Pricing Policies Contingent on Observed Product Quality

Abstract

Expanded use of incentive contracts has created interest in procurement arrangements in which unit purchase price varies as a function of observed product quality. Under the assumption that at a known cost, a producer can control the true quality of his output, a production and procurement situation is described in which a riskaverse producer and consumer both attempt to maximize expected profit-the consumer by selecting a pricing strategy and sample size, and the producer by then selecting the product quality. Let product quality be denoted by p. The consumer will desire the selected product quality to be some p*. If at a fixed sample size, n, a price schedule exists which is acceptable to the risk-averse producer and also maximizes producer expected profit at p*, this price schedule is a “motivating” price schedule. For fixed (n, p), a motivating price schedule must be the solution to a specified linear programming problem. It will be a piecewise constant function of the observed quality and need have n...