Markus Reisinger: Vertical Product Differentiation, Market Entry, and Welfare

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1 Markus Reisinger: Vertical Product Differentiation, Market Entry, and Welfare Munich Discussion Paper No Departent of Econoics University of Munich Volkswirtschaftliche Fakultät Ludwig-Maxiilians-Universität München Online at

2 Vertical Product Differentiation, Market Entry, and Welfare Markus Reisinger 22nd Deceber 2004 JEL classification: D43, L13, L65 Keywords: Entry Deterrence, Price Discriination, Vertical Differentiation. I would like to thank Florian Englaier, Sven Rady, Ray Rees, Klaus Schidt, Arin Schutzler and participants at the annual eeting of the Geran Econoic Association, Zurich 2003, for helpful coents. I a also grateful to Marc Gruber and Ingrid Koenigbauer for discussion of exaples. Departent of Econoics, University of Munich, Kaulbachstr. 45, Munich, e ail: arkus.reisinger@lrz.uni-uenchen.de

3 Vertical Product Differentiation, Market Entry, and Welfare 1 Abstract This paper analyses a odel of vertical product differentiation with one incubent and one entrant fir. It is shown that if firs can produce only one quality level welfare in this entry gae can be lower than in onopoly. This is the case if qualities are strategic copleents because the incubent ay distort its quality downwards. If firs can produce a quality range and practice non-linear pricing welfare in case of entry deterrence is higher than in onopoly because the incubent enlarges its product line. If entry is accoodated consuer rent increases but the consequences on welfare are abiguous.

4 Vertical Product Differentiation, Market Entry, and Welfare 2 1 Introduction There are a lot of different ways how an incubent fir reacts when facing the threat of entry. For exaple, in the pharaceutical arket after patent expiration soe forerly protected onopolists introduced their own generics to keep copetitors out of the arket 1 while others abstained fro such practice and increased its price after entry generic copetitors. 2 Another exaple is the airline industry. In Canada in fall 2000 the low cost carrier CanJet Airlines entered the Toronto-Halifax arket. The reaction of Air Canada, the incubent, was not to increase its price like in the pharaceutical industry but to lower its fares. 3 A quite different strategy was pursued by British Airways. Its reaction on the entry of low cost carriers on long haul routes was to reduce econoy class capacity and enlarge preiu class capacity thereby increasing its average prices. 4 Many flag carriers instead tried to deter entry of low cost airlines by establishing their own no-frills -airline. This was done by British Airways on short-haul routes with the subsidiary GO. In 2000 the Dutch carrier KLM followed and established Basiq Air and in 2002 the low cost carrier Geranwings was founded. 5 Geranwings is an affiliate copany of Eurowings. In turn, Eurowings is controlled by the Geran flag carrier Lufthansa. So a couple of questions arise. Why do incubents pursue so any different strategies to seeingly the sae proble, naely threat of entry? Does an incubent s strategy differ if it can produce only one quality level or a whole quality range? What are the welfare consequences of this potential copetition, i.e. does welfare always increase in such a scenario or is it possible that a protected onopoly is better? This paper tries to answer these questions in a vertical product differentiation fraework. We copare a odel where each fir can produce a single quality with one where price discriination over a quality range is possible. We show 1 See Hollis (2003). 2 See Grabowski & Vernon (1992) or Frank & Salkever (1997). 3 See Gillen (2002). 4 See Johnson & Myatt (2003). 5 See Gilroy, Lukas, & Volpert (2003).

5 Vertical Product Differentiation, Market Entry, and Welfare 3 that in the single quality case welfare with potential copetition can be lower than in onopoly. The intuition is that if qualities are strategic copleents the incubent lowers its quality in coparison to onopoly and produces soe iddle range quality to deter entry because it is ipossible then for an entrant to find a profitable entry segent. Even in case of entry such a quality reduction ight be profitable, causing the entrant to produce a low quality and reducing price copetition. If qualities are strategic substitutes the incubent produces higher quality and welfare increases. If firs can produce a quality range we find that consuer rent with potential copetition is higher than under onopoly. The intuition is that in order to deter entry the incubent enlarges its product line to occupy the lower segent as well. In this case welfare increases as well. If entry cannot be deterred there is a gap between the two firs s quality ranges which reduces copetition. In this case consuer rent always increases because of lower prices while the consequences on welfare are unclear. The reason is that soe consuers buy a higher quality but others buy a lower one. Specifically, we analyse a odel of vertical product differentiation with entry. In the first stage the incubent produces a quality which cannot be changed in the sequel. After observing this quality level the entrant decides if it wants to enter and if so which quality level it wants to produce. In the third stage firs copete in prices dependent on the produced quality levels. 6 We copare this situation of potential copetition with a situation of onopoly. In onopoly the fir produces too low a level of quality. The reason is that the onopolist can only charge one price which is the valuation of the arginal consuer. The valuation of the infraarginal consuer is higher but cannot be represented in the price. In the scenario of potential entry the incubent can deter entry by varying its quality level. If qualities are strategic copleents in the sense of Bulow, Geanakoplos, & Kleperer (1985) a reduction of the incubent s quality leads to a reduction of the entrant s quality which lowers the entrant s profit. 7 If 6 Throughout the paper we assue that it is ore profitable for the incubent to be the high quality fir than the low quality fir. 7 In a different terinology which is used by Fudenberg & Tirole (1984) the strategy where the

