Competition with Targeted Product Design: Price, Variety, and Welfare

Transcription

1 Competition with Targeted Product Design: Price, Variety, and Welfare Miguel González-Maestre Universidad de Murcia Lluís M. Granero Universitat de València February, 2017 Abstract We consider the price and welfare effects of competition in targeted product design, in the context of the Salop circle model. Changes in product design lead to demand rotations that set the stage for our analysis. With an exogenous number of firms, we show that under reasonable conditions price-increasing competition takes place, for intermediate levels of the number of firms. This effect is associated with the possibility of lower consumer welfare. With endogenous firm entry, an interesting insight from our analysis is that in some situations an increase in market size or a technological progress that reduces entry costs both might reduce consumers welfare. Keywords: price-increasing competition, welfare, targeted product design, generic product design. JEL Classification: D43, L11, L13, M31. We are grateful to Andrea Galeotti, Nikolaos Georgantzis and Konstantinos Serfes for helpful comments. We acknowledge financial support from the Spanish Ministry of Economy and Competitiveness, under projects ECO P (M González-Maestre) ECO R (M González-Maestre and LM Granero. The usual disclaimer applies. Corresponding author. Departamento de Fundamentos del Análisis Económico, Universidad de Murcia, Murcia, Spain. mmaestre@um.es; Phone: ; Fax: Departament d Anàlisi Econòmica, Facultat d Economia, Universitat de València, Avda. dels Tarongers s/n, València, Spain. lmgraner@uv.es. 1

2 1 Introduction This paper examines competition in product design and the implications of that competition on pricing and welfare. The analysis suggests that strategic trade-offs fromthedegreeoftargetedproductdesignimpactonbothpricing and welfare to a relevant extent, and that this occurs both when firm entry is exogenous and when it is endogenous. In order to explore the welfare effects of product design and pricing, we consider the Salop (1979) circle model of product location, and in particular the setting by Bar-Isaac et al. (2014). These authors examine targeted product design and pricing for given market structures in order to determine whether firms adopt an extreme or an intermediate product design. Consumer location offers a natural interpretation of demand-based preferred varieties of the product, which sets the stage for an analysis of the degree of targeted design. Specifically, design has two components: a horizontal decision of which type of consumer to target, and the degree to which the product is tailored to this type of consumer (customization). A less generic product implies a higher valuation by targeted consumers, but it also implies alowervaluation forotherconsumers withdifferent tastes. This leads to a trade-off in designing the product and differentiates the setting from others with quality differentials where ceteris paribus all consumers prefer the highquality product (e.g., see Ungern-Sternberg, 1988, Weitzman, 1994, Hendel and Neiva de Figueiredo, 1997, and Loginova and Wang, 2011). Under such circumstances, Bar-Isaac et al. (2014) show that a monopolist can choose the degree to which the product is tailored to consumers such that product design can be extreme (completely generic or completely tailored) or rather only partially tailored. In particular, a higher marginal cost induces the monopolist to choose a targeted design. 1 In addition, these authors extend their analysis to heterogeneous duopolists, showing that the firms with higher marginal costs choose a nicher product design. Our model is based on these authors approach, but we focus on the analysis of strategic pricing, variety and welfare. In contrast to these authors, instead of restricting the analysis to a duopoly, we consider firms with strategic interaction, which allows us to examine the impact of changes in the number of active firms on equilibrium price and welfare. Our analysis shows that this impact is relevant and may lead to unconventional results. 1 This insight is extended to a search model of monopolistic competition. 2

