ECON 115. Industrial Organization

Transcription

1 ECON 115 Industrial Organization

2 1. Review the Quiz 2. Reprise 3 rd Degree Price Discrimination 3. A problem and its implications 4. Introduction to non-linear (1 st & 2 nd Degree) Price Discrimination

3 First Hour Review of the quiz. Review third-degree price discrimination MR = MR = MC 3 rd Degree Price Discrimination Problem Analyzing the Problem Second Hour First-Degree Price Discrimination. Two-tiered pricing Bundling Introduction to Second- Degree Price Discrimination.

4 Two issues confront a firm wishing to price discriminate: 1. Identification: can the firm identify demands of different types of consumer or in separate markets easier in some markets than others: e.g tax consultants, doctors 2. Arbitrage: can the firm prevent consumers charged a low price from reselling to consumers charged a high price prevent re-importation of prescription drugs to the United States

5 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

6 There are three types of price discrimination: Type Name Example First Degree Personalized Pricing Maximum price charged to each consumer Second Degree Menu Pricing Quantity discounts Third Degree Group Pricing Group discounts ( early bird special senior discount )

7 Third-degree price discrimination: Group pricing. Consumers differ by some observable characteristic(s). A uniform price is charged to everyone in the group. This is linear pricing. Different uniform prices are charged to different groups: children under 12 are free senior discounts high variety of airline ticket prices early-bird specials 7

8 RULE 1: If demands are linear price discrimination results in the same aggregate output as no price discrimination price discrimination increases profit because allocated more profitably across two markets RULE 2 (Elasticity of Demand): consumers with low elasticity of demand are charged a high price. consumers with high elasticity of demand are charged a low price. RULE 3 (Marginal Revenue): marginal revenue must be equalized in each market. marginal revenue must equal aggregate marginal cost. 8

9 Exploring 3 rd Degree Price Discrimination Further: disaggregating the demand function. 9

10 From last week s in-class problem: Aggregate Demand: P = 12 Q/20 Marginal Revenue: MR = 12 Q/10 MAX Profit (MR = MC): 3 = 12 Q/10 Q = 90 and P = $7.50 Plugging these values back into the Daytime and Evening demand curves: Daytime: P = 10 Q/10; Q = 25 Evening: P = 14 Q/10; Q = 65 10

11 Suppose that there are two markets with the same MC. MR in market i is given by MR i = P i (1 1/h i ) where h i is (absolute value of) elasticity of demand From Rule 3 (above) MR 1 = MR 2 so P 1 (1 1/h 1 ) = P 2 (1 1/h 2 ) Therefore: 1 P 1 = (1 ) h 2 = h h h P 2 ( ) h h 1 h 2 h 2 1 Price is lower in the market with the higher demand elasticity 11

12 Question 1: what are the elasticities of demand of these two functions? Daytime: P = 10 Q/10; Q = 25 Evening: P = 14 Q/10; Q = 65 Therefore the we should be charging a higher price for the evening customers. 12

13 Question 2: what are the different MRs for each demand function at P = $7.50? Daytime Demand: P = 10 Q/10; Q = 25 Daytime Marginal Revenue: MR = 10 Q/5 Plug in 25; MR = 5!!!!! Evening Demand: P = 14 Q/19; Q = 65 Evening Marginal Revenue: MR = 14 Q/5 Plug in 65; MR = 1!!!!! MR daytime > MR evening 13

14 Just like the situation between Europe and the US in the bookselling example, here our theater owner can improve on this outcome by using more 3 rd degree price discrimination. Note that MR MC in both markets: MR > MC for daytime customers MR < MC evening customers Therefore, the theater owner wants more customers in the daytime than evening. 14

15 The demand function for the daytime is P = 10 Q/10. MR daytime = 10 Q/5 At MC = 3, Q = 35 and price = $6.50. Profits = $ $3.00 = $3.50/person x 35 persons = $ This superior result allowed us to grow our overall profits from $405 to $425. Now let s push this further... 15

16 Suppose we could further disaggregate the daytime demand function, P = 10 Q/10. Let s say there are two distinct groups of customers who attend movies in the afternoon: retired people and UC Merced ECON students. Each group has a different demand function: RETIRED: P = 12 Q/5; MR = 12 Q/2.5 ECON: P = 8 Q/5; MR = 8 Q/2.5 16

17 Both groups pay the $6.50 price discrimination charge. Disaggregating the Daytime Demand function, we see Q retired = 27.5 and Q ECON = 7.5. ( = 35). But the marginal revenue in each segment is now different: MR retired = $1 and MR ECON = $5. Therefore, we should further price discriminate with the goal of reducing the retired customers and adding ECON customers. Equating the MRs to $3, we get Q retired = 22.5 and Q ECON = New prices are P retired = $7.50 and P ECON = $5.50. New Profit = $ > $

