1. 1 Product Variety and Quality under Monopoly

2. 2 Introduction Most firms sell more than one product Products are differentiated in different ways –horizontally goods of similar quality targeted at consumers of different types –how is variety determined? –is there too much variety –vertically consumers agree on quality differ on willingness to pay for quality –how is quality of goods being offered determined?

3. 3 Horizontal product differentiation Suppose that consumers differ in their tastes –firm has to decide how best to serve different types of consumer –offer products with different characteristics but similar qualities This is horizontal product differentiation –firm designs products that appeal to different types of consumer –products are of (roughly) similar quality Questions: –how many products? –of what type? –how do we model this problem?

4. 4 A spatial approach to product variety The spatial model (Hotelling) is useful to consider –pricing –design –variety Has a much richer application as a model of product differentiation –“location” can be thought of in space (geography) time (departure times of planes, buses, trains) product characteristics (design and variety) –consumers prefer products that are “close” to their preferred types in space, or time or characteristics

5. 5 A Spatial approach to product variety 2 Assume N consumers living equally spaced along Main Street – 1 mile long. Monopolist must decide how best to supply these consumers Consumers buy exactly one unit provided that price plus transport costs is less than V. Consumers incur there-and-back transport costs of t per mile The monopolist operates one shop –reasonable to expect that this is located at the center of Main Street

6. 6 The spatial model z = 0z = 1 Shop 1 t x1x1 Price All consumers within distance x 1 to the left and right of the shop will by the product All consumers within distance x 1 to the left and right of the shop will by the product 1/2 VV p1p1 t x1x1 p 1 + txp 1 + t.x p 1 + tx 1 = V, so x 1 = (V – p 1 )/t What determines x 1 ? What determines x 1 ? Suppose that the monopolist sets a price of p 1 Suppose that the monopolist sets a price of p 1

7. 7 The spatial model 2 z = 0z = 1 Shop 1 x1x1 Price 1/2 VV p 1 x1x1 p 1 + t.x Suppose the firm reduces the price to p 2 ? Suppose the firm reduces the price to p 2 ? p2p2 x2x2 x2x2 Then all consumers within distance x 2 of the shop will buy from the firm Then all consumers within distance x 2 of the shop will buy from the firm

8. 8 The spatial model 3 Suppose that all consumers are to be served at price p. –The highest price is that charged to the consumers at the ends of the market –Their transport costs are t/2 : since they travel ½ mile to the shop –So they pay p + t/2 which must be no greater than V. –So p = V – t/2. Suppose that marginal costs are c per unit. Suppose also that a shop has set-up costs of F. Then profit is  (N, 1) = N(V – t/2 – c) – F.

9. 9 Monopoly pricing in the spatial model What if there are two shops? The monopolist will coordinate prices at the two shops With identical costs and symmetric locations, these prices will be equal: p 1 = p 2 = p –Where should they be located? –What is the optimal price p*?

10. 10 Location with two shops Suppose that the entire market is to be served Price z = 0z = 1 If there are two shops they will be located symmetrically a distance d from the end-points of the market If there are two shops they will be located symmetrically a distance d from the end-points of the market Suppose that d < 1/4 Suppose that d < 1/4 d VV 1 - d Shop 1Shop 2 1/2 The maximum price the firm can charge is determined by the consumers at the center of the market The maximum price the firm can charge is determined by the consumers at the center of the market Delivered price to consumers at the market center equals their reservation price Delivered price to consumers at the market center equals their reservation price p(d) Start with a low price at each shop Start with a low price at each shop Now raise the price at each shop Now raise the price at each shop What determines p(d)? What determines p(d)? The shops should be moved inwards The shops should be moved inwards

11. 11 Location with two shops 2 Price z = 0z = 1 Now suppose that d > 1/4 Now suppose that d > 1/4 d VV 1 - d Shop 1Shop 2 1/2 p(d) Start with a low price at each shop Start with a low price at each shop Now raise the price at each shop Now raise the price at each shop The maximum price the firm can charge is now determined by the consumers at the end-points of the market The maximum price the firm can charge is now determined by the consumers at the end-points of the market Delivered price to consumers at the end-points equals their reservation price Delivered price to consumers at the end-points equals their reservation price Now what determines p(d)? Now what determines p(d)? The shops should be moved outwards The shops should be moved outwards

12. 12 Location with two shops 3 Price z = 0 z = 1 1/4 VV 3/4 Shop 1 Shop 2 1/2 It follows that shop 1 should be located at 1/4 and shop 2 at 3/4 It follows that shop 1 should be located at 1/4 and shop 2 at 3/4 Price at each shop is then p* = V - t/4 Price at each shop is then p* = V - t/4 V - t/4 Profit at each shop is given by the shaded area Profit at each shop is given by the shaded area Profit is now  (N, 2) = N(V - t/4 - c) – 2F Profit is now  (N, 2) = N(V - t/4 - c) – 2F c c

13. 13 Three shops Price z = 0 z = 1 VV 1/2 What if there are three shops? What if there are three shops? By the same argument they should be located at 1/6, 1/2 and 5/6 By the same argument they should be located at 1/6, 1/2 and 5/6 1/65/6 Shop 1Shop 2Shop 3 Price at each shop is now V - t/6 Price at each shop is now V - t/6 Profit is now  (N, 3) = N(V - t/6 - c) – 3F Profit is now  (N, 3) = N(V - t/6 - c) – 3F

14. 14 Optimal number of shops A consistent pattern is emerging. Assume that there are n shops. We have already considered n = 2 and n = 3. When n = 2 we have p(N, 2) = V - t/4 When n = 3 we have p(N, 3) = V - t/6 They will be symmetrically located distance 1/n apart. It follows that p(N, n) = V - t/2n Aggregate profit is then  (N, n) = N(V - t/2n - c) – nF How many shops should there be? How many shops should there be?

