Spatial Price Discrimination Research Articles

Spatial Pricing in Uncontested Procurement Markets: Regulatory Implications

Abstract This study derives a general characterization of the misalignment between socially and privately optimal spatial pricing in an uncontested procurement market. In doing so it clarifies the link between firm-gate price markdown (pricing the input below its marginal value product at the firm’s location) and spatial price discrimination (varying markdown by distance). We subsequently examine the implications of our results for regulatory prescriptions. Our analysis reveals that, in the absence of regulation, increased firm-gate price markdown is necessarily accompanied by intensified spatial price discrimination, and that discrimination is always conducted against nearby producers. We find that if regulation targets price markdown at the firm gate, then spatial price discrimination is also inhibited resulting in welfare gains. In contrast, directly targeting spatial price discrimination (as generally prescribed by enacted and proposed legislation) cannot attain a first best, and may in fact result in efficiency losses relative to the unregulated equilibrium.

Quality Selection, Sectoral Heterogeneity and Chinese Exports

AbstractRecent models of international trade have identified product quality as an important determinant of bilateral trade flows. In this paper we examine the relationship between the characteristics of the export market and the aggregate quality of products using Chinese data. We find evidence that product unit values vary with standard gravity variables in a different manner across sectors of the Chinese economy and run contrary to earlier findings for the USA. These results are not compatible with existing heterogeneous firm trade models with constant mark‐up and the extension to include product quality. We construct a heterogeneous firm trade model with quality differences and spatial price discrimination, and show that the model provides plausible explanations for our empirical finds as well as other existing findings in the literature.

Spatial Pricing in Ride-Sharing Networks

We explore spatial price discrimination in the context of a ride-sharing platform that serves a network of locations. Riders at different locations are heterogeneous in terms of their destination preferences, as captured by the demand pattern of the underlying network. Drivers decide whether, when, and where to provide service so as to maximize their expected earnings given the platform’s pricing policy. Our findings highlight the impact of the demand pattern of the underlying network on the platform’s optimal profits and aggregate consumer surplus. In particular, we establish that both profits and consumer surplus are maximized when the demand pattern is “balanced” across the network’s locations. In addition, we show that profits and consumer surplus are monotonic with the balancedness of the demand pattern (as formalized by the pattern’s structural properties). Furthermore, we explore the widely adopted compensation scheme that allocates a constant fraction of the fare to drivers and identify a class of networks for which it can implement the optimal equilibrium outcome. However, we also showcase that generally this scheme leads to significantly lower profits for the platform than the optimal pricing policy especially in the presence of heterogeneity among the demand patterns in different locations. Together, these results illustrate the value of accounting for the demand pattern across a network’s locations when designing the platform’s pricing policy, and complement the existing focus on the benefits of dynamic (surge) pricing to deal with demand fluctuations over time.

How to license a transport innovation

This paper identifies the optimal method to license an innovation that reduces transport cost in a duopoly model of spatial price discrimination. An inside innovator finds licensing by a distance fee more profitable than by a fixed fee, an ad valorem royalty or a per unit royalty. Moreover, the social welfare associated with distance fee licensing is larger than that associated with not licensing. In contrast, an outside innovator never finds licensing by a distance fee the most profitable choice.

Consistent location conjectures under spatial price discrimination

This paper is the first to model consistent location conjectures under spatial price discrimination. With linear production cost, the well-known association of spatial price discrimination with efficiency vanishes as duopolists with consistent conjectures collocate at the center. With convex production cost, the duopolists do not collocate but continue to locate closer to the center than under Nash conjectures. Yet, with sufficient cost convexity, this movement to the center can actually increase welfare relative to Nash. We extend the results with linear costs to multiple private firms.

Endogenous market boundary and spatial price discrimination with a quadratic production cost function

This paper examines the welfare effects of spatial price discrimination. In the model a monopolist sells its product to a continuum of consumers distributed uniformly along a line market in which the market boundary is endogenously determined. We find that the monopolist always serves more consumers and sells more outputs under discriminatory pricing than under uniform pricing. Nevertheless, the welfare ranking between the two pricing policies is ambiguous. Results show that uniform pricing is more socially desirable than discriminatory pricing as long as the production cost function is sufficiently convex. This result is in sharp contrast to the finding in the literature that spatial price discrimination is more socially desirable than uniform pricing.

Foreign-owned firms and zoning under spatial price discrimination

This paper shows that the nationality of firms influences the design of the optimal zoning by a regulator in a duopoly model of spatial price discrimination. For high enough values of the bias of the regulator towards firms, the size of the zone in which firms are allowed to locate is greater when firms are partially foreign-owned than when firms are fully domestic-owned.

Spatial price discrimination, monopoly upstream and convex costs downstream

Under spatial price discrimination a critical cost of an upstream monopoly is the resulting distortion in downstream locations. While this is well-established for linear production costs it is examined here for the first time for convex production costs. Convex production costs create their own location distortions yet it is shown that the presence of the upstream monopoly has a smaller influence on efficiency with such costs.

Privatization and merger in a mixed oligopoly with spatial price discrimination

This paper is the first to investigate the impact of the presence of a public firm on the profitability of two-firm mergers in a spatial price discrimination model. The presence of the public firm may increase the set of mergers for two private firms to profitably merge. Merger increases social welfare in the presence of a public follower alone. However, privatizing the public firm never increases social welfare.

