Industrial OrganizationGraduate-level Lecture Notesby Oz Shywww.ozshy.comFile=gradio21.tex Revised=2007/12/11 12:19Contents1 Monopoly 11.1 Swans Durability Theorem 11.2 Durable Goods Monopoly 21.3 Monopoly and Planned Obsolescence 42 A Taxonomy of Business Strategies 72.1 Major Issues 72.2 Is there Any Advantage to the First Mover? 72.3 Classication of Best-Response Functions 82.4 The Two-stage Game 92.5 Cost reduction investment: makes rm 1 tough 102.6 Advertising investment: makes rm 1 soft 103 Product Dierentiation 123.1 Major Issues 123.2 Horizontal Versus Vertical Dierentiation 123.3 Horizontal Dierentiation: Hotellings Linear City Model 133.4 Horizontal Dierentiation: Behavior-based Pricing 153.5 Horizontal Dierentiation: Salops Circular City 183.6 Vertical Dierentiation: A Modied Hotelling Model 193.7 Non-address Approach: Monopolistic Competition 213.8 Damaged Goods 234 Advertising 254.1 Major Issues 254.2 Persuasive Advertising: Dorfman-Steiner Condition 254.3 Informative Advertising 265 R&D and Patent Law 305.1 Classications of Process Innovation 305.2 Innovation Race 315.3 R&D Joint Ventures 345.4 Patents 365.5 Appropriable Rents from Innovation in the Absence of Property Rights 386 Capacities and Preemption 406.1 Investment and entry deterrence 406.2 Spatial preemption 417 Limit Pricing 43(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)CONTENTS v8 Predation 458.1 Judo Economics 458.2 The Chain-Store Paradox 479 Facilitating Practices 489.1 A Meeting Competition Clause 489.2 Tying as a Facilitating Practice 49(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)Topic 1Monopoly1.1 Swans Durability Theorem Durability can be viewed as aspect of quality of a product. Suppose that rms control the durability for the products they produce. Of course, unit cost rises monotonically with durability. Loose formulation of Swans independence result: Durability (or even quality) does not vary withthe market structure. More accurate formulation: A monopoly will choose the same durability level as the social planner,which is the same as the one chosen by competitive rms. Intuition: It is sucient for a monopoly to exercise its power using a price distortion, so qualitydistortion need not be utilized. Therefore: A monopoly (or any producer) distorts quality only if it cannot set the monopolys prot-maximizing price. Example: Rent control in NYC: Landlords dont maintain their buildings.A light bulb illustration of Swans independence resultFor a more general formulation see Tirole p.102. $V = consumers maximum willingness to pay for lighting service per unit of time c1 = unit production cost of a light bulb which lasts for one unit of time. c2 = unit production cost of a light bulb which lasts for two unit of time. Assumption: 0 < c1 < V , 0 < c2 < 2V , and c1 < c2. Remark: At this stage we dont specify whether c2 < 2c1 (economies of durability production).Monopolys prot over 2 periods Produces nondurables: pm1 = $V , hence m1 = 2(V c1). Produces durables: pm2 = 2$V , hence m2 = 2V c2. Hence, m2 m1 if and only if c2 2c1 (cost consideration only).(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)1.2 Durable Goods Monopoly 2Competitive industry Many competing rms each oers long and short durability of light bulbs. Competitive prices: p1 = c1 and p2 = c2, both available in stores. Consumers buy durable if and only if 2V p2 2(V p1) implying that c2 2c1.Result: Monopoly and competitive markets produce the same durability which would be also chosen bythe social planner.1.2 Durable Goods Monopoly Coases Conjecture: A monopoly selling a durable good will charge below the price a monopolycharges for a nondurable (per period of usage). Two-period lived consumers, t, t = 1, 2. The good is per-period transportation services obtained from a car. A continuum of consumers having dierent valuations, v [0, 100]. Utility function of type v: U def= max{v pt, 0}.(Instructor : Explain the 2 interpretations of demand curves). Hence, inverse demand for one period of service: pt = 100 Qt. Monopoly sells a durable product that lasts for two periods (zero costs)

