Spatial price equilibrium sensitivity analysis

A direct approach to performing sensitivity analysis for a spatial price equilibrium problem with nonlinear transportation cost, commodity supply and commodity demand functions is presented. The first order derivatives of all decision variables with respect to parameter perturbations are shown to be expressable in a simple from which requires inversion of a matrix whose rank is the number of regions considered. A typical network usually involves several hundred regions and several thousand links; thus, by working with a matrix whose rank depends only on the number of regions rather than the number of links, computer storage is minimized and the necessary matrix inversion is made feasible, enabling us to perform the sensitivity analyses of very large nonlinear equilibrium problems. An example is presented to demonstrate application of the method. The approach taken here is also adaptable to the sensitivity analysis of Wardropian equilibrium problems.