قیمت گذاری تحویل داده شده در برابر قیمت گذاری غیرخطی کارخانه با ساختار بازار درون زا

This paper discusses a model where consumers differ according to one unobservable (preference for quality) and one observable characteristic (location), with nonlinear prices arising in equilibrium. The main question addressed is whether firms should be allowed to practice different nonlinear prices at each location (delivered nonlinear pricing) or should be forced to set a unique nonlinear contract (mill nonlinear pricing). Assuming that firms can costless relocate, we show that the free entry long-run number of firms may be smaller, equal, or higher under delivered nonlinear pricing. Moreover, delivered nonlinear pricing yields higher long-run welfare when (i) fixed costs are low and when (ii) fixed costs are intermediate and consumer types are not very similar.

Regulation theory has been one of the most active areas of research in the last decade. However, regulation of firms' pricing policies has been almost neglected within this wave of research. This paper revisits the issue of whether regulatory authorities should prohibit firms from practicing price discrimination among consumers who differ according to some observable characteristic. The currently accepted view that unregulated markets are more competitive has been justified by economic theory using spatial pricing models. Most of existing studies compare spatial discriminatory pricing with nondiscriminatory mill pricing1 for a given market structure (see, for example, Norman, 1983 and Thisse and Vives, 1988). Under spatial discriminatory pricing firms can price discriminate across locations, hence firms compete in each of them. On the other hand if firms have to practice the same price in every location, competition occurs only at the boundary of each firm's market. As a consequence, for a given market structure discriminatory pricing is more competitive than mill pricing. However, as pointed out by Norman and Thisse (1996), the previous analysis is incomplete if one does not consider the effect of pricing policies on market structure since entry incentives are not the same under both pricing policies. Norman and Thisse (1996) analyze the economic justification of firms' pricing policies regulation taking into account the effect of pricing policies on welfare for a given market structure and the effect of pricing policies on market structure. They consider a circular model of horizontal product differentiation where the location of each consumer is observable and firms may price discriminate (delivered pricing) or set a mill price (mill pricing). The free entry long-run equilibrium and its number of firms (number of product varieties2) is computed for each pricing policy and degree of spatial contestability (when firms' relocation is costless we have spatial contestability; when location is once-for-all we have spatial noncontestability). Their work illustrates an important trade-off: as delivered pricing implies fiercer competition and lower profits, in the long-run it acts as an entry deterrent and reduces the free entry number of firms. Therefore, mill pricing always leads to more variety than delivered pricing. However, this higher variety is not necessarily welfare improving. When relocation is costless, both mill and delivered pricing have too much product variety. Thus, the equilibrium number of firms under discriminatory pricing is closer to the socially optimal one and discriminatory pricing leads to higher social surplus. Under spatial noncontestability the welfare comparisons are less clear. In this case, there is too much product variety under mill pricing but too little product variety with delivered pricing. The previously mentioned works consider linear prices: mill linear price is compared to discriminatory linear price, in a setup where consumers differ according to one observable characteristic (location). However, if consumers differ according to one unobservable (e.g. quality preference) we would expect nonlinear prices to arise in equilibrium. In order to explore nonlinear pricing, our work adds vertical differentiation to the Norman and Thisse (1996) setup. This is an important extension since horizontally differentiated firms competing in product lines are notorious in various markets (e.g., car,3 telecommunications, airline, etc.). Within this more realistic setup, we assume that firms have uncertainty about consumers' quality preferences but observe their location (or brand preferences parameter). Under these circumstances, firms set price/quality nonlinear contracts that screen consumers according to their preference for quality. The regulatory issue4 is then whether firms should be allowed to practice different nonlinear price contracts at each location (delivered nonlinear pricing) or, on the contrary, should be forced to set a unique nonlinear price contract (mill nonlinear pricing). The regulatory issue of whether nonlinear price discrimination should or not be allowed has been implicit in the debate around price differentials in the European Union car market. The recent policy of the European Commission acts upon the cars' distribution sector in order to reduce/stop the practices on which car manufactures rely to prevent arbitrage (therefore acting upon a crucial feature for price discrimination). The economic justification of the European Commission is the need to create more competition to the advantage of European consumers: claiming that “the consumer should be in the driver's seat”, to build a single market may put pressure on price differentials.5 Our work builds on previous results on nonlinear pricing under oligopoly.6 The framework we use is similar to the one first presented by Stole (1995), who named it vertical uncertainty. Stole studies delivered nonlinear price contracts considering a continuous of consumer types. Delivered nonlinear pricing with a discrete number of consumer types was studied by Pires and Sarkar (2000) and Valletti (2002). Both analyze the locational equilibrium, the former considering price/quantity nonlinear contracts and the latter price/quality nonlinear contracts. The discrete case analysis shows that when firms use delivered nonlinear pricing, in equilibrium, there can be different market regions: monopoly, intermediate and competitive regions. On the other hand Villas-Boas and Schmidt-Mohr (1999) study mill nonlinear contracts under discrete vertical uncertainty. They analyze a credit-market setting where banks offer a menu of credit contracts (which include a gross interest rate and a collateral requirement) and show that those contracts and their screening level depend upon the degree of horizontal and vertical differentiation. In this paper we consider a model of vertical uncertainty with two types of consumers at each location where firms set price/quality nonlinear contracts. We compare two pricing policies: delivered nonlinear pricing – DNP – firms offer different nonlinear contracts at each location; and mill nonlinear pricing – MNP – firms are not allowed to discriminate among consumers at different locations and they must simultaneously offer a unique nonlinear contract. The first part of the paper compares the performance of the two pricing policies for a given market structure. The second part of the paper studies the long-run market structure and welfare under the two pricing policies assuming spatial contestability. For a given market structure we show that, for most parameters' values, discriminatory nonlinear prices lead to lower profits than mill nonlinear prices, which extends to our nonlinear setup the result under linear pricing. However, with two types of consumers there are parameters' values where firms cover only partially or do not cover at all the low valuation consumers under mill nonlinear pricing. When low valuation consumers are not covered under MNP we may have profits under DNP being higher, equal or smaller than profits under MNP. For a given market structure, we also show that welfare is the same under the two pricing as long as the whole market is covered under MNP, otherwise welfare is higher under DNP. Our long-run analysis shows that delivered nonlinear pricing may bring smaller, equal or higher free entry number of firms than mill nonlinear pricing. Moreover, long-run welfare is higher under delivered nonlinear pricing for low fixed costs and for intermediate fixed costs and consumer types sufficiently different. This paper will proceed as follows: Section 2 presents the circular city model with n identical firms, studies the equilibrium contracts and compares profits and welfare for both pricing policies for a given market structure. Section 3 analyzes the free entry long-run equilibrium under spatial contestability and compares both pricing policies in terms of long-run product variety and welfare. Our main conclusions are presented in Section 4.