`

`````````````````p1p2q2q1MR1(q1) MR2(q2)D2D1 q1 100 q12100 q1100100 q1100 `

Figure 1.1: Durable-good monopoly: the case of downward sloping demandThe monopoly has two options:Sell: for a price of pS(transfer all ownership rights)Rent (lease): For a price of pRt for period t (renter maintains ownership).(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)1.2 Durable Goods Monopoly 31.2.1 A renting (leasing) monopolyThe consumer leases Qt each period t = 1, 2. The monopoly solvesMR(Qt) = 100 2Qt = 0 = MC(Qt) = QRt = 50, pRt = 50, and Rt = 2, 500 for t = 1, 2.Hence, the life-time sum of prots of the renting monopoly is given by R= 5, 000.1.2.2 A seller monopoly The seller knows that those consumers who purchase the durable good in t = 1 will not repurchasein period t = 2. Thus, in t = 2 the monopoly will face a lower demand. The reduction in t = 2 demand equals exactly the amount it sold in t = 1. Therefore, in t = 2 the monopoly will have to sell at a lower price than in t = 1. We compute a SPE for this two-period game.The second period Suppose that the monopoly sells q1 units have been sold in t = 1. t = 2 residual demand is q2 = 100 q1 p2 or p2 = 100 q1 q2. In t = 2 the monopoly solvesMR2(q2) = 100 q1 2q2 = 0 = q2 = 50 q12 .Hence, the second period price and prot levels are given byp2( q1) = 100 q1

50 q12

= 50 q12 , and 2( q1) = p2q2 =

50 q12

2.The rst period Given expected p1 and p2, nd the consumer type v who is indierent between buying at t = 1 andpostponing to t = 2. The indierent consumer must satisfy 2 v p1 = v p2. Substitute v = 100 q1 (only high vs buy at t = 1) to obtain 2 v. .. .(100 q1) p1 = v. .. .(100 q1) q2.Hence,2(100 q1) p1 = (100 q1)

50 q12

. .. .q2.Solving for p1 yieldsp1 = 150 3 q12 .(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)1.3 Monopoly and Planned Obsolescence 4In a SPE the selling monopoly chooses a rst-period output level q1 that solvesmaxq1(1 +2) =

150 3q12

q1. .. .1+

50 q12

2. .. .2(1.1)yielding a rst-order condition given by0 = (1 +2)q1= 150 3q1 100 q12 = 100 5q12 .Denoting the solution values by a superscript S, we have that qS1 = 40, qS2 = 50 40/2 = 30,pS2 = 50 40/2 = 30 and pS1 = 100 40 + 30 = 90. Hence,S= pS1qS1 +pS2qS2 = 4, 500 < 5, 000 = pm.These results manifest Coases conjecture. Therefore, a monopoly selling a durable goods earns a lower prot than a renting monopoly. This result has led some economists to claim that monopolies have the incentives to produce lessthan an optimal level of durability (e.g., light bulbs that burn very fast). We discuss the (in)validity of this argument in Sections 1.1 and 1.31.3 Monopoly and Planned Obsolescence The literature on planned obsolescence may suggest that a monopoly my shorten durability in orderto enhance future sales. But, look at your old computer, old printer, old TV, old music player. Dont you want to replacethem with newer faster models? Arent they too durable? Here we ask: Is short durability really bad? Answer: No, according to Fishman, Gandal, and Shy (1993) short durability may have some welfareenhancing eects such as the introduction of new technologies. Overlapping generations model, each t = 1, 2, . . . one two-period lived consumer enters the market. One good that can be improved via innovation, many rms. Each rm can produced a durable which lasts for 2 periods with unit cost cD. Each rm can produced a nondurable which lasts 1 period with unit cost cND. Assumption: Production of a durable is less costly: cD< 2cND. The utility from the initial technology at t = 0 is v > 0 Utility from period t state-of-the-art technology under continuous innovation: tv, where > 1. Continuous innovation means that technology t1v prevailed at in t 1. Each t one rm is randomly endowed with ability to invest F and improve upon t 1 technology. Instructor : You must stress that this exposition compares only continuous innovation with continuousstagnation (simplication).(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)1.3 Monopoly and Planned Obsolescence 51.3.1 Welfare analysis of durabilityWelfare analysis: Continuous stagnation (No innovation) Per-period welfare given that only nondurables are sold: W = 2(v cND). Per-period welfare given that only durables are sold: W = 2v cD. Hence, welfare is higher when durables are produced since cD< 2cND. ()Welfare analysis: Continuous innovation Per-period welfare given that only nondurables are sold: W = 2(tv cND) F. Per-period welfare given that only durables are sold: W = tv + t1v cD F (old guys dontswitch to the new technology). Hence, welfare is higher when nondurables are produced if 2cNDcD t1( 1)v. In particular, it must hold in t = 1, hence, 2cNDcD ( 1)v. () Remark: In the paper we assume that the above condition holds.1.3.2 Prot-maximizing choice of durability and innovationInstructor : Explain that this paper does not solve for a SPE. It only searches for an outcome which ismore protable to rms in the long run.Prot under continuous stagnation (No innovation) Prices fall to marginal costs (no rm maintains any patent right): pD= cDand pND= cND. Consumers buy only durables since cD< 2cNDimplies UD= 2v cD> 2(v cND) = UND. ()Prot under continuous innovation The prices and prots below are for 2 consumption periods. Maximum price that can be charged for a nondurable is solved from: tv pND t1v cND,because consumers can always buy an outdated nondurable for a price of cND. Hence, pND t1( 1)v +cND. Therefore, ND= 2(pNDcND) F = 2t1( 1)v F. () Maximum price that can be charged for a durable is solved from: 2tvpD t1vcND+tvcND,because consumers can always buy an outdated nondurable for a price of cND. Hence, pD t1( 1)v + 2cND. Therefore, D= pDcDF = t1( 1)v cD+ 2cNDF. (selling to young only) () Remark: Notice that outdated durables are also available at competitive prices. Hence, we shouldalso verify that pDalso satises 2tv pD 2t1v cD.(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)1.3 Monopoly and Planned Obsolescence 6 Comparing the two prot levels marked by (), we conclude that, under continuous innovation,production of nondurables is more protable than durables, ND D 2cNDcD t1(1)v. In particular, it must hold in t = 1, hence, 2cNDcD ( 1)v. () Hence, if the production of ND is protable, it is also socially optimal.Summary of results: A welfare evaluation of prot decisionsContinuous stagnation: Comparing the two outcomes marked by (), production of nondurables is bothunprotable and socially undesirable.Continuous innovation: Comparing the two outcomes marked by (), production of durables is bothunprotable and socially undesirable 2cNDcD ( 1)v.Conclusion: Planned obsolescence (short durability) is essential for technology growth.(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)Topic 2A Taxonomy of Business Strategies2.1 Major Issues(1) Reinterprets Stackelberg (sequential-moves) equilibrium as a sequence of commitments, rather thanas a sequential-move output (production game).(2) Commitments (other than output and price, not really commitments) include:(a) investment in capital(b) advertising cost(c) choice of standard(d) contracts(e) brand diversity (brand prolication)(f) coupons and price commitment(3) Major question: should the rst mover engage in over or under investment in the relevant strategicvariable?(4) To provide a classication of dierent optimal behavior of the rst mover.2.2 Is there Any Advantage to the First Mover?Not necessarily! In sequential-move price games, or auction games, the last mover earns higher protthan the rst mover.q1 = 168 2p1 +p2 and q2 = 168 +p1 2p2. (2.1)The single-period game Bertrand prices and prot levels are pbi = 56 and bi = 6272 (assuming costlessproduction).We look for a SPE in prices where rm 1 sets its price before rm 2.In the rst period, rm 1 takes rm 2s best-response function as given, and chooses p1 that solvesmaxp11(p1, R2(p1)) =

168 2p1 + 168 +p14

p1. (2.2)The rst-order condition is0 = 1p1= 210 72p1.Therefore, ps1 = 60, hence, ps2 = 57. Substituting into (2.1) yields that qs1 = 105 and q2 = 114. Hence,s1 = 60 105 = 6300 > b1, and s2 = 57 114 = 6498 > b2.(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)2.3 Classication of Best-Response Functions 8Result 2.1Under a sequential-moves price game (or more generally, under any game where actions are strategicallycomplements):(a) Both rms collect a higher prot under a sequential-moves game than under the single-periodBertrand game. Formally, si > bi for i = 1, 2.(b) The rm that sets its price rst (the leader) makes a lower prot than the rm that sets its pricesecond (the follower).(c) Compared to the Bertrand prot levels, the increase in prot to the rst mover (the leader) issmaller than the increase in prot to the second mover (the follower). Formally, s1b1 < s2b2.Reason: Firm 1 is slightly undercut in the 2nd period. Therefore, it keeps the price above the Bertrandlevel.2.3 Classication of Best-Response FunctionsConsider a static two-rm Nash game.Action/Strategy space: xi strategic variable of rm i, i = 1, 2. xi [0, ]. If xi = qi, we haveCournot-quantity game. If xi = pi, we have Bertrand-price game.Payo Functions:i(xi, xj) = ( xi +xj)xi, > 0.Note: the sign of is not specied!Assumption 2.1Own-price eect: > 0, ( < 0), (also, need for concavity w/r/t xi)Cross eect: 2> 2may need to be assumed (meaning that own eect is stronger than the crosseect). This assumption also implies the following:Stability:

21(x1)2

22(x2)2

= 42> 2=

21(x1)(x2)

22(x1)(x2)

,meaning that the own-price coecient dominates the rivals price coecient.The rst-order conditions yield the best-response functionsxi = Ri(xj) = 2 + 2xj, i, j = 1, 2; i = j. (2.3)Definition 2.1(a) Players strategies are said to be strategic substitutes if the best-response functions are downwardsloping. That is, if R

i(pj) < 0 ( < 0 in our example).(b) Players strategies are said to be strategic complements if the best-response functions are upwardsloping. That is, if R

i(pj) > 0 ( > 0 in our example).Note: Strategic substitutes and complements are dened by whether a more aggressive strategyby 1 lowers or raises 2s marginal prot.Solving the two best-response function yieldxN1 = xN2 = 2 , and N1 = N2 = 2(2 )2. (2.4)(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)2.4 The Two-stage Game 9

x1x2````````````R1(x2)R2(x1)22xN1xN2

x1x2`>>>>>>>>>>>>>>>>/////////////R2(x1)R1(x2)xN2xN122Figure 2.1: Left: Strategic substitutes. Right: Strategic complements2.4 The Two-stage GameTwo-stage game.Stage 1: Incumbent chooses to invest k1.Stage 2: k1 = k1 is given. Incumbent and entrant play Nash in x1(k1) and x2(k1), respectively. Prots,N1 (x1(k1), x2(k1)) and N2 (x1(k1), x2(k1)), are collected.Remarks:(1) the post-entry market structure is given.(2) if N2 = 0, we say that entry is deterred.(3) assume that entry is accommodated.What is the eect of increasing k1 on 1? The total eect is dened byd1dk1....Total Eect= 1k1....Direct Eect+ 1x2dx2dk1. .. .Strategic Eect.Now,dx2dk1= x2x1 dx1dk1= R

2(x1) dx1dk1.Assumption 2.2(a) There are no direct eects. Formally,1k1= 0.(b)sign

1x2

= sign

2x1

.Hence,sign

1x2dx2dk1

= sign

2x1dx1dk1

sign

R

2

(2.5)(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)2.5 Cost reduction investment: makes rm 1 tough 10Definition 2.2Investment makes rm 1 tough ( soft) if2x1dx1dk1< 0 (> 0).Investment makes rm 1Tough SoftR

> 0 (complements) Puppy dog (underinvest) Fat cat (overinvest)R

< 0 (substitutes) Top dog (overinvest) Lean & hungry (underinvest)Table 2.1: Classication of optimal business strategies.2.5 Cost reduction investment: makes rm 1 toughStage 1: rm 1 chooses k1 which lowers its marginal costStage 2: rms compete in quantities or prices

`

`q1q2p1p2R1(q2)R2(q1)-

`R1(p2)R2(p1) .Figure 2.2: Investment makes 1 tough. Left: quantity game. Right: price game.Quantity game: k1 = q1 = 2 = 2q1dq1dk1< 0 = Tough!Hence, should overinvest (Top dog).Price game: k1 = p1 = 2 = 2p1dp1dk1< 0 = Tough!Hence, should underinvest (Puppy dog).2.6 Advertising investment: makes rm 1 softStage 1: rm 1 chooses k1 which boosts its demandStage 2: rms compete in quantities or prices(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)2.6 Advertising investment: makes rm 1 soft 11

`

`q1q2p1p2R1(q2)R2(q1)

`R1(p2)R2(p1)` `

Figure 2.3: Investment makes 1 soft. Left: quantity game. Right: price game.Quantity game: k1 = q1 = 2 = 2q1dq1dk1> 0 = Soft!Hence, should underinvest (Lean & hungry look).Price game: k1 = p1 = 2 = 2p1dp1dk1> 0 = Soft!Hence, should overinvest (Fat cat).(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)Topic 3Product Dierentiation3.1 Major Issues(1) Firms choose the specication of the product in addition to price. (Specication may be quality ingeneral and durability in particular).(2) Firms choose to dierentiate their brand to reduce competition (maintain higher monopoly power).(3) Policy question: Too much dierentiation? Or, too little?3.2 Horizontal Versus Vertical DierentiationWe demonstrate the dierence using Hotellings model.