6 Vertical Product Differentiation, Market Entry, and Welfare 4 fixed costs of entry are high enough entry is deterred by a quality reduction and welfare is lower than under onopoly. Even in the case where entry is accoodated it ight be profitable for the incubent to reduce its quality. The entrant lowers its quality as well which results in lessened price copetition. So even in case of copetition it is possible that welfare is lower than under onopoly. If products are strategic substitutes welfare rises in both cases (entry deterrence and accoodation) because the incubent increases its quality. 8 We also show that if arginal costs of production are low quality of the incubent in case of entry is higher than in onopoly. The intuition is that the incubent wishes to differentiate itself fro its copetitor by producing a higher quality. If arginal costs are low it is not very costly to do so and quality in case of entry is higher. We also analyse a odel where each fir can produce a whole range of different qualities and engage in second-degree price discriination. This odel is copared with the single quality case and we find that the results differ in soe respects. In the odel with price discriination the lowest quality of the incubent and the highest quality of the entrant are strategic copleents. So if the incubent enlarges its quality range the profit of the entrant decreases. Thus the incubent s entry deterrence strategy is to expand its product line which results in a welfare increase because ore consuers are served. This is different fro the single quality case where welfare in case of entry deterrence can be lower if qualities are strategic copleents. If fixed costs of entry are low and the incubent accoodates entry then we always get a gap between the two product lines of incubent and entrant in order to reduce price copetition. Thus soe qualities in the iddle range which are produced in onopoly are no longer produced in duopoly. But ore qualities in the lower segent are produced in duopoly. The result is that soe consuers buy higher quality in duopoly while others buy lower quality. Therefore the consequence on welfare is not clear. By contrast, it can be shown that consuer rent always increases in case of entry due to increased price copetition. incubent reduces quality to deter entry is called the lean and hungry look. 8 In the terinology of Fudenberg & Tirole (1984) this strategy is called Top Dog.

7 Vertical Product Differentiation, Market Entry, and Welfare 5 For both odels, single quality case and price discriination, we provide two epirical exaples fro different industries where firs behaviour is siilar to that predicted by our odel. The reainder of the paper is organised as follows. In the next section our odel is related to the existing literature. Section 3 presents the odel and the equilibriu without price discriination. Soe anecdotal evidence that supports the results is given in Section 4. Section 5 presents the odel, the equilibriu, and the welfare consequences if price discriination is possible. In Section 6 two practical exaples for such fir behaviour are given. Section 7 gives a short conclusion and soe policy iplications. Most proofs of the results are presented in the Appendix. 2 Related Literature Our odel relates to the literatures on vertical product differentiation, seconddegree price discriination, and arket entry. We will give the relation to each of the three branches and how our odel differs fro these literatures in turn. The literature on quality copetition started with the pioneering work of Gabszewicz & Thisse (1979) and Shaked & Sutton (1982). In their odels firs are restricted to produce one quality level and copete in prices. In Gabszewicz & Thisse (1979) firs qualities are exogenously given while in Shaked & Sutton (1982) firs decide siultaneously about their quality levels in the stage before price copetition. Shaked & Sutton (1982) show that firs will produce different quality levels to avoid fierce copetition in the last stage of the gae. Under soe paraeter constellations only two firs are active in the arket if there exist costs of entry. Shaked & Sutton (1982) were the first to analyse the now coon gae structure where firs are coitted to their quality levels when copeting in prices because prices can be changed at will while a quality change involves odifications of the production facilities. Ronnen (1991) analyses a odel with a siilar fraework as Shaked & Sutton (1982) but where a regulation authority can set a iniu quality standard before firs copete in qualities. In his odel qualities are strategic copleents.

8 Vertical Product Differentiation, Market Entry, and Welfare 6 Thus if the iniu quality standard is set (slightly) above the quality which is produced by the low quality fir in a gae without restriction, both qualities will rise in equilibriu. Price copetition is intensified and all consuers are better off while the high quality fir loses. Ronnen (1991) shows that with an appropriately chosen standard social welfare iproves. Cabrales (2003) looks at the consequence of a price ceiling. He shows that with a lower price ceiling the arket share of the high quality variant increases. The reason is that arket share depends on the ratio of price to quality. But the quality responds less than proportionally to the price ceiling if the cost function is convex. He applies his odel to regulation issues in the pharaceutical arket. In contrast to these odels y paper analyses a sequential ove gae in the quality decision. It ight therefore be possible for the first over to deter entry by an appropriate quality choice. Also welfare in this sequential structure is copared with a pure onopoly situation. There are several papers which analyse copetition between ultiproduct firs. 9 The closest to the odel considered here are Chapsaur & Rochet (1989) and Johnson & Myatt (2003). Chapsaur & Rochet (1989) analyse a duopoly where firs coit in the first stage to a quality range and in the second stage copete in prices for each produced quality. They show that firs produce non overlapping quality ranges (there is always a gap between the two product lines) to reduce price copetition. This result appears in y paper as well. The difference is that in y paper quality decisions are taken sequentially and one fir has a first over advantage. This influences prices and quality ranges and ay results in entry deterrence. I also provide a welfare analysis. Johnson & Myatt (2003) analyse an asyetric duopoly. One fir (which is called incubent by Johnson & Myatt (2003)) can produce the entire range of qualities while the other (the entrant ) is liited to soe range with an upper quality level. So the incubent can produce upgrade versions. Firs copete siultaneously 9 Spulber (1989) analyses a odel where firs are horizontally differentiated on a Hotelling line. He shows that each fir produces the first best quality for the consuer who is located exactly at the fir s position while qualities for all other consuers are distorted downwards. Stole (1995) in addition to Spulber (1989) considers the case where firs are uncertain about vertical preferences. He finds that a siilar result holds in this case.

9 Vertical Product Differentiation, Market Entry, and Welfare 7 in quantities for each quality level. As is shown by Johnson & Myatt (2003) the incubent ay produce fewer qualities ( product line pruning ) or ore qualities ( fighting brands ) in duopoly than in onopoly dependent on the cost function. If arginal revenue is decreasing the quality range is reduced while the quality range ight be broader if arginal revenue is increasing in soe regions. A odel of arket entry in a vertical product differentiation fraework is analysed by Donnenfeld & Weber (1995). 10 In their odel there are two incubents who face the entry threat of a third fir. They show that the equilibriu depends on the level of the fixed costs of entry. If these fixed costs are low entry is accoodated and the incubents select extree qualities to reduce price copetition. The entrant chooses a quality in the iddle. 11 If fixed costs are in soe iddle range incubents deter entry. They do this by producing siilar qualities which leads to harsh copetition and low profits. If fixed costs are so high that entry is blockaded incubents choose sharply differentiated products to reduce copetition. In contrast to Donnenfeld & Weber (1995), y odel analyses the behaviour of only one incubent but firs can produce quality ranges and engage in second degree price discriination. In short, odels of vertical product differentiation usually do not consider the possibility of price discriination if entry is possible. So this paper akes a first attept to analyse the equilibriu and the welfare consequences of such a strategy. 3 The Model without Price Discriination This section presents the odel where each fir can produce only one quality level. 10 For a odel of entry deterrence and horizontal preferences see Bonanno (1987). 11 A siilar result is obtained in Donnenfeld & Weber (1992) in the case without fixed costs. They show that in this case the entrant s profit is higher than the profit of the incubent which produces the lower quality.

