Recommended Methods to Re-Calculate Regional and Total Economic Surpluses after Solving Spatial Equilibrium Models by the Non-Linear Programming Method

The current non-linear programming method does not derive regional economic surpluses and may derive an imprecise maximized value of the total economic surplus. The main reason is that the integrals for supply functions will automatically take regional non-economic producer surpluses into account if any intercepts of supply functions is negative. Consequently, the derived values are always lower than the real regional and total economic surpluses. The unknown regional economic surpluses and the imprecise total economic surplus will limit the suitable application of the model for broader contexts including game theory analysis, international trade policy analysis, and even GDP calculation. This paper recommends two formulae applied for two types of functions, namely original and inverse supply and demand functions, to calculate the regional and total economic surpluses of commodities. The two methods can be converted to each other conveniently, for example by using an inverse matrix of coefficients of original supply and demand functions to solve coefficients of inverse supply and demand functions. A numerical example is used to illustrate the spatial equilibrium model for 2 products and 3 regions with original linear supply and demand functions.