Railways competition in a park-and-ride model

It is well understood that the way of use of automobiles within urban areas should be reconsidered for environmental improvements, such as reduction of CO2 or energy itself. In this paper, scale effect of city size and cost advantage of railway over automobiles is examined in a simple setting with so-called Park-and-Ride commuter system. Our results are as follows: The fare per mile charged by a monopoly railway firm may not be relevant to the city size; the fare in a symmetric equilibrium under monopolistic competition is decreasing with the city size; the fare in a symmetric zero-profit kinked equilibrium is increasing with the city size; the fare of social optimum is decreasing with the city size.