A Note on the Stability of Equilibrium Solutions of Production-Constrained Spatial-Interaction Models

In a recent paper an analysis of the stability of equilibrium solutions of production-constrained retailing models was undertaken by Harris and Wilson. It was argued that by examining equilibrium solutions in response to changes in a parameter, κ, jumps in the value of state variables, analogous to the fold catastrophe, could be expected. In this note it is shown that this is not necessarily always the case, and two different conditions are identified, one that gives rise to jump behaviours, and another that does not. The distinction arises from the nature of the κ parameter.