A Model of Sequential City Growth

There is strong evidence showing that in most countries cities develop sequentially, with the initially largest cities being the first to grow. This paper presents a growth model of optimal city size that rationalizes this growth pattern. Increasing returns to scale is the force that favors agglomeration of resources in a city, and convex costs associated with the stock of installed capital represent the congestion force that limits city size. The key to generate sequential growth is the assumption of irreversible investment in physical capital. The presence of a positive external effect of aggregate city capital on individual firms makes the competitive equilibrium inefficient.