SELF RATIONING WITH NONLINEAR PRICES
2018
Srinagesh, Padmanabhan
This paper is concerned with pricing problems that arise when a service and the capacity to consume that service are jointly sold to consumers with random demand. It builds on the work of Oren, Smith & Wilson (1985) and Panzar & Sibley (1978). We show that profit maximizing firms that can use fully nonlinear prices will satisfy the usual right end point condition: the last unit sold to the largest consumer will be marginally priced at marginal cost. We also provide conditions under which marginal prices exceed marginal cost. When the firm is restricted to using a partly nonlinear price structure, selling capacity at a linear price and the service itself at a nonlinear price, we show that marginal prices will generally lie below marginal cost over some portion of their domain. The intuition underlying this result can be found in the loss leader problem first studied by Allen.
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