Abstract: We consider a seller who wishes to sell K goods by time T. Potential buyers enter IID over time and are forward-looking, so can strategically time their purchases. At any point in time, profit is maximized by awarding the good to the agent with the highest valuation exceeding a cutoff. These cutoffs are characterized by a one-period-look-ahead rule and are deterministic, depending only on the number of units and time remaining. The cutoffs decrease over time and in the inventory size, and are independent of the buyers' arrival times. In the continuous time limit, the seller's profits are maximized by posting anonymous prices, with an auction for the last unit at time T. Unlike the cutoffs, the optimal prices depend on the history of past sales. Bio: Simon Board is an associate professor of Economics at UCLA. He received his Ph.D at Stanford Business School, and has taught at the University of Toronto and UCLA. Simon's research interests include pricing with strategic customers, optimal relational contracts and models of reputation. He teaches contract theory in the PhD program and e-commerce to undergraduates.