3 Akeyaspectoftargetedproductdesignisthatdesignchoicesleadto rotations in demand along the lines of Johnson and Myatt (2006). Design is thus considered as a decision that rotates demand in a context where design is mediated through product location. 2 In that context, the degree of design targeting depends on the extent to which profits are quasi-concave in design, and if profits are quasi-convex then design decisions are extreme. In the context of the Salop (1979) model of product location where consumers locate on the circumference of a circle, the demand rotations that we consider follow from location-based design decisions. In particular, product location along an arc captures a conventional horizontal differentiation, and product location into the interior of the circle along a ray captures the extent to which the product is tailored to the specific type of consumer located at the extreme point of that ray on the circumference of the circle. Then, extreme designs correspond to points on the circumference (fully tailored product), or on the center of the circle (fully generic product), whereas intermediate designs correspond to interior points of the circle. In our analysis, the impact of firm entry on the equilibrium price depends on two effects. On the one hand, there is a direct effect according to which, given product design, price falls with firm entry. On the other hand, there is an indirect product targeting effect according to which a higher degree of targeting makes closer target consumers better off and distant non-target consumers worse off. The direct effect is conventional and it is present in the Salop (1979) model and in most models of imperfect competition. In contrast, the product targeting effect relies exclusively on demand rotations from endogenous product design, and it is particularly relevant when it benefits target consumers to a large extent because it leads then to price-increasing competition. Price-increasing competition has been previously obtained in oligopoly models under incomplete information (e.g., Satterwhite, 1979, Schulz and Stahl, 1996, and Stiglitz, 1987) or for mixed strategy equilibria (Rosenthal, 1980). 3 In contrast, we consider complete information and pure strategies. 2 See also Lewis and Sappington (1994) for an analysis of the firms incentives to provide information to consumers. More recently, Hoffmann et al. (2012) have examined the impact of tailored advertising, and Bar-Isaac et al. (2012) have studied how product designs adapt as search costs fall. 3 Specifically, in Rosenthal (1980) firms sell to two different populations, a fully captured one and a fully competitive one. As more firms enter the competitive market, firms focus more in maximizing profits in their captured markets. In our setting, product design allows 3

4 Closer to our analysis, Chen and Riordan (2007) obtain price-increasing competition in the spokes model of non-localized competition. In the absence of product design, Chen and Riordan (2008) show that price-increasing competition can also take place when the market structure goes from a monopoly to a duopoly in a discrete choice model of product differentiation. We depart from these authors in considering localized competition in the standard circle model by Salop (1979) under endogenous product design. In our setting, it is product design that can lead to price-increasing competition through the product targeting effect. The available empirical evidence suggests that price-increasing competition can take place in a variety of contexts. For instance, Thomadsen (2007) documents that product positioning through location can lead to price-increasing competition in the fast food industry. In a related vein, Perloff et al. (2006) find evidence on higher prices from new entry in the antiulcer drug market. Empirical evidence on price-increasing competition can be also found in sectors such as the cable modem internet access (Chen and Savage, 2011) and food industries (Ward et al., 2002). In the pharmaceutical industry in the United States, Grabowski and Vernon (1992) document that new entry after the 1984 Drug Act implied higher pioneer brand prices and, remarkably, the introduction of relatively more targeted (i.e., customized) variants of the product. This evidence points to the product targeting effect in our analysis as a potential driving force of price-increasing competition. The current paper also investigates the welfare effects of product-market competition. 4 We characterize the resulting equilibrium configuration in comparison with a socially optimal configuration. Our results reveal that the interactions of product design, pricing and entry have a relevant impact on welfare. In particular, we find that with an exogenous number of firms, the equilibrium level of design targeting is too small from a social welfare point of view, but too large from consumers point of view. In fact, we show that competition can reduce consumer surplus due to a prominent product targeting effect that also generates price-increasing competition. This rethe firms to decide the extent of the captured market in a continuous way. Remarkably, while Rosenthal (1980) relies on mixed strategies in prices, our results obtain under pure strategies in prices and product design. 4 Johnson and Myatt (2006) consider a brief extension to a Cournot oligopoly (under homogeneous product), with comparative statics regarding exogenous change in the degree of product targeting. Here, we consider endogenous product targeting and the effects of entry. 4

5 sult helps understand the consequences of product design not only on price but also on surplus. This analysis extends to the case of endogenous entry, where we obtain that an increase in market size or a technological progress that reduces entry costs both might reduce consumers welfare. These findings suggest that the contribution of globalization and technological progress on welfare could lead to outcomes with non-monotonic patterns in situations with product design decisions and imperfect competition. The rest of the paper is organized as follows: Section 2 examines the basic model with an exogenous number of firms, Section 3 deals with endogenous entry, and Section 4 gathers the main conclusions. 2 The model with exogenous number of firms In this section we consider the classic Salop (1979) circle model, with an exogenous number of firms that compete in product design. This version of the model will set the stage for our subsequent analysis with an endogenous number of firms. We model product design as in the model by Bar-Isaac et al. (2014), in line with the conceptual framework by Johnson and Myatt (2006). Specifically, the design space available to each firm is given by one of rays of acircleofradiusnormalizedto1. Locationononeoftheserayssummarizes the design of each firm s product. The rays are distributed symmetrically around the circle and the location of firm is given by its distance from the center of the circle, along its radius. As in the Salop model, there is a mass of consumers, labeled by, whoareuniformlydistributedaroundthe circumference of the circle. Then, if a firm locates on the circumference of the circle (the situation in the Salop model), it tailors the characteristics of its product to a specific type of consumer,so that product design is extremely targeted for the type of consumer located at that point on the circumference. From that point, the product becomes more generic as the firm goes to the center along its ray. A completely generic product (i.e., no targeted design at all) will be achieved at the center of the circle. If a consumer located at angle from firm chooses to buy from it, then she obtains the following utility: = (1 ) (1) where (1 ) is the vertical cost in the terminology of Bar-Isaac et al. (2014), which is the transport cost of the distance from the outer circum- 5