0011xxAA BBFigure 3.1: Horizontal versus vertical dierentiation. Up: horizontal dierentiation; Down: vertical dierentia-tionUx

pA |x A| if he buys from ApB |x B| if she buys from B > 0. (3.1)Definition 3.1Let brand prices be given.(a) Dierentiation is said to be horizontal if, when the level of the products characteristic is augmentedin the products space, there exists a consumer whose utility rises and there exists another consumerwhose utility falls.(b) Dierentiation is said to be vertical if all consumers benet when the level of the products char-acteristic is augmented in the product space. In Figure 3.1, brands are horizontally dierentiated if A, B < 1, and vertically dierentiated whenA, B > 1. As increases, dierentiation increases. When 0 the brands become perfect substitutes, whichmeans that the industry becomes more competitive.(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)3.3 Horizontal Dierentiation: Hotellings Linear City Model 13 Alternative denition of vertical dierentiations is that if all brands are equally priced, all consumersprefer one brand over all others.3.3 Horizontal Dierentiation: Hotellings Linear City Model Firm B is located to the right of rm A, b units of distance from point L. Each consumer buys one unit of the product. Production is costless (not critical)0 LB A x b , a ,aL bFigure 3.2: Hotellings linear city with two rmsThe utility function of a consumer located at point x byUx

pA |x a| if he buys from ApB |x (L b)| if she buys from B. (3.2)Here there is no reservation utility. Adding a reservation utility may result in partial market coverage inthe sense that consumers around the center will prefer not to buy any brand.Formally, if a < x < L b, thenpA ( x a) = pB (L b x).Hence, x = pB pA2 + (L b +a)2 ,which is the demand function faced by rm A. The demand function faced by rm B isL x = pA pB2 + (L +b a)2 .We now look for a Bertrand-Nash equilibrium in price strategies. That is, Firm A takes pB as givenand chooses pA tomaxpAA = pBpA (pA)22 + (L b +a)pA2 . (3.3)The rst-order condition is given by0 = ApA= pB 2pA2 + (L b +a)2 . (3.4)Firm B takes pA as given and chooses pB tomaxpBB = pBpA (pB)22 + (L +b a)pB2 . (3.5)(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)3.3 Horizontal Dierentiation: Hotellings Linear City Model 14The rst-order condition is given by0 = BpB= pA 2pB2 + L +b a2 .Hence, the equilibrium prices are given byphA = (3L b +a)3 and phB = (3L +b a)3 . (3.6)The equilibrium market share of rm A is given by xh= 3L b +a6 . (3.7)Note that if a = b, then the market is equally divided between the two rms. The prot of rm A isgiven byhA = xhphA = (3L b +a)218 , (3.8)Shows the Principle of Minimum Dierentiation.Result 3.1(a) If both rms are located at the same point (a+b = L, meaning that the products are homogeneous),then pA = pB = 0 is a unique equilibrium.(b) A unique equilibrium exists and is described by (3.6) and (3.7) if and only if the two rms are nottoo close to each other; formally if and only if

L + a b3

2 4L(a + 2b)3 and

L + b a3

2 4L(b + 2a)3the unique equilibrium is given by (3.6), (3.7), and (3.8).Proof. (1) When a +b = 1...undercutting (Bertrand).To demonstrate assume a = b, a < L/2. Then, we are left to show that the equilibrium exists if andonly if L2 4La, or if and only if a L/4.When a = b, the distance between the two rms is L 2a.Also, if equilibrium exists, pA = pB = L.Figure 3.3 has three regions:Region I: Aa maximal prot is given by A = pAL.Region II: Substituting the equilibrium pB = L into (3.3) yieldsA = L2 + L2pA (pA)22 , (3.9)which is drawn in Region II of Figure 3.3. Maximizing (3.9) with respect to pA yields A = L2/2.Region III: High price, no market share.In equilibriumIIA = L22 IA = [L (L 2a)]L = 2aL,implying that a L/4.(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)3.4 Horizontal Dierentiation: Behavior-based Pricing 15

Region II Region I Region IIIApA. .. .L (L 2a). .. .L +(L 2a)L`L222aL Figure 3.3: Existence of equilibrium in the linear city: The prot of rm A for a given pB = L3.4 Horizontal Dierentiation: Behavior-based Pricing Suppose that rms can identify consumers who have purchased their brands before. How? For example, by product registration, frequent mileage, and trade-in. Therefore, they can set dierent prices for loyal consumers and consumers switching from competingbrands. Two rms, A located at x = 0, and B located at x = 1. Two periods: t = 0 is history. Price competition takes place at t = 1. History of consumer x [0, 1] is the function h(x) : [0, 1] {A, B} describing whether x haspurchased A or B in t = 0. Example: h(x) = A means that consumer x has purchased brand A in t = 0 (public information). Firm A sets pA for its loyal consumers, and qA for consumers switching from brand B. Firm B sets pB for its loyal consumers, and qB for consumers switching from brand A. AB and BA exogenously-given switching costs A to B, and B to A.Utility of a consumer indexed by x with a purchase history of brand h(x) A, B is dened byU(x) def=

pA x if h(x) = A and continues to purchase brand A qB (1 x) AB if h(x) = A and now switches to brand B pB (1 x) if h(x) = B and continues to purchase brand B qA x BA if h(x) = B and now switches to brand A. For our purposes, we now set AB = BA = 0.1 Assumption: As inherited market share constitutes of consumers indexed by x x0.1Gehrig et. al. 2007 demonstrate why AB > 0 and BA > 0 are needed for generating persistent dominance.(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)3.4 Horizontal Dierentiation: Behavior-based Pricing 16 Hence, consumers indexed by x > x0 have a history of buying brand B. Assumption: With no loss of generality x0 0.5 (A was dominant in t = 0).Figure 3.4 illustrates how the history of purchases relates to current brand preferences.

x0 1x012Purchased brand A Purchased BA-oriented B-oriented , ,Figure 3.4: Purchase history relative to current preferencesThe utility function implies that consumers indierent between switching brands and not switchingare given by

x0xA1 xB10xA A A B B B A BpA qB qA pBA B1h(x) = A h(x) = B , ,Figure 3.5: Consumer allocation between the brands Note: Arrows indicate direction of switching (if any). Pricesindicated the prices paid by the relevant range of consumers.xA1 = 12 + qB pA2 and xB1 = 12 + pB qA2 .Firms prot maximization problems are:maxpA,qAA(pA, qA) def= pAxA1 +qA(xB1 x0) (3.10)maxpB,qBB(pB, qB) def= pB(1 xB1 ) +qB(x0 xA1 ).yielding the Nash equilibrium pricespA = (2x0 + 1)3 , qA = (3 4x0)3 , pB = (3 2x0)3 , and qB = (4x0 1)3 .and thereforexA1 = 2x0 + 16 , xB1 = 2x0 + 36 , and A = B = 5(2x20 2x0 + 1)9 .DenemA1 = xA1 + (xB1 x0) = 2 x03 and mB1 = (x0 xA1 ) + (1 xB1 ) = 1 +x03 .(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)3.4 Horizontal Dierentiation: Behavior-based Pricing 17Results(1) The loyalty price of each rm increases with the rms inherited market share. Formally, pA increasesand pB decreases with an increase in x0.(2) Each rms poaching price decreases with the rms inherited market share. Formally, qA decreasesand qB increases with an increase in x0.(3) The dominant rm charges a loyalty premium. Formally, pA qA.(4) The small rm oers a loyalty discount pB < qB if and only if its inherited market share exceeds1/3 (i.e., x0 > 2/3).(5) With behavior-based price discrimination, the rm with inherited dominance is bound to lose itsdominance.22Gehrig et. al. 2007 reverses this result by assuming strictly positive switching costs: AB > 0 and BA > 0.(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)3.5 Horizontal Dierentiation: Salops Circular City 183.5 Horizontal Dierentiation: Salops Circular City Model advantages: (1) Number of rms (brands) is endogenously determined. (2) Can have servicetime dierentiation applications when the circle is interpreted as a clock. Notation: (1) N rms, endogenously determined. (2) F= xed cost, c= marginal cost. (3) qi andi(qi) the output and prot levels of the rm-producing brand i,i(qi) =

(pi c)qi F if qi > 00 if qi = 0. (3.11)Consumers:Then, assuming that rms 2 and N charge p,p1consumers buying from rm 1`` p2 = ppN = p1N.....>>>>. x

\\\\Figure 3.6: The position of rms on the unit circlep1 + x = p +(1/N x)Hence, x = p p12 + 12N. (3.12)q1(p1, p) = 2 x = p p1 + 1N. (3.13)Definition 3.2The triplet {N, p, q} is an equilibrium if(a) Firms: Each rm behaves as a monopoly on its brand; that is, given the demand for brand i (3.13)and given that all other rms charge pj = p, j = i, each rm i chooses p tomaxpii(pi, p) = piqi(pi) (F +cqi) = (pi c)

p pi + 1N

F.(b) Free entry: Free entry of rms (brands) will result in zero prots; i(q) = 0 for all i = 1, 2, . . . , N.The rst-order condition for rm is maximization problem is0 = i(pi, p)pi= p 2pi +c + 1N.Therefore, in a symmetric equilibrium, pi = p = c +/N.(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)3.6 Vertical Dierentiation: A Modied Hotelling Model 19To nd the equilibrium number of brands N, we set0 = i(p, p) = (p c) 1N F = N2 F.HenceN =

F , p = c + N = c + F, q = 1N. (3.14)The cost of the average consumer who is located half way between x = 1/(2N) and a rm.The average consumer has to travel 1/(4N), which yieldsT(N) = 4N. (3.15)minNL(F, , N) NF +T(N) +Ncq = NF + 4N +c. (3.16)The rst-order condition is 0 = LN = F /(4N2). Hence,N = 12

F < N. (3.17)3.6 Vertical Dierentiation: A Modied Hotelling Model Continuum of consumers uniformly distributed on [0, 1]. Two rms, denoted by A and B and located at points a and b (0 a b 1) from the origin,respectively.3 pA and pB are the price charged by rm A and B.

1 0 abrm A rm B(b a) , xFigure 3.7: Vertical dierentiation in a modied Hotelling modelUx(i)

ax pA i = Abx pB i = B (3.18)The indierent consumer is determined byU x(A) = a x pA = b x pB = U x(B). (3.19)Solving for x from (3.19) yields x = pB pAb a and 1 x = 1 pB pAb a . (3.20)(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)3.6 Vertical Dierentiation: A Modied Hotelling Model 20

` `x 1 10 0

Ux(A)Ux(B)Ux(A)Ux(B)z x pBpApApBxFigure 3.8: Determination of the indierent consumer among brands vertically dierentiated on the basis ofquality. Left: pA < pB, Right: pA > pBFormally, rm A and B solvemaxpAA(a, b, pA, pB) = pA x = pApB pAb a

(3.21)maxpBB(a, b, pA, pB) = pB (1 x) = pB1 pB pAb a

.Definition 3.3The quadruple < ae, be, peA(a, b), peB(a, b) > is said to be a vertically dierentiated industry equilibriumifSecond period: For (any) given locations of rms (a and b), pe1(a, b) and pe2(a, b) constitute a Nashequilibrium.First period: Given the second period-price functions of locations peA(a, b), peB(a, b), and x(peA(a, b), peB(a, b)),(ae, be) is a Nash equilibrium in location.3.6.1 The Second Stage: Choice of Prices Given LocationThe rst-order conditions to (3.21) are given by0 = ApA= pB 2pAb a and 0 = BpB= 1 2pB pAb a . (3.22)Hence,peA(a, b) = b a3 peB(a, b) = 2(b a)3 , and x = 13. (3.23)Result 3.2The rm producing the higher-quality brand charges a higher price even if the production cost forlow-quality products is the same as the production cost of high-quality products.3The assumption that a, b 1 is needed only for the two-stage game where in stage I rms choose their qualities, aand b, respectively. In general, vertical dierentiation can be dened also for a, b > 1.(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)3.7 Non-address Approach: Monopolistic Competition 21Substituting (3.23) into (3.21) yields thatA(a, b) = 1b a2(b a)29 (b a)29

= b a9 (3.24)B(a, b) = 1b a4(b a)29 2(b a)29

= 4(b a)9 .3.6.2 The rst Stage: Choice of Location (Quality)The following result is known as the principle of maximum dierentiation.Result 3.3In a vertically dierentiated quality model each rm chooses maximum dierentiation from its rival rm.Remark: Here the assumption that a, b [0, 1] (or any compact interval) is crucial. However, the modelcan be extended to a, b [0, ) provided that we assume and subtract the (convex) cost of developingquality levels, c(a) and c(b).3.7 Non-address Approach: Monopolistic CompetitionModel advantage: General equilibrium which is therefore suited to analyze welfare and internationaltrade.ConsumersRepresentative consumeru(q1, q2, . . .) i=1qi. (3.25)limqi0uqi= limqi012qi= +.

`q1q2