18 Nonlinear Price Discrimination (1 st and 2 nd Degree Price Discrimination) 18

19 A nonlinear pricing strategy depends upon the information available to the seller. That determines whether to employ first-degree (personalized) or second-degree (menu) pricing. Under first-degree price discrimination, the monopolist charges the maximum price that each consumer is willing to pay. Extracts all consumer surplus Since profit equals the total surplus, first-degree price discrimination is efficient. 19

20 Suppose you inherit five antique cars. Your research shows there are 5 collectors each with different reservation prices. Each is willing to pay: Linear Pricing: Personalized pricing $10000 $6000 $10000 $8000 $6000 $8000 $6000 $6000 $6000 $4000 $6000 $4000 $2000 $6000 $2000 Revenue under standard monopoly pricing = $18,000 Revenue under personalized pricing = $30,000 20

21 First-degree price discrimination is very profitable, And it leads to the efficient choice of output, since no value-creating exchanges are missed. However, it requires: 1. detailed customer information; and 2. the ability to avoid arbitrage. The information requirements appear insurmountable. Solvable if personal information is available (accounting services; university applicants) and prices 21 can be set after the customer has agreed to the contract.

22 Can a seller achieve a similar outcome if prices must be announced in advance? Yes, with non-linear prices Two-part pricing is an example of common non-linear pricing strategy. charge a quantity-independent fee (membership?), plus a per unit usage charge Block pricing is a second example. bundle total charge and quantity in a package 22

23 Example of Two-part pricing. A jazz club serves two types of customer: Old: demand for entry + Q o drinks is P = V o Q o Young: demand for entry + Q y drinks is P = V y Q y Cost of operating the jazz club C(Q) = F + cq Assumptions: V o > V y : Old will to pay more than Young Demand and costs are all in daily units Equal numbers of each type of customer. 23

24 Suppose that the jazz club owner applies traditional linear pricing: free entry and a fixed price for drinks. Aggregate demand is Q = Q o + Q y = (V o + V y ) 2P Set the equation equal to price: P = (V o + V y )/2 Q/2 MR therefore is MR = (V o + V y )/2 Q Maximize profits be equating MR and MC, where MC = c and solve for Q: 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 24

25 Under this linear pricing scheme: 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 25

26 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 4 + c 2 h i c k j MC MR Quantity V o Quantity V y V o +V y 2 - c Quantity Vo + V y Linear pricing leaves each type of consumer retaining the consumer surplus. 26

27 Jazz club owner can improve on this. Remember the 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 He can charge an entry fee (just less than): E o = CS o to each Old customer and E y = CS y to each Young customer; The club checks IDs to implement this policy. Each type will still be willing to frequent the club and buy the equilibrium number of drinks. This increases profit by E o for each Old and E y for each Young customer. 27

28 The jazz club can do better still! The club can 1. Reduce the price per drink; this increases consumer surplus; 2. Then extract the additional consumer surplus can through a higher entry fee. Let s consider the best the jazz club owner can do with respect to each type of consumer. 28

29 Set the unit price equal to marginal cost $/unit V i The entry charge converts consumer surplus into profit This gives consumer surplus of (V i - c) 2 /2 c MC Set the entry charge to (V i - c) 2 /2 MR V i - c V i Quantity Profit from each pair of Old and Young now d = [(V o c) 2 + (V y c) 2 ]/2 29

30 Set the unit price equal to marginal cost This gives consumer surplus of (V i - c) 2 /2 Set the entry charge to (V i - c) 2 /2 $/unit V i c The entry charge Using converts two-part consumer pricing surplus increases into profit the monopolist s profit MR V i - c V i MC Quantity Profit from each pair of Old and Young now d = [(V o c) 2 + (V y c) 2 ]/2 30

31 There s another pricing method the club owner can use called Block Pricing: offer a package Entry plus X number of drinks for $Y. Maximize profit by following these two rules: 1. Offer each consumer type an amount equal to how much that type would buy if price equaled marginal cost. 2. Set the total charge for each type equal to the total willingness to pay for the that quantity. 31

32 $ Old $ Young V o Willingness to pay of each Old customer Quantity supplied to each Old customer V y Willingness to pay of each Young Quantity customer supplied to each Young customer c MC c MC Q o Quantity V o Q y Quantity V y WTP o = (V o c) 2 /2 + (V o c)c = (V o2 c 2 )/2 WTP y = (V y c) 2 /2 + (V y c)c = (V y2 c 2 )/2 32

33 How to implement this block pricing policy? Here are the simple rules: 1. Card everyone at the door. 2. Give customers the requisite number of tokens that are exchanged for drinks. 33

34 What if the seller cannot distinguish between buyers? For example, perhaps they don t differ by age by rather by income, which is unobservable. Then the type of price discrimination just discussed is impossible. A high-income buyer will pretend to be a low-income buyer to avoid the high entry price and to pay the smaller total charge 34