6 ference of radius 1 to the inner circumference of radius,while is the horizontal cost, which is the transport cost from the consumer s preferred variety and firm s variety. Therefore, the vertical cost is the disutility associated with consuming a broad type of good instead of a tailored good, while the horizontal cost is the disutility associated with consuming a variety different from the one preferred by the consumer. In our analysis, we assume that the vertical cost is increasing, 0 (1 ) 0, andconvex, 00 (1 ) 0. Appendix 6.1 shows that the convexity of the vertical cost is necessary to ensure that second-order conditions for profit maximization hold in the case of an interior product design. Hereafter we focus on symmetric equilibria under simultaneous choice of price and product design. 5 Aconsumerwillbeindifferent about patronizing firm and any of its neighbor firms when ( (1 )+ )+ = ( (1 )+ ( 1 )) + (2) where and are the choices made by each of the rest of firms, at the symmetric equilibrium. Therefore, firm s total demand is given by =2 = µ 2 ( (1 ) (1 )) + ( + ) + (3) With zero marginal costs, and a fixed cost per firm, firm s profits follow as = µ 2 ( (1 ) (1 )) + ( + ) + (4) The first-order condition for profit maximizationwithrespectto gives = µ 2 ( (1 ) (1 )) + ( + ) + 2 =0 (5) Using (5) and (4) yields the reduced form profit functiongivenby 5 This timing is different from that in the duopoly model by Bar-Isaac et al (2014), where these authors assume sequential moves such that design is chosen before price. We believe that our assumption about the timing is reasonableinmanymarkets. Forinstance, restaurants usually announce their designed daily menus along with their price. 6

7 ( )= µ ( (1 ) (1 )) ( + ) + (6) Consider now product design. First-order conditions for an interior equilibrium involve ( ) = ( (1 ) (1 )) + + (7) 2 ( + ) 2 µ2 0 (1 )( + ) ( (1 ) (1 )) =0 At a symmetric configuration, these first-order conditions yield = (8) 0 (1 )= 1 (9) 2 where and indicate the interior symmetric equilibrium values for price and product design, given. As we show in Appendix 6.1, a lower bound 0 on is required to ensure that second-order conditions hold globally for an interior solution such that. When equals the lower bound, theproductbecomesgenerictothe largest possible extent. This product design follows from a corner solution at which 0 (1 ) 1 so that 2 =. Because 00 (1 ) 0, itturnsoutthat is a constant (given by = ) if is small enough, and it is increasing in otherwise. This is illustrated in Figure 1, where is the threshold value of above which we have the interior solution where (9) holds and increases with. Figure 2 illustrates the relationship between equilibrium price and. Because is constant in Region I, the equilibrium price,,decreaseswith in this region. However, in Regions II and III increases with, andthen two effects determine the price in equation (8): first, there is a direct effect according to which, given,agreater tends to decrease price; and second, there is an indirect product targeting effect according to which a greater means a higher degree of product targeting, which tends to increase price. In 7