15. 15 Optimal number of shops 2 Profit from n shops is  (N, n) = (V - t/2n - c)N - nF and the profit from having n + 1 shops is:  *(N, n+1) = (V - t/2(n + 1)-c)N - (n + 1)F Adding the (n +1)th shop is profitable if  (N,n+1) -  (N,n) > 0 This requires tN/2n - tN/2(n + 1) > F which requires that n(n + 1) < tN/2F.

16. 16 An example Suppose that F = $50,000, N = 5 million and t = $1 Then tN/2F = 50 For an additional shop to be profitable we need n(n + 1) < 50. This is true for n < 6 There should be no more than seven shops in this case: if n = 6 then adding one more shop is profitable. But if n = 7 then adding another shop is unprofitable.

17. 17 Some intuition What does the condition on n tell us? Simply, we should expect to find greater product variety when: –there are many consumers. –set-up costs of increasing product variety are low. –consumers have strong preferences over product characteristics and differ in these consumers are unwilling to buy a product if it is not “very close” to their most preferred product

18. 18 How much of the market to supply Should the whole market be served? –Suppose not. Then each shop has a local monopoly –Each shop sells to consumers within distance r –How is r determined? it must be that p + tr = V so r = (V – p)/t so total demand is 2N(V – p)/t profit to each shop is then  = 2N(p – c)(V – p)/t – F differentiate with respect to p and set to zero: d  /dp = 2N(V – 2p + c)/t = 0 So the optimal price at each shop is p* = (V + c)/2 If all consumers are served price is p(N,n) = V – t/2n –Only part of the market should be served if p(N,n)< p* –This implies that V < c + t/n.

19. 19 Partial market supply If c + t/n > V supply only part of the market and set price p* = (V + c)/2 If c + t/n < V supply the whole market and set price p(N,n) = V – t/2n Supply only part of the market: –if the consumer reservation price is low relative to marginal production costs and transport costs –if there are very few outlets

20. 20 Social optimum Are there too many shops or too few? Are there too many shops or too few? What number of shops maximizes total surplus? What number of shops maximizes total surplus? Total surplus is therefore NV - Total Cost Total surplus is therefore NV - Total Cost Total surplus is then total willingness to pay minus total costs Total surplus is then total willingness to pay minus total costs Total surplus is consumer surplus plus profit Consumer surplus is total willingness to pay minus total revenue Profit is total revenue minus total cost Total willingness to pay by consumers is N.V So what is Total Cost? So what is Total Cost?

21. 21 Social optimum 2 Price z = 0 z = 1 VV Assume that there are n shops Assume that there are n shops Consider shop i Consider shop i 1/2n Shop i t/2n Total cost is total transport cost plus set-up costs Total cost is total transport cost plus set-up costs Transport cost for each shop is the area of these two triangles multiplied by consumer density Transport cost for each shop is the area of these two triangles multiplied by consumer density This area is t/4n 2 This area is t/4n 2

22. 22 Social optimum 3 Total cost with n shops is, therefore: C(N,n) = n(t/4n 2 )N + nF = tN/4n + nF Total cost with n + 1 shops is: C(N,n+1) = tN/4(n+1)+ (n+1)F Adding another shop is socially efficient if C(N,n + 1) < C(N,n) This requires that tN/4n - tN/4(n+1) > F which implies that n(n + 1) < tN/4F The monopolist operates too many shops and, more generally, provides too much product variety The monopolist operates too many shops and, more generally, provides too much product variety If t = $1, F = $50,000, N = 5 million then this condition tells us that n(n+1) < 25 If t = $1, F = $50,000, N = 5 million then this condition tells us that n(n+1) < 25 There should be five shops: with n = 4 adding another shop is efficient

23. 23 Product variety and price discrimination Suppose that the monopolist delivers the product. –then it is possible to price discriminate What pricing policy to adopt? –charge every consumer his reservation price V –the firm pays the transport costs –this is uniform delivered pricing –it is discriminatory because price does not reflect costs

24. 24 Product variety and price discrimination Suppose that the monopolist delivers the product. –then it is possible to price discriminate What pricing policy to adopt? –charge every consumer his reservation price V –the firm pays the transport costs –this is uniform delivered pricing –it is discriminatory because price does not reflect costs

25. 25 Product variety and price discrimination 2 Should every consumer be supplied? –suppose that there are n shops evenly spaced on Main Street –cost to the most distant consumer is c + t/2n –supply this consumer so long as V (revenue) > c + t/2n This is a weaker condition than without price discrimination. Price discrimination allows more consumers to be served.

