GENERAL QUASI-EQUILIBRIUM PROBLEM AND ECONOMIC SIGNIFICANCE

Abstract

Balance is an extremely important state of all things. Especially in the economy, the balance between supply and demand is a state that both consumers and producers are always eager to achieve. The equilibrium problem in economics has been studied by many scientists. This paper presents the mathematical model in the form of a general quasi-equilibrium problem of the demand-supply model in economics and proves the existence of the solution of this problem when some conditions are satisfied. The general quasi-equilibrium problem includes many classes of optimal problems that we know as quasi-variational inclusion problem, quasi-variational relation problem, etc. Sufficient conditions for the existence of solutions to general quasi-equilibrium problem were studied by many authors. Here, the author proves the sufficient conditions for the existence of the solution of the general quasi-equilibrium problem when the utility function is a semi-continuous lower mapping based on the basic knowledge of multi-value analysis, especially Hahn - Banach theorem, and fixed point Ky Fan theorem. This is one of the important results of optimization theory.