The issue of whether price discrimination should be prohibited has been previously addressed in a setup where consumer differ according to one observable characteristic (location). Under this setup mill linear pricing and delivered linear pricing have been compared and it has been shown that, if there is spatial contestability (firms can costless relocate), then in the long-run delivered linear pricing yields higher welfare, and, consequently, discriminatory prices should be allowed. This paper considers a model where consumers have unit demands and simultaneously differ according to one unobservable (quality preferences) and one observable characteristic (location — brand preferences). In these circumstances nonlinear prices arise in equilibrium. The main question addressed in this work is whether firms should be allowed to discriminate according to the observable characteristic. In other words, should firms be allowed to practice different nonlinear contracts at each location (delivered nonlinear pricing) or should they be forced to set a unique nonlinear contract (mill nonlinear pricing)? Our work analyzes the effect of these two pricing policies on profits and welfare for a given market structure and their effect on the long-run market structure and welfare. For a given market structure we show that, when brand differentiation is very low and consequently competition is intense, nonlinear delivered pricing leads to lower profits and has no impact on social welfare, which generalizes the results obtained under linear pricing. However, when brand differentiation is higher the low valuation consumers are only partially covered or not covered at all under mill nonlinear pricing and, consequently, nonlinear delivered pricing increases welfare. When low valuation consumers are not covered under mill nonlinear pricing, which happens when the two types are similar, the profits comparison is ambiguous. There is a region where profits are precisely the same under the two pricing policies. In this region, both types are offered the social optimal qualities under delivered nonlinear pricing whereas under mill nonlinear pricing only high valuation consumers are served. And there exists a region where profits are higher under delivered nonlinear price. This last case holds when brand differentiation is close to the limit where firms stop competing for high valuation consumers under mill nonlinear pricing whereas under delivered nonlinear pricing firms may be able to practice monopoly nonlinear prices at locations closer to the firm. Since under monopoly nonlinear price discrimination increases profits while under intense competition nonlinear price discrimination leads to lower profits we interpret this last result as an intermediate case between oligopoly and monopoly results. Our long-run analysis shows that, when firms can costless relocate and set nonlinear contracts to screen consumers according to their preference for quality, delivered nonlinear pricing may bring smaller, equal or higher free entry equilibrium number of firms than mill nonlinear pricing, depending on the degree of asymmetric information and the degree of differentiation. The fact that the number of product varieties (free entry number of firms) may be higher under delivered nonlinear pricing is not present at Norman and Thisse (1996) and occurs when consumers types are similar and differentiation is close to the level where local monopolies for both types start to appear under mill nonlinear pricing. Our results corroborate Norman and Thisse (1996), under spatial contestability, in terms of too much product variety (excess of entry) with both mill nonlinear pricing and delivered nonlinear pricing since the free entry social optimal number of firms is always smaller than the free entry equilibrium number of firms. This also happens in terms of welfare, since delivered nonlinear pricing yields higher long-run welfare than mill nonlinear pricing, when (i) fixed costs are low and when (ii) fixed costs are intermediate and consumer types are sufficiently different. In addition, our numerical results suggest that long-run welfare is higher under delivered nonlinear pricing than under mill nonlinear pricing for other parameters' values, supporting the view that discriminatory nonlinear prices should not be prohibited. Interesting extensions of our work would be to consider scenarios where we have a different proportion of types at each location or where brand preferences interact with quality preferences.