26. 26 Product variety & price discrimination 3 How many shops should the monopolist operate now? —Suppose that the monopolist has n shops and is supplying the entire market. —Total revenue minus production costs is NV – Nc —Total transport costs plus set-up costs is C(N, n)=tN/4n + nF —So profit is  (N,n) = NV – Nc – C(N,n) —But then maximizing profit means minimizing C(N, n) —The discriminating monopolist operates the socially optimal number of shops.

27. 27 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 determined by its ability to generate profit; attitude of consumers to quality Consider 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

28. 28 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

29. 29 Demand and quality 2 Begin with a particular demand curve for a good of quality Z 1 Begin with a particular demand curve for a good of quality Z 1 Price Quantity P(Q, Z 1 ) P1P1 Q1Q1 If the price is P 1 and the product quality is Z 1 then all consumers with reservation prices greater than P 1 will buy the good If the price is P 1 and the product quality is Z 1 then all consumers with reservation prices greater than P 1 will buy the good R 1 (Z 1 ) These are the inframarginal consumers These are the inframarginal consumers This is the marginal consumer This is the marginal consumer Suppose that an increase in quality increases the willingness to pay of inframarginal consumers more than that of the marginal consumer Suppose that an increase in quality increases the willingness to pay of inframarginal consumers more than that of the marginal consumer Then an increase in product quality from Z 1 to Z 2 rotates the demand curve around the quantity axis as follows Then an increase in product quality from Z1 Z1 to Z2 Z2 rotates the demand curve around the quantity axis as follows R 1 (Z 2 ) P2P2 Quantity Q 1 can now be sold for the higher price P 2 Quantity Q1 Q1 can now be sold for the higher price P2P2 P(Q, Z 2 )

30. 30 Demand and quality 3 Price Quantity P(Q, Z 1 ) P1P1 Q1Q1 R 1 (Z 1 ) Suppose instead that an increase in quality increases the willingness to pay of marginal consumers more than that of the inframarginal consumers Suppose instead that an increase in quality increases the willingness to pay of marginal consumers more than that of the inframarginal consumers Then an increase in product quality from Z 1 to Z 2 rotates the demand curve around the price axis as follows Then an increase in product quality from Z1 Z1 to Z2 Z2 rotates the demand curve around the price axis as follows P(Q, Z 2 ) Once again quantity Q 1 can now be sold for a higher price P 2 Once again quantity Q1Q1 can now be sold for a higher price P2P2 P2P2

31. 31 Demand and quality 4 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(  - Q) where Z is an index of quality

32. 32 Demand and quality 5 P = Z(  - Q) Assume that marginal cost of output is zero: MC(Q) = 0 Cost of quality is C(Z) =  Z 2 This means that quality is costly and becomes increasingly costly This means that quality is costly and becomes increasingly costly Marginal cost of quality = dC(Z)/d(Z) = 2  Z The firm’s profit is:  (Q, Z) =PQ - C(Z)= Z(  - Q)Q -  Z 2

33. 33 Demand and quality 6 Again, profit is:  (Q, Z) =PQ - C(Z)= Z(  - Q)Q -  Z 2 The firm chooses Q and Z to maximize profit. Take the choice of quantity first: this is easiest. Marginal revenue = MR = Z  - 2ZQ MR = MC  Z  - 2ZQ = 0  Q* =  /2  P* = Z  /2

34. 34 Demand and quality 7 Total revenue = P*Q* =(Z  /2)x(  /2) =Z  2 /4 So marginal revenue from increased quality is MR(Z) =  2 /4 Marginal cost of quality is MC(Z) = 2  Z Equating MR(Z) = MC(Z) then gives Z* =  2 /8  Does the monopolist produce too high or too low quality?

35. 35 Demand and quality: multiple products What if the firm chooses to offer more than one product? –what qualities should be offered? –how should they be priced? Determined by costs and consumer demand

36. 36 Demand and quality: multiple products 2 An example: –two types of consumer –each buys exactly one unit provided that consumer surplus is nonnegative –if there is a choice, buy the product offering the larger consumer surplus –types of consumer distinguished by willingness to pay for quality This is vertical product differentiation

37. 37 Vertical differentiation Indirect utility to a consumer of type i from consuming a product of quality z at price p is V i =  i (z – z i ) – p –where  i measures willingness to pay for quality; –z i is the lower bound on quality below which consumer type i will not buy –assume  1 >  2 : type 1 consumers value quality more than type 2 –assume z 1 > z 2 = 0: type 1 consumers only buy if quality is greater than z 1 : never fly in coach never shop in Wal-Mart only eat in “good” restaurants –type 2 consumers will buy any quality so long as consumer surplus is nonnegative

38. 38 Vertical differentiation 2 Firm cannot distinguish consumer types Must implement a strategy that causes consumers to self- select –persuade type 1 consumers to buy a high quality product z 1 at a high price –and type 2 consumers to buy a low quality product z 2 at a lower price, which equals their maximum willingness to pay Firm can produce any product in the range MC = 0 for either quality type z, z

