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Chapter 4

Chapter 4. Product and Pricing Strategies for the Multiproduct Monopolist. Introduction. A monopolist can offer goods of different varieties multiproduct firms The “big” issues: pricing product variety: how many? product bundling: how to bundle how to price

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Chapter 4

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  1. Chapter 4 Product and Pricing Strategies for the Multiproduct Monopolist Industrial Organization: Chapter 4

  2. Introduction • A monopolist can offer goods of different varieties • multiproduct firms • The “big” issues: • pricing • product variety: how many? • product bundling: • how to bundle • how to price • whether to tie the sales of one product to sales of another • Price discrimination Industrial Organization: Chapter 4 4-1

  3. Price Discrimination • This is a natural phenomenon with multiproduct firms • restaurant meals: table d’hôte or à la carte • different varieties of the same car • airline travel • “goods” of different quality are offered at very different prices • Note the constraints • arbitrage • ensuring that consumers buy the “appropriate” good • identification • How to price goods of different quality? Industrial Organization: Chapter 4

  4. Price discrimination and quality • Extract all consumer surplus from the low quality good • Use screening devices • Set the prices of higher quality goods • to meet incentive compatibility constraint • to meet the constraint that higher price is justified by higher quality • One interesting type of screening: crimping the product • offer a product of reasonably high quality • produce lower quality by damaging the higher quality good • student version of Mathematica • different versions of Matlab • the “slow” 486SX produced by damaging the higher speed 486DX • why? • for cost reasons Industrial Organization: Chapter 4

  5. A Spatial Approach to Product Variety • Approach to product quality in Chapter 3 is an example of vertical product differentiation • products differ in quality • consumers have similar attitudes to quality: value high quality • An alternative approach • 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 Industrial Organization: Chapter 4

  6. A Spatial Approach to Product Variety (cont.) • 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) Industrial Organization: Chapter 4

  7. A Spatial Approach to Product Variety (cont.) • 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 unit • The monopolist operates one shop • reasonable to expect that this is located at the center of Main Street Industrial Organization: Chapter 4

  8. The spatial model Suppose that the monopolist sets a price of p1 Price Price p1+ t.x p1 + t.x V V All consumers within distance x1 to the left and right of the shop will by the product t t What determines x1? p1 x = 0 x1 x1 x = 1 1/2 Shop 1 p1 + t.x1 = V, so x1 = (V – p1)/t Industrial Organization: Chapter 4

  9. The spatial model Price Price p1+ t.x Suppose the firm reduces the price to p2? p1 + t.x V V Then all consumers within distance x2 of the shop will buy from the firm p1 p2 x = 0 x2 x1 x1 x2 x = 1 1/2 Shop 1 Industrial Organization: Chapter 4

  10. The spatial model • 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 p(N, 1) = N(V – t/2 – c) – F. Industrial Organization: Chapter 4

  11. 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: p1 = p2 = p • Where should they be located? • What is the optimal price p*? Industrial Organization: Chapter 4

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

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

  14. V V Location with Two Shops 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 Price V - t/4 V - t/4 Profit at each shop is given by the shaded area c c 1/4 1/2 3/4 x = 0 x = 1 Shop 2 Shop 1 Profit is now p(N, 2) = N(V - t/4 - c) – 2F Industrial Organization: Chapter 4

  15. V V By the same argument they should be located at 1/6, 1/2 and 5/6 What if there are three shops? Three Shops Price Price Price at each shop is now V - t/6 V - t/6 V - t/6 x = 0 1/6 1/2 5/6 x = 1 Shop 1 Shop 2 Shop 3 Profit is now p(N, 3) = N(V - t/6 - c) – 3F Industrial Organization: Chapter 4

  16. Optimal Number of Shops • A consistent pattern is emerging. Assume that there are n shops. They will be symmetrically located distance 1/n apart. How many shops should there be? 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 It follows that p(N, n) = V - t/2n Aggregate profit is then p(N, n) = N(V - t/2n - c) – n.F Industrial Organization: Chapter 4

