Urban hierarchies tell us about the general organization of cities and yield some important insights.
Paul Krugman proposes that, in the case of cities, the power law operates according to the percolation theory.
The urban hierarchy has been described in detail in the United States where the power law has held consistently for over a century.
Henderson's model of urban system relies on three sets of factors that influence the size of cities: land inputs, labor, and capital.
Eventually, the greater costs lead to diminishing returns to scale and cities tend towards an optimal equilibrium size, assuming they all share the same attributes.
[5] Henderson relaxed the assumption of identical cities to explore the implications of a diversified economy of traded goods.
The extension of the model underlies the urban system literature and gives rise to the finding that cities will differ in size to account for the factor rewards associated with traded goods of varying degrees of return to scale and intensity of land use.
Examples of primate cities include Paris in France, London in the United Kingdom, and Tokyo in Japan.