39. 39 Vertical differentiation 3 For type 2 consumers charge maximum willingness to pay for the low quality product: p 2 =  2 z 2 Suppose that the firm offers two products with qualities z 1 > z 2 Now consider type 1 consumers: firm faces an incentive compatibility constraint  1 (z 1 – z 1 ) – p 1 >  1 (z 2 – z 1 ) – p 2 Type 1 consumers prefer the high quality to the low quality good  1 (z 1 – z 1 ) – p 1 >  Type 1 consumers have nonnegative consumer surplus from the high quality good These imply that p 1 <  1 z 1 – (    -  2 )z 2 There is an upper limit on the price that can be charged for the high quality good

40. 40 Vertical differentiation 4 Take the equation p 1 =  1 z 1 –  1 –  2 )z 2 –this is increasing in quality valuations –increasing in the difference between z 1 and z 2 –quality can be prices highly when it is valued highly –firm has an incentive to differentiate the two products’ qualities to soften competition between them monopolist is competing with itself What about quality choice? –prices p 1 =  1 z 1 – (  1 –  2 )z 2 ; p 2 =  2 z 2 check the incentive compatibility constraints –suppose that there are N 1 type 1 and N 2 type 2 consumers

41. 41 Vertical differentiation 5 Profit is  N 1 p 1 + N 2 p 2 = N 1  1 z 1 – (N 1  1 – (N 1 + N 2 )  2 )z 2 This is increasing in z 1 so set z 1 as high as possible: z 1 = For z 2 the decision is more complex (N 1  1 – (N 1 + N 2 )  2 ) may be positive or negative z

42. 42 Vertical differentiation 6 Case 1: Suppose that (N 1  1 – (N 1 + N 2 )  2 ) is positive Then z 2 should be set “low” but this is subject to a constraint Recall that p 1 =  1 z 1 – (    -  2 )z 2 So reducing z 2 increases p 1 But we also require that  1 (z 1 – z 1 ) – p 1 >  Putting these together gives: The equilibrium prices are then:

43. 43 Vertical differentiation 7 Offer type 1 consumers the highest possible quality and charge their full willingness to pay Offer type 2 consumers as low a quality as is consistent with incentive compatibility constraints Charge type 2 consumers their maximum willingness to pay for this quality –maximum differentiation subject to incentive compatibility constraints

44. 44 Vertical differentiation 8 Case 1: Now suppose that (N 1  1 – (N 1 + N 2 )  2 ) is negative Then z 2 should be set as high as possible The firm should supply only one product, of the highest possible quality What does this require? From the inequality offer only one product if: Offer only one product: if there are not “many” type 1 consumers if the difference in willingness to pay for quality is “small” Should the firm price to sell to both types in this case? YES!

45. 45 Empirical Application: Price Discrimination and Imperfect Competition Although we have presented price discrimination and product design (versioning) issues in the context of a monopoly, these same tactics also play a role in more competitive settings of imperfect competition Imagine a two-store setting again Assume N customers distributed evenly between the two stores, each with maximum willingness to pay of V. No transport cost—Half of the consumers always buys at nearest store. Other half always buys at cheapest store.

46. 46 Price Discrimination and Imperfect Competition 2 If both stores operated by a monopolist, set price = V. Cannot set it higher of there will be no customers. If Store 1 cuts its price  below V. It loses N  /2 from all current customers Setting it lower though gains nothing. What if stores operated by separate firms? Imagine P 1 = P 2 = V. Store 1 serves N/4 price- sensitive customers and N/4 price-insensitive ones. The same is true for Store 2. It gains N(V -  )/4 by stealing all price- sensitive customers from Store 2

47. 47 Price Discrimination and Imperfect Competition 3 MORAL 1: Both firms have a real incentive to cut price. This ultimately proves self-defeating Cutting their price does not increase their likelihood of shopping at a particular place. It just loses revenue. MORAL 2: Unlike the monopolist who sets the same price to everyone, these firms have an incentive to discriminate and so continue to charge a high price to loyal consumers while pricing low to others. In equilibrium, both still serve N/2 customers but now do so at a price closer to cost. This is especially frustrating in light of the “brand- loyal” or price-insensitive customers

48. 48 Price Discrimination and Imperfect Competition 4 The intuition then is that price discrimination may be associated with imperfect competition and become more prominent as markets get more competitive (but still less than perfectly competitive). This idea is tested by Stavins (2001) with airline prices. Restrictions such as a required Saturday night stay-over or an advanced purchase serve as screening mechanism for price-sensitive customers. Hence, restrictions lead to lower ticket price. Stavins (2001) idea is that price reduction associated with flight restrictions will be small in markets that are not very competitive.

49. 49 Price Discrimination and Imperfect Competition 6 Stavins (2001) looks at nearly 6,000 tickets covering 12 different city-pair routes in September, 1995. She finds strong support for the dual hypothesis that: In highly competitive (low HHI) markets, a Saturday night restriction leads to a $253 price reduction but only a $165 reduction in less competitive ones. a) passengers flying on a ticket with restrictions pay less; b) price reduction shrinks as concentration rises In highly competitive (low HHI) markets, an Advance Purchase restriction leads to a $111 price reduction but only a $41 reduction in less competitive ones.

50. 50 Price Discrimination and Imperfect Competition 5 Variable Coefficient t-Statistic Coefficient t-Statistic Saturday Night Stay – 0.408 – 4.05 ----- ----- Required Saturday Night Stay 0.792 3.39 ----- ----- RequiredxHHI Advance Purchase ----- ----- – 0.023 –5.53 Required Advance Purchase ----- ----- 0.098 8.38 RequiredxHHI NOTE: HHI is the Herfindahl Index. A Saturday Night Stay or an Advance Purchase lowers the price significantly. But the HHI terms show that this effect weakens as market concentration increases.

