Regulatory Models for Pricing and Evaluation of Transport Services

Abstract

A variety of objectives and constraints are presented for use by a regulatory agency in pricing public services and evaluating capacities under conditions where the demands are random variables with probability distributions that depend on prices in different parts of the system. The models studied include a maximization of the joint probability of achieving at least specified levels of consumers' surpluses in these interacting markets, as well as models that constrain the choices of prices and services to ensure that these surpluses are satisfied to at least specified levels of probability, while observing expected fair return constraints for the producers. Chance constrained programming formulations and reductions to deterministic equivalents are developed to use for evaluating levels of service, etc. Some new “coefficients conditions” establishing concavity for quadratic forms are stated and proved in the Appendix to this paper. This also establishes convexity for the deterministic equivalents developed in this paper and hence provides access to Kuhn-Tucker and other conditions that depend on convexity. This then yields yet another (dual) problem that is also deterministic and that makes it possible to extend the procedures for constraint evaluations in terms of their welfare and regulatory implications.