The Panexponential Monocentric Model

We derive declining exponential rent and density functions for a monocentric city from a new set of assumptions, which place restrictions on commuting costs rather than on the demand for land. The utility function is Cobb-Douglas with unrestricted income expenditure shares for land and for the numeraire good. The marginal commuting cost is assumed to be proportional to income-earning potential and exponentially declining in distance from the center at a particular constant rate. These assumptions capture realistic properties of congested cities. Under these assumptions, equilibrium land rent, residential density, and numeraire consumption all decline exponentially with distance, although at different rates. If it is also assumed that traffic speed at the edge of a city is equal to free-flow speed, then the rates of decline in rent, residential density, and numeraire consumption all increase with the city's physical size. We also suggest a new statistical procedure for estimating negative exponential density functions from a cross section of cities of various sizes.