10 Vertical Product Differentiation, Market Entry, and Welfare Description of the Model There is a continuu of consuers of ass 1. Each consuer purchases a single unit of a good. If a consuer decides to purchase fro fir i she gets a good of quality q i at price p i. Consuers tastes are described by the paraeter θ which is distributed between 0 and 1 with distribution function F (θ) and density function f(θ). The utility fro purchasing fro fir i can therefore be denoted as U(q i, θ, p i ) = u(q i, θ) p i, where u is assued to be strictly concave in q and in θ and thrice continuously differentiable. Consuers reservation value fro not buying is noralised to zero. We proceed by aking a few assuptions on the utility and the distribution function. A1 : Single Crossing Property : u qθ (q, θ) > 0 A2 : u qθθ (q, θ) 0, u qqθ (q, θ) 0 ( ) A3 : Monotone Hazard Rate Condition : 1 F (θ) θ f(θ) 0. A1 is the single crossing property. It states that utility and arginal utility go in the sae direction if θ increases. It iplies that indifference curves cross only once. This assuption is standard in the literature. A2 iposes two technical assuptions that guarantee that the second order conditions are satisfied. A3 is a standard assuption in the adverse selection literature and is called onotone hazard rate condition. It is satisfied by any distribution functions like the unifor distribution, the noral distribution etc. There are two firs i = 1, 2. Fir 1 is the incubent and fir 2 the potential entrant. If a fir decides to produce quality q it has to incur developent costs c(q) with c (q) > 0 and c (q) > c(q) is the sae for both firs. Marginal costs are denoted v and are the sae for both firs as well. The gae structure is as follows. The gae has three stages. In stage 1 fir 1 chooses q 1. Fir 2 decides about arket entry in stage 2 after observing the choice 12 c(q) satisfies the standard Inada-conditions li q 0 c (q) = 0 and li q c (q) =.

11 Vertical Product Differentiation, Market Entry, and Welfare 9 of fir 1. If fir 2 decides not to enter fir 1 is a onopolist in stage three and decides about p 1. If fir 2 enters it has to incur fixed costs of arket entry of F 13 and chooses q 2 in stage 2. Fir 1 observes q 2 and in stage 3 both firs set their prices p 1 and p 2 conditional on q 1 and q 2. The iportant feature of the odel is that both firs are coitted to the quality they produce. In particular it is not possible for fir 1 to ake a later change in the quality to which it has coitted in stage This tie structure represents the idea that it is easy and alost costless possible to change prices but it takes a considerable aount of tie and costs to change the quality of a good Monopoly Situation First let us look at the onopoly case as a benchark which is later copared with the results of the entry gae. So suppose fir 1 is a onopolist and there is no potential entrant. In other words stage 2 of the gae does not exist and fir 1 chooses first q 1 and then p 1. Let the arginal consuer who is served by the onopolist be called θ on. If quality is q 1 this arginal consuer is given by u(q 1, θ on ) p 1 = 0. So all types θ on while all types θ < θ on θ 1 are buying fro the onopolist are not buying. In the last stage the onopolist chooses its price given quality q 1. The axiisation proble is thus Since θ on variables and let θ on 1 ax Π 1 = p 1 θ on [p 1 vq 1 ]f(θ)dθ c(q 1 ). is deterined by p 1 it is convenient to ake a change in the decision be the decision variable. Thus we have ax θ on Π 1 = 1 θ on [u(q 1, θ on ) vq 1 ]f(θ)dθ c(q 1 ). 13 These entry costs ight contain advertising expenditures to infor consuers about the entrant s product, investent in transportation channels and so on. 14 For a odel where such coitent is only partially possible see Henkel (2003). 15 This line of reasoning is followed in ost odels of vertical product differentiation, see for exaple Shaked & Sutton (1982) or Ronnen (1991).

12 Vertical Product Differentiation, Market Entry, and Welfare 10 This results in a first order condition of Π 1 θ on = f(θ on )[u(q 1, θ on ) vq 1 ] + (1 F (θ on ))u θ (q 1, θ on ) = 0. (1) Because of Assuption A3 the second order condition is globally satisfied. The first order condition as usual states that the arginal gain fro serving an additional consuer type (first ter) is equal to the loss on all other consuers because of the price reduction (second ter). Turning to the first stage where the fir decides about quality q 1 we get a first order condition of 16 Π 1 q 1 = (1 F (θ on ))[u q1 (q 1, θ on ) v] c (q 1 ) = 0. (2) The second order condition is globally satisfied because of u q1 q 1 (q 1, θ on ) < 0 and c (q 1 ) > 0. Thus we get that θ on is given by (2). is given by (1), p on = u(q1 on, θ on ) and q on 1 A coparison of the onopolistic outcoe with the welfare axiising outcoe yields Proposition 1 Copared with the welfare-axiizing θ W F and q W F a onopolist serves too few consuers, θ on q W F > q on 1. Proof See the Appendix. > θ W F, and provides too low a quality The result that too few consuers are served by a onopolist is standard. The intuition for the quality distortion is that the onopolist can charge only one price naely p on 1 = u(q1 on, θ on ) for its produced quality. So by increasing quality it can only increase its price by the aount that the utility of the arginal consuer 16 Because of the Envelope Theore ters with Π1 θ on the first order condition. θ on q 1 = 0 and can therefore be ignored in

