Sensitivity analysis for the general spatial economic equilibrium problem

We consider the general spatial economic equilibrium problem where the supplies and demands at each market for each commodity may depend on the price on this as well as other prices of other commodities at other markets and the transportation cost on each link for each commodity may depend on the flow on this as well as other flows of other commodities on other links in the network. For this model we perform stability and sensitivity analysis. Assuming that the supply, demand, and transportation cost functions are monotone, we first show that the multicommodity equilibrium price pattern depends continuously upon the market supply and demand functions and the multicommodity equilibrium shipment pattern depends continuously upon the transportation cost functions. We then focus on the delicate question of predicting the direction of the change in the price and shipment pattern and the incurred supplies, demands, and transportation costs resulting from changes in the supply, demand, and transportation cost functions and we demonstrate that certain phenomena may prevail. Our analysis depends crucially on the fact that the governing equilibrium conditions can be formulated as a variational inequality