8 Figure 2, the product targeting effect dominates in the intermediate Region II, whereas the direct effect becomes dominant in Region III. The threshold determines which of these two effects prevails. Formally, a prevailing product targeting effect requires the following assumption: Assumption 1 ( ) 0 (1 ) 00 (1 ) 0. This assumption ensures the existence of a non-empty interval ( ) where the equilibrium price increases with. For simplicity, we also adopt the following assumption ensuring the existence of a unique threshold : Assumption 2 00 ( ) is non-increasing. The role of assumptions 1 and 2 is as follows. Given that 00 ( ) 0, Assumption 2 implies that ( ) is strictly decreasing, which means that Assumption 1 is satisfied for values of sufficiently far away from 1. Therefore, in economic terms, our assumptions merely mean that the model allows for a relevant range of firms decisions on product design. Otherwise, that is, if approaches 1, the model collapses into the standard Salop model with an exogenous (and fully specialized) product design. Under assumptions 1 and 2, the following proposition holds: Proposition 1 Under assumptions 1 and 2, there exist thresholds and, where 0, suchthat: (i) if then =, and decreases with ; (ii) if ( ) then both and increase with ; (iii) if then increases and decreases with. Proof. At the corner solution with =, whichamountsto,we have that is negative from (8). This shows part (i). Next, at an interior solution, equation (9) yields = (1 ) Making use of (8) and (9), we can write =2 0 (1 ) 8 0

9 from where =2 ( 0 (1 ) 00 (1 )) =2 00 (1 ) µ 0 (1 ) 00 (1 ) In the limit where approaches from above, increases with whenever 0 (1 ) 0. Therefore, with an interior product design, 00 (1 ) increases with whenever 00 ( ) is non-increasing and 0 (1 ) 0. In addition, 00 (1 ) an interior product design requires a lower bound on from the secondorder condition for profit maximization. Specifically, from Appendix 6.1, that second-order condition leads to 0 (1 ) 4 00 (1 ) which is compatible with 0 (1 ) 0for 00 (1 ) close to. Consequently,for non-increasing, bounded 00 ( ) there exist cost functions ( ), extremeproduct design, andthresholds and such that at the interior solution is negative for relatively large,, andpositiveforintermediatevaluesof,. Hence,theresultfollows. The basic intuition of this result is that when there is a relatively small number of firms, each firm chooses generic (non-niche) designs so as to appeal to much of the market, which corresponds to case (i) in Proposition 1, where = and thus the indirect product targeting effect is zero. As more competitors exist, it is more important to produce targeted products. In fact, in the intermediate case (ii) of Proposition 1, product design is very sensitive to changes in, sothattheindirectproducttargetingeffect prevails over the direct effect, and the equilibrium price increases with. Finally,in case (iii) of Proposition 1, the degree of competition is so large that product design is already very close to 1 (almost totally targeted design), and then is almost insensitive to changes in. This result means that there exist plausible values of and conventional functional forms of ( ) such that in equilibrium an increase in leads to a decrease or an increase in price depending on the effects discussed above. For example, consider the quadratic case where (1 )= 2 (1 ) 2 with 0. Then, with extreme product design we have = and =,sothat decreases with. Withaninteriorproductdesign,wehave =1 1.This 2 design must be such that 1,whichmeansthat Then, the equilibrium price is = (1 1 ),sothat 2 9 2(1 ) ;and 1. = 1 R 0 3

10 as Q = 1. Here, when the interior value of approaches we obtain 1 =. In these circumstances, for an interior product design, 2(1 ) ³ increases with for,whichcorrespondstoregioniiin 1 2(1 ) 1 Figure 2, whereas decreases with for 1, which corresponds to Region III. The quadratic example helps understand intuitively conditions that lead to the direct and the product targeting effects associated with entry. Specifically, can arise from product specifications that limit the extent to which the product can be fully generic, and measures the intensity of the vertical cost in terms of consumer preferences (i.e., the cost of non-targeted product design). Then, only depends on, whereas also depends on. The economic interpretation of price-increasing competition (Region II in Figure 2) relies on a prevailing product targeting effect from the demand rotations induced by product design: more competition, as measured by an increase in, inducesahigherdegreeofproducttargetingthatbenefits closer target consumers, but it also makes distant non-target consumers worse off because these consumers prefer a more generic product than a product tailored to consumers very close to the firm. The magnitude of the product targeting effect increases with target consumer benefit, which depends on both and. Inparticular,given, thelargerthevalueof, thelowerthemagnitude of the target consumer benefit becausethepotential foradditionalproduct targeting is reduced when increases. In the quadratic example, this can be seen by noticing that the condition only holds when 1 2. Then, with a relevant target consumer benefit, firms have an incentive to set higher prices in the face of more competition for ( ). Beyondthisregion,a large value of implies that the direct effect dominates and price-reducing competition takes place (Region III in Figure 2). We now examine the impact of these effects on welfare. 2.1 Welfare analysis with exogenous number of firms In order to explore the impact on welfare of endogenous product targeting, we first examine the welfare-maximizing level of product targeting. To that end, consider that the social planner maximizes total social surplus (sum of consumer and producer surplus), which is equivalent to minimize the following total costs: 10

