Dynamic Pricing and Inventory Decisions under Concave Costs.

This paper considers the relationship between pricing and inventory decisions for a retailer facing a known, stationary demand function (demand-price relationship), who incurs a fixed cost each time he places an order, and whose marginal purchasing costs and holding costs are constant. The retailer is assumed to be able to continuously vary his selling price over time. In this deterministic, concave cost setting, we introduce a notion of instantaneous margin, and use it to derive profit maximizing conditions for the retailer. Surprisingly, the model predicts that the retailer will increase his price over the inventory cycle. In the case of the linear demand function, we find expressions for the optimal cycle length and the optimal dynamic price. We also compare revenues and profits to the case where the retailer cannot vary his selling price over time.