13 Vertical Product Differentiation, Market Entry, and Welfare 11 rises. But the utility of all types θ > θ on rises ore fro a quality increase than the utility of the arginal consuer because of the single crossing property. Thus fro a welfare point of view quality in onopoly is too low. Since the onopolist also serves too few consuers the downward distortion of quality is intensified. 3.3 Potential Copetition Now let us turn to the three stage gae in which fir 2 can enter the arket in stage 2. In the following let us define q 2 (q 1 ) as the best answer of fir 2 if it enters in response to fir 1 producing q 1. Before starting with the analysis we need two additional assuptions: A4 : Π 2 (q on 1, q 2 (q on 1 )) > 0 A5 : Π 1 (q H 1, q 2 (q H 1 )) > Π 1 (q L 1, q 2 (q L 1 )) whenever q H 1 > q 2 (q H 1 ) and q L 1 < q 2 (q L 1 ). The first assuption states that the profit of fir 2 is positive if fir 1 produces its optial onopoly quality. The assuption is ade to avoid the uninteresting case that it is an equilibriu if fir 1 produces its onopoly quality and fir 2 stays out of the arket. In the terinology of Bain (1956) this would ean that entry is blockaded. Assuption A5 states that fir 1 s profit is higher if it is the high quality fir, i.e. produces such a quality in stage 1 that the optial response of fir 2 is to produce a lower quality in stage 2. As usual the gae is solved by backwards induction. In the third stage there are two possibilities. Either fir 2 has entered in stage 2 and there is copetition or fir 2 stayed out of the arket and fir 1 is a onopolist. If fir 1 is a onopolist the arginal consuer is deterined in the sae way as in the last subsection and θ on is given by (1) given the quality q 1 fir 1 has produced in stage 1 (which is different fro q on 1 because of Assuption A4.) If fir 2 has entered the arket in stage 2 firs copete for consuers in stage 3. Because of Assuption A5 fir 1 will always produce a quality q 1 such that it is optial for fir 2 to produce q 2 < q 1. It is therefore apparent that fir 1

14 Vertical Product Differentiation, Market Entry, and Welfare 12 will serve higher consuer types. The arginal consuer θ duo 1 who is indifferent between buying fro fir 1 and buying fro fir 2 is given by u(q 1, θ duo 1 ) p 1 = u(q 2, θ duo 1 ) p 2 or p 1 = p 2 + u(q 1, θ duo 1 ) u(q 2, θ duo 1 ). Thus fir 1 s profit function is given by Π 1 = 1 θ duo 1 Maxiising this with respect to θ duo 1 yields [p 2 + u(q 1, θ duo 1 ) u(q 2, θ duo 1 ) vq 1 ]f(θ)dθ c(q 1 ). Π 1 θ duo 1 = f(θ duo 1 )[p 2 + u(q 1, θ duo 1 ) u(q 2, θ duo 1 ) vq 1 ]+ (1 F (θ duo 1 ))(u θ (q 1, θ duo 1 ) u θ (q 2, θ duo 1 )) = 0. (3) The second order condition is globally satisfied because of Assuptions A2 and A3. Concerning fir 2 the arginal consuer θ duo 2 who is indifferent between buying at fir 2 and buying nothing is given by u(q 2, θ duo 2 ) p 2 = 0 or p 2 = u(q 2, θ duo 2 ). Thus the profit function of fir 2 is Π 2 = θ duo 2 θ duo 1 The first order condition is [u(q 2, θ duo 2 ) vq 2 ]f(θ)dθ c(q 2 ) F. Π 2 θ duo 2 = f(θ duo 2 )[u(q 2, θ duo 2 ) vq 2 ] + (1 F (θ duo 2 ))u θ (q 2, θ duo 2 ) = 0. (4) Again because of Assuption A3 the second order condition is satisfied. In equilibriu arginal consuers θ 1 and θ 2 are given by (3) and (4) and equilibriu prices are given by p 1 = u(q 2, θ 2)+u(q 1, θ 1) u(q 2, θ 1) and p 2 = u(q 2, θ 2). 17 Now let us look at stage 2 and suppose for the oent that fir 2 has entered. In this case fir 2 axiises its profit with respect to q 2 which yields Π 2 q 2 = (F (θ 1) F (θ 2))(u q (q 2, θ 2) v) + [u(q 2, θ 2) vq 2 ]f(θ) θ 1 q 2 c (q 2 ) = 0. (5) 17 Variables arked with a star indicate equilibriu values of the gae after fir 2 has entered.

15 Vertical Product Differentiation, Market Entry, and Welfare 13 The second order condition is satisfied because of u qq (q, θ) < 0 and c (q) > 0. q 2 is given by (5) and since θ 1 is dependent on q 1, q 2 is dependent on q 1 as well. Fir 2 only enters if θ 2 θ 1 [u(q 2, θ 2) vq 2]f(θ)dθ c(q 2) > F. Fir 1 in stage 1 does now take into account that q 2 depends on q 1. Its first order condition if fir 2 enters is given by Π 1 q 1 = (1 F (θ 1))(u q1 (q 1, θ 1) v [u q2 (q 2, θ 1) u q2 (q 2, θ 2) u θ (q 2, θ 2)] θ 2 q 2 q 2 q 1 ) c (q 1 ) = 0. (6) But if F is high enough then fir 1 also has the possibility to choose q 1 in such a way that fir 2 does not enter. Let us denote the quality that deters entry of fir 2 by q ED 1. It is given by θ 2 θ 1 [u(q 2(q ED 1 ), θ 2) vq 2(q ED 1 )]f(θ)dθ c(q 2(q ED 1 )) = F. If fir 1 produces this q ED 1 it is a onopolist in stage 3 and earns profits of 1 Π ED 1 = [u(q θ 1 ED, θ(q 1 ED )) vq1 ED ]f(θ)dθ c(q1 ED ). (qed 1 ) Thus fir 1 engages in entry deterrence if and only if Π ED 1 = 1 θ(q 1 ED ) [u(qed 1, θ(q 1 ED )) vq1 ED ]f(θ)dθ c(q1 ED ) > 1 θ1 [u(q 2, θ2) + u(q1, θ1) u(q2, θ1) vq1]f(θ)dθ c(q1) = Π duo 1. We are now in a position to state the equilibriu of the gae: If Π ED 1 > Π duo 1 then fir 1 chooses q ED 1, fir 2 does not enter in stage 2 and p 1 = u(q ED 1, θ ) where θ is given by (1) with q 1 = q ED 1. If Π ED 1 Π duo 1 then q 1 is given by (6), fir 2 enters in stage 2 and q 2 is given by (5). θ 1 and θ 2 are given by (3) and (4) and p 1 = u(q 2, θ 2) + u(q 1, θ 1) u(q 2, θ 1) and p 2 = u(q 2, θ 2).