faFigure 3.9: CES indierence curves for N = 2Ni=1piqi I L +Ni=1piqi. (3.26)(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)3.7 Non-address Approach: Monopolistic Competition 22We form the LagrangianL(qi, pi, ) Ni=1qi I Ni=1piqi.The rst-order condition for every brand i is0 = Lqi= 12qipi i = 1, 2, . . . , N.Thus, the demand and the price elasticity (i) for each brand i are given byqi(pi) = 142(pi)2, or pi(qi) = 14qi qipipiqi= 2. (3.27)Brand-producing rmsEach brand is produced by a single rm.TCi(qi) =

F +cqi if qi > 00 if qi = 0. (3.28)Dening a monopolistic-competition market structureDefinition 3.4The triplet {Nmc, pmci , qmci , i = 1, . . . , Nmc} is called a Chamberlinian monopolistic-competitionequilibrium if(1) Firms: Each rm behaves as a monopoly over its brand; that is, given the demand for brand i(3.27), each rm i chooses qmci to maxqi i = pi(qi)qi (F cqi).(2) Consumers: Each consumer takes his income and prices as given and maximizes (3.25) subject to(3.26), yielding a system of demand functions (3.27).(3) Free entry: Free entry of rms (brands) will result in each rm making zero prots; i(qmci ) = 0for all i = 1, 2, . . . , N.(4) Resource constraint: Labor demanded for production equals the total labor supply;Ni=1(F+cqi) =L.Solving for a monopolistic-competition equilibriumMRi(qi) = pi

1 + 1

= pi

1 + 12

= pi2 = c = MC(qi).Hence, the equilibrium price of each brand is given by pmci = 2c (twice the marginal cost).The zero-prot condition implies0 = i(qmci ) = (pmci c)qmci F = cqmci F.Hence, qmci = F/c.The resource-constraint condition: that N[F +c(F/c)] = L. Hence, N = L/(2F). Altogether, wehave it thatpmci = 2c; qmci = Fc ; Nmc= L2F .(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)3.8 Damaged Goods 233.7.1 Monopolistic competition in international marketsNf= L/F = 2Na, where f and a denote equilibrium values under free trade and under autarky.Also, (qfi = qai = F/c), but the entire population has doubled, under free trade each consumer (country)consumes one-half of the world production (F/(2c)).uf= Nf

qfi = LF

F2c = L2cF(3.29)> L2cF= L2F

Fc = Na

qai = ua.3.8 Damaged Goods Manufacturers intentionally damage some features of a good or a service in order to be able to pricediscriminate among the consumer groups. A proper implementation of this technique may even generate a Pareto improvement. The most paradoxical consequence of this technique is that the more costly to produce good (thedamaged good) is sold for a lower price as it has a lower quality. Deneckere and McAfee (1996), Shapiro and Varian (1999), and McAfee (2007) list a wide variety ofindustries where this technique is commonly observed. For example:Costly delay: Overnight mail carriers, such as Federal Express and UPS, oer deliveries at 8:30 a.m. or10 a.m., and a standard service promising an afternoon delivery. Carriers make two trips to thesame location instead of delivering the standard packages during the morning.Reduced performance: Intel has removed the math coprocessor from its 486DX chip and renamed it as486SX in order to be able to sell it for a low price of $333 to low-cost consumers, as comparedwith $588 that it charged for the undamaged version (in 1991 prices).Delay in Internet services: Real-time information on stock prices is sold for a premium, whereas twenty-minute delayed information is often provided for free. A good (service ) is produced (delivered) at a high quality level, H, with a unit cost of H = $2. The seller posses a technology of damaging the good so it becomes a low quality product denotedby L. The cost of damaging is D = $1. The cost of damaging is D = $1. Therefore, the total unit cost of producing good L is L = H+D.The seller has to to consider the following options:Selling H to type 2 consumers only: This is accomplished by not introducing a damaged version andby setting a suciently high price, pH = $20, under which consumer = 1 will not buy. Theresulting prot is = 100(20 2) = $1, 800.Selling H to both consumer types: Again, selling only the original high-quality good but at a muchlower price, pH = $10, in order to induce consumer = 1 to buy. The resulting prot is = (100 + 100)(10 2) = $1, 600.(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)3.8 Damaged Goods 24i (Quality) = 1 = 2 i (Unit Cost)H (Original) VH1 = $10 VH2 = $20 $2L (Damaged) VL1 = $8 VL2 = $9 $2+$1N

(# consumers) N1 = 100 N2 = 100Table 3.1: Maximum willingness for original and quality-damaged product/service.Selling H to type 2, and L to type 1 consumers: Introducing the damaged good into the market. Con-sumer 2 will choose H over L if VH2 pH VL2 pL. Thus, the seller must set pH VH2 VL2 + pL = 11 + pL. To induce type 1 consumers to buy the damaged good L, theseller should set pL = $8 which implies that pH = 11 + 8 = $19. Total prot is therefore = 100(19 2) + 100(8 2 1) = $22, 000. Most protable !!! Note: Selling H to type 2 and L to type 1 makes no one worse o compared with selling only H totype 2 only. Introducing the damaged good L lowers the price of the H good to pH = 19 thereby increasing thewelfare of type 2 consumers. Type 1 consumers remain indierent. Sellers prot is enhanced to = $22, 000 from = $18, 000.Figure 3.10 below illustrates buyers decisions on which quality to purchase in the pLpH space.`

pL$19VL1 = $8pH0

pL = pH 11 pL = pH 1$1 $9 $11type 1 buys H type 1 buys Ltype 2 buys H type 2 buys LSegmented market$20VL2 = $9Figure 3.10: Segmenting the market with a damaged good. Note: The three bullet marks represent candidateprot-maximizing price pairs.(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)Topic 4Advertising4.1 Major Issues Integral part of our life, in many forms: TV, radio, printed media, billboards, buses, trains, junk mail,junk e-mail, Internet. Very little is understood about the eects of advertising. In developed economies: about 2% of GNP is spent, 3% of personal expenditure Ratio of advertising/sales vary across industry (low for vegetables, 20% to 80% in cosmetics anddetergents). Is this ration correlated with size? The Big-3 are among the largest advertisers. In 1986, GM (largestproducer) spends $63/car, Ford $130/car, Chrysler $113/car (although over all less). Kaldor (1950): manipulative, hence welfare reducing due to reduced competition (prices of advertisedbrands rise above MC). More recently, Tesler (1964), Nelson (1970, 1974), Demetz (1979): tool for information transmission,thereby reducing consumers search cost. Nelson distinguishes: search goods, and experience goods. Economics literature: persuasive v. informative advertising.4.2 Persuasive Advertising: Dorfman-Steiner Condition Monopoly, TC(q, s) = C(q) +s (s advertising expenditure). Market demand: Q = D(p, s), D1 < 0, D2 > 0. What is the monopolys prot maximizing advertising level?Dene

pdef= D(p, s)ppD(p, s), and sdef= D(p, s)ssD(p, s).The monopoly solvesmaxp,sM= pD(p, s) C(D(p, s)) s.(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)4.3 Informative Advertising 260 = Mp = Q+pDp C

()Dp0 = Ms = pDs C

()Ds 1Rearranging,pMc

pM = QMDp= 1Ds

pMQMs

sDsQM

=

DppMQM

sMpMQM = s

p.4.3 Informative Advertising Do sellers provide optimal amount of advertising? Butters (1977): All rms sell identical brands; advertising is only for price Grossman & Shapiro (1984): Advertising also conveys information about products attributes. Benham (1972): nds that state laws prohibiting eyeglass advertising had higher-than-average prices.The (unit circle) Grossman & Shapiro (1984) modied to the linear city in Tirole p.292: 2 rms i = 1, 2, locate on the edges of [0, 1] Continuum, uniform density of consumers, =transportation cost parameter. utility of consumer located at x from rm i isUx =

x pA buy from A (1 x) pB buy from B x pA does not buy from any store. i= fraction of consumers receiving an ad from rm i Later on assume that i {12, 1} Cost of i = 12 = aL. Cost of i = 1 = aH aL. (Grossman & Shapiro A(1) = ) Two assumptions: (1) c + 4 112 4aL +c. (2) aL 38 . To be explained below. Consumers do not know the existence of a store unless they received an ad from the specic store.= (1 2)1= the fraction that receives ads only from store 1 = buy from store 1= (1 1)2= the fraction that receives ads only from store 2 = buy from store 2= 12 = fraction that receives both rms ads. These consumers obtain information on locationand prices, thus will follow Hotellings basic model x = p2 p1 +2 .= Aggregate demand facing store x = 11 2 +2

p2 p1 +2

(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)4.3 Informative Advertising 27= Checking the eect of advertising on price elasicity:

1def= xp1p1 x = 122p1 x =

1=2p1=p22p(1 /2) = p(2 ) [decreases (more elastic) with ] Two-stage game: Stage I : Stores invest in advertising, 1 and 2. Stage II : Price game, p1 and p2.Stage II: Equilibrium in prices for given advertising levelsWe look for a Nash equilibrium in (p1, p2). Firm 1 takes 1, 2, and p2 as given and solvesmaxp11 = 11 2 +2

p2 p1 +2

(p1 c)

a where a {aL, aH}0 = 1p1= 1[2(c 2p1 +p2) +(2 2)]2 = p1(p2) = (2 2)22+ p2 +c2 .Firm 2 takes 1, 2, and p1 as given and solvesmaxp22 = 21 1 +1

1 p2 p1 +2

(p2 c)

a where a {aL, aH}0 = 2p2= 2[1(c 2p2 +p1) +(2 1)]2 = p2(p1) = (2 1)21+ p1 +c2 .Solving the two price best-response functions yield the equilibrium prices as functions of the advertisinglevelsp1 = c + [22 1(32 4)]312and p2 = c + [42 1(32 2)]312.Hence,p1 p2 = 2(1 2)312 0 1 2,which means that the rm that places more ads charges a higher price.Substituting the prices into the prot functions yields1(1, 2) = [1(32 4) 22]21812a1 and 2 = [1(32 2) 42]21812a2.Stage I: Equilibrium in advertising levels Each store i = 1, 2 chooses its advertising level i {12, 1} . Cost of advertising a(12) = aL, a(1) = aH, where aH aL 0.Result 4.1(a) Prices and prot are higher under 1 = 2 = 12 compared with 1 = 2 = 1 (less advertinggenerates more prots).(b) p1 p2 = 1 2 (more advertising leads to a higher price)(c) 1 = 2 = 1 (maximum advertising) is NOT a Nash equilibrium.(d) 1 = 2 = 12 is a Nash equilibrium if aH aL > 1772(e) Otherwise, there are two equilibria: 1, 2 = 12, 1 and 1, 2 = 1, 12

(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)4.3 Informative Advertising 28Store 2:1 2 = 12 2 = 11 = 12 c + 3 c + 3 c + 53 c + 731 = 1 c + 73 c + 53 c + c +Store 2:1 2 = 12 2 = 11 = 1298 aL98 aL2536 aL4936 aH1 = 1 4936 aH2536 aL2 aH2 aHTable 4.1: Equilibrium prices (p1, p2) (left) and prots (1, 2) (right) under varying advertising levelsStore 2:1 2 = 12 2 = 11 = 1238385127121 = 1 7125121212Store 2:1 2 = 12 2 = 11 = 12121256161 = 1 16561212Table 4.2: Equilibrium sales (q1, q2) (left) and x (right) under varying advertising levelsResult 4.2(a) The store that advertises more serves more consumers than the store that advertises less. Formally,1 2 implies that q1 q2. However,(b) it serves less consumers that receive both adds, formally, x = 16.The role of our 2 assumptionsThe rst assumption was c + 4 112 4aL + c. The left part, c + 4 , is needed so thatpi = c + 3 0 for the case where A = B = 12 in Table 4.1.The right part, 112 4aL +c is needed to prevent a rm from raising the price to unboundedlevels, lose all the market with shared information, and monopolize the market for consumers who receiveonly one ad. To monopolize, this rm can raise to price to a maximum of . This is not protableif14( c) < 98 aL = 112 4aL +c.The above assumption implies that the second assumption, aL 38 , is needed to have a nonemptyinterval for . Formally,c + 4 112 4aL +c = aL 38 .Socially optimal advertising level Computing social welfare for the outcomes 1, 2 = 12, 1 and 1, 2 = 1, 12 would require thecomputation of transportation costs (distorted because x = 16 or x = 56. We omit this analysis. Table 4.2 shows that 1 = 2 = 12 results in an exclusion of 12 consumers. Therefore for suciently-high value of (basic valuation), 1 = 2 = 1 should yield higher social welfare than1 = 2 = 12. For example, take that satises 4 > 2(aH aL).(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)4.3 Informative Advertising 29Results from Grossman & Shapiro circular city model(1) Under xed # brands: advertising is excessive (excessive competition over market shares(2) Under free entry: the equilibrium # of brands exceeds the socially optimal, in this case, too littleadvertising.(3) In general, advertising increases eciency if it leads to a reduction of over-priced brands.(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)Topic 5R&D and Patent Law5.1 Classications of Process Innovation classies process (cost-reducing) innovation according to the magnitude of the cost reduction gener-ated by the R&D process. industry producing a homogeneous product rms compete in prices. initially, all rms possess identical technologies: with a unit production cost c0 > 0.