11 = + + (1 ) (10) 4 The first-order condition for an interior social optimum implies: = 4 0 (1 ) =0 from where the socially optimal value of for given, denotedas,is determined by 0 (1 )= 1 (11) 4 Again, because 00 (1 ) 0 it follows that the degree of design targeting is increasing in the number of firms. 6 Nevertheless, the comparison of with reveals that 0 (1 ) 0 (1 ) (12) where the last inequality follows from the fact that 00 (1 ) 0. We can summarize our previous findings in the following result: Proposition 2 If the number of firms is exogenous, then both the equilibrium and the socially optimal level of design targeting are increasing in the number of firms. Moreover, for any given number of firms, the socially optimal level of (partially tailored) design targeting is greater than the equilibrium level of targeting. Similarly, for given we can also compare socially optimal product targeting with the levels of targeting that maximize, respectively, consumers surplus, denoted by,andindustryprofits, denoted by,wherethe superscript stands for collusive. Those comparisons are summarized in the following: Proposition 3 For given, thefollowingchainofinequalitiesholds: =1. 6 Note that assuming 00 (1 ) 0 ensures the second-order condition for an interior welfare optimum because 2 2 = 00 (1 ) 0 11

12 Proof. From equation (8), consumer surplus is given by from where = (1 ) 5 4 = 0 (1 ) 5 4 =0 so that 0 (1 )= ,andthen from (9) and 00 ( ) 0. In asymmetricconfiguration with (8) and =, standardcalculationsleadto = and thus 2 =1. Intuitively, the previously discussed impact of product targeting on price explains that the equilibrium level of targeting,,exceedsthelevelthat maximizes consumer surplus. Recall that Assumption 1 yields a prevailing product targeting effect, that is, an interval ( ) with price-increasing competition. In turn, a more restrictive condition is required to ensure that price-increasing competition reduces consumer surplus: 3 Assumption 1 0 (1 ) (1 ) The following proposition identifies the circumstances under which consumer surplus falls from competition: Proposition 4 Under assumptions 1 and 2, there exist thresholds, b, and, where0 b, suchthat: (i) if,consumersurplusincreaseswith ; (ii) if ( b ), consumersurplusdecreases; (iii) if b, consumersurplusincreaseswith. Proof. From equation (8), consumer surplus is given by = (1 ) 4 = (1 ) 5 4 The corner solution with = takes place for.atthissolution,we have = (1 ) 5,whichincreaseswith. This shows part 4 (i). Next, at an interior solution, equation (9) yields = (1 ) 12 0

13 and = (1 ) (1 ), fromwhere µ = 0 (1 ) (1 ) (1 ) µ = (1 ) 00 (1 00 (1 ) ) 2 Hence, R 0 as 3 0 (1 ) R 0, 5 00 (1 ) andinthelimitwhere goes to from above, 0 as 3 0 (1 ) 0 from Assumption 1. Recall that 5 00 (1 ) an interior product design requires a lower bound on from the second-order condition for profit maximization,sothat 0 (1 ),whichiscompatible 4 00 (1 ) with Assumption 1. Therefore, given that 0 (1 ) 3 0 (1 ),underassumptions 1 and 2 there will exist values of 0such that the threshold 4 00 (1 ) 5 00 (1 ) b ( ) exists as given by the value of such that 3 0 (1 ) =0under 5 00 (1 ) (9), so that Q 0 as Q b for (interior product design). Intuitively, the interpretation of the pattern in Proposition 4 is that an increase in leads to three effects on consumer surplus, = (1 ) 4 : (i) Targeting cost effect: The vertical cost, (1 ), fallsbecausethe degree of product targeting increases with. (ii) Direct price-variety effect: For any given,boththehorizontalcost and the equilibrium price 4 = decrease with. (iii) Indirect price-variety effect: For any given, theincreaseinthe targeting level,,tendstoincreaseboththehorizontalcost and the 4 equilibrium price. While the two first effects are beneficial in terms of consumers welfare, the third one is harmful. When is small, is constant at and thus only the socially beneficial direct price-variety effect takes place. For intermediate values of, turns out to depend on and then the harmful indirect pricevariety effect takes place and prevails over the direct price-variety effect. Moreover, for intermediate-low values of, thenegativeoverallprice-variety effect prevails over the targeting cost effect. The intuition is that for this range of intermediate-low, anincreaseinthedegreeofproducttargeting (from a small increase in ) issociallyharmfulbecausemostconsumersare far away from their preferred varieties and the increased degree of targeting exacerbates this problem by increasing both their variety and price costs. Figure 3 shows how affects consumer surplus under assumptions 1 13

