Price Discrimination and Monopoly Chapter 5: Price Discrimination and Monopoly

Chapter 5: Price Discrimination and Monopoly Introduction Prescription drugs are cheaper in Canada than the United States Textbooks are generally cheaper in Britain than the United States Examples of price discrimination presumably profitable should affect market efficiency: not necessarily adversely is price discrimination necessarily bad – even if not seen as “fair”? Chapter 5: Price Discrimination and Monopoly

Feasibility of price discrimination 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 Chapter 5: Price Discrimination and Monopoly

Introduction to First-Degree Price Discrimination 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 Chapter 5: Price Discrimination and Monopoly

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 Chapter 5: Price Discrimination and Monopoly

First-degree price discrimination 3 Suppose that you own five antique cars Market research shows there are collectors of different types keenest is willing to pay $10,000 for a car, second keenest $8,000, third keenest $6,000, fourth keenest $4,000, fifth keenest $2,000 sell the first car at $10,000 sell the second car at $8,000 sell the third car to at $6,000 and so on total revenue $30,000 Contrast with linear pricing: all cars sold at the same price set a price of $6,000 sell three cars total revenue $18,000 Chapter 5: Price Discrimination and Monopoly

First-degree price discrimination 4 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 Chapter 5: Price Discrimination and Monopoly

First-degree price discrimination 5 The information requirements appear to be insurmountable but not in particular cases tax accountants, doctors, students applying to private universities No arbitrage is less restrictive but potentially a problem 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 Chapter 5: Price Discrimination and Monopoly

Chapter 5: Price Discrimination and Monopoly Two-part pricing Jazz club serves two types of customer Old: demand for entry plus Qo drinks is P = Vo – Qo Young: demand for entry plus Qy drinks is P = Vy – Qy Equal numbers of each type Assume that Vo > Vy: 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 Chapter 5: Price Discrimination and Monopoly

Chapter 5: Price Discrimination and Monopoly 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 = Qo + Qy = (Vo + Vy) – 2P invert to give: P = (Vo + Vy)/2 – Q/2 MR is then MR = (Vo + Vy)/2 – Q equate MR and MC, where MC = c and solve for Q to give QU = (Vo + Vy)/2 – c substitute into aggregate demand to give the equilibrium price PU = (Vo + Vy)/4 + c/2 each Old consumer buys Qo = (3Vo – Vy)/4 – c/2 drinks each Young consumer buys Qy = (3Vy – Vo)/4 – c/2 drinks profit from each pair of Old and Young is U = (Vo + Vy – 2c)2 Chapter 5: Price Discrimination and Monopoly

Chapter 5: Price Discrimination and Monopoly Two part pricing 3 This example can be illustrated as follows: Price Quantity V o y + MC MR (a) Old Customers (b) Young Customers (c) Old/Young Pair of Customers +V 2 - c c 4 h i j k a b d e f g Linear pricing leaves each type of consumer with consumer surplus Chapter 5: Price Discrimination and Monopoly

Chapter 5: Price Discrimination and Monopoly Two part pricing 4 Jazz club owner can do better than this Consumer surplus at the uniform linear price is: Old: CSo = (Vo – PU).Qo/2 = (Qo)2/2 Young: CSy = (Vy – PU).Qy/2 = (Qy)2/2 So charge an entry fee (just less than): Eo = CSo to each Old customer and Ey = CSy 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 Eo for each Old and Ey for each Young customer Chapter 5: Price Discrimination and Monopoly

Chapter 5: Price Discrimination and Monopoly 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 Chapter 5: Price Discrimination and Monopoly

Two-Part Pricing Using two-part pricing increases the monopolist’s profit $/unit Vi The entry charge converts consumer surplus into profit Set the unit price equal to marginal cost This gives consumer surplus of (Vi - c)2/2 c MC MR Set the entry charge to (Vi - c)2/2 Vi - c Vi Quantity Profit from each pair of Old and Young now d = [(Vo – c)2 + (Vy – c)2]/2 Chapter 5: Price Discrimination and Monopoly

Chapter 5: Price Discrimination and Monopoly 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: Chapter 5: Price Discrimination and Monopoly

