24 Aggregate these demands Q = Q U + Q E = 9 – P/4 for $36 ≥ P ≥ $24 At these prices only the US market is active Q = Q U + Q E = 15 – P/2 for P < $24 Now both markets are active

10 The example (cont.) Invert the direct demands P = 36 – 4Q for Q < 3 P = 30 – 2Q for Q > 3 $/unit Quantity Marginal revenue is MR = 36 – 8Q for Q < 3 MR = 30 – 4Q for Q < 3 Demand MR Set MR = MC MC Q = 6.5 P = $ Price from the demand curve

11 The example (cont.) Substitute price into the individual market demand curves: Q U = 9 – P/4 = 9 – 17/4 = 4.75 million Q E = 6 – P/4 = 6 – 17/4 = 1.75 million Aggregate profit = (17 – 4)x6.5 = $84.5 million

12 The example: price discrimination The firm can improve on this outcome Check that MR is not equal to MC in both markets –MR > MC in Europe –MR < MC in the US –the firms should transfer some books from the US to Europe This requires that different prices be charged in the two markets Procedure: –take each market separately –identify equilibrium quantity in each market by equating MR and MC –identify the price in each market from market demand

13 The example: price discrimination 2 Demand in the US: P U = 36 – 4Q U $/unit Quantity Demand Marginal revenue: MR = 36 – 8Q U 36 9 MR MC = 4 MC4 Equate MR and MC Q U = 4 Price from the demand curveP U = $

14 The example: price discrimination 3 Demand in the Europe: P E = 24 – 4Q U $/unit Quantity Demand Marginal revenue: MR = 24 – 8Q U 24 6 MR MC = 4 MC4 Equate MR and MC Q E = 2.5 Price from the demand curveP E = $

15 The example: price discrimination 4 Aggregate sales are 6.5 million books –the same as without price discrimination Aggregate profit is (20 – 4)x4 + (14 – 4)x2.5 = $89 million –$4.5 million greater than without price discrimination

16 No price discrimination: non-constant cost The example assumes constant marginal cost How is this affected if MC is non-constant? –Suppose MC is increasing No price discrimination procedure –Calculate aggregate demand –Calculate the associated MR –Equate MR with MC to give aggregate output –Identify price from aggregate demand –Identify market demands from individual demand curves

17 The example again Applying this procedure assuming that MC = Q/2 gives: D U MR U Price (a) United States Quantity D E MR E Price (b) Europe Quantity D MR MC Price (c) Aggregate Quantity

18 Price discrimination: non-constant cost With price discrimination the procedure is –Identify marginal revenue in each market –Aggregate these marginal revenues to give aggregate marginal revenue –Equate this MR with MC to give aggregate output –Identify equilibrium MR from the aggregate MR curve –Equate this MR with MC in each market to give individual market quantities –Identify equilibrium prices from individual market demands

19 The example again Applying this procedure assuming that MC = Q/2 gives: Price (a) United States Quantity D U MR U 4 Price (b) Europe Quantity D E MR E Price (c) Aggregate Quantity MR MC

20 Some additional comments Suppose that demands are linear –price discrimination results in the same aggregate output as no price discrimination –price discrimination increases profit For any demand specifications two rules apply –marginal revenue must be equalized in each market –marginal revenue must equal aggregate marginal cost

21 Third-degree price discrimination 2 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

22 Other mechanisms for price discrimination Impose restrictions on use to control arbitrage –Saturday night stay –no changes/alterations –personal use only (academic journals) –time of purchase (movies, restaurants) Damaged goods Discrimination by location

23 Discrimination by location Suppose demand in two distinct markets is identical –P i = A = BQ i But suppose that there are different marginal costs in supplying the two markets –c j = c i + t Profit maximizing rule: –equate MR with MC in each market as before –  P i = (A + c i )/2; P j = (A + c i + t)/2 –  P j – P i = t/2  c j – c i –difference in prices is not the same as the difference in costs

24 Introduction to Nonlinear Pricing Annual subscriptions generally cost less in total than one-off purchases Buying in bulk usually offers a price discount –these are price discrimination reflecting quantity discounts –prices are nonlinear, with the unit price dependent upon the quantity bought –allows pricing nearer to willingness to pay –so should be more profitable than third-degree price discrimination How to design such pricing schemes? –depends upon the information available to the seller about buyers –distinguish first-degree (personalized) and second-degree (menu) pricing

25 First-degree price discrimination 2 Monopolist can charge maximum price that each consumer is willing to pay Extracts all consumer surplus Since profit is now total surplus, find that first-degree price discrimination is efficient

26 First-degree price discrimination 3 First-degree price discrimination is 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 –no value-creating exchanges are missed

27 First-degree price discrimination 4 The information requirements appear to be insurmountable –but not in particular cases tax accountants, doctors, students applying to private universities But there are pricing schemes that will achieve the same outcome –non-linear prices –two-part pricing as a particular example of non-linear prices charge a quantity-independent fee (membership?) plus a per unit usage charge –block pricing is another bundle total charge and quantity in a package

28 Two-part pricing Jazz club serves two types of customer –Old: demand for entry plus Q o drinks is P = V o – Q o –Young: demand for entry plus Q y drinks is P = V y – Q y –Equal numbers of each type –Assume that V o > V y : Old are willing to pay more than Young –Cost of operating the jazz club C(Q) = F + cQ Demand and costs are all in daily units