14 and 2. If Assumption 1 were satisfied but Assumption 1 (which is more restrictive) were not, the graph would be the same except for the fact that the entire Region II would correspond to Region II.2 (that is, the interval that leads to Region II.1 would be empty). On the graph, Regions I, II.2 and III are conventional in that consumer surplus increases with. InRegionII.1, however, consumer surplus decreases with competition. This situation arises from a prominent product targeting effect that causes price to be increasing in. In the quadratic case where (1 )= (1 2 ) 2 with 0, wehave 3 0 (1 ) = (1 ),fromwhere 0 if and only if 3(1 5 ), i.e., 3 8. Then,inaccordancewith(9), 4 0 if and only if b =. 5 1 Given that = = 1 for 1 2, we have b. 2(1 ) That is, under assumptions 1 and 2, consumer surplus increases with for small values of ( in Region I of Figure 3), it decreases with for intermediate values of ( b in Region II.1 of Figure 3), and it increases in for the rest of values (b in Region II.2 in Figure 3, and in Region III). For example, if = 1 and = 1 then =75, b =80, and =100,fromwhere decreases with competition for 75 80, which is a subset of the value of that leads to price-increasing competition, Themodelwithendogenousnumberoffirms Now we deal with the number of firms as determined by free entry. Our analysis extends to a context with free entry under assumptions 1 and 2 in the previous section. For simplicity, we focus on the quadratic case with (1 )= 2 (1 ) 2,where 0, and 1 3. The lower bound on follows from the fact that the symmetric free-entry equilibrium is unique in this quadratic case for 1 3 (see Appendix 6.2). As is explained in Appendix 6.2, for a small market size the equilibrium product design is given by =. However,formarketsizelargeenough, increases with market size. The following analysis focuses on this case, where we consider =1 3 for the sake of simplicity. Nevertheless, the qualitative conclusions from our analysis in this section hold under more general conditions. In order to investigate the welfare effects of technology improvements and the increase in market size, we can write the free-entry equilibrium counter- 14

15 part of (9) as 7 (1 )= 1 2 µ 1 2 In order to gain intuition, we can represent this graphically. To that end, it is easier to write this expression as ( ) (13) (1 ) 2 where stands for the relative market size, and 1. This 4 2 function is strictly increasing in if 1 3, whichisensuredtohold for =1 3. Therefore, if (1 3) the equilibrium level of targeting is strictly increasing in the relative size of the market. If (1 3) then the first-order conditions for a symmetric equilibrium imply = =1 3. In contrast, if (1 3) then is strictly increasing according to (13). Figure 4 plots the relationship between and. Next, we investigate the welfare effects of changes in as a result of either changes in market size or changes in the fixed entry cost. Under free entry, profits equal zero and welfare is given by consumers net utility. Therefore, total equilibrium welfare is given by = ( ) = µ 2 (1 ) 2 4 (14) where = 2 (1 ) 2 is the vertical cost paid by each consumer, = 4 is the average horizontal cost paid by each consumer, and = is the equilibrium price. We define the per capita welfare as. Then,with (9) and (1 3), thepreviousexpressionsimplifies to = 2 (1 ) 2 5 (1 ) 2 Hence, = 1 2 (4 +1)(1 ) (15) 7 Note that the free-entry value of is found by setting (4) equal to zero and solving. In our analysis we ignore integer constraints on. 15

