Since consumers do not react to price cuts in practice as standard models of price competition predict, recent studies have introduced `switching costs' to reconcile their behaviour with rational decision-making. These raise the cost of reacting to price cuts and thus provide a theoretical rationale for consumers' loyalty to firms from which they have purchased in the past. In Discussion Paper No. 846, Research Affiliate Jorge Padilla develops an infinite-horizon model of price competition with consumer switching costs in which the latter are initially large enough to deter all switching irrespective of relative prices in the market. For all parameter constellations this has a unique stationary equilibrium, with unambiguously higher prices and profits than that of an otherwise identical market with no switching costs. The size of a firm's customer base is the fundamental determinant of its future profitability, and firms' equilibrium prices are increasing functions of that size.

Padilla then extends this model to show first that its results also apply when consumers are not necessarily locked into their previous suppliers, i.e. their switching costs are small. Second, tacit collusion is more difficult to sustain with switching costs than in an otherwise identical market without them. While switching costs relax competition and thus reduce the severity of the optimal punishments in any period, they also raise the costs of undercutting, which reduces incentives to deviate from a collusive agreement; but the first effect always dominates. Third, for a version of the model with one entrant and one incumbent, the latter can profitably deter entry by rationing (i.e. by restricting the size of its customer base in each period), which credibly commits itself to fight any potential entrant. Finally, Padilla concludes by generalizing the basic model to consider more general demand systems.

Revisiting Dynamic Duopoly with Consumer Switching Costs
A Jorge Padilla

Discussion Paper No. 846, October 1993 (AM)