Price Discrimination 1

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1 Price Discrimination 1

2 Introduction Price Discrimination describes strategies used by firms to extract surplus from customers Examples of price discrimination presumably profitable should affect market efficiency: not necessarily adversely is price discrimination necessarily bad even if not seen as fair? 2

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

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 easier in some markets than others: e.g tax consultants, doctors arbitrage: prevent consumers who are charged a low price from reselling to consumers who are charged a high price prevent re-importation of prescription drugs to the United States 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 4

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 the number of different economy fares charged can be very large indeed! early-bird specials; first-runs of movies 5

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 6

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 7

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 8

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 Q = Q U + Q E = 15 P/2 for P < $24 At these prices only the US market is active Now both markets are active 9

10 The example (cont.) Invert the direct demands P = 36 4Q for Q < 3 P = 30 2Q for Q > 3 Marginal revenue is MR = 36 8Q for Q < 3 MR = 30 4Q for Q < 3 Set MR = MC Q = 6.5 $/unit MR Price from the demand curve P = $ Demand MC 15 10

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 11

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 12

13 The example: price discrimination 2 Demand in the US: P U = 36 4Q U $/unit 36 Marginal revenue: 20 MR = 36 8Q U MC = 4 4 MR Demand MC Equate MR and MC Q U = 4 Price from the demand curve P U = $

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

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 15

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 16

17 The example again Applying this procedure assuming that MC = Q/2 gives: (a) United States (b) Europe (c) Aggregate Price 40 Price 40 Price DU DE D 10 MRU 10 MRE 10 MR MC

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 18

19 The example again Applying this procedure assuming that MC = Q/2 gives: Price 40 (a) United States Price 40 (b) Europe Price 40 (c) Aggregate 30 D U MRU MR E 0 D E MR 10 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 20

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 21

22 Product differentiation and price discrimination Suppose that demand in each submarket is P i = A i B i Q i Assume that marginal cost in each submarket is MC i = c i Finally, suppose that consumers in submarket i do not purchase from submarket j Equate marginal revenue with marginal cost in each submarket It is highly unlikely that the difference in prices will equal the difference in marginal costs A i 2B i Q i = c i Q i = (A i c i )/2B i P i = (A i + c i )/2 P i P j = (A i A j )/2 + (c i c j )/2 22

23 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

24 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

25 Third-degree rice discrimination and welfare Does third-degree price discrimination reduce welfare? not the same as being fair relates solely to efficiency so consider impact on total surplus 25

26 Price discrimination and welfare Suppose that there are two markets: weak and strong Price The discriminatory price in the weak market is P 1 Price The discriminatory price in the strong market is P 2 D 1 The maximum gain in surplus in the weak market is G The uniform price in both market is P U P 2 MR 2 D 2 The minimum loss of surplus in the strong market is L P U P U P 1 G L MR 1 MC MC ΔQ 1 ΔQ 2 26

27 Price discrimination and welfare Price D 1 Price Price discrimination cannot cannot increase surplus surplus unless unless it it increases aggregate output output Price P 2 MR 2 D 2 P U P U P 1 MR 1 G L MC MC ΔQ 1 ΔQ 2 It follows that ΔW < G L = (P U MC)ΔQ 1 + (P U MC)ΔQ 2 = (P U MC)(ΔQ 1 + ΔQ 2 ) 27

28 Price discrimination and welfare 2 Previous analysis assumes that the same markets are served with and without price discrimination This may not be true uniform price is affected by demand in weak markets firm may then prefer not to serve such markets without price discrimination price discrimination may open up weak markets The result can be an increase in aggregate output and an increase in welfare 28

29 New markets: an example Demand in North is P N = 100 Q N ; in South is P S = Q S Marginal cost to supply either market is $20 North South Aggregate $/unit $/unit $/unit Demand MC MC MC MR 29

30 New Markets: the example 2 Aggregate demand is P = (1 + )50 Q/2 provided that both markets are served Equate MR and MC to get equilibrium output Q A = (1 + )50-20 Get equilibrium price from aggregate demand P = $/unit P Aggregate Demand MC Q A MR 30

31 New Markets: the example 3 Now consider the impact of a reduction in $/unit Aggregate Aggregate demand changes Marginal revenue changes It is no longer the case that both markets are served P N Demand The South market is dropped Price in North is the monopoly price for that market MR MR' MC D' 31

