Self-Financing of Congestible Facilities in a Growing Economy by

The basic static self-financing result for congestible facilities, due to Mohring 1 and Harwitz (1962) and Strotz (1965), is that if the facility exhibits constant long-run average costs, then the revenue from the optimal toll exactly covers the cost of constructing and operating the optimal capacity. More generally, if the user cost function is homogeneous of degree zero in capacity and usage, then the degree of self-financing at the optimum equals the degree of homogeneity of the capacity cost function. 2 These self-financing results are useful since they indicate for a first-best environment, the proportion of a congestible facility's capacity costs that should be covered from user fees/tolls and the proportion that should be financed out of general revenues. The results are receiving increased attention in policy circles 3 (especially transportation policy – highways, public transit, airports). In the current fiscal climate, policy makers find the results attractive since they typically justify an increase in cost recovery over current levels. Policy economists too find them attractive since they provide a politically appealing argument in favor of congestion pricing. The self-financing results were derived and promulgated on the basis of static models. Remarkably, no one seems to have enquired whether they carry over to intertemporal settings. 4 The aim of this paper is to address this oversight. We examine the form of the self-financing results in a variety of intertemporal economic environments – continuous additions to capacity with and without adjustment costs, operating costs, depreciation, and irreversibility; and intermittent additions to capacity, where the intermittence may be due to fixed costs of capacity additions, increasing returns to the scale of capacity additions, natural discreteness of capacity increments (e.g., airport runways), or the technology of the planning process. We find, with one exception which is readily explainable, that the self-financing results do extend to intertemporal environments in present value terms. We also explain why the results extend. Section 2 briefly reviews previous work on the self-financing of congestible facilities in a 2 static environment. Section 3 examines self-financing results in intertemporal environments with continuous additions to capacity, and Section 4 treats intermittent capacity additions. Section 5 provides a brief ex post literature review. And Section 6 concludes. To set the stage, we provide brief geometric and algebraic derivations of the self-financing results in a static context. To simplify notation, we assume throughout the paper that individuals are identical. The results can be …