  17. Optimal number of shops (cont.) Profit from n shops is p(N, n) = (V - t/2n - c)N - n.F and the profit from having n + 1 shops is: p*(N, n+1) = (V - t/2(n + 1)-c)N - (n + 1)F Adding the (n +1)th shop is profitable if p(N,n+1) - p(N,n) > 0 This requires tN/2n - tN/2(n + 1) > F which requires that n(n + 1) < tN/2F. Industrial Organization: Chapter 4

  18. An example Suppose that F = $50,000 , N = 5 million and t = $1 Then t.N/2F = 50 So we need n(n + 1) < 50. This gives 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. Industrial Organization: Chapter 4

  19. 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. Industrial Organization: Chapter 4

  20. 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 p = 2N(p – c)(V – p)/t – F • differentiate with respect to p and set to zero: • dp/dp = 2N(V – 2p + c)/t = 0 • So the optimal price at each shop is p* = (V + c)/2 • If all consumers are to be served then 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. Industrial Organization: Chapter 4

  21. 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 Industrial Organization: Chapter 4

  22. Are there too many shops or too few? Social Optimum What number of shops maximizes total surplus? 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 surplus is then total willingness to pay minus total costs Total willingness to pay by consumers is N.V Total surplus is therefore N.V - Total Cost So what is Total Cost? Industrial Organization: Chapter 4

  23. V V Assume that there are n shops Social optimum (cont.) Price Price Transport cost for each shop is the area of these two triangles multiplied by consumer density Consider shop i Total cost is total transport cost plus set-up costs t/2n t/2n 1/2n 1/2n x = 0 x = 1 Shop i This area is t/4n2 Industrial Organization: Chapter 4

  24. Social optimum (cont.) Total cost with n shops is, therefore: C(N,n) = n(t/4n2)N + n.F = tN/4n + n.F If t = $1, F = $50,000, N = 5 million then this condition tells us that n(n+1) < 25 Total cost with n + 1 shops is: C(N,n+1) = tN/4(n+1)+ (n+1).F There should be five shops: with n = 4 adding another shop is efficient 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 Industrial Organization: Chapter 4

  25. Monopoly, 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 • 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. Industrial Organization: Chapter 4

  26. Price Discrimination and Product Variety • 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 N.V – N.c Total transport costs plus set-up costs is C(N, n)=tN/4n + n.F So profit is p(N,n) = N.V – N.c – C(N,n) But then maximizing profit means minimizing C(N, n) The discriminating monopolist operates the socially optimal number of shops. Industrial Organization: Chapter 4

  27. Bundling • Firms sell goods as bundles • selling two or more goods in a single package • complete stereo systems • fixed-price meals in restaurants • Firms also use tie-in sales: less restrictive than bundling • tie the sale of one good to the purchase of another • computer printers and printer cartridges • constraining the use of spare parts • Why? • Because it is profitable to do so! Industrial Organization: Chapter 4

  28. Bundling: an example How much can be charged for Godzilla? How much can be charged for Casablanca? • Two television stations offered two old Hollywood films • Casablanca and Son of Godzilla • Arbitrage is possible between the stations • Willingness to pay is: If the films are sold separately total revenue is $19,000 $7,000 Willingness to pay for Casablanca Willingness to pay for Godzilla $2,500 Station A $8,000 $2,500 Station B $7,000 $3,000 Industrial Organization: Chapter 4

  29. How much can be charged for the package? Bundling is profitable because it exploits aggregate willingness pay Bundling: an example Now suppose that the two films are bundled and sold as a package If the films are sold as a package total revenue is $20,000 Willingness to pay for Casablanca Willingness to pay for Godzilla Total Willingness to pay Station A $8,000 $2,500 $10,500 Station B $7,000 $3,000 $10,000 $10,000 Industrial Organization: Chapter 4

  30. Bundling (cont.) • Extend this example to allow for • costs • mixed bundling: offering products in a bundle and separately Industrial Organization: Chapter 4

  31. y py2 x px2 px1 py1 Consumer y has reservation price py1 for good 1 and py2 for good 2 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 Bundling: another example Suppose that the firm sets price p1 for good 1 and price p2 for good 2 All consumers in region B buy only good 2 All consumers in region A buy both goods Consumer x has reservation price px1 for good 1 and px2 for good 2 R2 B A All consumers in region C buy neither good All consumers in region D buy only good 1 Consumers split into four groups p2 D C p1 R1 Industrial Organization: Chapter 4

