Long-Run Urban Growth with Agglomeration Economies

It is widely recognized that agglomeration economies are a crucially important factor in explaining the existence and growth of urban areas, and therefore should be explicitly taken into consideration in long-run urban growth analysis. Once such economies are introduced, however, the urban economy tends to diverge from a steady state equilibrium and may ‘explode’ without limit. A possible way to solve this dilemma is shown. First, a simple urban growth model with production and factor migration functions in the presence of agglomeration economies is set up. It is proved that the urban economy with agglomeration economies tends to approach a kind of balanced growth path in the long run, although the growth rate itself is accelerating without limit. It is also shown that if the total demand for the output of the city is growing at an exogenously given rate, a sustainable steady growth equilibrium exists and is unique and globally stable. Then, land is introduced to show that the availability of the third factor of production will make it more likely to achieve a steady growth equilibrium in the presence of agglomeration economies. Last, the model is generalized to include many factors of production.