OPTIMAL PRICING WITH SUNK COST AND UNCERTAINTY James Alleman Paul

The efficiency results of marginal-cost pricing have been used to justify the imposition of regulatory policy tools to determine optimal pricing. In the more sophisticated form, Ramsey pricing methodology is recommended as a pricingpolicy tool. These methods are static. Nevertheless, they are applied to major infrastructure industries such as telecommunications. At best, these methods assume prospective events with certainty; they do not account for stochastic changes in cash flows. However, uncertainty can make a substantial difference in the vector of optimal prices. Moreover, significant sunk (irreversible) costs are incurred by the incumbent firm in these industries. Once the sunk costs are incurred, the firm no longer has the delay option available. This opportunity cost has not been acknowledged by the regulatory community in its pricing decisions. In addition to the neglect of opportunity costs, regulators have additional impacts on the incumbent firm’s cost of capital. In this regard, the regulators’ principal impact is on the magnitude and cost of the firm’s investment, directly and, perhaps just as importantly, indirectly. We first develop a model with sunk costs which determines the optimal price in the spirit of traditional marginal-cost pricing. This model demonstrates the role of sunk cost in determining opportunity cost for the firm of immediate investment. We use the techniques of real options methodology to analyze the cash flows which in turn have an impact on investment valuations. One uniqueness of the model is allowing the economic depreciation to be determined endogenously, in the spirit of Hotelling, rather than exogenously. The market value of the asset is determined by its prospective cash flows, which in turn determines its depreciation for the period. It is the interaction of stochastic consumer demand with the investment valuations which determines depreciation endogenously. We then solve for the social welfare maximum, namely, the maximization of the discounted value of producer’s and consumers’ surplus. (Because they fail to note the interaction between demand and economic depreciation, models which assume that depreciation is exogenously determined are in error.) Because the options * University of Colorado – Boulder & Columbia University; Temple University & Columbia University; and Darby & Associates, respectively. The authors would like to thank Alain deFontenay, Gary Madden, Eli Noam, and Scott Savage for useful comments and discussion of the ideas developed in this paper. Of course, the usual disclaimer applies.