16 Vertical Product Differentiation, Market Entry, and Welfare 14 Now this equilibriu with potential copetition can be copared with the onopoly equilibriu. First look at the case where fir 2 enters. In this case fixed costs of arket entry are so low that it does not pay for fir 1 to choose q ED 1 such that fir 2 does not enter. Instead fir 1 sets q 1 according to (6). Proposition 2 q 1 > q on 1 if and only if v < u q1 (q on 1, θ 1) q 2 q 1 [(u q2 (q 2, θ 1) + u q2 (q 2, θ 2) u θ (q 2, θ 2)) θ 2 q 2 )]( 1 F (θ on ) F (θ 1 )) (7) Proof q on 1 is given by (2), Π 1 q 1 = (1 F (θ on ))(u q1 (q 1, θ on ) v) c (q 1 ) = 0, while q 1 is given by (6), Π 1 q 1 = (1 F (θ 1))(u q1 (q 1, θ 1) v (u q2 (q 2, θ 1) + u q2 (q 2, θ 2) u θ (q 2, θ 2)) θ 2 q 2 Evaluated at q on 1, (6) becoes q 2 q 1 c (q 1 ) = 0. [F (θ on ) F (θ1)](u q1 (q1 on, θ1) v) ((u q2 (q2, θ1) + u q2 (q2, θ2) u θ (q2, θ2)) θ ) q q2 2 q 1, which can be greater or saller than zero. Solving for v yields u q1 (q1 on, θ1) [(u q (q2, θ1) + u q2 (q2, θ2) u θ (q2, θ2)) θ q q2 2 q 1 ] ( > ) 1 F (θ on ) F (θ1 ) = v. < If > is true the first derivative of the profit function of fir 1 after

17 Vertical Product Differentiation, Market Entry, and Welfare 15 entry is increasing at q on 1 while it is zero at q 1. Since the function is globally concave q on 1 < q duo 1. q.e.d. This shows that the quality level of the incubent increases after entry if and only if arginal costs are lower than a given threshold. At first glance one ay would have guessed that the quality level of fir 1 in duopoly is always higher achieving a higher degree of differentiation fro the entrant s quality. But with high arginal costs this is not true. The reason is that in case of copetition it is harder for the incubent to extract consuer rent. Thus it does not pay to produce high quality if this coes at high costs. More specifically, let us have a closer look at inequality (7). It is obvious fro equation (2) that u q1 (q on 1, θ 1) > v. Thus if the ter [ q 2 q 1 [(u q2 (q 2, θ 1) + u q2 (q 2, θ 2) u θ (q2, θ2)) θ 2 1 )]( q2 F (θ on ) F (θ1 ))] is greater than zero the right hand side of (7) is higher than the left hand side and we have q1 > q1 on. To get an intuition for the result suppose that θ 1 < θ on positive if q 2 q 1 (and thus F (θ1) < F (θ on )). 18 Then this ter is < 0, i.e. qualities are strategic substitutes. In this case an increase in q 1 has a favourable ipact for fir 1 on q 2, naely a reduction of q 2. Thus q 1 unabiguously increases with copetition. If instead q 2 > 0 the qualities are q1 strategic copleents. In this case it ight be optial for fir 1 to set q1 < q1 on to induce fir 2 to lower its quality as well. Fir 1 will do so if variable costs are high because then costs can be reduced and copetition is lowered by the reaction of fir 2. To gain soe insights into welfare coparisons between onopoly and potential copetition we have to give a bit ore structure to the odel. Proposition 3 Let u(q, θ) = θq. If qualities are strategic substitutes welfare unabiguously rises with entry. 18 In the next proposition it is shown that this is always the case if u(q, θ) = θq.

18 Vertical Product Differentiation, Market Entry, and Welfare 16 Proof See the Appendix. If u(q, θ) = θq fir 1 serves ore consuers in duopoly than in onopoly. The reason is that the quality deflated price p 1 is lower. 19 This follows fro the fact q1 that θ1 < θ on which for the specific utility function eans that p 1 p 2 < pon q1 1, q 2 q1 on and the fact that p 2 < pon q2 1. Taken together this iplies that p q1 on 1 < pon q1 1. Thus ore q1 on consuers are buying fro the incubent. If its quality in duopoly is higher as well then welfare in duopoly is for sure higher. This is the case if qualities are strategic substitutes because then fir 2 reduces its quality as reaction to a quality increase of fir 1, which is profitable for fir 1. It should be entioned that if qualities are strategic substitutes welfare necessarily increases. But the "only if" stateent is not true. Even in case if qualities are strategic copleents welfare can rise because ore consuers are buying in duopoly. But it is also possible that welfare decreases because the incubent reduces its quality and this quality reduction effect doinates the effect that ore consuers are served. Now let us turn to the case where fir 1 deters entry of fir 2. In this case fir 1 produces q ED 1 and is a onopolist thereafter. Fro Proposition 1 we know that a onopolist distorts quality downwards. So whether welfare in case of entry deterrence is higher than welfare in a pure onopoly situation depends on q ED 1 in coparison with q on 1. If q ED 1 > (<)q on 1 welfare in case of entry deterrence is higher (lower). But this depends on the reaction of q 2 on q 1. If e.g. q 2 q 1 < 0 the incubent has to increase its quality to keep the entrant out of the arket. p on 1 is always given by p on 1 = u(q on in p on 1 of u q on 1 (q on proposition. 1, θ on 1, θ on ) but θ on ). Thus a change in q on 1 leads to a change stays unchanged and we get the following Proposition 4 If qualities are strategic substitutes welfare in case of entry deterrence 19 This result is obtained in any odels of quality copetition, see e.g. Bae & Choi (2003) or Banerjee (2003). In these odels quality is exogenous. In the paper here it is shown that this result holds for endogenous quality choice as well.

19 Vertical Product Differentiation, Market Entry, and Welfare 17 is higher than in a protected onopoly. If qualities are strategic copleents the reverse is true. This shows that the threat of entry can either increase or decrease welfare depending on the strategic reaction of fir 2 to the quality of fir 1. In the ost general odel it is ipossible to assess whether qualities are strategic substitutes or copleents. But we can ake a general conclusion in the specific fraework of Mussa & Rosen (1978). In their odel θ is uniforly distributed, u(q, θ) = θq, v = 0, and c(q) = 1 2 q2. Proposition 5 In the linear-unifor-quadratic case of Mussa & Rosen (1978) qualities are strategic copleents. Proof See the Appendix. So in the unifor-linear-quadratic case welfare decreases with potential entry if fixed costs fro entry are high enough such that entry is deterred. The reason is that the incubent distorts its quality further downwards so that it is not profitable for the entrant to occupy the low quality segent and therefore the entrant stays out of the arket. But this downward distortion of quality lowers welfare. In Section 5 this result will be contrasted with a odel where both firs can produce any different quality levels. 4 Discussion The preceding analysis points to cost-and deand-function-based reasons for an incubent to increase or decrease its quality and price after entry. In this section we turn to a discussion of soe epirical exaples fro different arkets that give anecdotal evidence for our results.

