- Text
- Bundling,
- Equilibrium,
- Consumers,
- Prices,
- Conglomerate,
- Proposition,
- Shoppers,
- Conglomerates,
- Discount,
- Bundle,
- Multimarket,
- Collusive,
- Cemfi

Multimarket Contact, Bundling and Collusive Behavior - Cemfi

a collection of cities that are ordered according to some distribution () in ∈ [0 12].A full range of correlations in preferences can be produced varying () –for example,the uniform distribution of consumers over the square city is obtained with () =2forall – with results that follow closely those in figure 4.Another message from this latter exercise is that it is not innocuous the way in whichcorrelations are produced. A simple example can help illustrate the point. Suppose thatinstead of letting vary,aswehavedonesofar,weconsiderconsumerslocatedintwo(extreme) cities, =0**and** =12, **and** let the proportion of consumers allocated toeach city, (1 + )2 **and** (1 − )2, respectively, vary with ∈ [1 −1]. Thiswaywecanproduce any aggregate correlation we want. Not surprisingly, the equilibrium outcomesare quite different from those in Propositions 1 **and** 2 except when =1**and** = −1. Asshown in Appendix C, the pure bundling (mixed-strategy) equilibrium moves gradually**and** monotonically from linear pricing ( =1) to marginal-cost pricing ( = −1). Again,this is not surprising because allocating more consumers to city =0can never restorethe price-discrimination effect simply because we are adding consumers with perfectlypositive correlations for which bundling is irrelevant. In other words, we are "liquefying"the pro-competitive (i.e., business-stealing) effect of bundling without really changing theform of the equilibrium.We conclude the section with a remark on the second profit profile depicted in Figure4–thedottedline.ItisdrawnupontheanalysisinAppendixesA**and**B**and**capturesthe evolution of (relative) bundling profits when 6= ,**and**( + )2 = so profitsunder linear pricing remain unchanged. One immediate implication is that the (profirm)equilibrium in Proposition 1 can extend well into negative correlations (even allthe way if ˆ 0 = 12). The other is that the gap between bundling **and** benchmarkprofits closes with transport cost heterogeneity. Neither implication is really surprisingafter we underst**and** that introducing such heterogeneity is equivalent to considering amore positive correlation in preferences. In fact, when one of the markets is perfectlycompetitive (e.g., =0), a consumer that buys product − from is ready to buy from the same conglomerate (or from the other conglomerate for that matter). **Bundling**becomes irrelevant when one of the markets is perfectly competitive or, which is thesame, when there is a perfectly positive correlation.4 CollusionIn the first part of the section we ask what is the optimal collusive agreement conglomeratescan fashion, as if they were infinitely patient or → 1, **and** only then look at theissue of sustaining such an agreement or a less ambitious one. Throughout the sectionwe maintain the assumption that = = . But when we look at the sustainabilityof the agreement we make also explicit that = = **and** = = (actually,with full coverage it suffices to assume that − = − ), so we can fully isolatethe Bernheim **and** Whinston’s effect of multimarket contact on collusion from that of18

undling. In the last part of the section we incorporate the Bernheim **and** Whinston’seffect by relaxing these latter assumptions.4.1 **Collusive** bundlingThe question here is whether **and** how a cartel agreement of the two conglomerates canmake use of bundling to raise profits above those obtained when charging the (linear)monopoly prices **and** . Figure 5 below provides a hint. Figure 5a considers a cartelcharging monopoly prices to consumers living in city =12 (i.e., = −1). There isessentially only two-stop shoppers: the half on the left of the city will buy from 1 **and** from 2 **and** the half on the right will buy from 2 **and** from 1. Only consumers exactlylocated halfway between 1 **and** 1 (**and** 2 **and** 2) areindifferent between shoppingat either conglomerate or at different conglomerates; **and** these consumers are preciselythe ones left with no surplus. All remaining consumers enjoy a surplus, particularly thoselocated close to the firms.*** figure 5 here or below ***The cartel can get a h**and** on some of that surplus by introducing non-linear pricing:by raising st**and**-alone prices above monopoly levels while maintaining the monopolyprices for the one-stop shoppers (i.e., = + ). As indicated by the dashed linesin the figure, this would reduce the number of two-stop shoppers **and** create a strictlypositive mass of one-stop shoppers, all with zero surplus. Obviously, the cartel doesnotwanttoincreasethest**and**-alonepricesallthewayastoeliminateallthetwo-stopshoppers (we come back shortly with the optimal increase).Figure 5b considers the other extreme, that of a cartel charging monopoly pricesto consumers living in city = 0 (i.e., = 1). Now, there are essentially no twostopshoppers: consumers on the upper half of the city will buy everything from 1 **and**those on the lower half from 2. Only consumers exactly located halfway between 1**and** 2 (**and** 1 **and** 2) areindifferent between shopping at either conglomerate or atdifferent conglomerates; **and** these consumers are again the ones left with no surplus.As before, the cartel can get a h**and** on some the surplus enjoyed by most consumers byintroducing non-linear pricing. But unlike in =12, here the cartel would like to chargea premium, as opposed to a discount, to the one-stop shoppers while maintaining thest**and**-alone prices at the monopoly levels. As indicated by the dashed lines in the figure**and** assuming that the cartel can perfectly monitor sales, this would reduce the numberof one-stop shoppers **and** create a strictly positive mass of two-stop shoppers, all withzero surplus. Again, the cartel would not introduce a premium that would eliminate allthe one-stop shoppers but something smaller. The exact amount is made precise in thefollowing proposition.Proposition 3 Acartelalwaysbenefits from non-linear pricing, sometimes charging a19

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