Durable Goods Sales with Dynamic Arrivals and Changing Values

I study a pro…t-maximizing monopolist selling a durable good to buyers who arrive over time. Buyers are forward looking and their values for the good evolve stochastically. I …rst suppose that the seller commits to a path of posted prices in a stationary environment. Contrary to the case where values remain constant, optimal prices ‡uctuate over time. This is consistent with the use of sales or periodic discounts. If the arrival rate varies with time, the seller favors discounting when the rate is at its fastest, suggesting an explanation for the common empirical …nding of countercyclical markups. A path of posted prices, however, is not the most pro…table mechanism. Because values evolve over time, higher pro…t can be obtained with more sophisticated mechanisms. In particular, the unrestricted optimal mechanism can be implemented by selling options to purchase the good at future dates. As is the case for optimal posted prices, buyers who arrive later expect to earn less rent and expect to wait longer to obtain the good. Contracts agreed at later dates are therefore less e¢ cient. JEL classi…cation : D82. Keywords : changing types, durable goods, dynamic mechanism design, price cycles, sales, countercyclical markups This paper has bene…ted from detailed comments from my advisor, Alessandro Pavan, as well as the helpful suggestions of Je¤ Ely, Igal Hendel, Alexander Koch, Konrad Mierendor¤, Aviv Nevo, Bill Rogerson, Bruno Strulovici and Rakesh Vohra. Thank you also to seminar participants at Aarhus University, Northwestern University and at the Arne Ryde Memorial Lectures at the University of Lund. I am solely accountable for any errors. yThis paper previously circulated under the title ‘Durable Goods Sales with Changing Values and Unobservable Arrival Dates’.