Ex post vs. ex ante pricing: Optional calling plans and tapered tariffs

We study optimal nonuniform pricing in a setting where a customer's demand at the start of a billing period contains a random variable whose realization becomes known by the end of the billing period. In this context, an optional calling plan is a tariff which the consumer must select based on his/her expectations about the random variable, whereas, under a tapered tariff, the consumer's choice of usage charge is made after he/she knows the realization of the random variable. We show that for low to moderate levels of uncertainty about the random variable entering the demand function, the optional calling plan approach to nonuniform pricing yields higher expected profit than does the tapered tariff approach, given risk-neutral consumers. We illustrate this finding with a case study and argue that it is consistent with the historical evolution of tariffs in the interexchange telecommunications market.