The Optimal Congestion Charge When Equity Matters

Abstract

The optimal congestion charge has been the subject of several recent papers appearing in this journal and elsewhere. Oakland (1969, 1972) derives the conditions for the optimal pricing of congested facilities under conditions of unlimited and fixed capacity. He concludes that the optimal congestion charge is equal to the congestion damage accompanying the use of the facility by one more person and that the charge should be uniform over all users. Sandmo (1973, 1974), using a different approach, reaches the same conclusion. The optimality conditions derived in these studies have normative significance only so long as lump-sum income transfers are available for moving us to the Pareto frontier. The present article begins with the premise that incomes are not justly distributed and that a transfer system that would correct the income distribution is infeasible both from an administrative and from a political point of view. In this situation, the traditional pricing rules for congested facilities must be modified to reflect distributive considerations. It is shown in this paper that the optimal price of a congested facility is not, in general, proportional to marginal cost but must reflect society's evaluation of the worth of an additional dollar to each household. A balance must be achieved between considerations of equity and considerations of efficiency. The approach of this study was suggested by the works of Diamond and Mirrlees (1971a, b) and Feldstein (1972a, b, c), who derived optimality conditions and pricing rules for the pricing of private goods produced by a central authority constrained to raise a fixed amount of revenue but without the power to redistribute incomes through lump-sum taxes and transfers. The present study extends their work to the situation where the goods in question are subject to crowding and, hence, are of a quasi-public goods nature. (Although Diamond and Mirrlees (1971b, Section IX) discuss the optimal pricing of pure public goods, they nowhere treat the quasi-public good pricing problem.) A major conclusion of this study is that, if a congested facility is primarily utilized by low-income households, its price should be moderated accordingly. This conclusion holds under fairly general assumptions and corresponds to the Diamond-Mirrlees and Feldstein results for pure private goods. In Section I of this paper a general methodology for analysing the problem is developed, and in Section II a pricing rule is derived which must be met for full optimality in the economy. Section III considers the special case where cross-elasticities of demand are zero; Section IV takes up the possibility of non-uniform prices and Section V discusses applications and limitations.