``````````````````````````````` Qpc0c2c1pm(c1)pm(c2)p1 = p0MR(Q)DQ1 Q0 Q2Figure 5.1: Classication of process innovationDefinition 5.1Let pm(c) denote the price that would be charged by a monopoly rm whose unit production cost isgiven by c. Then,(a) Innovation is said to be large (or drastic, or major) ifpm(c) < c0. That is, if innovation reduces the cost to a level where the associated pure monopolyprice is lower than the unit production costs of the competing rms.(b) Innovation is said to be small (or nondrastic, or minor) ifpm(c) > c0.(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)5.2 Innovation Race 31Example: Consider the linear inverse demand function p = a bQ. Then, innovation is major ifc1 < 2c0 a and minor otherwise.5.2 Innovation RaceTwo types of models:Memoryless: Probability of discovery is independent of experience (thus, depends only on current R&Dexpenditure).Cumulating Experience: Probability of discovery increases with cumulative R&D experience (like capitalstock).5.2.1 Memoryless modelLee and Wilde (1980), Loury (1979), and Reinganum. The model below is Exercise 10.5, page 396 inTirole. n rms race for a prize V (present value of discounted benets from getting the patent) each rm is indexed by i, i = 1, 2, . . . , n xi 0 is a commitment to a stream of R&D investment (at any t, t [0, )). h(xi) is probability that rm i discovers the at t when it invests xi in this time interval, whereh

