Explaining the size distribution of cities: Extreme economies

The empirical regularity known as Zipf's law or the rank-size rule has motivated development of a theoretical literature to explain it. We examine the assumptions on consumer behavior, particularly about their inability to insure against the city-level productivity shocks, implicitly used in this literature. With either self-insurance or insurance markets, and either an arbitrarily small cost of moving or the assumption that consumers do not perfectly observe the shocks to firms' technologies, the agents will never move. Even without these frictions, our analysis yields another equilibrium with insurance where consumers never move. Thus, insurance is a substitute for movement. We propose an alternative class of models, involving extreme risk against which consumers will not insure. Instead, they will move, generating a Fréchet distribution of city sizes that is empirically competitive with other models.