Optimal Pricing in Markets with Non-Convex Costs

32 Pages Posted: 3 May 2019

See all articles by Navid Azizan

Navid Azizan

California Institute of Technology

Yu Su

California Institute of Technology

Krishnamurthy Dvijotham

Google DeepMind

Adam Wierman

California Institute of Technology

Date Written: April 1, 2018

Abstract

We consider a market run by an operator, who seeks to satisfy a given consumer demand for a commodity by purchasing the needed amount from a group of competing suppliers with non-convex cost functions. The operator knows the suppliers' cost functions and announces a price/payment function for each supplier, which determines the payment to that supplier for producing different quantities. Each supplier then makes an individual decision about how much to produce, in order to maximize its own profit. The key question is how to design the price functions. To that end, we propose a new pricing scheme, which is applicable to general non-convex costs, and allows using general parametric pricing functions. Optimizing for the quantities and the price parameters simultaneously, and the ability to use general parametric pricing functions allows our scheme to find prices that are typically economically more efficient and less discriminatory than those of the existing schemes. In addition, we supplement the proposed method with a polynomial-time approximation algorithm, which can be used to approximate the optimal quantities and prices. Our framework extends to the case of networked markets, which, to the best of our knowledge, has not been considered in previous work.

Keywords: non-convexities, pricing, start-up cost, uplift, market-clearing price, networked market

JEL Classification: D4, Q4

Suggested Citation

Azizan Ruhi, Navid and Su, Yu and Dvijotham, Krishnamurthy and Wierman, Adam, Optimal Pricing in Markets with Non-Convex Costs (April 1, 2018). Available at SSRN: https://ssrn.com/abstract=3365416 or http://dx.doi.org/10.2139/ssrn.3365416

Navid Azizan Ruhi (Contact Author)

California Institute of Technology ( email )

Pasadena, CA 91125
United States

HOME PAGE: http://www.caltech.edu/~nazizanr

Yu Su

California Institute of Technology ( email )

Pasadena, CA 91125
United States

Krishnamurthy Dvijotham

Google DeepMind ( email )

Adam Wierman

California Institute of Technology ( email )

Pasadena, CA 91125
United States

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