1. Chapter 7: Product Variety and Quality under Monopoly 1 Product Variety and Quality under Monopoly

2. Chapter 7: Product Variety and Quality under Monopoly 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. Chapter 7: Product Variety and Quality under Monopoly 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. Chapter 7: Product Variety and Quality under Monopoly 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. Chapter 7: Product Variety and Quality under Monopoly 5 An geographic example of product variety McDonald’sBurger KingWendy’s

6. Chapter 7: Product Variety and Quality under Monopoly 6 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

7. Chapter 7: Product Variety and Quality under Monopoly 7 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

8. Chapter 7: Product Variety and Quality under Monopoly 8 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

9. Chapter 7: Product Variety and Quality under Monopoly 9 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.

10. Chapter 7: Product Variety and Quality under Monopoly 10 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*?

11. Chapter 7: Product Variety and Quality under Monopoly 11 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

12. Chapter 7: Product Variety and Quality under Monopoly 12 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

13. Chapter 7: Product Variety and Quality under Monopoly 13 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

14. Chapter 7: Product Variety and Quality under Monopoly 14 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

15. Chapter 7: Product Variety and Quality under Monopoly 15 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?

16. Chapter 7: Product Variety and Quality under Monopoly 16 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.

17. Chapter 7: Product Variety and Quality under Monopoly 17 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.

18. Chapter 7: Product Variety and Quality under Monopoly 18 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

19. Chapter 7: Product Variety and Quality under Monopoly 19 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.

20. Chapter 7: Product Variety and Quality under Monopoly 20 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

21. Chapter 7: Product Variety and Quality under Monopoly 21 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?

22. Chapter 7: Product Variety and Quality under Monopoly 22 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

23. Chapter 7: Product Variety and Quality under Monopoly 23 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

24. Chapter 7: Product Variety and Quality under Monopoly 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. Chapter 7: Product Variety and Quality under Monopoly 25 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

26. Chapter 7: Product Variety and Quality under Monopoly 26 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.

27. Chapter 7: Product Variety and Quality under Monopoly 27 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.

28. Chapter 7: Product Variety and Quality under Monopoly 28 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

29. Chapter 7: Product Variety and Quality under Monopoly 29 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

30. Chapter 7: Product Variety and Quality under Monopoly 30 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 )

31. Chapter 7: Product Variety and Quality under Monopoly 31 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

32. Chapter 7: Product Variety and Quality under Monopoly 32 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

33. Chapter 7: Product Variety and Quality under Monopoly 33 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

34. Chapter 7: Product Variety and Quality under Monopoly 34 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

35. Chapter 7: Product Variety and Quality under Monopoly 35 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?

36. Chapter 7: Product Variety and Quality under Monopoly 36 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

37. Chapter 7: Product Variety and Quality under Monopoly 37 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

38. Chapter 7: Product Variety and Quality under Monopoly 38 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

39. Chapter 7: Product Variety and Quality under Monopoly 39 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

40. Chapter 7: Product Variety and Quality under Monopoly 40 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

41. Chapter 7: Product Variety and Quality under Monopoly 41 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

42. Chapter 7: Product Variety and Quality under Monopoly 42 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

43. Chapter 7: Product Variety and Quality under Monopoly 43 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:

44. Chapter 7: Product Variety and Quality under Monopoly 44 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

45. Chapter 7: Product Variety and Quality under Monopoly 45 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!

46. Chapter 7: Product Variety and Quality under Monopoly 46 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.

47. Chapter 7: Product Variety and Quality under Monopoly 47 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

48. Chapter 7: Product Variety and Quality under Monopoly 48 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

49. Chapter 7: Product Variety and Quality under Monopoly 49 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.

50. Chapter 7: Product Variety and Quality under Monopoly 50 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.

51. Chapter 7: Product Variety and Quality under Monopoly 51 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.

52. Chapter 7: Product Variety and Quality under Monopoly 52 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

53. Chapter 7: Product Variety and Quality under Monopoly 53 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

54. Chapter 7: Product Variety and Quality under Monopoly 54 Demand and quality Derivation of aggregate demand Order consumers by their reservation prices Aggregate individual demand horizontally Price Quantity 12345678

55. Chapter 7: Product Variety and Quality under Monopoly 55 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.

56. Chapter 7: Product Variety and Quality under Monopoly 56 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.