51. 51 Demand and quality A1 Price Quantity  Z1Z1 P(Q,Z 1 ) How does increased quality affect demand? How does increased quality affect demand? Z2Z2 P(Q, Z 2 ) MR(Z 1 ) MR(Z 2 )  /2 Q* P 1 = Z 1  /2 P 2 = Z 2  /2 When quality is Z 1 price is Z 1  /2 When quality is Z 1 price is Z 1  /2 When quality is Z 2 price is Z 2  /2 When quality is Z 2 price is Z 2  /2

52. 52 Demand and quality A2 Price Quantity  Z1Z1 Z2Z2  /2 Q* P 1 = Z 1  /2 P 2 = Z 2  /2 An increase in quality from Z 1 to Z 2 increases revenue by this area An increase in quality from Z 1 to Z 2 increases revenue by this area Social surplus at quality Z 1 is this area minus quality costs Social surplus at quality Z 1 is this area minus quality costs Social surplus at quality Z 2 is this area minus quality costs Social surplus at quality Z 2 is this area minus quality costs So an increase is quality from Z 1 to Z 2 increases surplus by this area minus the increase in quality costs So an increase is quality from Z 1 to Z 2 increases surplus by this area minus the increase in quality costs The increase in total surplus is greater than the increase in profit. The monopolist produces too little quality

53. 53 Demand and quality Derivation of aggregate demand Order consumers by their reservation prices Aggregate individual demand horizontally Price Quantity 12345678

54. 54 Location choice 1 d < 1/4 We know that p(d) satisfies the following constraint: p(d) + t(1/2 - d) = V This gives:p(d) = V - t/2 + td  p(d) = V - t/2 + td Aggregate profit is then:  (d) = (p(d) - c)N = (V - t/2 + td - c)N This is increasing in d so if d < 1/4 then d should be increased.

55. 55 Location choice 2 d > 1/4 We now know that p(d) satisfies the following constraint: p(d) + td = V This gives:p(d) = V - td Aggregate profit is then:  (d) = (p(d) - c)N = (V - td - c)N This is decreasing in d so if d > 1/4 then d should be decreased.

56. 56 Commodity Bundling and Tie-In Sales

57. 57 Introduction Firms often bundle the goods that they offer –Microsoft bundles Windows and Explorer –Office bundles Word, Excel, PowerPoint, Access Bundled package is usually offered at a discount Bundling may increase market power –GE merger with Honeywell Tie-in sales ties the sale of one product to the purchase of another Tying may be contractual or technological –IBM computer card machines and computer cards –Kodak tie service to sales of large-scale photocopiers –Tie computer printers and printer cartridges Why? To make money!

58. 58 Bundling: an example Two television stations offered two old Hollywood films –Casablanca and Son of Godzilla Arbitrage is possible between the stations Willingness to pay is: Station A Station B Willingness to pay for Casablanca Willingness to pay for Godzilla $8,000 $7,000 $2,500 $3,000 How much can be charged for Casablanca? How much can be charged for Casablanca? $7,000 How much can be charged for Godzilla? How much can be charged for Godzilla? $2,500 If the films are sold separately total revenue is $19,000

59. 59 Bundling: an example 2 Station A Station B Willingness to pay for Casablanca Willingness to pay for Godzilla $8,000 $7,000 $2,500 $3,000 Total Willingness to pay $10,500 $10,000 Now suppose that the two films are bundled and sold as a package Now suppose that the two films are bundled and sold as a package How much can be charged for the package? How much can be charged for the package? $10,000 If the films are sold as a package total revenue is $20,000 Bundling is profitable because it exploits aggregate willingness pay

60. 60 Bundling Extend this example to allow for –costs –mixed bundling: offering products in a bundle and separately

61. 61 All consumers in region A buy both goods All consumers in region A buy both goods Bundling: another example R2R2 R1R1 Consumer x has reservation price p x1 for good 1 and p x2 for good 2 Consumer x has reservation price p x1 for good 1 and p x2 for good 2 x p x2 p x1 y p y2 p y1 Consumer y has reservation price p y1 for good 1 and p y2 for good 2 Consumer y has reservation price p y1 for good 1 and p y2 for good 2 Suppose that the firm sets price p 1 for good 1 and price p 2 for good 2 Suppose that the firm sets price p 1 for good 1 and price p 2 for good 2 p1p1 p2p2 Suppose that there are two goods and that consumers differ in their reservation prices for these goods Suppose that there are two goods and that consumers differ in their reservation prices for these goods Each consumer buys exactly one unit of a good provided that price is less than her reservation price Each consumer buys exactly one unit of a good provided that price is less than her reservation price A B D C Consumers split into four groups Consumers split into four groups All consumers in region B buy only good 2 All consumers in region B buy only good 2 All consumers in region C buy neither good All consumers in region C buy neither good All consumers in region D buy only good 1 All consumers in region D buy only good 1

