Selling to Heterogeneous Customers with Uncertain Valuations under Returns Policies
32 Pages Posted: 20 Oct 2008
Date Written: October, 17 2008
Abstract
This paper considers a firm that sells a product with a finite inventory to a market with a random population size. Each customer's valuation of the product consists of two components: the customer's intrinsic value of the product which is privately known by him before purchase, and the product's fitness which is ex ante uncertain and revealed to him only after purchase. The customers are heterogeneous in the sense that they differ in their intrinsic values. Because of its lack of knowledge about the customer's intrinsic value before purchase and about the fitness value after purchase, the firm essentially faces a sequential screening problem. It has been established in the literature that when the firm has an unlimited inventory, the firm's optimal selling policy takes the form of a menu of returns policies that serves the entire population. However, we show that this result no longer holds when the firm has a finite inventory or has to decide the inventory level before selling to the market. In particular, we study three commonly-used selling policies: 1) the single returns policy that serves only a fraction of the population; 2) the menu of returns policies that serves the entire population; 3) the inventory rationing policy. We show that the firm may be better off under 1) or 3) relative to 2). We derive the results as to how the firm's preference over these selling policies depends on the customer heterogeneity, the customer's ex ante valuation uncertainty, the firm's inventory level, and the firm's procurement cost.
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