Equilibrium commuting

We consider the role of a nonlinear commuting cost function in determination of the equilibrium commuting pattern where all agents are mobile. Previous literature has considered only linear commuting cost, where in equilibrium, all workers are indifferent about their workplace location. We show that this no longer holds for nonlinear commuting cost. The equilibrium commuting pattern is completely determined by the concavity or convexity of commuting cost as a function of distance. We show that a monocentric equilibrium exists when the ratio of the firm agglomeration externality to commuting cost is sufficiently high. We also show that equilibrium residential land rent is decreasing and convex in distance to the business district under concave commuting cost given that the total land used for offices is smaller than that used for housing. Finally, we find empirical evidence of both long and short commutes in equilibrium, implying that the commuting cost function is likely concave.