62. 62 Bundling: another example 2 R2R2 R1R1 c1c1 c2c2 Now consider pure bundling at some price p B Now consider pure bundling at some price p B pBpB pBpB Consumers now split into two groups Consumers now split into two groups E All consumers in region E buy the bundle All consumers in region E buy the bundle F All consumers in region F do not buy the bundle All consumers in region F do not buy the bundle Consumers in these two regions can buy each good even though their reservation price for one of the goods is less than its marginal cost Consumers in these two regions can buy each good even though their reservation price for one of the goods is less than its marginal cost

63. 63 Mixed bundling R2R2 R1R1 p1p1 p2p2 Now consider mixed bundling Now consider mixed bundling pBpB pBpB Good 1 is sold at price p 1 Good 1 is sold at price p 1 Good 2 is sold at price p 2 Good 2 is sold at price p 2 The bundle is sold at price p B < p 1 + p 2 The bundle is sold at price p B < p 1 + p 2 Consumers split into four groups: buy the bundle buy only good 1 buy only good 2 buy nothing Consumers split into four groups: buy the bundle buy only good 1 buy only good 2 buy nothing p B - p 1 p B - p 2 Consumers in this region are willing to buy both goods. They buy the bundle Consumers in this region are willing to buy both goods. They buy the bundle Consumers in this region also buy the bundle Consumers in this region also buy the bundle Consumers in this region buy nothing Consumers in this region buy nothing Consumers in this region buy only good 1 Consumers in this region buy only good 1 Consumers in this region buy only good 2 Consumers in this region buy only good 2 This leaves two regions This leaves two regions In this region consumers buy either the bundle or product 1 In this region consumers buy either the bundle or product 1 In this region consumers buy either the bundle or product 2 In this region consumers buy either the bundle or product 2

64. 64 Mixed bundling 2 R2R2 R1R1 p1p1 p2p2 pBpB pBpB p B - p 1 p B - p 2 x p 1x p 2x p 1x +p 2x Consider consumer x with reservation prices p 1x for product 1 and p 2x for product 2 Consider consumer x with reservation prices p 1x for product 1 and p 2x for product 2 Her aggregate willingness to pay for the bundle is p 1x + p 2x Her aggregate willingness to pay for the bundle is p 1x + p 2x Consumer surplus from buying the bundle is p 1x + p 2x - p B Consumer surplus from buying the bundle is p 1x + p 2x - p B Which is this measure Which is this measure Consumer surplus from buying product 1 is p 1x - p 1 Consumer surplus from buying product 1 is p 1x - p 1 The consumer x will buy only product 1 The consumer x will buy only product 1 All consumers in this region buy only product 1 All consumers in this region buy only product 1 Similarly, all consumers in this region buy only product 2 Similarly, all consumers in this region buy only product 2

65. 65 Mixed bundling 3 What should a firm actually do? There is no simple answer –mixed bundling is generally better than pure bundling –but bundling is not always the best strategy Each case needs to be worked out on its merits

66. 66 An Example Four consumers; two products; MC 1 = $100, MC 2 = $150 Consumer Reservation Price for Good 1 Reservation Price for Good 2 Sum of Reservation Prices A B C D $50$450$500 $250$275$525 $300$220$520 $450$50$500

67. 67 The example 2 Consider simple monopoly pricing Consider simple monopoly pricing Good 1: Marginal Cost $100 PriceQuantityTotal revenueProfit $450 $300 $250 $50 1 2 3 4 $450 $600 $750 $200 $350 $400 $450 -$200 $250 Good 2: Marginal Cost $150 PriceQuantityTotal revenueProfit $450 $275 $220 $50 1 2 3 4 $450 $550 $660 $200 $300 $200 $210 -$400 $450 Good 1 should be sold at $250 and good 2 at $450. Total profit is $450 + $300 = $750 Good 1 should be sold at $250 and good 2 at $450. Total profit is $450 + $300 = $750

68. 68 The example 3 Consumer Reservation Price for Good 1 Reservation Price for Good 2 Sum of Reservation Prices A B C D $50$450$500 $250$275$525 $300$220$520 $450$50$500 Now consider pure bundling Now consider pure bundling The highest bundle price that can be considered is $500 The highest bundle price that can be considered is $500 All four consumers will buy the bundle and profit is 4x$500 - 4x($150 + $100) = $1,000 All four consumers will buy the bundle and profit is 4x$500 - 4x($150 + $100) = $1,000

69. 69 The example 4 Consumer Reservation Price for Good 1 Reservation Price for Good 2 Sum of Reservation Prices A B C D $50$450$500 $250$275$525 $300$220$520 $450$50$500 Take the monopoly prices p 1 = $250; p 2 = $450 and a bundle price p B = $500 $500 $250 All four consumers buy something and profit is $250x2 + $150x2 = $800 All four consumers buy something and profit is $250x2 + $150x2 = $800 Now consider mixed bundling Now consider mixed bundling Can the seller improve on this? Can the seller improve on this?

