Perfect competition in a continuous spatial economy

We present a model of spatial adjustments of economic agents across perfectly competitive locations distributed along a continuous geographical space. The evolution of the spatial economy is governed by a set of partial differential equations. We perform a local stability analysis around the uniform steady-state by using the method of normal modes. Examples are presented for the case of two consumer types and two local goods. The spatial stability of the uniform steady-state depends crucially on whether the law of demand holds.