Qualitative Properties of Systems of Linear Constraints

Systems of linear constraints are examined from a qualitative point of view. A property is said to be qualitative if it holds for all possible parameter values of certain prefixed sign patterns. In economics, such an approach has been traditionally taken within the perspective of comparative static analysis. However, the results obtained in this area appear somewhat limited in practical applicability. This paper extends qualitative approach to the system of linear constraints in general, and presents necessary and sufficient conditions for qualitative feasibility/infeasibility, qualitative boundedness/unboundedness offeasible regions, and qualitative boundedness/unboundedness of objective functions. Duality theorem for linear programming problems is reconsidered from the qualitative point of view. Possible application areas of such an approach are also discussed.