> 0, h

< 0, h(0) = 0, h

(0) = , h

(+) = 0 i date rm i discovers (random variable) idef= minj=i{j(xj)} date in which rst rival rm discovers (random variable).Probability that rm i discovers before or at t isPr(i(xi) t) = 1 eh(xi)t, density is: h(xi)eh(xi)tProbability that rm i does not discover by tPr(i(xi) > t) = eh(xi)tProbability that all n rms do NOT discover before tPr( i t) = 1 Pr{j > t i} = 1

1 e

ni=1 h(xi)t

= e

ni=1 h(xi)tDene aidef= j=ihj(xj).Remark: Probability at least one rival discovers before tPr( i t) = 1 Pr{j > t j = i} = 1 eaitThe expected value of rm i isVi =

0ertet

ni=1 h(xi)[h(xi)V xi] dt = h(xi)V xir +ai +h(xi)(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)5.2 Innovation Race 32Result 5.1R&D investment actions are strategically complementsProof. Let xj = x for all j = i. Then, ai = (n 1)h(x). First order condition is,0 = Vixi= 1()2[h

(xi)V 1][(n 1)h(x) +h(xi) +r] h

(xi)[h(xi)V xi].Using the implicit function theorem,xix = [h

(xi)V 1](n 1)h

(x) where = V h

(xi)[(n1)h(x) +h(xi) +r] +h

(xi)[h

(xi)V 1] [h

(xi)V 1]h

(xi) h

(xi)[h(xi)V xi].The second and third terms cancel out so, = V h

(xi)[(n 1)h(x) +h(xi) +r] h

(xi)[h(xi)V xi] < 0Therefore, xi/x > 0.Lee and Wilde show a series of propositions:(1) give condition under which x/n > 0.(2) i/n < 0(3) Vi/n < 0(4) x > x (excessive R&D, where social optimal is calculated by maximizing nV )5.2.2 Cumulating experience modelFudenberg, Gilbert, Stiglitz, and Tirole (1983) provide a model with cumulative experience. V is prize (only to winner), c per-unit of time R&D cost ti innovation starting date of rm i, i = 1, 2 Assumption: t2 > t1 = 0 (rm 1 has a head start) i(t) = experience (length of time) rm i is engaged in R&D hence, 1(t2) > 2(t2) = 0. Note that 2(t) = 0 for t t2. i(t)def= (i(t)) = probability of discovering at t +dt Hence, 1(t) > 2(t) for all t > 0. Also 2(t) = 0 for t t2. c = (ow) cost of engaging in R&D.(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)5.2 Innovation Race 33Expected instantaneous prot conditional that no rm having yet made the discovery isi(t)V cProbability that neither rm makes the discovery before te

t0[1(1())+2(2())]dWhen both rms undertake R&D, from t1 and t2, respectively,Vi =

tie[rt+

t0[1(1())+2(2())]d][i(i(t))V c] dtAssumptions:(1) R&D is potentially protable for the monopolist. Formally, there exists > 0 such that ()V c >0 for all > ; and (0)V c < 0.(2) R&D is protable for a monopolist. Formally,

0e[rt+

t0[()]d][(t)V c] dt > 0.(3) R&D is unprotable for a rm in a duopoly. Formally,

0e[rt+

t0[2()]d][(t)V c] dt < 0.

`21V2 > 0V2 < 0V1 < 0actual patht245V2(1, 2) = 0V2(1, 2) = 0Firm 1 stays inFirm 2 stays inBoth stay inFigure 5.2: Locuses of Vi(1(), 2()) = 0, i = 1, 2 (note: t2 > t1 = 0)(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)5.3 R&D Joint Ventures 34Results:(1) -preemption. That is, rm 2 does not enter the race.(2) if we add another stage of uncertainty (associated with developing the innovation), leapfrogging ispossible and there is no -preemption5.3 R&D Joint VenturesMany papers (see Choi 1993; dAspremont and Jacquemin 1988; Kamien, Muller, and Zang 1992; Katz1986, and Katz and Ordover 1990). two-stage game: at t = 1, rms determine (rst noncooperatively and then cooperatively) how muchto invest in cost-reducing R&D and, at t = 2, the rms are engaged in a Cournot quantity game market for a homogeneous product, aggregate demand p = 100 Q. xi the amount of R&D undertaken by rm i, ci(x1, x2) the unit production cost of rm ici(x1, x2)def= 50 xi xj i = j, i = 1, 2, 0.Definition 5.2We say that R&D technologies exhibit (positive) spillover eects if > 0.Assumption 5.1Research labs operate under decreasing returns to scale. Formally,TCi(xi) = (xi)22 .We analyze 2 (out of 3) market structures:(1) Noncoordination: Look for a Nash equilibrium in R&D eorts: x1 and x2.(2) Coordination (semicollusion): Determine each rms R&D level, x1 and x2 as to maximize jointprot, while still maintaining separate labs.(3) R&D Joint Venture (RJV semicollusion): Setting a single lap. The present model does not t thismarket structure.5.3.1 Noncooperative R&DThe second periodi(c1, c2)|t=2 = (100 2ci +cj)29 for i = 1, 2, i = j. (5.1)(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)5.3 R&D Joint Ventures 35The rst periodmaxxii = 19[100 2(50 xi xj) + 50 xj xi]2 (xi)22= 19[50 + (2 )xi + (2 1)xj]2 (xi)22 . (5.2)The rst-order condition yields0 = ixi= 29[50 + (2 )xi + (2 1)xj](2 ) xi.x1 = x2 xnc, where xncis the common noncooperative equilibriumxnc= 50(2 )4.5 (2 )(1 +). (5.3)5.3.2 R&D CoordinationThe rms seek to jointly choose x1 and x2 to1maxx1,x2(1 +2),where i, i = 1, 2 are given in (5.1). The rst-order conditions are given by0 = (1 +2)xi= ixi+ jxi.The rst term measures the marginal protability of rm i from a small increase in its R&D (xi), whereasthe second term measures the marginal increase in rm js prot due to the spillover eect from anincrease in is R&D eort. Hence,0 = 29[50 + (2 )xi + (2 1)xj](2 ) xi+ 29[50 + (2 )xj + (2 1)xi](2 1).Assuming that second order conditions for a maximum are satised, the rst order conditions yield thecooperative R&D levelxc1 = xc2 = xc= 50( + 1)4.5 ( + 1)2. (5.4)We now compare the industrys R&D and production levels under noncooperative R&D and coop-erative R&D.Result 5.2(a) Cooperation in R&D increases rms prots.(b) If the R&D spillover eect is large, then the cooperative R&D levels are higher than the noncoop-erative R&D levels. Formally, if > 12, then xc> xnc. In this case, Qc> Qnc.(c) If the R&D spillover eect is small, then the cooperative R&D levels are lower than the noncoop-erative R&D levels. Formally, if < 12, then xc< xnc. In this case, Qc< Qnc.1See Salant and Shaer (1998) for a criticism of the symmetry of R&D assumption.(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)5.4 Patents 365.4 Patents We search for the socially optimal patent life T (is it 17 years?) Process innovation reduces the unit cost of the innovating rm by x For simplicity, we restrict our analysis to minor innovations only. market demand given by p = a Q, where a > c.

``````````````M DLcc xa c a (c x) a QpaFigure 5.3: Gains and losses due to patent protection (assuming minor innovation)M(x) = (a c)x and DL(x) = x22 . (5.5)5.4.1 Innovators choice of R&D level for a given duration of patentsDenote by (x; T) the innovators present value of prots when the innovator chooses an R&D levelof x. Then, in the second stage the innovator takes the duration of patents T as given and chooses inperiod t = 1 R&D level x tomaxx(x; T) =Tt=1t1M(x) TC(x). (5.6)That is, the innovator chooses R&D level x to maximize the present value of T years of earning monopolyprots minus the cost of R&D. We need the following Lemma.Lemma 5.1Tt=1t1= 1 T1 .(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)5.4 Patents 37Proof.Tt=1t1=T1t=0t= 11 TT+1T+2. . .= 11 T(1 + +2+3+. . .)= 11 T1 = 1 T1 .Hence, by Lemma 5.1 and (5.5), (5.6) can be written asmaxx1 T1 (a c)x x22 ,implying that the innovators optimal R&D level isxI= 1 T1 (a c). (5.7)Hence,Result 5.3(a) The R&D level increases with the duration of the patent. Formally, xIincreases with T.(b) The R&D level increases with an increase in the demand, and decreases with an increase in the unitcost. Formally, xIincreases with an increase in a and decreases with an increase in c.(c) The R&D level increases with an increase in the discount factor (or a decrease in the interestrate).5.4.2 Societys optimal duration of patentsFormally, the social planner calculates prot-maximizing R&D (5.7) for the innovator, and in periodt = 1 chooses an optimal patent duration T tomaxTW(T) t=1t1

CS0 +M(xI)

+t=T+1t1DL(xI) (xI)22s.t. xI= 1 T1 (a c). (5.8)Sincet=T+1t1= Tt=0t= T1 and using (5.5), (5.8) can be written as choosing T to maximizeW(T) = CS0 + (a c)xI1 (xI)221 T1 s.t. xI= 1 T1 (a c). (5.9)Thus, the government acts as a leader since the innovator moves after the government sets the patentlength T, and the government moves rst and chooses T knowing how the innovator is going to respond.(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)5.5 Appropriable Rents from Innovation in the Absence of Property Rights 38We denote by T the societys optimal duration of patents. We are not going to actually performthis maximization problem in order to nd T. In general, computer simulations can be used to nd thewelfare-maximizing T in case dierentiation does not lead to an explicit solution, or when the discretenature of the problem (i.e., T is a natural number) does not allow us to dierentiate at all. However,one conclusion is easy to nd:Result 5.4The optimal patent life is nite. Formally, T < .Proof. It is sucient to show that the welfare level under a one-period patent protection (T = 1)exceeds the welfare level under the innite patent life (T = ). The proof is divided into two parts forthe cases where < 0.5 and 0.5.First, for < 0.5 when T = 1, xI(1) = a c. Hence, by (5.9),W(1) = CS0 + (a c)21 (a c)221 21 = CS01 + (a c)21 1 + 22 . (5.10)When T = +, xI(+) = ac1. Hence, by (5.9),W(+) = CS01 + (a c)2(1 )2 (a c)22(1 )2 = CS01 + (a c)22(1 )2. (5.11)A comparison of (5.10) with (5.11) yields thatW(1) > W() (a c)21 1 + 22 > (a c)22(1 )2 < 0.5. (5.12)Second, for 0.5 we approximate T as a continuous variable. Dierentiating (5.9) with respectto T and equating to zero yieldsT = ln[3 +

6 +2 6 ] ln(3)ln() < .Now, instead of verifying the second-order condition, observe that for T = 1, dW(1)/dT = [(a c)2(1 5) ln()]/[2(1 )2] > 0 for > 0.2.5.5 Appropriable Rents from Innovation in the Absence of Property RightsFollowing Anton an Yao (AER, 1994), we show that Even without patent law, a non-reproducible innovation can provide with a substantial amount ofprot. This holds true also for innovators with no assets (poor innovators).The model One innovator, nancially broke Mprot level if only one rm gets the innovation Dprot level to each rm if two rms get the innovation(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)5.5 Appropriable Rents from Innovation in the Absence of Property Rights 39 Innovator reveals the innovation one rm then, the informed rm oers a take-it-or-leave-it contract R = (RM, RD) = payment to innovatorin case innovator does not reveal to a second rm (RM), or he does reveal (RD). Innovator approaches another rm and asks for a take-it-or-leave-it oer before revealing the innova-tion Innovator accepts/rejects the new contract .Innovator approaches rm 1 Approaches rm 2Firm 1 oers contractR = (RM, RD)

Does not approachrm 2Innovator approaches rm 2Firm 2 oers contract SS I= RM1= MRM

I= RM1= MRMInnovator rejects.AcceptsI= RD +S2= D S1= D RDFigure 5.4: Sequence of moves: An innovator extracting rents from rmsWill the innovator reveal to a second rm?Suppose that innovator already has a contract from rm 1, R = (RM, RD).Without revealing, innovator will accept a second contract, S from rm 2 ifRD +S > RMHence, rm 2 will oer a take-it-or-leave-it contact of S = RM RD +.Firm 2 will oer a contract S if 2= DS > 0, or S < D.Firm 1s optimal contract oeringHence, rm 1 will set contract R to satisfy RM RD D> S to ensure rejection. Hence, rm 1maximizes prot by oering R = (RM, RD) = (D, 0).(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)Topic 6Capacities and Preemption6.1 Investment and entry deterrence Relaxing the Bain, Sylos-Labini postulate (Spence) using Dixit (1980) Two-stage game, Stage 1: rm 1 (incumbent) chooses a capacity level k that would enable rm 1 toproduce without cost q1 k units of output Stage 2: if incumbent chooses to expand capacity beyond k in the second stage, then the incumbentincurs a unit cost of c per each unit of output exceeding k. Entrant makes entry decision in 2nd stage.`mc1(q1)

q1MC1(q1)kFigure 6.1: Capacity accumulation and marginal cost