  32. Bundling: the example (cont.) Now consider pure bundling at some price pB R2 All consumers in region E 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 pB E Consumers now split into two groups All consumers in region F do not buy the bundle F c2 c1 pB R1 Industrial Organization: Chapter 4

  33. Mixed Bundling Now consider mixed bundling In this region consumers buy either the bundle or product 2 Consumers in this region buy only good 2 Good 1 is sold at price p1 R2 Consumers in this region are willing to buy both goods. They buy the bundle Consumers in this region also buy the bundle Good 2 is sold at price p2 pB This leaves two regions Consumers split into four groups: buy the bundle buy only good 1 buy only good 2 buy nothing p2 In this region consumers buy either the bundle or product 1 Consumers in this region buy nothing Consumers in this region buy only good 1 The bundle is sold at price pB < p1 + p2 pB - p1 pB - p2 p1 pB R1 Industrial Organization: Chapter 4

  34. Mixed Bundling (cont.) Similarly, all consumers in this region buy only product 2 R2 The consumer x will buy only product 1 pB Consider consumer x with reservation prices p1x for product 1 and p2x for product 2 p2 All consumers in this region buy only product 1 Which is this measure Consumer surplus from buying product 1 is p1x - p1 Consumer surplus from buying the bundle is p1x + p2x - pB Her aggregate willingness to pay for the bundle is p1x + p2x pB - p1 x p2x pB - p2 p1 pB p1x R1 p1x+p2x Industrial Organization: Chapter 4

  35. Mixed Bundling (cont.) • 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 Industrial Organization: Chapter 4

  36. An Example Four consumers; two products; MC1 = $100, MC2 = $150 Reservation Price for Good 1 Reservation Price for Good 2 Sum of Reservation Prices Consumer A $50 $450 $500 B $250 $275 $525 $300 $220 $520 C D $450 $50 $500 Industrial Organization: Chapter 4

  37. The example (cont.) Good 1: Marginal Cost $100 Consider simple monopoly pricing Price Quantity Total revenue Profit $450 1 $450 $350 $300 2 $400 $600 Good 1 should be sold at $250 and good 2 at $450. Total profit is $450 + $300 = $750 $250 $250 3 $750 $450 $50 4 $200 -$200 Good 2: Marginal Cost $150 Price Quantity Total revenue Profit $450 $450 1 $450 $300 $275 2 $200 $550 $220 3 $660 $210 $50 4 $200 -$400 Industrial Organization: Chapter 4

  38. The example (cont.) Now consider pure bundling Reservation Price for Good 1 Reservation Price for Good 2 Sum of Reservation Prices Consumer 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 A $50 $450 $500 B $250 $275 $525 $300 $220 $520 C D $450 $50 $500 Industrial Organization: Chapter 4

  39. The example (cont.) Now consider mixed bundling Take the monopoly prices p1 = $250; p2 = $450 and a bundle price pB = $500 All four consumers buy something and profit is $250x2 + $150x2 = $800 Reservation Price for Good 1 Reservation Price for Good 2 Sum of Reservation Prices Consumer Can the seller improve on this? A $50 $450 $500 $500 B $250 $275 $525 $500 $250 $300 $220 $520 C D $450 $250 $50 $500 Industrial Organization: Chapter 4

  40. The example (cont.) This is actually the best that the firm can do Try instead the prices p1 = $450; p2 = $450 and a bundle price pB = $520 All four consumers buy and profit is $300 + $270x2 + $350 = $1,190 Reservation Price for Good 1 Reservation Price for Good 2 Sum of Reservation Prices Consumer A $50 $450 $450 $500 B $250 $275 $520 $525 $300 $220 $520 $520 C D $450 $450 $50 $500 Industrial Organization: Chapter 4

  41. Bundling (cont.) • Bundling does not always work • Requires that there are reasonably large differences in consumer valuations of the goods • 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 Industrial Organization: Chapter 4

  42. Tie-in Sales • 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 that marginal costs of the film and of making the camera are zero (to keep things simple) • suppose also that there are two types of consumer: high-demand and low-demand Industrial Organization: Chapter 4

