Simon's Steady State Assumption: A Critique of Okabe's Critique

Abstract

Simon's model of city-size distributions has been a classical way of explaining the rank-size rule. But the steady state condition he uses to solve his model was shown by Okabe to be mathematically inconsistent with the basic postulates of the model. Okabe is correct as long as the difference between individual city size and total population is small. But when t (total number of population units) is only moderately larger than i (individual city size), as it always would be in actual applications of this model, Simon's steady state assumption is found to be very reasonable. Thus, users of the Simon model need not concern themselves with the fine points and complexities of Okabe's exposition since Simon's steady state assumption holds for any value of t that might be empirically observed.