CONTINGENT PRICING POLICIES
Abstract
A production and procurement situation is described in which the producer and consumer of some commodity negotiate a contract under which the consumer purchases a batch of N items and pays a unit price, phi(x), determined by the result of sampling n (< or = N) items from the batch. It is assumed that the producer can control the quality, p, of the commodity to a known degree at a known cost, h(p), and further that given phi(x) and n the producer selects p to maximize expected net return. Therefore the consumer must choose phi(x) and n to maximize his own net return under the producer's optimal action. Under the additional assumptions that phi(x) is bounded and that the contract must provide for protection against incorrect payment due to sampling variation it is shown that at a fixed (n,p) optimal price schedules must be solutions to a specified linear programming problem, and that for fixed n, if the consumer desires the producer to select p = p sub o, and seeks phi(x) to both maximize producer expected net return at p sub o and minimize the mean square difference between actual producer profit at p sub o and negotiated profit, under weak conditions the optimal phi(x) is piecewise linear. A computational procedure for seeking optimal price functions is described, and several hypothetical examples are presented.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 30, 1964
- Accession Number
- AD0611541
Entities
People
- Eugene P. Durbin
Organizations
- Stanford University