Emergent Cities: A Microeconomic Explanation for Zipf's Law

A model of city formation and evolution is elaborated, based on a multi-agent model of endogenous firm formation. Agents have heterogeneous abilities, are boundedly rational, and interact directly with one another out of equilibrium in team production environments. Each agent works in a firm and each firm has a location. Agents periodically search for positions in other firms that would give them higher utility. Moves between firms are migrations when they involve changes in location. Agents can also start-up new firms if it is welfare-improving to do so. With high probability the location of a new firm is identical with the current location of its founder. However, there is a small chance that a new firm starts up in a different location, with the new location chosen at random. This makes it possible for new cities to occasionally emerge. Over time the movement of individuals across firms combines with the movement of firms across locations to yield clusters of agents and firms in particular locations, i.e., cities. It is demonstrated that under a wide range of conditions these locational clusters reproduce the so-called ÎZipf lawÌ for city sizes, i.e., a Pareto-distribution with exponent 1. This model also yields empirically-significant wage-city size effects, city growth rate distributions, and dependence of city growth rate variance on size. Apparently, this model constitutes the first microeconomic explanation of these phenomena.