Spatial Economics through a Mathematical Lens: City Structure and the Breakdown of General Equilibrium

In this paper we present contemporary theories of economic geography in their mathematical forms. Specifically, we discuss the agglomeration and dispersion forces that determine city structure and human organization as well as the breakdown of general equilibrium in a spatial economy. We begin with an introduction of basic economic concepts like supply and demand and increasing return to scale. Subsequently, we discuss why traditional general equilibrium theories fail in the context of a spatial economy. We then present some major contemporary economic theories that take geographic factors into consideration and discuss their implications. Real-world examples of these theories are analyzed critically and include the organization of rice farms in Japan, social stratification of cities such as Detroit and Paris, and city shapes in India