Block pricing 2 Old Young $ $ Willingness to pay of each Old customer Willingness to pay of each Young customer Vo Quantity supplied to each Old customer Quantity supplied to each Young customer Vy c MC c MC Qo Vo Qy Vy Quantity Quantity WTPo = (Vo – c)2/2 + (Vo – c)c = (Vo2 – c2)/2 WTPy = (Vy – c)2/2 + (Vy – c)c = (Vy2 – c2)/2 Chapter 5: Price Discrimination and Monopoly

Chapter 5: Price Discrimination and Monopoly Block pricing 3 How to implement this policy? card at the door give customers the requisite number of tokens that are exchanged for drinks Chapter 5: Price Discrimination and Monopoly

Chapter 5: Price Discrimination and Monopoly A final comment One final point average price that is paid by an Old customer = (Vo2 – c2)/2(Vo – c) = (Vo + c)/2 average price paid by a Young customer = (Vy2 – c2)/2(Vo – c) = (Vy + c)/2 identical to the third-degree price discrimination (linear) prices but the profit outcome is much better with first-degree price discrimination. Why? consumer equates MC of last unit bought with marginal benefit with linear pricing MC = AC (= average price) with first-degree price discrimination MC of last unit bought is less than AC (= average price) so more is bought Chapter 5: Price Discrimination and Monopoly

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 Chapter 5: Price Discrimination and Monopoly

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 Chapter 5: Price Discrimination and Monopoly

Third degree price discrimination: example Harry Potter volume sold in the United States and Europe Demand: United States: PU = 36 – 4QU Europe: PE = 24 – 4QE Marginal cost constant in each market MC = $4 Chapter 5: Price Discrimination and Monopoly

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 Chapter 5: Price Discrimination and Monopoly

The example (npd cont.) United States: PU = 36 – 4QU Invert this: QU = 9 – P/4 for P < $36 Europe: PU = 24 – 4QE Invert At these prices only the US market is active QE = 6 – P/4 for P < $24 Aggregate these demands Now both markets are active Q = QU + QE = 9 – P/4 for $36 < P < $24 Q = QU + QE = 15 – P/2 for P < $24 Chapter 5: Price Discrimination and Monopoly

Chapter 5: Price Discrimination and Monopoly The example (npd cont.) Invert the direct demands $/unit P = 36 – 4Q for Q < 3 36 P = 30 – 2Q for Q > 3 Marginal revenue is 30 MR = 36 – 8Q for Q < 3 17 MR = 30 – 4Q for Q < 3 MR Demand Set MR = MC MC Q = 6.5 6.5 15 Quantity Price from the demand curve P = $17 Chapter 5: Price Discrimination and Monopoly

Chapter 5: Price Discrimination and Monopoly The example (npd cont.) Substitute price into the individual market demand curves: QU = 9 – P/4 = 9 – 17/4 = 4.75 million QE = 6 – P/4 = 6 – 17/4 = 1.75 million Aggregate profit = (17 – 4)x6.5 = $84.5 million Chapter 5: Price Discrimination and Monopoly

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 Chapter 5: Price Discrimination and Monopoly

The example: price discrimination 2 $/unit Demand in the US: 36 PU = 36 – 4QU Marginal revenue: 20 MR = 36 – 8QU Demand MR MC = 4 4 MC Equate MR and MC 4 9 Quantity QU = 4 Price from the demand curve PU = $20 Chapter 5: Price Discrimination and Monopoly

The example: price discrimination 3 $/unit Demand in the Europe: 24 PE = 24 – 4QU Marginal revenue: 14 MR = 24 – 8QU Demand MR MC = 4 4 MC Equate MR and MC 2.5 6 Quantity QE = 2.5 Price from the demand curve PE = $14 Chapter 5: Price Discrimination and Monopoly

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 Chapter 5: Price Discrimination and Monopoly

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 Chapter 5: Price Discrimination and Monopoly

Chapter 5: Price Discrimination and Monopoly The example again Applying this procedure assuming that MC = 0.75 + Q/2 gives: 5 10 20 30 40 D U MR 17 4.75 Price (a) United States Quantity 5 10 20 30 40 D E MR 1.75 17 Price (b) Europe Quantity 5 10 15 20 30 40 D MR MC 24 6.5 17 Price (c) Aggregate Quantity Chapter 5: Price Discrimination and Monopoly

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 Chapter 5: Price Discrimination and Monopoly