16 = 1 2 ( 3+8 ) R 0 as R 3 (16) 8 An interesting implication from this derivative is that any increase in the relative market size in the interval ( (1 3) (3 8)) implies a reduction in per capita welfare. In other words, if increases (due to a market expansion or a technological progress that reduces the entry cost), then the resulting increase in the number of competitors reduces the net utility of each consumer. In fact, equation (15) implies that any shock which increases from (1 3) to (5 12) will reduce per capita welfare. Therefore, we have the following Proposition 5 Any technological progress or market expansion that increases relative market size from the threshold (1 3) to any value below the threshold (5 12) will reduce the per capita level of welfare in the economy. This proposition is illustrated in figures 5 and 6. For (1 3), Figure 5plotstherelationshipbetweenthelevelsofper capita welfare,, and equilibrium product targeting, (which is increasing in ). In addition, Figure 6 plots the relationship between and the free-entry equilibrium number of firms,.inordertointerpretthesefigures, consider an increase in either from a technological progress associated with a decrease in the entry cost or from a market expansion associated with an increase in. In the example plotted in Figure 6, if as a result of this change the free-entry equilibrium number of firms increases from =75to [76 85], then Figure 6 shows that this change is socially harmful. 8 The economic interpretation of this pattern is analogous to the intuition of Proposition 4. According to (14), an increase in leads to an increase in the equilibrium number of firms which causes three (per capita)welfare effects: (i) targeting cost effect from the vertical cost = (1 2 ) 2 ;(ii) direct price-variety effect from both the horizontal cost = and the 4 equilibrium price = ;and(iii)indirectprice-varietyeffect from both the horizontal cost and the equilibrium price. Recall that the two first effects are socially beneficial and the third one is harmful. For and small, = and only the beneficial second effect works. For intermediate and large values of, equation(15)impliesthattheoverall 8 To see this, recall that ( ) = 1 1 2, so that ( ) = 1 2 1, and then 50 (0 333) = ( ) = , and 50 (0 417) = ( ) = (approximating to the third decimal number, i.e., 1 3 ' 0 333, and5 12 ' 0 417). 16 1

17 price-variety effect is given by the derivative of 5 (1 ) 2 with respect to. For intermediate-low levels of product targeting that derivative is positive, and for large levels it is negative. Therefore, for intermediate-low values of (associated with intermediate-low ), the harmful indirect price-variety effect is very large and dominates over the direct price-variety effect. In fact, for that range of intermediate-low,anincreaseinthedegreeofproduct targeting (from a small increase in )issociallyharmfulbecausemostconsumers are far away from their preferred varieties and the increased degree of targeting exacerbates this problem by increasing both their variety and price costs. 9 4 Conclusions We have considered the impact on price and welfare of endogenous targeted product design under imperfect spatial competition. With an exogenous number of firms, the analysis shows that price-increasing competition can emerge in equilibrium. In these circumstances, we show that consumer surplus can fall as a result of increased competition. In contrast with most standard imperfect competition models, an interesting insight from our analysis is that,underfreeentry,an increaseinmarket size or a technological progress that reduces entry costs both might reduce consumers welfare. Therefore, our model shows that incorporating explicitly the firms choice of product design might lead to relevant policy conclusions. Specifically, in our model, an institutional deregulation that reduces entry costs increases price and reduces consumer surplus for intermediate initial entry costs. 5 References Bar-Isaac, H., G. Caruana and V. Cuñat (2012). Search, design, and market structure, American Economic Review 102(2) Given that our main welfare results rest on price-increasing competition, it is worth noting that the equilibrium number of firms in our model is more than proportional to market size in the region of price-increasing competition. Consequently, equilibrium firm size (as measured by the mass of consumers per firm) decreases with market size in that region, which can be seen as a testable insight from the model. 17

18 Bar-Isaac, H., G. Caruana and V. Cuñat (2014). Targeted product design: locating inside the Salop circle, mimeo, CEMFI. Chen, Y. and M.H. Riordan (2008). Price-increasing competition, Rand Journal of Economics 39(4), Chen, Y. and M.H. Riordan (2007). Price and variety in the spokes model, Economic Journal 117(522), Chen, Y. and S.J. Savage (2011). The effects of competition on the price for cable modem internet access, Review of Economics and Statistics 93(1), Grabowski, H.G. and J.M. Vernon (1992). Brand loyalty, entry, and price competition in pharmaceuticals after the 1984 Drug Act, Journal of Law and Economics 35, Johnson, J.P. and D.P. Myatt (2006). On the simple economics of advertising, marketing, and product design, American Economic Review 96(3), Hendel, I. and J. Neiva de Figueiredo (1997). Product differentiation and endogenous disutility, International Journal of Industrial Organization 16(1), Hoffmann, F., R. Inderst and M. Ottaviani (2012). Tailored advertising and consumer privacy, mimeo, IMFS. Lewis, T.R. and D.E.M. Sappington (1994). Supplying information to facilitate price discrimination, International Economic Review 95(2), Loginova, O. and X.H. Wang (2011). Customization with vertically differentiated products, Journal of Economics and Management Strategy 20(2), Rosenthal, R.W. (1980). A model in which an increase in the number of sellers leads to a higher price, Econometrica 48(6), Perloff, J.M.V.Y.SuslowandP.J.Seguin(2006).Higherpricesfromentry: pricing of brand-name drugs, mimeo, University of California - Berkeley. Salop, S. (1979). Monopolistic competition with outside goods, Bell Journal of Economics 10(1), Satterthwaite, M.A. (1979). Consumer information, equilibrium industry price, and the number of sellers, Bell Journal of Economics 10(2),

