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A Note on Optimal Tolls in an Imperfect Environment

Maurice Marchand

Abstract

Levy-Lambert shows in [3], for a specific example, how the marginal cost pricing principle must be modified to take into account an imperfect environment. The author studies the case of two existing, perfectly substitutable facilities, namely a turnpike and a highway, connecting two given locations. It is well known that an optimal resource allocation can be attained only by levying a toll on users during congested hours. These tolls must be such that the private cost of the trip on each facility is equal to its marginal social cost. In practice, however, there are often constraints that prevent reaching this goal. Thus, what is the optimal toll to be charged on the turnpike, when it is impossible to levy a toll on the highway? We owe the answer to this question to Levy-Lambert. The purposes of the present note are: (i) to derive explicitly Levy-Lambert's result from a general equilibrium model and in the process to exhibit a minor qualification; (ii) to derive a few additional results, especially about the optimal redistribution of incomes; and (iii) to illustrate by a simple example a general methodology for analyzing "second best" models, already used with success in other fields.