20 Vertical Product Differentiation, Market Entry, and Welfare Pricing of Pharaceuticals after Generic Entry In the arket for pharaceuticals, patents protect drug developers after the developent of a new pharaceutical. The ai of these patents is to give developing firs an incentive to develop new pharaceuticals because they can earn onopoly rents during the patent period. After the expiry of the patent, entry of generic drugs is possible. In the US the Watchan-Hax Act in 1984 akes it easier for generic firs to enter the arket. 20 This akes the pharaceutical arket a suitable exaple for applying the results of the previous section. By Proposition 2 our theory predicts that if variable arginal costs of production are low, quality and price of the brand-nae drug should increase after entry. In the production of pharaceuticals arginal costs are very low copared with research and developent costs. For exaple, in the US the pharaceutical industry has spent the largest fraction of its sales receipts to research and developent aong all US industries with coparable data (US Federal Trade Coission (1985)). So one would predict that prices increase after generic entry. This is confired by epirical studies. Scherer (2000) gives an exaple of the expiry of the product patent covering the cephalosporin antibiotic cephalexin in April This was sold under the brand nae Keflex. After entry the price of Keflex rose fro around $60 (per 100 capsules) to $85 in During this tie the prices of generics went down fro $30 to $15. Frank & Salkever (1997) looked at 45 drugs which faced generic copetition for the first tie after the Watchan-Hax Act. They found that brand-nae prices increased by 50% five years after generic entry. Siilar pricing patterns were obtained in the studies by Grabowski & Vernon (1992) and Scherer (1996). This supports the prediction that if variable arginal costs are low prices will rise after entry. Rising quality is a bit harder to explain because norally quality of drugs stayed unchanged. But the brand-nae producers tried to increase consuers perceived quality via advertising during the period of patent protection. Scherer (2000) states 20 The reason is that testing requireents for generics have been relaxed. It is only necessary to deonstrate that the drug has the sae ingredients as the original, that the forulation was absorbed in the blood strea at ore or less the sae tie, and to docuent good anufacturing practices of the generic fir. See Scherer (2000), p

21 Vertical Product Differentiation, Market Entry, and Welfare 19 that in 1998 in the USA producers spend about $1 billion on direct-to-consuer advertising. 21 This aount can not only be seen as inforative advertising but is also done to convince consuers of the product s quality and to separate fro generics. After entry, advertiseent was reduced because of the fear that this would also spur the sales of the new copetitors. Thus in the arket for pharaceuticals brand-nae producers did not increase the real quality of the drugs. Instead they increased perceived quality when faced with the threat of entry. 4.2 The Market for Fragrance and Cosetics In Singapore for a long tie cosetics were sold exclusively by authorised distributors and listed retailers. These firs deand high prices and had high price-cost argins. For exaple, consuers had to pay $35 to $38 for a lipstick at cosetic counters of departent stores but it costs only US $0.50 to anufacture a lipstick. 22 These lipsticks are iported fro the US or Europe so one had to add transportation costs. Still price cost argins were high. In the late 1980s the parallel iporter B&N entered the arket. B&N iported the sae products as the authorised distributors but had a siple business strategy, naely price cuts. It sold a Christian Dior lipstick at $19 or $20 23 and in general offered the cosetics up to 50% below the prices of listed retailers. The products are qualitatively siilar but disadvantages for B&N were that the copany was unknown at the beginning of their business and that authorised distributors placed their products on preiu space and had set up cosetic counters at departent stores. What was the reaction of distributors to the entry of B&N? Beside negative advertising about parallel iports and lawsuits their ain response consisted in price cuts. For exaple they lowered the lipstick price fro $34 to $ In contrast to the pharaceutical arket in the arket for fragrance and cosetics arginal costs play the iportant role copared to developent costs. The only source of developent costs is the building up of connections to iporters. But 21 See also Caves, Whinston & Hurwitz (1991). 22 See Lee, Li & Tan (2001). 23 "Parallel Iporters Make Cosetic Firs See Red", The Straits Tie, October 7, 1994, p "Parallel Iports: Copyright Owners Fight Back", The Straits Tie, August 12, 1996, p.31.

22 Vertical Product Differentiation, Market Entry, and Welfare 20 the ain bulk of costs a retailer has to bear are the delivering costs of lipsticks, the advertising costs, and the rents to be paid to departent stores for display on preiu space. In this respect the retailers also reduced the quality of their offers. They set up fewer cosetic counters in stores and spend less oney on costly advertising. 25 But especially with cosetics and fragrance the conveyed life-style of the products is very iportant and this can be ainly given by advertising. Since the retailers do not anufacture the cosetics theselves the physical quality if the products stays the sae. But the quality was reduced fro the perspective of the consuers since the products are no longer displayed on preiu space and are less advertised. Thus the observations in this arket go in line with the predictions of our theory that an incubent s price and quality decrease if arginal variable costs are high. 5 The Model with Price Discriination This section analyses a odel where firs can produce any different qualities which can be sold at different prices. The results of this odel are later copared with the results of Section Model Fraework Consuers utility functions, the distribution of preferences, firs cost functions, and the gae structure is the sae as in Section 3. The only difference is that each fir can now produce not only one quality but any different qualities which are sold at different prices. We are therefore in a proble of adverse selection. We assue that for each quality a fir produces it has to bear developent costs c(q) 26 and variable costs v. Assuptions A1, A2, and A3 are kept as well. 25 See Lee, Li & Tan (2001). 26 Theoretically the assuption of developent costs for each quality is necessary to avoid that fir 1 can coit costless to the whole range of qualities. If this is possible we get trivial equilibria in which fir 2 is always kept out of the arket.

