Existence and Stability of City-Size Distribution in the Gravity and Logit Models

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Abstract
An attempt is made to analyze reasons for and consequences of migration under zero population growth by use of a system of simultaneous differential equations. Intercity migration is assumed to take place based upon differences in utilities, where the utility function is expressed as a function of city size. It is revealed that a deterministic specification of the utility leads to an unstable distribution of city sizes, whereas a stochastic specification does not. Existence and stability of equilibria are examined for two representative stochastic migration models: the origin-constrained gravity model and the logit model. It is then argued that population concentration can be explained by an increase in urbanization economies, and population decentralization can be due to a decrease in intercity transportation and communication costs.

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