The golden rule of urban transportation investment

The purpose of this paper is to find an optimal taxation rule for transportation investment in an ever growing urban economy. First we dynamize a standard circular-city model with identical residents by introducing population growth and transportation improvements over time. Assuming that utility functions are of a constant-elasticity form and transportation investment is financed by an income tax, we prove the existence, uniqueness and stability of a balanced growth equilibrium for each given tax rate. Then, an optimal tax rate is determined so as to maximize the balanced growth equilibrium level of utility for every resident in the city. It is also shown that our simple rule remains valid in the case of two income classes.