70. 70 The example 5 Consumer Reservation Price for Good 1 Reservation Price for Good 2 Sum of Reservation Prices A B C D $50$450$500 $250$275$525 $300$220$520 $450$50$500 Try instead the prices p 1 = $450; p 2 = $450 and a bundle price p B = $520 $450 $520 $450 All four consumers buy and profit is $300 + $270x2 + $350 = $1,190 All four consumers buy and profit is $300 + $270x2 + $350 = $1,190 This is actually the best that the firm can do

71. 71 Bundling again Bundling does not always work Mixed bundling is always more profitable than pure bundling Mixed bundling is always better than no bundling But pure bundling is not necessarily better than no bundling –Requires that there are reasonably large differences in consumer valuations of the goods Bundling is a form of price discrimination May limit competition

72. 72 Tie-in sales What about tie-in sales? –“like” bundling but proportions vary –allows the monopolist to make supernormal profits on the tied good –different users charged different effective prices depending upon usage –facilitates price discrimination by making buyers reveal their demands

73. 73 Tie-in sales 2 Suppose that a firm offers a specialized product – a camera – that uses highly specialized film cartridges Then it has effectively tied the sales of film cartridges to the purchase of the camera –this is actually what has happened with computer printers and ink cartridges How should it price the camera and film? –suppose also that there are two types of consumer, high- demand and low-demand, with one-thousand of each type –high demand P = 16 – Q h ; low demand P = 12 - Q l –the company does not know which type is which

74. 74 Tie-in sales 3 Film is produced competitively at $2 per picture –so film is priced at $2 per picture Suppose that the company leases its cameras –if priced so that all consumers lease then we can ignore production costs of the camera these are fixed at 2000c Now consider the lease terms

75. 75 Tie-in sales: an example 2 High-Demand Consumers Low-Demand Consumers Demand: P = 16 - Q Demand: P = 12 - Q $ Quantity $16 16 $12 $ 12 Recall that the film sells at $2 per picture $2 14 Low-demand consumers take 10 pictures 10 Consumer surplus for low-demand consumers is $50 $50 Consumer surplus for high-demand consumers is $98 $98 High-demand consumers take 14 pictures So the firm can set a lease charge of $50 to each type of consumer: it cannot discriminate Profit is $50 from each low-demand and high- demand consumer. Total profit is $100,000 Profit is $50 from each low-demand and high- demand consumer. Total profit is $100,000

76. 76 Tie-in sales example 3 This is okay but there may be room for improvement Redesign the camera to tie the camera and the film –technological change that makes the camera work only with the firm’s film cartridge Suppose that the firm can produce film at a cost of $2 per picture Implement a tying strategy that makes it impossible to use the camera without this film

77. 77 Tie-in sales: an example 2 $16 16 $12 12 High-Demand Consumers Low-Demand Consumers Demand: P = 16 - Q Demand: P = 12 - Q $ Quantity $ $2 12 Low-demand consumers take 8 pictures 8 Consumer surplus for low-demand consumers is $32 Each high-demand consumer will lease the camera at $32 Aggregate profit is now $48,000 + $56,000 = $104,000 $4 $32 Lease the camera at $32. Profit is $32 plus $16 in film profits = $48 $16 $32 Profit is $32 plus $24 in film profits = $56 $24 High-demand consumers take 12 pictures Tying increases the firm’s profit Tying increases the firm’s profit

78. 78 Tie-in sales example 3 Why does tying increase profits? –high- demand consumers are offered a quantity discount under both the original and the tied lease arrangement –but tying solves the identification and arbitrage problems film exploits its monopoly in film supply high-demand consumers are revealed by their film purchases quantity discount is then used to increase profit arbitrage is not an issue: both types of consumers pay the same lease and the same unit price for film

79. 79 Tie-in sales example 4 Can the firm do even better? Redesign the camera so that the film cartridge is integral –offer two types of integrated camera/film package: high capacity and low capacity –what capacities? This is similar to second-degree price discrimination –design two cameras with socially efficient capacities: 10 picture and 14 picture –lease these as integrated packages

80. 80 Tie-in sales: an example 2 $16 16 $12 12 High-Demand Consumers Low-Demand Consumers Demand: P = 16 - Q Demand: P = 12 - Q $ Quantity $ $2 Low-demand consumers will pay up to $70 to lease the 10-picure camera Aggregate profit is now $50,000 + $58,000 = $108,000 $70 10 14 10 12 High-demand consumers get $40 consumer surplus by leasing the 10- picure camera $40 $70 $16 So high-demand consumers can be charged $86 to lease the 14-picture camera

81. 81 Complementary goods Complementary goods are goods that are consumed together –nuts and bolts –PC monitors and computer processors How should these goods be produced? How should they be priced? Take the example of nuts and bolts –these are perfect complements: need one of each! Assume that demand for nut/bolt pairs is: Q = A - (P B + P N )

82. 82 Complementary goods 2 Demand curve can be written individually for nuts and bolts For bolts: Q B = A - (P B + P N ) For nuts: Q N = A - (P B + P N ) This gives the inverse demands: P B = (A - P N ) - Q B P N = (A - P B ) - Q N These allow us to calculate profit maximizing prices Assume nuts and bolts are produced by independent firms Each sets MR = MC to maximize profits MR B = (A - P N ) - 2Q B MR N = (A - P B ) - 2Q N Assume MC B = MC N = 0

83. 83 Complementary goods 3 Therefore Q B = (A - P N )/2 and P B = (A - P N ) - Q B = (A - P N )/2 by a symmetric argument P N = (A - P B )/2 The price set by each firm is affected by the price set by the other firm The price set by each firm is affected by the price set by the other firm In equilibrium the price set by the two firms must be consistent In equilibrium the price set by the two firms must be consistent

