Introduction

In the last chapter we showed that a properly chosen set of n+l selfselecting two-part tariffs could Pareto dominate a set of n self-selecting two-part tariffs. The reason for this welfare dominance is that the set of n+1 two-part tariffs gives each type of consumer the ability to find a two-part tariff more closely attuned to his willingness to pay than under the original set of n two-part tariffs. Because of the relationship between a set of n self-selecting two-part tariffs and a single nonuniform price schedule with n rate steps, this result suggests that welfare can be made progressively higher by constructing nonuniform price schedules with more and more rate steps, each one progressively smaller in length, obtaining in the limit a continuously varying nonuniform price schedule.

In the upper panel of Figure 4.14 we depicted four self-selecting two-part tariffs which form the shaded piecewise-linear outlay schedule. The associated marginal price schedule is the declining block schedule in the lower part of that figure. If we were to let the number of optimally chosen self-selecting tariffs tend to infinity, then the resulting outlay schedule would be the smooth lower envelope of the two-part tariffs given as R(Q) in Figure 5.1. The corresponding smooth marginal price schedule is given as the curve P(Q) in the lower panel.

In this chapter we will explore the properties of smooth nonuniform price schedules which maximize total surplus, subject to the firm breaking even.