This paper examines the problem of a monopolist setting an optimal non
linear pricing schedule in the face of consumers of unknown type who a
rrive randomly over time and self-select a choice of hire period. The
major determinant of pricing policy is the customer arrival distributi
on, with the overall level of price higher than in the atemporal yield
management/nonuniform pricing solution by a margin which increases wi
th the average frequency with which potential customers arrive. By con
trast, the solution is generally fairly insensitive to variations in t
he time rate of discount, although there is a tendency for the rate of
price discount to increase with increases in the time discount rate.