84. 84 Complementary goods 4 PBPB PNPN Pricing rule for the Bolt Producer: P B = (A - P N )/2 Pricing rule for the Bolt Producer: P B = (A - P N )/2 A/2 A Pricing rule for the Nut Producer: P N = (A - P B )/2 Pricing rule for the Nut Producer: P N = (A - P B )/2 A/2 A Equilibrium is where these two pricing rules intersect Equilibrium is where these two pricing rules intersect P B = (A - P N )/2 P N = (A - P B )/2  P N = A/2 - (A - P N )/4 = A/4 + P N /4  3P N /4 = A/4  P N = A/3  P B = A/3 A/3  P B + P N = 2A/3  Q = A - (P B +P N ) = A/3 Profit of the Bolt Producer = P B Q B = A 2 /9 Profit of the Nut Producer = P N Q N = A 2 /9

85. 85 Complementary goods 5 What happens if the two goods are produced by the same firm? The firm will set a price P NB for a nut/bolt pair. Demand is now Q NB = A - P NB so that P NB = A - Q NB $ Quantity  MR NB = A - 2Q NB A A Demand MR MR = MC = 0  Q NB = A /2 A/2  P NB = A /2 Profit of the nut/bolt producer is P NB Q NB = A 2 /4 Merger of the two firms results in consumers being charged lower prices and the firm making greater profits Why? Because the merged firm is able to coordinate the prices of the two goods

86. 86 Complementary goods 6 Don’t necessarily need a merger to get these benefits –product network ATM networks airline booking systems –one of the markets is competitive price equals marginal cost in this market leads to the “merger” outcome There may also be a countervailing force –network externalities value of a good to consumers increases when more consumers use the good

87. 87 Network externalities Product complementarities can generate network effects –Windows and software applications substantial economies of scale strong network effects –leads to an applications barrier to entry new operating system will sell only if applications are written for it but… So product complementarities can lead to monopoly power being extended

88. 88 Anti-trust and bundling The Microsoft case is central –accusation that used power in operating system (OS) to gain control of browser market by bundling browser into the OS –need\ to show monopoly power in OS OS and browser are separate products with no need to be bundled abuse of power to maintain or extend monopoly position –Microsoft argued that technology required integration –further argued that it was not “acting badly” consumers would benefit from lower price because of the complementarity between OS and browser

89. 89 Microsoft and Netscape Complementarity products –so merge? –what if Netscape refuses? –then Microsoft can develop its own browser –MC ≈ 0 so competition in the browser market drives price close to zero –but then get the outcome of merger firm through competition So Microsoft is not “acting badly” But –JAVA allows applications to be run on Internet browsers –Netscape then constitutes a threat –need to reduce their market share

90. 90 And now… This view gained more force & support in Europe –bundling of Media Player into Windows –Competition Directorate found against Microsoft Microsoft Appealed Microsoft finally lost its appeal in September, 2007 –Result: Microsoft ordered to stop bundling and forced to pay fine of €497 (finally settled in October, 2007) –Some economists upset by this decision arguing that as price discrimination, bundling often expands the market, AND also that bundling/tying can reflect competition and not just market power

91. 91 Competitive Bundling/Tying Bundling and tying are very commonly observed phenomena –Perhaps too commonly observed to be just the outcome of monopoly power –Is there a way to understand competitive bundling? Yes! Salinger and Evans (2005) and Evans (2006) It may well be the case that the structure of demand and the nature of scope and scale economies force competitive firms to bundle tie their goods

92. 92 Competitive Bundling/Tying 2 Consider the table on the next slide and assume consumer willingness to pay is $20 for most preferred option –Competitive firm can’t offer pain reliever & decongestant separately, To do so incurs total fixed cost of $600 Marginal cost of $4 Breakeven price = $6 –50 by pain relief alone and pay $6 per unit –50 by decongestant alone and pay $6 per unit –100 buy both and pay $12 per combined unit Total Revenue = $1800; Total cost = $600 + $4x150 + $4x150 = $1800 –Rival could sell bundled product for $10 and steal all 100 customers interested in joint goods who now pay $12

93. 93 Competitive Bundling/Tying 3 Product Pain ReliefDecongestantBundle Demand 50 100 Costs Fixed Cost $300 Marginal Cost $4 $7 Feasible Prices Separate Goods $6 ----- Pure Bundling ---- $8.50 Mixed Bundling $10 Bundle + Good 1 $10----$9 Bundle + Good 2 ----$10$9 $8.50 is lowest feasible price and is achieve by only offering the bundled product Moral: competitive pressure may be the underlying reason for much bundling

94. 94 Antitrust and tying arrangements Tying arrangements have been the subject of extensive litigation Current policy –tie-in violates antitrust laws if there exists distinct products: tying product & tied one firm tying the products has sufficient market power in the tying market to force purchase of the tied good tying arrangement forecloses or has the potential to foreclose a substantial volume of trade As time passes, approach is more and more of a rule-of- reason standard with increasing recognition that whether price discrimination or competitive pressure is the reason, bundling/tying is often welfare-improving