Group purchasing, nonlinear tariffs, and oligopoly

Loyalty discounts are nonlinear tariffs that condition rebates or marginal prices on meeting aggregate purchase or market share targets. These discounts are widespread, and are often the impetus for consumers to form buying groups, or group purchase organizations (GPOs). This paper models the competitive effects of the introduction of a GPO into a market within which the preferences of the GPO's members are horizontally differentiated. While nonlinear tariffs are an effective way for a monopolist to extract consumer surplus, when two suppliers compete using such schedules, the results are far more competitive in comparison to simple Bertrand-Nash competition with linear tariffs. This result holds when the product of each of the suppliers is attractive to a substantial portion of consumers. In our model, the nonlinear schedule puts all customers “in play” to a degree that contrasts sharply with the competition at the margin characteristic of constant per unit prices. Moreover, competing in nonlinear tariffs removes allocative inefficiency that can result from single price competition.