Spatial Price Discrimination Research Articles

Public firms on an international border: A model of spatial price discrimination

This paper uniquely examines an international mixed oligopoly in a model of spatial price discrimination. It isolates the importance of the location of the border showing a variety of equilibria depending on the nationality and placement of the private rivals. While the presence of a public firm often improves domestic welfare, it need not. Moreover, a prisoner's dilemma can exist in which each country would benefit from the privatization of both public firms but neither country has a unilateral incentive to privatize. The implications are discussed.

Urban/rural spatial price discrimination with online competition

Urban/rural spatial price discrimination with online competition

Endogenous price discrimination with asymmetric firms

We explore a third-degree spatial price discrimination model within the context of asymmetric duopolies. We find that if the degree of asymmetry is small, both firms charge uniform price is the unique sub-game perfect Nash equilibrium. As the degree of asymmetry reaches intermediate, there exists no pure strategy sub-game perfect Nash equilibrium. In the mixed strategy equilibrium, both firms price discriminate with certain probability. When the degree of asymmetry is large, there exists one or two asymmetric equilibria: the advantaged firm price discriminating and the disadvantaged firm uniformly pricing IN and vice versa in the other NI. In both equilibria, the price-discriminating firm consistently benefits, and the uniform-pricing firm also experiences higher profits when the degree of asymmetry is large, despite being driven out of the smaller market. Moreover, when the asymmetry is large enough, social welfare can also be higher.

Spatial price discrimination with a ‘must-have’ component

An upstream firm provides a valuable component with either an exclusive or nonexclusive contract to two downstream firms on a horizontal market. The downstream firms engage in either uniform pricing or spatial price discrimination. The component provider is more likely to sign an exclusive contract under discriminatory pricing. Discriminatory pricing generates higher welfare when both pricing methods result in exclusive contracts and generates the same welfare when both methods result in nonexclusive contracts. Importantly it generates lower welfare when discriminatory pricing results in exclusive contracts and uniform pricing results in nonexclusive contracts. These results prove robust to a variety of model variations.

Spatial price discrimination in a mixed duopoly input market

We uniquely examine an upstream mixed duopoly engaging in spatial price discrimination across a continuum of downstream markets. The monopoly firms in those markets face elastic final demand creating double marginalization. The upstream public firm faces a cost disadvantage relative to its private rival that declines as it is partially privatized. We show that the fully public firm improves social welfare relative to a private duopoly when it is not overly inefficient and when differentiation is sufficiently large. We also show that whenever this is the case, there exists an optimal degree of partial privatization that better aligns the trade-off between production costs and pricing distortions.

Nash versus consistent equilibrium: A comparative perspective on a mixed duopoly location model of spatial price discrimination with delegation

We argue that under the presence of a public firm, discriminatory pricing according to location leads to an efficient consistent equilibrium. We consider a mixed ownership duopoly delegation model with spatial price discrimination and constant, albeit different, marginal production costs. In contrast to what holds true for a private duopoly, we prove that the Nash equilibrium, absent delegation, is both consistent and socially optimal. The consistent equilibrium remains socially optimal regardless of the order in the delegation process. Under Nash conjectures, in most cases, firm owners have a strong incentive to delegate location decisions to managers. In such cases, duopolists locate closer to each other. Nash, compared to consistency of conjectures, leads to lower prices, lower profits, for both firms, and increased surplus for the consumer. The result surprises as it contrasts with respective findings regarding a private duopoly.

Quality, Location and Collusion under Spatial Price Discrimination

Abstract We present the first demonstration of the influence of a quality rivalry on location choices under spatial price discrimination. The rivalry is shown to generate the socially efficient quality but to push locations inefficiently close together, a result not found under Hotelling pricing. We apply this new equilibrium to the anti-trust policy issue of collusion showing that introducing the quality rivalry reduces the likelihood of collusion.

