Simple monopoly price theory in a spatial market

Abstract

D42, R32,

Spatial monopoly pricing under non-constant marginal costs

“…Because the left hand side of this inequality has its minimum at = 1∕2 , the condition is always satisfied if the second-order necessary condition for a profit maximum is satisfied ( 2 (f )∕ f 2 < 0 ) and transport costs are sufficiently small, formally: ◻ Proposition 1 extents previous findings (e.g. Greenhut et al 1987;Hsu 2006) by showing that the monopolist's optimal prices are only independent of transport costs if marginal costs are constant. Under variable marginal costs, however, optimal prices change with the level of transport costs.…”

“…The opposite is true if consumer demand is concave. However, Hsu (2006) shows that these results do not generally hold in a framework of endogenous market size, where mill pricing is always superior to uniform pricing in terms of consumer surplus and…”

“…The firm's pricing decision crucially affects profit, output, and social welfare (Beckmann 1976;Greenhut et al 1987). Yet the ranking of alternative spatial price strategies (based on economic benefits) depends, e.g., on the shape of individual consumer demand functions (Smithies 1941;Cheung and Wang 1996) or whether the firm is able to optimize its market area (Hsu 2006). Always, however, conclusions are derived for the case of constant marginal costs.…”

“…The objective of this paper is to relax this assumption and to examine the effect of variable marginal costs on the ranking of uniform and mill pricing in a general monopoly framework. We focus on these two pricing options because they are easy to administer (Espinosa 1992), important in different markets and regions (Greenhut 1981), most previous studies (including Hsu 1983;Cheung and Wang 1996;Hsu 2006;Lederer 2012) compare these options, which provides a point of reference, and both price strategies represent the limits of no (mill pricing) and full (uniform pricing) freight costs absorption.…”

“…Most relevant to the present paper is the work by Cheung and Wang (1996) and Hsu (2006) because of their general formulations of individual demand functions under spatial monopoly. While I generally follow Hsu (2006) by allowing the firm to optimize its market area, I also investigate the fixed market setting studied by Cheung and Wang (1996). The critical deviation from these and other papers, however, is the introduction of a general cost function by comparing mill and uniform pricing.…”