Computing Prices for Target Profits in Contracts

TL;DR

This paper develops a mathematical framework for price discrimination aimed at achieving target profits in contract-based services, especially when user type distributions are unknown or uncertain.

Contribution

It introduces a novel approach to price discrimination with target profits, providing methods to compute pricing menus and demand estimates under uncertainty.

Findings

Provided sufficient conditions for target profit achievement.

Developed constructive methods to compute quality-price menus.

Illustrated methods with practical design examples.

Abstract

Price discrimination for maximizing expected profit is a well-studied concept in economics and there are various methods that achieve the maximum given the user type distribution and the budget constraints. In many applications, particularly with regards to engineering and computing, it is often the case than the user type distribution is unknown or not accurately known. In this paper, we therefore propose and study a mathematical framework for price discrimination with \emph{target} profits under the contract-theoretic model. We first consider service providers with a given user type profile and determine sufficient conditions for achieving a target profit. Our proof is constructive in that it also provides a method to compute the quality-price tag menu. Next we consider a dual scenario where the offered service qualities are predetermined and describe an iterative method to obtain nominal demand values that best match the qualities offered by the service provider while achieving a target profit-user satisfaction margin. We also illustrate our methods with design examples in both cases.