Diffusion of Growth and Cycles in Continuous Time and Space

Spatial economics can be formatted in two different ways. One can see geographical space as a set of locations connected by arcs. Or one can see it as a continuous plane in two dimensions. Activities, such as production and consumption can be represented in both, and so can flows, of trade or migrants. When space is the continuous plane such flows are represented by continuous fields as in physics. The continuous outlook was the traditional both in economics and geography. However, it does not so easily lend itself to computations and fitting to actual data as in the discrete representation. The disadvantage of seeing space as a matrix of locations and connecting arcs is that space, in the sense of geometric shape and size slips out. In the twentieth century there were presented two ingenious economic models using continuous space, Hotelling (A mathematical theory of migration, MA Thesis, University of Washington, reprinted in Environment and Planning A, 10, 1223–1239) who dealt with migration, and Beckmann (1952) who dealt with trade and pricing in a spatially dispersed market. Here we take a simpler case dealing with the diffusion of growth and business cycles in continuous geographical space.