Non-linear pricing by convex duality

Date
2015
Authors
Pınar, M. Ç.
Advisor
Instructor
Source Title
Automatica
Print ISSN
0005-1098
Electronic ISSN
1873-2836
Publisher
Elsevier
Volume
53
Issue
Pages
369 - 375
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Abstract

We consider the pricing problem of a risk-neutral monopolist who produces (at a cost) and offers an infinitely divisible good to a single potential buyer that can be of a finite number of (single dimensional) types. The buyer has a non-linear utility function that is differentiable, strictly concave and strictly increasing. Using a simple reformulation and shortest path problem duality as in Vohra (2011) we transform the initial non-convex pricing problem of the monopolist into an equivalent optimization problem yielding a closed-form pricing formula under a regularity assumption on the probability distribution of buyer types. We examine the solution of the problem when the regularity condition is relaxed in different ways, or when the production function is non-linear and convex. For arbitrary type distributions, we offer a complete solution procedure.

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Book Title
Keywords
Asymmetric information, Convex optimization, Mechanism design, Nonlinear pricing, Shortest paths, Convex optimization, Economics, Graph theory, Machine design, Optimization, Probability distributions, Sales, Asymmetric information, Mechanism design, Non-linear pricing, Nonlinear utility functions, Optimization problems, Regularity assumption, Shortest path, Shortest path problem, Costs
Citation
Published Version (Please cite this version)