Chapter 5: Price Discrimination and Monopoly The example again Applying this procedure assuming that MC = 0.75 + Q/2 gives: Price (a) United States Quantity 5 10 20 30 40 D U MR 4 Price (b) Europe Quantity 4 5 10 20 30 40 D E MR 1.75 14 Price (c) Aggregate Quantity 5 10 15 20 30 40 MR MC 24 6.5 17 4 Chapter 5: Price Discrimination and Monopoly

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 Chapter 5: Price Discrimination and Monopoly

Price discrimination and elasticity Suppose that there are two markets with the same MC MR in market i is given by MRi = Pi(1 – 1/hi) where hi is (absolute value of) elasticity of demand From rule 1 (above) MR1 = MR2 so P1(1 – 1/h1) = P2(1 – 1/h2) which gives Price is lower in the market with the higher demand elasticity P1 (1 – 1/2) 12 – 1 = = 12 – 2 P2 (1 – 1/1) Chapter 5: Price Discrimination and Monopoly

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 Chapter 5: Price Discrimination and Monopoly

Product differentiation and price discrimination Suppose that demand in each submarket is Pi = Ai – BiQi Assume that marginal cost in each submarket is MCi = ci Finally, suppose that consumers in submarket i do not purchase from submarket j “I wouldn’t be seen dead in Coach!” “I never buy paperbacks.” 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 Ai – 2BiQi = ci  Qi = (Ai – ci)/2Bi  Pi = (Ai + ci)/2  Pi – Pj = (Ai – Aj)/2 + (ci – cj)/2 Chapter 5: Price Discrimination and Monopoly

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) “Crimp” the product to make lower quality products Mathematica® Discrimination by location Chapter 5: Price Discrimination and Monopoly

Discrimination by location Suppose demand in two distinct markets is identical Pi = A = BQi But suppose that there are different marginal costs in supplying the two markets cj = ci + t Profit maximizing rule: equate MR with MC in each market as before  Pi = (A + ci)/2; Pj = (A + ci + t)/2  Pj – Pi = t/2  cj – ci difference in prices is not the same as the difference in prices Chapter 5: Price Discrimination and Monopoly

Third-degree price 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 Chapter 5: Price Discrimination and Monopoly

Price discrimination and welfare Suppose that there are two markets: “weak” and “strong” The discriminatory price in the strong market is P2 The discriminatory price in the weak market is P1 Price Price D2 The minimum loss of surplus in the strong market is L The maximum gain in surplus in the weak market is G The uniform price in both market is PU MR2 D1 P2 PU PU G L P1 MR1 MC MC ΔQ1 Quantity ΔQ2 Quantity Chapter 5: Price Discrimination and Monopoly

Price discrimination and welfare cannot increase surplus unless it increases aggregate output D1 MR1 D2 MR2 MC P1 P2 ΔQ1 ΔQ2 Price Quantity PU G L It follows that ΔW < G – L = (PU – MC)ΔQ1 + (PU – MC)ΔQ2 = (PU – MC)(ΔQ1 + ΔQ2) Chapter 5: Price Discrimination and Monopoly

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 Chapter 5: Price Discrimination and Monopoly

New markets: an example Demand in “North” is PN = 100 – QN ; in “South” is PS = 100 - QS Marginal cost to supply either market is $20 North South Aggregate $/unit $/unit $/unit 100 100 Demand MC MC MC MR Quantity Quantity Quantity Chapter 5: Price Discrimination and Monopoly

New Markets: the example 2 Aggregate demand is P = (1 + )50 – Q/2 provided that both markets are served $/unit Aggregate Quantity MC Demand MR Equate MR and MC to get equilibrium output QA = (1 + )50 - 20 Get equilibrium price from aggregate demand P = 35 + 25 P QA Chapter 5: Price Discrimination and Monopoly

New Markets: the example 3 $/unit Aggregate Quantity MC Demand MR Now consider the impact of a reduction in  Aggregate demand changes Marginal revenue changes PN It is no longer the case that both markets are served The South market is dropped D' Price in North is the monopoly price for that market MR' Chapter 5: Price Discrimination and Monopoly

Chapter 5: Price Discrimination and Monopoly The example again Previous illustration is too extreme Quantity $/unit Aggregate MC Demand MR MC cuts MR at two points So there are potentially two equilibria with uniform pricing At Q1 only North is served at the monopoly price in North PN At Q2 both markets are served at the uniform price PU PU Switch from Q1 to Q2: decreases profit by the red area increases profit by the blue area If South demand is “low enough” or MC “high enough” serve only North Q1 Q2 Chapter 5: Price Discrimination and Monopoly

