A new way of evaluating the optimality of a transportation improvement in a class of urban land use models

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At the optimum, the cost of, and resource savings from an infinitesimal transportation improvement are equal. The improvement changes the equilibrium allocation. In first-best economies, however by the envelope theorem, this reallocation does not have a first-order effect; therefore, the resource savings can be measured at the pre-improvement allocation. When the pre-improvement allocation is expressed in terms of physical location, the resource savings equal the reduction in the aggregate transportation costs induced by the improvement. By using a transformation of variables first introduced in Arnott and Stiglitz (1981), this paper derives a new way of evaluating the optimality of a transportation improvement. We express the pre-improvement allocation in terms of the transportation cost location instead of the physical location. From this perspective, the transportation improvement changes the transportation cost shape of the city by essentially generating new land. The optimality implies that the aggregate differential land rent of the generated land evaluated at the pre-improvement rents equals the cost of the transportation improvement. The fact that the optimality refers to the pre-improvement rents only carries policy relevance, say in the impact evaluation of the transportation improvement. This paper demonstrates the generality of this optimality, synthesizes and reinterprets the results in the literature from this alternative perspective, and discusses some insights that it generates.