A review of the formulation and application of the spatial equilibrium models to analyze policy

Abstract

This paper reviews alternative market equilibrium models for policy analysis. The origin of spatial equilibrium models and their application to wood and wood-processing industries are described. Three mathematical programming models commonly applied to solve spatial problems — namely linear programming, non-linear programming and mixed complementary programming — are reviewed in terms of forms of objective functions and constraint equalities and inequalities. These programming are illustrated with numerical examples. Linear programming is only applied in transportation problems to solve quantities transported between regions when quantities supplied and demanded in each region are already known. It is argued that linear programming can be applied in broader context to transportation problems where supply and demand quantities are unknown and are linear. In this context, linear programming is seen as a more convenient method for modelers because it has a simpler objective function and does not require as strict conditions, for instance the equal numbers of variables and equations required in mixed complementary programming. Finally, some critical insights are provided on the interpretation of optimal solutions generated by solving spatial equilibrium models.

Keywords

simplex method / reduced-gradient / linear programming / nonlinear programming / mixed complementary programming