Optimal three-part tariff pricing with Spence-Mirrlees reservation prices

Jianqing Fisher Wu () and Banafsheh Behzad ()
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Jianqing Fisher Wu: California State University, Long Beach
Banafsheh Behzad: California State University, Long Beach

Mathematical Methods of Operations Research, 2023, vol. 97, issue 2, No 5, 233-258

Abstract: Abstract We study the pricing of three-part tariffs (3PTs), where service providers charge a fixed fee with an allowance of free units, and a per-unit fee for additional units above the allowance. This is a pricing strategy that has been widely used in a variety of industries, including telecommunications and internet services. Many papers study the properties of the optimal solution of 3PTs. However, the existing solution approaches proposed in prior papers can only be used to solve 3PT problems under certain restricted conditions. Solving 3PT problems with multiple consumer types has been considered as “intractable” in the literature. In this paper, we provide an optimal solution for 3PT problem with multiple consumer types. We first provide a solution approach to solve 3PT problem with discrete units and multiple discrete consumer types whose willingness-to-pays for different units follow Spence-Mirrlees single-crossing property. The cost of our solution approach is low-rank polynomial to the problem size. We then extend the discrete solution to solve 3PT problems when the consumer types and unit amounts are not required to be discrete. The solution values for the continuous problems are within arbitrary prespecified error tolerances.

Keywords: Pricing; Three-part tariff; Non-linear pricing; Price discrimination (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00186-023-00813-4

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