  43. Suppose that the firm leases the product for $72 per period Profit is $72 from each type of consumer So this gives profit of $144 per pair of high-and low-demand consumers Tie-In Sales: an Example High-Demand Consumers Low-Demand Consumers Is this the best that the firm can do? Demand: P = 16 - Q Demand: P = 12 - Q $ $ $16 Low-demand consumers are willing to buy 12 units $12 High-demand consumers buy 16 units $128 $72 16 12 Quantity Quantity Industrial Organization: Chapter 4

  44. Tie-In Sales: an Example Suppose that the firm sets a price of $2 per unit Profit is $70 from each low-demand consumer: $50 + $20 and $78 from each high-demand consumer: $50 + $28 giving $148 per pair of high-demand and low-demand So the firm can set a lease charge of $50 to each type of consumer: it cannot discriminate High-Demand Consumers Low-Demand Consumers Demand: P = 16 - Q Demand: P = 12 - Q Consumer surplus for low-demand consumers is $50 $ $ Consumer surplus for high-demand consumers is $98 $16 $12 Low-demand consumers buy 10 units High-demand consumers buy 14 units $98 $50 $2 $2 14 16 10 12 Quantity Quantity Industrial Organization: Chapter 4

  45. Suppose that the firm can bundle the two goods instead of tie them Tie-In Sales: an Example Profit is $72 from each low-demand consumer and $80 from each high-demand consumer giving $150 per pair of high-demand and low-demand High-Demand Consumers Low-Demand Consumers Produce a bundled product of camera plus 12-shot cartridge So produce a second bundle of camera plus 16-shot cartridge Demand: P = 16 - Q Demand: P = 12 - Q $ $ High-demand consumers get $48 consumer surplus from buying it $16 High-demand consumers will pay $80 for this bundled camera ($128 - $48) $12 Low-demand consumers can be sold this bundled product for $72 $48 $72 $72 $8 12 16 12 Quantity Quantity Industrial Organization: Chapter 4

  46. 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 - (PB + PN) Industrial Organization: Chapter 4

  47. Complementary goods (cont.) This demand curve can be written individually for nuts and bolts For bolts: QB = A - (PB + PN) For nuts: QN = A - (PB + PN) These give the inverse demands: PB = (A - PN) - QB PN = (A - PB) - QN These allow us to calculate profit maximizing prices Assume that nuts and bolts are produced by independent firms Each sets MR = MC to maximize profits MRB = (A - PN) - 2QB Assume MCB = MCN = 0 MRN = (A - PB) - 2QN Industrial Organization: Chapter 4

  48. Complementary goods (cont.) Therefore QB = (A - PN)/2 and PB = (A - PN) - QB = (A - PN)/2 by a symmetric argument PN = (A - PB)/2 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 Industrial Organization: Chapter 4

  49. Complementary goods (cont.) PB = (A - PN)/2 PN = (A - PB)/2 Pricing rule for the Nut Producer: PN = (A - PB)/2 PB  PN = A/2 - (A - PN)/4 Equilibrium is where these two pricing rules intersect A = A/4 + PN/4 Pricing rule for the Bolt Producer: PB = (A - PN)/2  3PN/4 = A/4  PN = A/3  PB = A/3 A/2  PB + PN = 2A/3 A/3  Q = A - (PB+PN) = A/3 Profit of the Bolt Producer = PBQB = A2/9 A/3 A/2 A PN Profit of the Nut Producer = PNQN = A2/9 Industrial Organization: Chapter 4

  50. Complementary goods (cont.) Merger of the two firms results in consumers being charged lower prices and the firm making greater profits What happens if the two goods are produced by the same firm? The firm will set a price PNB for a nut/bolt pair. Why? Because the merged firm is able to coordinate the prices of the two goods Demand is now QNB = A - PNB so that PNB = A - QNB $  MRNB = A - 2QNB MR = MC = 0 A  QNB = A /2  PNB = A /2 A/2 Profit of the nut/bolt producer is PNBQNB = A2/4 Demand MR A/2 A Quantity Industrial Organization: Chapter 4

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