A Spatial Model of City Growth and Formation

We introduce a model in which city populations grow at rates proportional to the area of their "sphere of influence", where the influence of a city depends on its population (to power α) and distance from city (to power -β) and where new cities arise according to a certain random rule. A simple non-rigorous analysis of asymptotics indicates that for β> 2α$the system exhibits "balanced growth" in which there are an increasing number of large cities, whose populations have the same order of magnitude, whereas for β< 2α$ the system exhibits "unbalanced growth" in which a few cities capture most of the total population. Conceptually the model is best regarded as a spatial analog of the combinatorial "Chinese restaurant process".

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