29 Two-part pricing 2 Suppose that the jazz club owner applies “traditional” linear pricing: free entry and a set price for drinks –aggregate demand is Q = Q o + Q y = (V o + V y ) – 2P –invert to give: P = (V o + V y )/2 – Q/2 –MR is then MR = (V o + V y )/2 – Q –equate MR and MC, where MC = c and solve for Q to give –Q U = (V o + V y )/2 – c –substitute into aggregate demand to give the equilibrium price –P U = (V o + V y )/4 + c/2 –each Old consumer buys Q o = (3V o – V y )/4 – c/2 drinks –each Young consumer buys Q y = (3V y – V o )/4 – c/2 drinks –profit from each pair of Old and Young is  U = (V o + V y – 2c) 2 / 8

30 Two part pricing 3 This example can be illustrated as follows: Price Quantity V o V o Price Quantity V y V y Price Quantity V o V o +V y MC MR (a) Old Customers(b) Young Customers(c) Old/Young Pair of Customers V o +V y 2 - c c V o +V y 4 + c 2 h i j k a b d e f g Linear pricing leaves each type of consumer with consumer surplus

31 Two part pricing 4 Jazz club owner can do better than this Consumer surplus at the uniform linear price is: –Old: CS o = (V o – P U ).Q o /2 = (Q o ) 2 /2 –Young: CS y = (V y – P U ).Q y /2 = (Q y ) 2 /2 So charge an entry fee (just less than): –E o = CS o to each Old customer and E y = CS y to each Young customer check IDs to implement this policy –each type will still be willing to frequent the club and buy the equilibrium number of drinks So this increases profit by E o for each Old and E y for each Young customer

32 Two part pricing 5 The jazz club can do even better –reduce the price per drink –this increases consumer surplus –but the additional consumer surplus can be extracted through a higher entry fee Consider the best that the jazz club owner can do with respect to each type of consumer

33 Two-Part Pricing $/unit Quantity ViVi ViVi MR MC c Set the unit price equal to marginal cost Set the unit price equal to marginal cost This gives consumer surplus of (V i - c) 2 /2 This gives consumer surplus of (V i - c) 2 /2 The entry charge converts consumer surplus into profit V i - c Set the entry charge to (V i - c) 2 /2 Set the entry charge to (V i - c) 2 /2 Profit from each pair of Old and Young now  d = [(V o – c) 2 + (V y – c) 2 ]/2 Using two-part pricing increases the monopolist’s profit Using two-part pricing increases the monopolist’s profit

34 Block pricing There is another pricing method that the club owner can apply –offer a package of “Entry plus X drinks for $Y” To maximize profit apply two rules –set the quantity offered to each consumer type equal to the amount that type would buy at price equal to marginal cost –set the total charge for each consumer type to the total willingness to pay for the relevant quantity Return to the example:

35 Block pricing 2 Old $ Quantity VoVo VoVo Young $ Quantity VyVy VyVy MC cc Quantity supplied to each Old customer Quantity supplied to each Young customer QoQo QyQy Willingness to pay of each Old customer Willingness to pay of each Young customer WTP o = (V o – c) 2 /2 + (V o – c)c = (V o 2 – c 2 )/2 WTP y = (V y – c) 2 /2 + (V y – c)c = (V y 2 – c 2 )/2

36 Block pricing 3 How to implement this policy?

37 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 Take a specific example –P h = 16 – Q h –P l = 12 – Q l –MC = 4

38 Second-degree price discrimination 2 First-degree price discrimination requires : –High Income: entry fee $72 and $4 per drink or entry plus 12 drinks for a total charge of $120 –Low Income: entry fee $32 and $4 per drink or entry plus 8 drinks for total charge of $64 This will not work –high income types get no consumer surplus from the package designed for them but get consumer surplus from the other package –so they will pretend to be low income even if this limits the number of drinks they can buy Need to design a “menu” of offerings targeted at the two types

39 Second-degree price discrimination 3 The seller has to compromise Design a pricing scheme that makes buyers –reveal their true types –self-select the quantity/price package designed for them 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 Use quantity discounting

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

41 Second degree price discrimination 5 High-Income Low-Income $ Quantity MC4 12 $ Can the club- owner do even better than this? Can the club- owner do even better than this? 8 Yes! Reduce the number of units offered to each low-income consumer Yes! Reduce the number of units offered to each low-income consumer Suppose each low-income consumer is offered 7 drinks 7 Each consumer will pay up to $59.50 for entry and 7 drinks $59.50 Profit from each ($59.50, 7) package is $31.50: a reduction of $0.50 per consumer $31.50 A high-income consumer will pay up to $87.50 for entry and 7 drinks 7 $87.50 $28 So buying the ($59.50, 7) package gives him $28 consumer surplus So entry plus 12 drinks can be sold for $92 ($ = $92) $92 $28 Profit from each ($92, 12) package is $44: an increase of $4 per consumer $44 $48 The monopolist does better by reducing the number of units offered to low-income consumers since this allows him to increase the charge to high-income consumers

42 Second-degree price discrimination 6 Will the monopolist always want to supply both types of consumer? There are cases where it is better to supply only high- demand types –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

43 Second-degree price discrimination 7 Suppose both types of consumer are served –two packages are offered ($57.50, 7) aimed at low-income and ($92, 12) aimed at high-income –profit is $31.50xN l + $44xN h Now suppose only high-income 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 < = There should not be “too high” a fraction of high-demand consumers

44 Second-degree price discrimination 8 Characteristics of second-degree price discrimination –extract all consumer surplus from the lowest-demand group –leave some consumer surplus for other groups –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

45 Tying Tying is a seller’s conditioning the purchase of one product on the purchase of another –Technological ties Printer cartridges –Contractual ties Car dealer and car parts Why tying?

46 Quality Discrimination Why is Quality Discrimination a form of Price Discrimination? –First / business class airfare vs economy class Reduction in quality of the lower-quality good to reduce the incentive of people with high willingness to pay to switch from the high-quality good when the firm increases its price –“Damaged goods”