35 Take a specific example: P h = 16 Q h P l = 12 Q l MC = 4 To capture the consumer surplus using 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. 35

36 This will not work. High-Income types get no consumer surplus from the package designed for them, but get consumer surplus from the low-income package. Therefore, they will pretend to be lowincome even if this limits the number of drinks they can buy. To address this problem, the seller designs a menu of offerings targeted at the two types. 36

37 This alternative offer must be what economists call incentive compatible. Any offer made to high-demand consumers must provide as much consumer surplus as they would get from an offer designed for lowdemand consumers. 37

38 In designing this pricing scheme, the seller endeavors to make buyers: 1. Reveal their true types; 2. Self-select the quantity/price package designed for them. This is the essence of second-degree price discrimination. Without the ability to identify different types of buyers, a two-part tariff is ineffective because it allows deception by buyers. The best option is quantity discounting. 38

39 $ 16 High-income So will the highincome consumers: because the ($64, 8) package gives them $32 consumer surplus Low-Income The low-demand consumers will b willing to buy this ($64, 8) package $32 8 $32 $64 $40 $32 4 $24 $8 MC 4 MC $32 $16 $ Quantity Quantity $ 12 Offer the low-income consumers a package of entry plus 8 drinks for $64 $8 39

40 This is the incentive High-income compatibility constraint Low-Income So any other package offered to high-income $ $ 16 consumers must offer at least $32 consumer 12 surplus $32 8 $32 $64 $40 $32 $8 4 $24 MC 4 MC $32 $16 $32 $ Quantity Quantity 40

41 Low income Industrial Organization So they can be offered a package consumers will not of ($88, 12) (since $ = 88) buy the ($88, 12) and they will buy this package since they High-income Low-Income are willing to pay Profit from each only $72 for 12 high-income High income consumers are drinks consumer is $ willing to pay up $ to $120 for 16$40 entry plus 12 drinks if no other And profit from ($88-12 x $4) package is 12 available each low-income consumer is $32 ($64-8x$4) $32 8 $32 $64 $40 $32 4 $24 $8 MC 4 MC $32 $16 $32 $ Quantity Quantity 41

42 $ 16 High-income $ 12 Low-Income These packages exhibit quantity discounting: highincome pay $7.33 per unit and low-income pay $8 $32 8 $32 $64 $40 $32 4 $24 $8 MC 4 MC $32 $16 $32 $ Quantity Quantity 42

43 High-Income $ 16 $28 Can the clubowner do even better than this? $ 12 Low-Income Yes! Reduce the number of units offered to each low-income consumer $87.50 $44$92 $59.50 $ MC 4 MC $28$48 $ Quantity Quantity 43

44 A high-income consumer will pay up to $87.50 for entry and 7 High-Incomedrinks $ 16 $28 So buying the ($59.50, 7) package gives him $28 consumer surplus So entry plus 12 drinks can be sold for $92 ($ = $92) $ Profit from each ($92, 12) package is $44: an increase 12 of $4 per consumer Suppose each low-income consumer is offered 7 drinks Each consumer will pay up to Low-Income $59.50 for entry and 7 drinks Profit from each ($59.50, 7) package is $31.50: a reduction of $0.50 per consumer $87.50 $44$92 $59.50 $ MC 4 MC $28$48 $ Quantity Quantity 44

45 $ 16 Industrial Organization A high-income consumer will pay High-Income up to $87.50 for entry and 7 The monopolist does better by So buying the drinks ($59.50, 7) package Suppose each low-income gives him reducing $28 consumer the surplus number of units consumer is offered 7 drinks So entry offered plus 12 drinks Can to low-income can the be clubowner do $ even sold consumers Each consumer will pay up to Low-Income Profit from for each since $92 ($120 ($92, this - 12) 28 allows = $92) him to increase $59.50 for entry and 7 drinks package is $44: an increase the better charge of $4 than to this? high-income Yes! Profit Reduce from each the ($59.50, number 7) per consumer consumers 12 of units package offered is $31.50: to a reduction each $28 of $0.50 per consumer low-income consumer $87.50 $44$92 $59.50 $ MC 4 MC $28$48 $ Quantity Quantity 45

46 Reducing the number of units to each low-income consumer begs the question: does the monopolist always want to supply both types of consumer? There are cases where it is better to supply only high-income types: high-end restaurants golf and country clubs To return to our example, suppose there are N l low-income and N h high-income consumers. 46

47 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 28 = There should not be too high a fraction of high-demand consumers. If the fraction is 47

48 Summarizing second-degree price discrimination: 1. Extract all consumer surplus from the lowestdemand group. 2. Leave some consumer surplus for other groups... to satisfy the incentive compatibility constraint 3. Offer less than the socially efficient quantity to all groups other than the highest-demand group. 4. 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. 48

49 Next Week: A reprise of 2 nd Degree Price Discrimination A 2 nd Degree Problem The welfare implications of price discrimination A bonus lecture on Standard Oil 49