Price discrimination and welfare Again In this case only North is served with uniform pricing Quantity $/unit Aggregate MC Demand MR Q1 PN But MC is less than the reservation price PR in South So price discrimination will lead to South being supplied PR Price discrimination leaves surplus unchanged in North But price discrimination generates profit and consumer surplus in South So price discrimination increases welfare Chapter 5: Price Discrimination and Monopoly

Price discrimination and welfare One more time Suppose only North is served with a uniform price Also assume that South will be served with price discrimination Welfare in North is unaffected Consumer surplus is created in South: opening of a new market Profit is generated in South: otherwise the market is not opened As a result price discrimination increases welfare. Chapter 5: Price Discrimination and Monopoly

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 Ph = 16 – Qh Pl = 12 – Ql MC = 4 Chapter 5: Price Discrimination and Monopoly

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 Chapter 5: Price Discrimination and Monopoly

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 Chapter 5: Price Discrimination and Monopoly

Second degree price discrimination 4 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 $24 $8 4 MC 4 MC $16 $32 $32 $8 8 12 16 8 12 Quantity Quantity Chapter 5: Price Discrimination and Monopoly

Second degree price discrimination 5 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 A high-income consumer will pay up to $87.50 for entry and 7 drinks High-Income So buying the ($59.50, 7) package gives him $28 consumer surplus Can the club- owner do even better than this? Suppose each low-income 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 Low-Income $ $ 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-income consumer Profit from each ($59.50, 7) package is $31.50: a reduction of $0.50 per consumer 12 $28 $87.50 $44 $31.50 $92 $59.50 4 MC 4 MC $28 $48 $28 7 12 16 7 8 12 Quantity Quantity Chapter 5: Price Discrimination and Monopoly

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 Nl low-income consumers and Nh high-income consumers Chapter 5: Price Discrimination and Monopoly

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 $31.50xNl + $44xNh Now suppose only high-income 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 This requires that Nh 31.50 < = 1.125 Nl 28 There should not be “too high” a fraction of high-demand consumers Chapter 5: Price Discrimination and Monopoly

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 Chapter 5: Price Discrimination and Monopoly

Non-linear pricing and welfare Non-linear price discrimination raises profit Does it increase social welfare? suppose that inverse demand of consumer group i is P = Pi(Q) marginal cost is constant at MC – c suppose quantity offered to consumer group i is Qi total surplus – consumer surplus plus profit –is the area between the inverse demand and marginal cost up to quantity Qi Price Demand Total Surplus c MC Qi Qi(c) Quantity Chapter 5: Price Discrimination and Monopoly

Non-linear pricing and welfare 2 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 Quantity Demand c MC Qi Qi(c) Total Surplus Q’i Chapter 5: Price Discrimination and Monopoly

Non-linear pricing and welfare 3 First-degree price discrimination always increases social welfare extracts all consumer surplus but generates socially optimal output output to group i is Qi(c) this exceeds output with uniform (non-discriminatory) pricing Price Quantity Demand c MC Qi Qi(c) Total Surplus Chapter 5: Price Discrimination and Monopoly

Non-linear pricing and welfare 4 Low demand offered less than the socially optimal quantity Price Menu pricing is less straightforward suppose that there are two markets low demand high demand PU L Uniform price is PU MC Menu pricing gives quantities Q1s, Q2s Qls QlU Quantity Price Welfare loss is greater than L High demand offered the socially optimal quantity Welfare gain is less than G PU G MC QhU Qhs Quantity Chapter 5: Price Discrimination and Monopoly

Non-linear pricing and welfare 5 Price Quantity MC PU QlU QhU Qls Qhs L G It follows that ΔW < G – L = (PU – MC)ΔQ1 + (PU – MC)ΔQ2 = (PU – MC)(ΔQ1 + ΔQ2) A necessary condition for second-degree price discrimination to increase social welfare is that it increases total output “Like” third-degree price discrimination But second-degree price discrimination is more likely to increase output Chapter 5: Price Discrimination and Monopoly

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 Chapter 5: Price Discrimination and Monopoly