Fluctuations, Instability, and Agglomeration

Recent models in economic geography suggest that there may be very large numbers of equilibrium spatial structures. Simulations suggest, however, that the structures that emerge are surprisingly orderly, and often seem approximately to follow simple rules about the spacing of urban sites. This paper offers an explanation in terms of the process by which a spatial economy diverges away from an even distribution of activity across the landscape. It shows that a small divergence of activity away from spatial uniformity, even if it is highly irregular, can be regarded as the sum of a number of simple periodic fluctuations at different spatial 'wavelengths'; these fluctuations grow at different rates. There is a particular 'preferred wavelength' that grows fastest; provided that the initial distribution of activity across space is flat enough, this preferred wavelength eventually dominates the spatial pattern and becomes the typical distance between cities. The approach suggests that surprisingly simple principles of self-organization may lie beneath the surface of models that appear at first to yield hopelessly complex possibilities.