19 Schulz, N. and K. Stahl (1996). Do consumers search for the higher price? Oligopoly equilibrium and monopoly optimum in differentiated-products markets, Rand Journal of Economics 27(3), Stiglitz, J.E. (1987). Competition and the number of firms in a market: are duopolists more competitive than atomistic markets? Journal of Political Economy 95 (5), Thomadsen, R. (2007). Product positioning and competition: the role of location in the fast food industry, Marketing Science 26(6), von Ungern-Sternberg, T. (1988). Monopolistic competition and general purpose products, Review of Economic Studies 55(2), Ward, M.R., J.P. Shimshack, J.M. Perloff, andj.m. Harris. (2002). Effects of the private-label invasion in food industries, American Journal of Agricultural Economics 84: Weitzman, M. (1994). Monopolistic competition with endogenous specialization, Review of Economic Studies 61(1), Appendix 6.1 Second-order conditions for a symmetric equilibrium From (5) we obtain: 2 = ( + ) and the second-order conditions with respect to are satisfied. According to (7), the sign of is determined by ( )=2 0 (1 )( + ) ((1 ) (1 )). Therefore,toensurethatthesecond-order condition holds globally we need: ( ) = ( 2 00 (1 )( + )+ 0 (1 )) 0 ( 1) which is satisfied if and only if 0 (1 ) 00 (1 ) 2( + ) ( 1) 19

20 In turn, this condition is ensured by 0 (1 ),fromwheretheglobal 4 00 (1 ) quasiconcavity of the profit functionfollows. Inthequadraticcase,with (1 )= (1 2 ) 2,wehave 0 (1 )= (1 ) and 00 (1 )=, which inserted into the above expression yields ( ) = ( 2 ( + )+ (1 )) Therefore, is globally quasiconcave in,andthesecond-orderconditions with respect to are satisfied for 1 4. InSection3thiscondition is satisfied. In these circumstances, Appendix 6.2 shows the existence of a unique free-entry symmetric equilibrium. 6.2 Existence and uniqueness of a free-entry symmetric equilibrium In the free-entry counterpart of (9), the first-order condition for a symmetric and interior free-entry equilibrium implies 0 (1 )= With a quadratic product targeting function (1 ) = (1 2 ) 2,thiscondition can be rewritten as (1 )= 1 1 2, 2 or ( 1 ) =. 4 2 (1 ) 2 Some properties of the function ( ) are as follows. Given that ( ) = 1 (3 1) R 0 as R 1 3, ( ) attains its minimum at = 4 2 (1 ) 3 ( ) for any 1 3. This implies that if (1 3) then (1 ) 1 2 (0 1), andinthiscasewehaveauniqueequilibriumwith =. If (1 3) then the previous derivative indicates that if 1 3then there is a unique free-entry equilibrium with If 1 3 and ( ( ) (1 3)) then we have two free-entry equilibria: one with = and another with The proof of this result is available upon request. 20

21 s n 1 B n n Figure 1 Equilibrium product targeting and number of rms 21

22 p n I II III c n n n Figure 2 Equilibrium price and number of rms 22

23 CS n I II.1 II.2 III n nˆ n n Figure 3 Consumer surplus and number of rms 23

24 s* Z Figure 4 Relative market size and equilibrium product targeting ( =100) 24

25 w s* Figure 5 ConsumersP welfare and equilibrium product targeting ( =2000, = 1, =40000)

26 w n* Figure 6 ConsumersP welfare and equilibrium number of rms ( =2000, = 1, =40000)