````````Monopoly Outcome Cournot GameSTAY-OUT ENTERII. Entrant moves

kk 0`````` I. Incumbent movesFigure 6.2: Relaxing the Bain-Sylos postulate(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)6.2 Spatial preemption 41The 2nd stage BR functions are

q2q1

q2 q2q1 q1

` ` `k1 k2 k3 q1 = R1(q2) q1 = R1(q2) q1 = R1(q2)R2(q1)R2(q1) R2(q1)E1E2 E3`` ```````````````````````Figure 6.3: Best-response functions with xed capacity: Left: low capacity; Middle: medium capacity; Right:High capacityResult 6.1An incumbent rm will not prot from investing in capacity that will not be utilized if entry occurs. Inthis sense, limit pricing will not be used to deter entry.6.2 Spatial preemption How a dierentiated brands monopoly provider reacts to partial entry? Judd (1985): monopoly rm (rm 1) which owns two restaurants, Chinese (denoted by C) andJapanese (denoted by J). zero production cost 2 types of consumers: Chinese-food oriented, Japanese-food orientedUC

pCif eats Chinese food pJif eats Japanese food (6.1)UJ

pCif eats Chinese food pJif eats Japanese food > 0 denotes the slight disutility a consumer has from buying his less preferred food. Assume < < 2Before entrypC= pJ= in each restaurant, and the monopolys total prot 1 = 2.Entry occurs in the market for Chinese foodIf monopoly ghts: pC1 = pC2 = 0.Maximal price for Japanese: pJ= sinceUJ(J) = pJ= pC= UJ(C).Hence, 1 = .(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)6.2 Spatial preemption 42Incumbent withdraws from the Chinese restaurantLemma 6.1The unique duopoly price game between the Chinese and the Japanese restaurants results in the con-sumer oriented toward Japanese food buying from the Japanese restaurant, the consumer orientedtoward Chinese food buying from the Chinese restaurant, and equilibrium prices given by pJ1 = pC2 = .Proof. We have to show that no restaurant can increase its prot by undercutting the price of thecompeting restaurant. If the Japanese restaurant would like to attract the consumer oriented towardChinese food it has to set pJ= pC = . In this case, 2 = 2( ). However, when it doesnot undercut, 2 = > 2( ) since we assumed that < 2. A similar argument reveals why theChinese restaurant would not undercut the Japanese restaurant.Result 6.2When faced with entry into the Chinese restaurants market, the incumbent monopoly rm wouldmaximize its prot by completely withdrawing from the Chinese restaurants market.Proof. The prot of the incumbent when it operates the two restaurants after the entry occurs is 1 = .If the incumbent withdraws from the Chinese restaurant and operates only the Japanese restaurants,Lemma 6.1 implies that 1 = > .(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)Topic 7Limit Pricing 2 periods, t = 1, 2. demand each period p = a bQ = 10 Q. Stage 1: rm 1 chooses q11. Stage 2: rm 2 chooses to enter or not Stage 2: Assumption: Entry occurs: Cournot; Does not: Monopolyt = 1 t = 2Firm 1 chooses q11Firm 2 EntersDoesnt EnterCournotFirm 1 isgamea monopoly.............------------- Firm 2: c2 = unit cost; F = entry cost. Let c2 = 1 and F2 = 9. Firm 1:c1 =

