Overage Charge or Loyalty Discount : When Should Consumptions be Penalized or Rewarded?

It is prevalent in many markets that customers are provided menus of tariffs with usage-dependent marginal prices. One instance of such nonlinear pricing scheme is additional payments on excess consumptions (e.g., overage charge, late fee, add-on charge for ancillary features or services). Conversely, firms may offer loyalty credit for repeated purchases or consumptions (e.g., quantity-discount contracts, redemption points or mileage in reward programs). Interestingly, both increasing and diminishing marginal prices may exist across and within markets, but not concurrently on a menu. In this paper we present a new perspective on whether and when firms should penalize or reward extra consumptions. We consider the standard problem of how a monopoly firm may design a menu of tariffs to sequentially screen consumers with multiple-period consumptions who are heterogenous in consumption value distribution and demand frequency. To relinquish less information rent to the high-type consumers, the optimal design should involve a tariff with increasing (respectively, diminishing) marginal price when the demand frequency of the high-value consumers is above or sufficiently lower (respectively, slightly lower) than that of the low-value consumers. This general pattern continues to hold under alternative settings on consumer heterogeneity and on uncertainty resolution about multiple-unit demand