Cities' power laws: the stochastic scaling factor
The power law is a fundamental scaling relationship in the dynamics of organisms and ecological systems. That cities exhibit this law with increasing returns to scale is an empirical finding reported by recent studies. I formulate a microeconomic model of urban systems that supports this evidence assuming a stochastic model, which is based on extreme value theory and random choice to describe all urban agents' rational stochastic behavior and on Alonso's urban economic principles. Thus, the observed superlinear increase in rents and wealth emerges, in addition to the classical scale economies, from individuals' and firms' behavior due to population diversity and size. A dynamic model of cities' growth follows, allowing us to predict the expected evolution of urban organizations.