Dynamic Pricing and Demand Estimation for a Single Unique Asset

We address the situation of a firm that needs to dispose of a large, expensive asset (e.g., car, machine tool, earth mover, turbine, house, airplane), with or without a given deadline (and either known or unknown to the buyer). If a deadline exists, the asset is salvaged at a known value which may be zero, or even negative if there is a disposal cost. The asset has a known holding cost and may also have an initial nominal (undiscounted) price. The question is how, if at all, the price should be discounted as time progresses to maximize the expected proceeds. We use a dynamic recursion where each decision stage can be optimized based on classic economic monopoly pricing theory with a demand intensity function estimated from sales data, and show that the model is well-behaved in the sense that the optimal price and optimal expected revenue monotonically decline as the deadline approaches. We test the model by comparing its optimal price pattern to the official pricing policy practiced at a used-car dealer. We then extend the model to situations where the buyer knows the seller's deadline and thus may alter his behavior as the deadline approaches.