Optimal three-part tariff plans

Gadi Fibich*, Roy Klein, Oded Koenigsberg, Eitan Muller

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


Service providers, such as cell phone carriers, often offer three-part tariff plans that consist of three levers:Afixed fee, an allowance of free units, and a price per 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 nonsmooth, however, it could only be solved in a fewsimple cases. In this studywe employ a different methodology that 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 rational, 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.

Original languageEnglish
Pages (from-to)1177-1189
Number of pages13
JournalOperations Research
Issue number5
StatePublished - 1 Sep 2017


  • Nonlinear pricing
  • Nonsmooth optimization
  • Three-part tariff


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