Partial Privatization Upstream with Spatial Price Discrimination Downstream

We consider a mixed duopoly selling to downstream retailers that are engaged in spatial price discrimination. We show that the optimal degree of privatization falls below—often far below—the level that is implied in the absence of the vertical chain. The size of this reduction in privatization reflects the extent to which increasing transport cost (differentiation) increases double marginalization in contested market regions—as opposed to simply reducing demand in uncontested market regions. Moreover, we show that despite higher costs of production, a fully public monopoly upstream can be welfare-superior to the optimal mixed duopoly. This would not be the case in the absence of downstream differentiation.

Spatial pricing and collusion

AbstractThe stability of collusion is compared assuming quadratic transport costs under two spatial pricing schemes, uniform mill pricing and spatial price discrimination. This comparison uniquely allows fully endogenous location choice and examines when two firms collude, when two of three firms collude and when three firms collude. Spatial price discrimination facilitates collusion more than uniform pricing in the first two of the three examinations but not in the third. This heterogeneity argues that the presence of price discrimination by itself does not inform antitrust authorities about the likelihood of collusion.

Does price discrimination make collusion less likely? a delivered pricing model

This paper compares the stability of collusion under delivered spatial price discrimination and under uniform pricing. Uniquely using a model of elastic demand, we show that collusion under price discrimination can be more stable thus facilitating collusion and making it more likely. This result holds only when the entire market is competitive. Whenever there exist natural monopoly portions of the spatial market, collusion on the remaining market is less stable with spatial price discrimination making such collusion less likely relative to uniform pricing.

Location decisions and welfare under spatial price discrimination

The welfare effects of regulation are of crucial importance to policy makers. To this end, we present a model of n firms with differentiated costs competing in a linear market within the framework of spatial price discrimination. We prove that the Nash equilibrium locations of firms are always socially optimal irrespective of the number of competitors, the distribution of consumers, firms' cost heterogeneity, the level of privatization, and the number and/or the varieties of the produced goods. We also provide an algorithm on how to find the unique Nash equilibrium in the case of uniformly distributed consumers.

Spatial Differentiation and Market Power in Input Procurement: Evidence from a Structural Model of the Corn Market

We estimate the cost of transporting corn and the resulting degree of spatial differentiation among downstream firms that buy corn from upstream farmers and examine whether such differentiation softens competition enabling buyers to exert market power (defined as the ability to pay a price for corn that is below its marginal value product net of processing cost). We estimate a structural model of spatial competition using corn procurement data from the U.S. state of Indiana from 2004 to 2014. We adopt a strategy that allows us to estimate firm-level structural parameters while using aggregate data. Our results return a transportation cost of $0.12 per bushel per mile (5% of the corn price under average distance traveled), which provides evidence of spatial differentiation among buyers. The estimated average markdown is $0.80 per bushel (16% of the average corn price in the sample), of which $0.34 is explained by spatial differentiation and the rest by the fact that firms operated under binding capacity constraints. We also find that corn prices paid to farmers at the mill gate are independent of distance between the plant and the farm, providing evidence that firms do not engage in spatial price discrimination. Finally, we evaluate the effect of hypothetical mergers on input markets and farm surplus. A merger between nearby ethanol producers eases competition, increases markdowns by 20%, and triggers a sizable reduction in farm surplus. In contrast, a merger between distant buyers has little effect on competition and markdowns.

Spatial price discrimination, sequential location and convex production costs

Simultaneous location is known to be socially superior to sequential location under spatial price discrimination given constant marginal production costs. For the first time I demonstrate that sequential location can be socially superior to simultaneous location given convex production costs. The asymmetric sequential locations lower the sum of production and transport cost below the symmetric but inefficiently distant simultaneous locations.

Resale price maintenance and spatial price discrimination

In this article, we examine resale price maintenance (RPM) in a classic model of downstream retailers engaging in spatial price discrimination. We show that a resale price floor increases the total profit of the upstream monopoly when transport cost (product differentiation) is relatively low. Importantly, this profitable RPM floor can also enhance social welfare and even consumer surplus. A resale price ceiling can also be profitable and always improves consumer surplus and social welfare. We argue that such findings support a rule of reason approach to RPM.