23 Vertical Product Differentiation, Market Entry, and Welfare Monopoly Situation As in Section 3 before solving the gae consider the benchark case where fir 1 is a onopolist. In this case we are in a standard echanis design proble of second-degree price discriination. The fir s proble is to choose the optial quality-payent schedule and the arginal consuer θ on participation and incentive copatibility constraints, subject to the standard ax q(θ),p(θ),θ on Π 1 = 1 θ on [p(θ) vq(θ)]f(θ)dθ 1 θ on c(q)dθ s.t. u(q(θ), θ) p(θ) 0 θ θ on u(q(θ), θ) p(θ) u(q(ˆθ), θ) p(ˆθ) θ, ˆθ θ on. The equilibriu is characterised in the following lea: Lea 1 The optial q(θ) on, p(θ) on, θ on are given by the following equations: p on (θ) = u(q on (θ), θ) θ θ on u(q on (τ), τ) dτ, (8) θ u(q on (θ), θ) q ( 1 F (θ) f(θ) ) 2 u(q on (θ), θ) q θ v c (q on (θ)) f(θ) = 0, (9) [u(q on (θ on ), θ on = (1 F (θ on ) vq on (θ on )]f(θ on ) c(q on (θ)) )) u(qon (θ on ),θ ) θ on. (10) Proof See the Appendix. The first two equations are standard in second degree price discriination. The first states that the price for each type θ is the utility type θ gets fro buying a

24 Vertical Product Differentiation, Market Entry, and Welfare 22 good of quality q on (θ) inus a ter which is increasing in θ. So higher types get a higher utility to prevent the fro choosing the contract designed for the lower types. The second equation states that the quality a type θ gets is increasing in θ but is always lower than the optial quality except for θ = 1. This is the faous nodistortion-at-the-top-result. The third equation states that the arginal consuer is characterised in such a way that the net gain of serving hi (the left hand side of (10)) is exactly equal to the loss that occurs to the fir because it has to give a higher rent to the infraarginal consuers (the right hand side of (10)). Concerning welfare the fir offers a whole range of qualities where higher types get higher quality. But except for the highest type quality is distorted downwards. 5.3 Analysis of the Duopoly Situation In the following we denote the quality range of fir 1 Q 1 = [q1, q 1 + ] and the quality range of fir 2 Q 2 = [q2, q 2 + ]. Q 2 (Q 1 ), as in Section 3, is the best response of fir 2 after entry if fir 1 produces a quality range Q 1. If the quality ranges do not overlap, i.e. the lowest quality of fir i, qi, is higher than the highest quality of fir j, q j +, we say that Q i > Q j. 27 Again before starting with the analysis of the entry gae we ake two assuptions which are odifications of assuptions A4 and A5 of Section 3. A4 : Π 2 (Q on 1, Q 2 (Q on 1 )) > 0. Q on 1 is the quality range fir 1 produces in the onopoly case and A4 states that fir 2 enters if fir 1 produces Q on 1. A5 : Π 1 (Q H 1, Q 2 (Q H 1 )) > Π 1 (Q L 1, Q 2 (Q L 1 )) whenever Q H 1 > Q 2 (Q H 1 ) and Q L 1 < Q 2 (Q L 1 ). Assuption A5 states that it is profitable for fir 1 to be the high quality fir, i.e. producing a quality range which is above the one of fir In Lea 2 we show that in equilibriu this is always the case.

25 Vertical Product Differentiation, Market Entry, and Welfare 23 Again the gae is solved by backwards induction. First look at the case where fir 2 did not enter in stage 2. By the sae calculations as in the onopoly case we get that prices are p (θ) = u(q(θ), θ) θ θ the ends of the quality range fir 1 has produced in stage 1. u(q(τ),τ) dτ. This prices are independent of θ Now let us turn to the case where fir 2 entered in stage We have to deterine the prices given that fir 1 produces quality range Q 1 and fir 2 produces quality range Q For siplicity let us assue first that q 1 > q + 2. We will later show that this is always the case. The arginal consuer θ who is indifferent between buying q 1 and q + 2 is given by u(q 1, θ ) p 1 (θ(q 1 )) = u(q + 2, θ ) p 2 (θ(q + 2 )) or p 1 (θ(q 1 )) = p 2 (θ(q + 2 )) + u(q 1, θ ) u(q + 2, θ ). Fir 1 s axiisation proble in stage 3 can be written as ax p1 (θ),p 1 (q 1 ) Π 1 = 1 θ(q )[p 1(θ) vq(θ)]f(θ)d(θ)+ 1 θ(q 1 ) θ [p 1 (q1 ) vq1 ]f(θ)dθ 1 θ(q 1 ) c(q(θ))dθ s.t. u(q(θ), θ) p 1 (θ) u(q + 2, θ) p 2 (q + 2 ) θ θ u(q(θ), θ) p 1 (θ) u(q(ˆθ), θ) p 1 (ˆθ) θ, ˆθ θ, where θ(q 1 ) is the highest type who buys quality q 1. Fir 2 s axiisation proble in stage 3 is ax p2 (θ),p 2 (q + 2 ) Π 2 = θ(q + 2 ) θ 2 [p 2 (θ) vq(θ)]f(θ)d(θ) + θ θ(q + )[p 2(q 2 + ) vq 2 + ]f(θ)dθ θ(q + 2 ) θ 2 c(q(θ))dθ 2 s.t. u(q(θ), θ) p 2 (θ) u(q 1, θ) p 1 (q 1 ) θ < θ u(q(θ), θ) p 2 (θ) u(q(ˆθ), θ) p 2 (ˆθ) θ, ˆθ < θ, where θ(q + 2 ) is the lowest type who buys quality q The analysis in this section draws heavily on Chapsaur & Rochet (1989). The difference is that firs choose qualities siultaneously in Chapsaur & Rochet (1989) while in y odel qualities are chosen sequentially. But the analysis of the second and the third stage is quite siilar. 29 In principle we should analyse the third stage for arbitrary (Q 1, Q 2 ). However, this is clearly ipossible to do. But one can put the restriction on (Q 1, Q 2 ) that there is never a whole in one of two quality ranges for the sae reason as for the onopolist. For a discussion on that issue and why it is reasonable to conduct the analysis in the way as it is done in this chapter see Chapsaur & Rochet (1989).