32 The example again Previous illustration is too extreme MC cuts MR at two points So there are potentially two equilibria with uniform pricing At Q 1 only North is served at the monopoly price in North At Q 2 both markets are served at the uniform price P U Switch from Q 1 to Q 2 : decreases profit by the red area increases profit by the blue area P N P U $/unit Aggregate Demand MC MR If South demand is low enough or MC high enough serve only North Q 1 Q 2 32

33 Price discrimination and welfare Again In this case only North is served with uniform pricing But MC is less than the reservation price P R in South So price discrimination will lead to South being supplied Price discrimination leaves surplus unchanged in North But price discrimination generates profit and consumer surplus in South P N P R $/unit Aggregate Demand MC MR So price discrimination increases welfare Q 1 33

34 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 34

35 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 35

36 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 36

37 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 37

38 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 38

39 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 39

40 Two part pricing 3 This example can be illustrated as follows: Price (a) Old Customers (b) Young Customers (c) Old/Young Pair of Customers Price Price Vo a V o V y e d b g f Vo+V y + c 4 2 h i c k j MC MR V o V y V o +V y 2 - c Vo + V y Linear pricing leaves each type of consumer with consumer surplus 40

41 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 41

42 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 42

43 Two-Part Pricing Set Set the the unit unit price price equal to to marginal cost cost This This gives gives consumer surplus of of (V (V i - i -c) c) 2 2 /2 /2 Set Set the the entry entry charge to to (V (V i - i -c) c) 2 2 /2 /2 $/unit V i c The entry charge Using two-part converts consumer pricing surplus increases into the the profit monopolist s profit MR V i - c V i MC Profit from each pair of Old and Young now d = [(V o c) 2 + (V y c) 2 ]/2 43

44 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: 44

45 Block pricing 2 $ Old $ Young V o Willingness to pay of each Old customer supplied to each Old customer V y Willingness to pay of each Young customer supplied to each Young customer c MC c MC Q o V o WTP o = (V o c) 2 /2 + (V o c)c = (V o2 c 2 )/2 Q y V y WTP y = (V y c) 2 /2 + (V y c)c = (V y2 c 2 )/2 45

46 Block pricing 3 How to implement this policy? 46

47 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 47

48 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 48

49 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 allows deception by buyers Use quantity discounting 49

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

51 Second degree price discrimination 5 $ 16 A high-income consumer will pay High-Income up to $87.50 for entry and 7 So buying the drinks ($59.50, 7) package gives him $28 consumer surplus The monopolist does better by reducing the number of units offered Can to low-income the clubowner allows do even him to increase consumers since this the better charge than to this? high-income consumers So entry plus 12 drinks can be sold Profit from for each $92 ($120 ($92, owner - 12) 28 = $92) do $ even package is $44: an increase of $4 per consumer 12 $28 Suppose each low-income consumer is offered 7 drinks Each consumer will pay up to Low-Income $59.50 for entry and 7 drinks Yes! Yes! Profit Reduce from each the the number ($59.50, 7) of package of units units offered is $31.50: to to a each each reduction low-income of $0.50 per consumer consumer $87.50 $44$92 $59.50 $ MC 4 MC $28 $48 $

52 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 highdemand 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 52

53 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 53

54 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 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 54

55 Non-linear pricing and welfare 1 Pricing policy affects distribution of surplus output of the firm First is welfare neutral Second affects welfare Does it increase social welfare? Price discrimination increases social welfare of group i if it increases quantity supplied to group i Price c Demand Total Surplus MC Q i Q i Q i (c) 55

56 Non-linear pricing and welfare 2 First-degree price discrimination always increases social welfare extracts all consumer surplus but generates socially optimal output output to group i is Q i (c) this exceeds output with uniform (nondiscriminatory) pricing 56

57 Non-linear pricing and welfare 3 Menu pricing is less straightforward suppose that there are two markets low demand high demand Uniform price is P U Menu pricing gives quantities Q 1s, Q 2 s Welfare loss is greater than L Welfare gain is less than G 57

58 Non-linear pricing and welfare 4 It follows that Price ΔW < G L = (P U MC)ΔQ 1 + (P U MC)ΔQ 2 = (P U MC)(ΔQ 1 + ΔQ 2 ) A necessary condition for seconddegree price discrimination to increase social welfare is that it increases total output Like third-degree price discrimination P U Price L Q l s Q l U MC But second-degree price discrimination is more likely to increase output P U G MC Q h U Q h s 58

59 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 59

60 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? 60

61 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 61

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