Spatial Price Discrimination in Input Markets with an Endogenous Market Boundary

This paper examines the welfare effect of third-degree price discrimination in a vertically related market with one upstream monopolist that sells its input to a continuum of downstream markets. Assume that the market boundary of the monopolist is endogenously determined. It is found that social welfare is necessarily lower under discriminatory than uniform pricing, even if the market area of the former is greater than that of the latter. This finding is contrary to that in the extant literature on price discrimination in final goods markets.

Spatial Price Discrimination in the Spokes Model

The spokes model allows to address nonlocalized spatial competition between firms. In a spatial context, firms can price discriminate using location‐contingent pricing. Nonlocalized competition implies that neighboring effects are not relevant to firms. This paper analyzes spatial price discrimination and location choices in the spokes model. Highly asymmetric location patterns are one outcome if the number of firms is sufficiently high: in that case, one firm supplies a generally appealing product whereas others focus on a specific niche. Moreover, multiple equilibria arise for intermediate values of the number of firms. In this case, the location patterns do not always globally minimize the sum of transport costs: asymmetric configurations distribute more efficiently the cost between firms.

Strategic delegation under spatial price discrimination

AbstractThis paper introduces strategic delegation into the traditional model of spatial price discrimination. We examine cases of both simultaneous and sequential location and find that delegating location choices to managers causes firms to move towards each other. This movement typically reduces social welfare. While exceptions exist for high cost convexity and for some cases of elastic demand, this reduction reverses the increase in welfare associated with delegation in common quantity games outside the spatial context.

ZONING UNDER SPATIAL PRICE DISCRIMINATION

This paper investigates zoning in a duopoly model of spatial price discrimination. We find that the zone in which the firms are not allowed to locate depends on the bias of the regulator. A bias toward firms is deduced when locations around the central area are forbidden, and a bias toward consumers exists when firms are only allowed to locate at places around the central area. The design of the zoned area guarantees that firms locate optimally and works under simultaneous or sequential choice of locations by the two firms. (JEL L13, R38)

Cournot and Bertrand Competition in a Model of Spatial Price Discrimination with Differentiated Products

AbstractThis study investigates spatial price discrimination with two types of market competition – price competition and quantity competition – and two kinds of cross-relations between goods – substitutes and complements – with endogenous location choices in a barbell model. The results herein present that the maximum differentiation (end point agglomeration) is the unique location equilibrium with substitutes (complements), irrespective of what type of competition. We demonstrate that if the unit transportation rate is sufficiently high, then consumer surplus, profits, and social welfare are higher under price competition than under quantity competition for both substitutes and complements. This means that introducing a spatial barrier to competition generated through transportation costs may solve the problem of inconsistency from the conflict interests between consumers, firms, and a social planner.

Spatial price discrimination and location choice with labor markets

This paper generalizes Hwang and Mai’s (Am Econ Rev 80:567–575, 1990) model to include labor markets and shows that their results are still valid when the difference of inverse demand slopes is large enough, while, when this difference is small, a monopoly firm always chooses the same (boundary) location under different pricing scenarios. In the latter situation, total outputs are identical in different pricing scenarios, while the social welfare under discriminatory pricing is definitely less than that of the mill pricing. Our results are robust, no matter whether the commuting costs are paid by the firm or workers, and no matter whether wages are discriminatory or uniform.

Spatial price discrimination and mergers with convex production costs

We examine duopolists that have convex production costs and locate under spatial price discrimination in anticipation of a merger. We show that the merger frequently results in locations that reduce social cost. This contrasts with the well-known result that with linear production costs the merger distorts locations to increase social cost. While mergers in our model can generate location asymmetry and so higher production costs, the locations frequently reduce transport cost sufficiently that the sum of transport and production costs is reduced.

Sequential entry and merger in spatial price discrimination

This paper newly introduces sequential entry into previous models of spatial price discrimination that examine location choices made in anticipation of a potential merger. While merger with simultaneous entry routinely reduces social welfare, we show that mergers frequently improve welfare. The extent of welfare improving mergers varies inversely with the timing advantage of an excluded rival. When the rival locates alone in the first stage, the merger harms welfare. When the rival locates alone in the last stage, the merger improves welfare. These results hold true when allocating three firms across either two or three location stages. Thus, allowing staged entry dramatically alters and often reverses the conclusion previously drawn on the basis of simultaneous entry.

ENDOGENOUS FLEXIBILITY IN THE FLEXIBLE MANUFACTURING SYSTEM

We investigate flexible manufacturing system (FMS) by using the spatial price discrimination framework of Pal (1998). The level of flexibility when producing variants is increased by increasing investment or production cost and is endogenously determined. Our result is that private incentives for increasing flexibility are excessive from the viewpoint of social welfare. We also show that allowing continuous level of flexibility like in von Ungern

The locations of firms on intersecting roadways

With Bertrand-Nash mill-price competition, travel costs proportional to distance squared, and three firms on an interval, the equilibrium locations of the peripheral firms are further from the center than is socially optimal. If there is a central intersection, with four (or more) finite roadway segments radiating outward from the center (a small city spread along two intersecting roadways), and with one firm at the center and one on each radial segment, then the equilibrium locations of the peripheral firms are closer to the center than is socially optimal. Extensions include competition with spatial price discrimination, a more complicated system of intersecting roadways, and more than one firm on each roadway segment.

Spatial Price Discrimination with Heterogeneous Firms

In this paper we aim to explain intuitively heterogeneous firms’ optimal location decisions in a simple spatial market. To do so, we present and solve a four‐stage game of entry, location, pricing and consumption in a spatial price discrimination framework with arbitrarily many heterogeneous firms. We provide a unique equilibrium outcome without imposing restrictions on the distribution of marginal costs across firms.