26 Vertical Product Differentiation, Market Entry, and Welfare 24 Solving for p 1 (θ) and p 2 (θ) yields for the sae reasons as in Lea 4.1 p 1 (θ) = u(q(θ), θ) θ θ(q 1 ) u(q(τ), τ) θ dτ + p 1 (q 1 ) u(q 1, θ(q 1 )), (11) and p 2 (θ) = u(q(θ), θ) θ θ 2 u(q(τ), τ) θ dτ + p 2 (q + 2 ) u(q + 2, θ(q + 2 )). (12) Plugging this back in the profit function and solving for p 1 (q 1 ) and p 2 (q + 2 ) gives p 1(q1 ) = vq1 + 1 F (θ ) [u θ (q1, θ ) u θ (q 2 +, θ )], (13) f(θ ) p 2(q 2 + ) = vq F (θ ) F (θ 2 ) [u θ (q1, θ ) u θ (q 2 +, θ )]. (14) f(θ ) Having solved stage 3 of the gae we can go back one stage to stage 2 where fir 2 chooses its optial quality range. The proble of fir 2 is thus ax q(θ),q + 2,θ Π 2 2 = θ(q θ ) [u(q(θ), θ) θ u(q(τ),τ) θ 2 θ +p 2(q + 2 ) u(q + 2, θ(q + 2 )) vq(θ) c(q(θ)) f(θ) ]f(θ)d(θ)+ θ θ(q + 2 )[p 2(q + 2 ) vq + 2 ]f(θ)dθ. dτ Differentiating with respect to θ 2 and q(θ) yields (F (θ ) F (θ 2 ))( u(q (θ ),θ ) ) f(θ 2) [u θ f(θ ) θ(q1, θ ) u θ (q 2 +, θ )] = f(θ 2 )[u(q(θ 2 ), θ 2 ) c(q(θ 2)) f(θ 2 + p ) 2(q 2 + ) u(q 2 +, θ(q 2 + )) vq(θ 2 )] (15) and u(q (θ),θ) q ( ) 1 F (θ) 2 u(q (θ),θ) v c (q (θ)) = 0, f(θ) q θ f(θ) θ with θ(q + 2 ) > θ θ 2. (16) Before differentiating with respect to q + 2 it is helpful to decopose the profit func-

27 Vertical Product Differentiation, Market Entry, and Welfare 25 tion as Chapsaur & Rochet (1989) do. Inserting p 2(q + 2 ) in Π 2 yields Π 2 = (F (θ) F (θ 2)) 2 f(θ ) [u θ (q1, θ ) u θ (q 2 +, θ )]+ θ(q + 2 ) θ 2 [u(q(θ), θ)) θ u(q(τ),τ) θ 2 θ vq(θ) + vq + 2 c(q(θ)) f(θ) ]]f(θ)d(θ). dτ u(q + 2, θ(q + 2 )) (17) The first ter is dependent on q 1 and q + 2 while the second ter (the integral ter) is independent of q In the following we denote the integral ter by I(q + 2 ). This decoposition also shows that q + 2 is only dependent on q 1 but not on the other qualities fir 1 produces. The first order condition for q + 2 (F (θ ) F (θ 2 )) 2 u θq (q 2 +, θ ) + I(q+ 2 ) f(θ ) q It is now possible to show that q + 2 < q 1. Lea 2 is thus given by = 0 (18) There is always a gap between the quality ranges of fir 1 and fir 2. Proof See the Appendix. This result is different to Chapsaur & Rochet (1989). If firs decide siultaneously about their qualities there can be equilibria where the quality ranges overlap and firs ake zero profits with these overlapping qualities. 31 We can get an additional result. Differentiating equation (17) with respect to q 1 we get by using the Envelope Theore Π 2 q 1 = (F (θ ) F (θ 2 )) 2 u θq (q1, θ ) > 0, (19) f(θ ) where the inequality coes fro the Single Crossing Property. 30 Chapsaur & Rochet (1989) call the first ter pure differentiation profit and the second ter pure segentation profit. 31 Chapsaur & Rochet (1989) assue that there are no developent costs, i.e. c(q) = 0. If such developent costs exists firs would ake losses with overlapping qualities and they ay decide not to produce the even in the siultaneous ove gae. Despite this, in the sequential ove gae even if c(q) = 0 product ranges would never overlap.

28 Vertical Product Differentiation, Market Entry, and Welfare 26 So fir 2 s profit is increasing if fir 2 produces a saller quality range. But this also iplies that q+ 2 > 0 so the lowest quality of fir 1 and the highest quality of q 1 fir 2 are strategic copleents. Fir 1 will take this into account in its decision of Q 1 in stage 1. Let us now turn to stage 1. As in Section 3 fir 1 has two possibilities either to accoodate entry or to deter entry. Let us look at each case in turn. If fixed costs are low fir 1 finds it optial to accoodate entry. Decoposing fir 1 s profit function in the sae way as fir 2 s profit function before we get a axiisation proble of ax q(θ),q 1 (1 F (θ))2 Π 1 = f(θ ) [u θ (q1, θ ) u θ (q 2 +, θ )]+ 1 θ(q )[u(q(θ), θ)) θ u(q(τ),τ) 1 θ(q 1 ) dτ u(q θ 1, θ(q1 )) vq(θ) + vq 1 c(q(θ)) f(θ) ]]f(θ)d(θ). In the following we call the integral ter I(q 1 ). We get two first order conditions u(q (θ),θ) q ( ) 1 F (θ) 2 u(q (θ),θ) v c (q (θ)) = 0, f(θ) q θ f(θ) θ with θ(q 1 ) θ 1. (20) and 1 F (θ )) 2 (u θq (q1, θ ) u θq (q 2 +, θ ) q+ 2 f(θ ) q1 ) + I(q 1 ) q = 0. (21) Fro the first of these two equations it is apparent that all types θ(q 1 ) θ 1 get the sae quality as in onopoly because this equation coincides with equation (9). All types θ θ < θ(q 1 ) get a higher quality because they buy q 1 which is above q(θ) in the onopoly case given by equation (9). The ter u θq (q 2 +, θ ) q+ 2 in equation (21) is greater than zero because we know q 1 that q+ 2 > 0. This expresses that with a change in q q 1 fir 1 can change fir 2 s 1 reaction in stage 2. In the odel of Chapsaur & Rochet (1989) this ter does not exist because qualities are chosen siultaneously. Thus the incubent produces a larger quality range than with a siultaneous quality choice to shift fir 2 s upper quality downwards.