Dynamic Pricing with Uncertainty

Abstract

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-Boiteux pricing methodology is recommended as a pricing-policy 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 determination 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, that is the firm cannot wait-and-watch how the market develops, but must invest immediately. 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.

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. We then solve for the social welfare maximum, namely, the maximization of the discounted value of producer’s and consumers’ surplus. Because the options values/opportunity costs are not recognized in a static view of the world, the resultant price vectors of the traditional models are a poor policy guide.

Without regulatory constraints on prices, the model shows that the uncertainty prices differ significantly from the results of both the traditional marginal-cost price and the Ramsey-Boiteux pricing vector. The policy implications of the result are material. For the telecommunications industry, the telecommunications element long-run incremental cost (TELRIC) rates are theoretically incorrect, and, even if the rates derived from the static theoretical construct were exactly as TELRIC would require, they would be erroneous. These results are applicable to other network industries.