A Spatial Model of Cartel Stability: The Influence of Production Cost Convexity

Abstract

We 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.

Spatial pricing and collusion

“…Matsumura and Matsushima (2005) show that having three firms in this model increases stability but that this does not carry over to four firms. Andree et al (2018) examine two firms with inelastic demand assuming convex rather than linear production costs. They demonstrate that collusion stability increases not only in cost convexity, but also with firm dispersion.…”

“…It also fits with Posada and Straume (2004) who demonstrate the strong theoretical incentive to relocate as firms enter or break an agreement to cooperate. Andree et al (2018) argue that such flexibility presents a sensible alternative in cases where relocating in product or physical space is not overly costly.…”

“…Andree et al. (2018) examine two firms with inelastic demand assuming convex rather than linear production costs. They demonstrate that collusion stability increases not only in cost convexity, but also with firm dispersion.…”

“…Alternatively, a single location choice happens at the very beginning of a game made in anticipation of whether collusion is stable or not. The stability condition then reflects that fixed but chosen location (see Andree et al, 2018; Heywood & Wang, 2020 for examples).…”

“…Andree et al. (2018) argue that such flexibility presents a sensible alternative in cases where relocating in product or physical space is not overly costly.…”