A SPATIAL MODEL OF CARTEL STABILITY: THE INFLUENCE OF PRODUCTION COST CONVEXITY

ABSTRACTWe uniquely introduce convex production costs into a cartel model involving spatial price discrimination. We demonstrate that greater convexity improves cartel stability and that for sufficient convexity first best locations will be adopted. We show that allowing locations to vary over the game reduces cartel stability but that greater convexity continues to improve that stability. Moreover, when the degree of convexity does not support the first best collusive locations, other collusive locations exist that require less stability and these may either increase or decrease social welfare relative to competition. Critically, these locations that require less stability are more dispersed in sharp contrast to the known result assuming linear production costs.

Location choices and third‐degree spatial price discrimination

AbstractThis paper studies how firms choose their product differentiation levels when they engage in third‐degree price discrimination in the following product market competition in a location‐price model. We show that firms will not choose to locate at the two endpoints if different consumer groups have similar sizes. Hence, the principle of maximum differentiation does not hold, resulting in a more intense product market price competition. Only if the size of one group of consumers is sufficiently larger than that of the other group, would firms make their products as differentiated as possible by choosing the two endpoints as their locations.

Can Banning Spatial Price Discrimination Improve Social Welfare?

We analyze a two-stage sequential-move model of location and pricing to identify firm’s location, output, and welfare. We consider two pricing regimes (mill pricing and spatial price discrimination) and, unlike previous literature, allow in each of them for a non-uniform population density, non-constant location costs (i.e., the setup costs, such rental costs and land prices, differ by firm’s location), and endogenous market boundaries. Under constant location costs, our results show the firm locates at the city center under both mill and discriminatory pricing, and that output is larger under spatial price discrimination. Welfare comparisons are, however, ambiguous. Under non-constant location costs, we find the optimal location can move away from the city center, and does not coincide across pricing regimes. Compared with mill pricing, spatial price discrimination generates a higher level of output. We also find that welfare is higher (lower) under mill than under discriminatory pricing when transportation rates are low (high, respectively).

Endogenous Spatial Price Discrimination with Elastic Demand

We relax two common assumptions in the Hotelling model with third-degree price discrimination: inelastic demand and exogenously assumed price discrimination. Based on the constant elasticity of substitution (CES) representative consumer model, we allow firms to endogenously choose whether to acquire consumer information and price discriminate. We find that when the information cost is sufficiently low, there exist two symmetric sub-game perfect Nash equilibria irrespective of the demand elasticity: both firms acquiring information and price discriminating, and neither firm acquiring information and charging a uniform price. This implies that the widely discussed prisoners' dilemma, in which both firms are exogenously assumed to price discriminate, is not in fact a dilemma. A comparison of social welfare shows that when the demand elasticity is large enough, price discrimination improves social welfare. This is in contrast to the finding -- price discrimination harms social welfare -- in the existing literature assuming perfect inelastic demand.

R&D investment under spatial price discrimination

This paper uniquely examines an R&D rivalry under spatial price discrimination and compares two alternative timings. When firms invest first, they locate efficiently but overinvest in cost‐reducing R&D if spillover is modest. When firms locate first, they locate inefficiently and always underinvest in cost‐reducing R&D. Although the R&D investment improves social welfare under either timing, profit always declines and so it would never be undertaken if firms cooperate. Both timings are relevant as we identify circumstances under which each will endogenously be chosen in a premarket stage. Critically, the equilibrium timing is often not the socially beneficial timing.

Retail Price Regulation in the British Energy Industry

In this paper, we revisit the 2009–2012 episode in which Ofgem imposed a nondiscrimination clause on large retailers in the UK energy market. The Standard Licence Condition 25A (SLC 25A) was introduced to prevent suppliers from charging their incumbent customers higher prices than their out-of-area customers. The SLC 25A included a “sunset clause”, to allow the condition to lapse three years after its implementation. Several IO economists protested that the prohibition of spatial price discrimination would eventually lead to competition weakening. At the end of the three-year period, Ofgem decided not to renew SLC 25A for any period. To further our understanding of Ofgem's motives and its opponents' arguments, we build a model where two local monopolists compete on a third market. We determine conditions where the obligation to set the same price in and out of the local market can result in a better or a worse situation for consumers. We show that even when the ban on price discrimination weakens competition, the average consumer can be better off.