0 with probability 0.54 with probability 0.5. (7.1) Prots: In the above table, the column labeled ENTER is based on the Cournot solution given byIncumbents Firm 2 (potential entrant)cost: ENTER DO NOT ENTERLow (c1 = 0) c1(0) = 13.44 c2(0) = 1.9 m1 (0) = 25 2 = 0High(c1 = 4) c1(4) = 1 c2(4) = 7 m1 (4) = 9 2 = 0Table 7.1: Prot levels for t = 2 (depending on the entry decision of rm 2). Note: All prots are functionsof the cost of rm 1 (c1); m1 is the monopoly prot of rm 1; ci is the Cournot prot of rm i,i = 1, 2.qci = a 2ci +cj3b , pc= a +c1 +c23 , and ci = b(qi)2.(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)44Solving the game assuming a high-cost incumbentEc2 = 12c2(0) + 12c2(4) = 12(1.9) + 127 > 0,Hence, rm 2 will enter.Given that entry occurs at t = 2, rm 1 should play monopoly at t = 1.q11(4) = 5 and therefore earn 1(4) = m1 (4) +c1(4) = 9 + 1 = 10. (7.2)Solving the game assuming a low-cost incumbentIf c1 = 0, c2(0) < 0, hence, no entry. However, entrant does not know for sure that 1 is a low-cost.Result 7.1A low-cost incumbent would produce q11 = 5.83, and entry will not occur in t = 2.Sketch of Proof. In order for the incumbent to convince rm 2 that it is indeed a low-cost rm, it has todo something heroic. More precisely, in order to convince the potential entrant beyond all doubts thatrm 1 is a low-cost one, it has to do something that a high-cost incumbent would never do namely,it has to produce a rst-period output level that is not protable for a high-cost incumbent!We look for rst period incumbents output level q11 so that(10 q11)q11 4q11 + m1 (4). .. .entry deterred< m1 (4) + c1(4). .. .entry accommodated= 9 + 1 + 10.Now, a high-cost incumbent would not produce q11 > 5.83 since9.99 = (10 5.83) 5.83 4 5.83 +m1 (4) < m1 (4) +c1(4) = 9 + 1 = 10. (7.3)That is, a high-cost incumbent is better o playing a monopoly in the rst period and facing entry inthe second period than playing q11 = 5.83 in the rst period and facing no entry in t = 2.Finally, although we showed that q11 = 5.83 indeed transmits the signal that the incumbent is a low-cost rm, why is q11 = 5.83 the incumbents prot-maximizing output level, given that the monopolysoutput level is much lower, qm1 (0) = 5. Clearly, the incumbent wont produce more than 5.83 sincethe prot is reduced (gets higher above the monopoly output level). Also (7.3) shows that any outputlevel lower than 5.83 would induce entry, and given that entry occurs, the incumbent is best o playingmonopoly in t = 1.Hence, we have to show, for a low-cost rm, that deterring entry by producing q11 = 5.83 yieldsa higher prot than accommodating entry and producing the monopoly output level q11 = 5 in t = 1.That is,1(0)|q11=5 = 25 + 13 = 38 < 49.31 = (10 5.83) 5.83 0 5.83 + 25 = 1(0)|q11=5.83,hence, a low-cost incumbent will not allow entry and will not produce q11 < 5.83.(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)Topic 8Predation8.1 Judo Economics Focus on entrants decision (rather than on only incumbent) Entrant adopts judo economics strategy, Gelman & Salop (1983), which means choosing to enterwith a limited amount of capacity (small scale operation). Demonstrates that entry deterrence is costly 2 stage game:(1) Entrant Moves: decides whether to enter, capacity (max output) k, and pe.(2) Incumbent Moves: decides on pI. Homogeneous product: p = 100 Q.qI=

100 pIif pI pe100 k pIif pI> pe and qe=

k if pe< pI0 if pe pI. (8.1) Incumbent strategy: sets pI(two options):(1) undercut entrant: pI= peor,(2) accommodate entrant pI> pe, facing residual demand qI= 100 k pI.Incumbent deters entryID = pe(100 pe).Incumbent accommodates entrymaxpI>peI= pI(100 k pI),yielding a rst-order condition given by 0 = 100 k 2pI. Therefore, pIA = (100 k)/2, henceqIA = (100 k)/2 and IA = (100 k)2/4.Comparing deterrence with accommodation (for the incumbent)IA ID and (100 k)24 pe(100 pe). (8.2)(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)8.1 Judo Economics 46First stage: entrance chooses k and peUnder entry accommodation, the entrant earns e= pek > 0. The entrant chooses peto maximizee= pek > 0 subject to (8.2).

`kID = pe(100 pe)IA = (100k)24 10024I100 0 kAccommodateDeterFigure 8.1: Judo economics: How an entrant secures entry accommodation(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)8.2 The Chain-Store Paradox 478.2 The Chain-Store ParadoxSelten (1978): An incumbent rm has 20 chain stores in dierent locations Dierent potential entrant in each location : .EnterStay outEntrant .Collude DeterI= 0E= 0I= 2E= 2I= 5E= 1IncumbentFigure 8.2: Chain-store paradox: The game in each locationPotential EntrantEnter Stay OutIncumbent Accommodate 2 2 5 1Fight 0 0 5 1Table 8.1: Chain-store paradox: the game in each location Working backwards, after 19 stores enter, the 20th should enter and the incumbent should accom-modate Working backwards, entrant 19 should enter, and incumbent should accommodate. That is, in a game in which the entrant decides before the incumbent, in the unique SPE, AccommodateEnter will be played in each period. In reality, an incumbent will probably ght the rst few stores that enter.(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)Topic 9Facilitating Practices9.1 A Meeting Competition Clause A sales agreement (like a warranty) between a seller and a buyer Three types:Most Favored Nation (MFN): two types:Rectroactive: Any future price discounts to other buyers before delivery takes place will berebated to consumers. Common in industries where delivery comes long after ordering takesplace.Contermporaneous MFN: Agreement made only with repeated purchases allowing them to ben-et from temporary price cuts made to other consumers. This is a lower commitment bythe rm since it protects only a selected group of buyers.Meeting the Competition Clause: Two types:Meet or Release (MOR): If a buyer discovers a lower price elsewhere, the seller will either matchthe discounted price, or release the customer to buy elsewhere. Purpose: to detect any secretprice cuts made by other sellers, and avoiding deterction cost.Note: It is likely that the seller will choose to release.No-release MCC: Here there is no release. Seller must match (and even take a loss). Providemuch stronger threat on rivals not to reduce prices.A Example of MCC GameIn a market for luxury cars there are two rms competing in prices. Each rm can choose to set a highprice given by pH, or a low price given by pL, where pH > pL 0. The prot levels of the two rms asa function of the prices chosen by both rms is given in Table 9.1. The rules of this two-stage marketFirm 2pH pLFirm 1 pH 100 100 0 120pL 120 0 70 70Table 9.1: Meet the competition clausegame are as follows:Stage I.: Firm 1 sets its price p1 {pH, pL}.(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)9.2 Tying as a Facilitating Practice 49Stage II.: Firm 1 cannot reverse its decision, whereas rm 2 observes p1 and then chooses p2 {pH, pL}.Stage III.: Firm 1 is allowed to move only if rm 2 played p2 = pL in stage II. This stage demonstratesthe MCC commitment.We can derive the SPE directly by formulating the extensive form game which is illustrated in Figure 9.1.In this case, the SPE if given by

````pL pHpHpL pLpHFirm 1Firm 21 = 702 = 70 1 = 1202 = 0 1 = 02 = 120 1 = 1002 = 100

````

pL1 = 702 = 70Firm 1(II.:)(I.:)(III.:)Figure 9.1: Sequential price game: Meet the competition clausep2 =

pH if p1 = pHpL if p1 = pLand p1 = pH,implying that the rms charge the industrys prot maximizing price and earn a prot of 100 each.9.2 Tying as a Facilitating Practice Tying as a tool to dierentiate brands, Seidmann (1991), Horn and Shy (1996) Segmenting markets by tying service with products 2 rms, homogeneous product, pSprice with service, pNw/o service Continuum of consumers indexed by s [0, 1]Us=

B pNif the product is bought without servicesB +s pSif bought tied with services. (9.1) m unit production cost, w unit service cost (wage rate)Market-dividing condition: B + s pS= B pN s =

1 if pSpN 1pSpNif 0 < pSpN 10 if pS pN.(9.2)An equilibrium: one rm ties and the other does not as the pair ( pS, pN), such that for a given pN, thebundling rm chooses pSto maximize S= (pSmw)(1 s), subject to s satisfying (9.2); and fora given pS, the nontying rm chooses pNto maximize N= (pNm) s, subject to s satisfying (9.2).(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)9.2 Tying as a Facilitating Practice 500 = SpS = 1 2pS+pN+m+w and 0 = NpN = pS 2pN+m. (9.3)Therefore, the reaction functions are given by, respectively,pS=

pNif pN> m+w + 112(1 +m+w +pN) if m+w 1 pN m+w + 1[pN+ 1, ) if pN< m+w 1(9.4)and pN=

pS 1 if pS> m+ 212(m+pS) if m pS m+ 2[pS, ) if pS< m.Solving the middle parts of the reaction functions given in (9.4) shows that an interior solution existsand is given by pS= 23(1 +w) +m; 1 s = 13(2 w); S= 19(2 w)2(9.5) pN= 13(1 +w) +m; s = 13(1 +w); N= 19(1 +w)2.Result 9.1(a) In a two-stage game where rms choose in the rst period whether to tie their product with services,one rm will tie-in services while the other will sell the product with no service.(b) An increase in the wage rate (in the services sector) would(i) increase the market share of the nontying rm (the rm that sells the product without service)and decrease the market share of the tying rm (decreases 1 s).(ii) increase the price of the untied good and the price of the tied product (both pSand pNincrease).(c) S Nif and only if w 12.The socially optimal provision of serviceThe socially optimal number of consumers purchasing the product without service, denoted by s

, isobtained under marginal-cost pricing. Thus, let pS= m + w and pN= m. Then, s

pS pN= w.It can easily be veried that s s

if and only if w 12. Hence,Result 9.2(a) If the wage rate in the services sector is high, that is, when w > 12, the equilibrium number ofconsumers purchasing the product tied with service exceeds the socially optimal level. That is,1 s > 1 s

.(b) If the wage rate is low, that is, when w < 12, the equilibrium number of consumers purchasing theproduct tied with service is lower than the socially optimal level. That is, 1 s < 1 s

.(Downloaded from www.ozshy.com) (draft=gradio21.tex 2007/12/11 12:19)