Optimal Three-Part Tariff Plans

37 Pages Posted: 11 May 2015 Last revised: 27 Dec 2016

See all articles by Gadi Fibich

Gadi Fibich

Tel Aviv University - School of Mathematical Sciences

Roy Klein

Tel Aviv University - School of Mathematical Sciences

Oded Koenigsberg

London Business School - Department of Marketing

Eitan Muller

New York University (NYU) - Department of Marketing; Interdisciplinary Center (IDC) Herzliyah

Date Written: December 1, 2016

Abstract

Service providers, such as cell phone carriers, often offer three-part tariff plans that consist of three levers: A fixed fee, an allowance of free units, and a price per each unit above the allowance. In previous studies the optimal three-part tariff contract was characterized using the standard first-order conditions approach. Because this optimization problem is non-smooth, however, it could only be solved in a few simple cases. In this study we employ a different methodology which is based on obtaining a global bound for the firm profit, and then showing that this bound is attained by the optimal plan. This approach allows us to explicitly calculate the optimal three-part tariff plan under quite general conditions, where consumers are strategic, they have a general utility function, they experience psychological costs when they exceed the number of free units, they have deterministic or stochastic consumption rates, they are homogeneous or heterogeneous, and the firm costs are fixed or depend on the usage level.

Keywords: non-linear pricing; three-part tariff ; non-smooth optimization

JEL Classification: C61, L8, L9, M31, D4

Suggested Citation

Fibich, Gadi and Klein, Roy and Koenigsberg, Oded and Muller, Eitan, Optimal Three-Part Tariff Plans (December 1, 2016). Available at SSRN: https://ssrn.com/abstract=2599985 or http://dx.doi.org/10.2139/ssrn.2599985

Gadi Fibich

Tel Aviv University - School of Mathematical Sciences ( email )

Tel Aviv 69978
Israel

Roy Klein (Contact Author)

Tel Aviv University - School of Mathematical Sciences ( email )

Tel Aviv 69978
Israel

Oded Koenigsberg

London Business School - Department of Marketing ( email )

Sussex Place
Regent's Park
London, NW1 4SA
United Kingdom

Eitan Muller

New York University (NYU) - Department of Marketing ( email )

Henry Kaufman Ctr
44 W 4 St.
New York, NY
United States

Interdisciplinary Center (IDC) Herzliyah ( email )

P.O. Box 167
Herzliya, 46150
Israel

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