  A patient seller aims to sell a good to an impatient buyer (i.e., one who
discounts utility over time). The buyer will remain in the market for a period
of time $T$, and her private value is drawn from a publicly known distribution.
What is the revenue-optimal pricing-curve (sequence of (price, time) pairs) for
the seller? Is randomization of help here? Is the revenue-optimal pricing curve
computable in polynomial time? We answer these questions in this paper. We give
an efficient algorithm for computing the revenue-optimal pricing curve. We show
that pricing curves, that post a price at each point of time and let the buyer
pick her utility maximizing time to buy, are revenue-optimal among a much
broader class of sequential lottery mechanisms. I.e., mechanisms that allow the
seller to post a menu of lotteries at each point of time cannot get any higher
revenue than pricing curves. We also show that the even broader class of
mechanisms that allow the menu of lotteries to be adaptively set, can earn
strictly higher revenue than that of pricing curves, and the revenue gap can be
as big as the support size of the buyer's value distribution.
