On the birth and growth of cities:. Laissez-faire and planning compared

In a growing laissez-faire economy, the optimal time when the large cities should be decentralized into new settlements is missed because such timing requires collective migration to the same place by many self-interested agents. New cities are born at stochastically determined times when existing cities are larger than their optimal sizes and unstable. With negligible migration costs, such city births are associated with panic-migrations and related economic shocks. Thus, laissez-faire city systems develop in cycles of booms and busts. The planned timing of settlements smooths these cycles by rounding the tops and raising the troughs in the per capita utility profile over time.Efficient growth requires alternating cycles of laissez-faire and planning. Planning establishes each new city at the optimal time and nurses it through an initial period of instability. As the economy grows large, the duration of the necessary planning periods vanishes asymptotically. In a declining laissez-faire economy, cities are abandoned at deterministic times and at smaller sizes than the sizes at which they would be born during growth. The decline path cannot be obtained by reversing the growth path, and a hysteresis effect is present.