Nonlinear Pricing

Nonlinear Pricing

Nonlinear Pricing

Nonlinear Pricing


What do phone rates, frequent flyer programs, and railroad tariffs all have in common? They are all examples of nonlinear pricing. Pricing is nonlinear when it is not strictly proportional to the quantity purchased. The Electric Power Research Institute has commissioned Robert Wilson to review the various facets of nonlinear pricing. The work starts with a general non-mathematical discussion, followed by a more technical presentation intended for readers with a fairly advanced background. Thorough and detailed, this study has ample examples of case studies from a variety of industries.


This monograph stems from work with Shmuel Oren and Stephen Smith, and later Hung-po Chao. In 1979, at the Xerox Palo Alto Research Center, we began studies of the pricing of differentiated products, and in 1984, at the Electric Power Research Institute, we continued this work with studies of the pricing of capacity and usage. With Hung-po Chao at EPRI, our project continued with studies of priority service. I am grateful to these superb colleagues. Doing research with them has been interesting and challenging, and happily, also fun. Many of the ideas herein came from them, and therefore they are co-authors in spirit at least.

At EPRI my mentor on nonlinear pricing has been Philip Hanser, to whom I am indebted for continual encouragement and help, as well as for the resources to bring the project to fruition. My experience at EPRI has been informative and stimulating in other respects as well, especially in the ways it has enabled me to learn about the practical problems of pricing and service design in the electric power industry. The value of theory is its usefulness in addressing practical problems, and my contacts at EPRI have proved again that for the theorist, the problems encountered by practitioners provide a wealth of topics.

The National Science Foundation provided grants for research during summer months, for which I am grateful. My home base is the Stanford Business School, to which I am always most indebted--for wonderful colleagues and continuing institutional support. Portions of this material, taught in a course on Pricing for seven years, has been derived from ideas in my students' term papers, many of which were very insightful. I am especially grateful to Timothy McGuire for the material on which §2.1 is based. Computer programs for numerical examples were developed using versions of APL PLUS and APL II contributed by the STSC, Inc. (now called Manugistics, Inc.).

The first draft of this monograph appeared originally as a technical report in September 1989. Several colleagues, some anonymously as referees, provided comments on the manuscript. Scott Davis of Washington University gave me line-by-line commentary; Karen Clay of Stanford and Bridger Mitchell of RAND helped me with specific aspects of telecommunications pricing. I am especially grateful to David Sibley of Bell Communications Research and the University of Texas for insightful suggestions; and to Mark Armstrong and James Mirrlees of . . .

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