Applications of Optimization Theory to Social Benefit Maximizations in Macroeconomics with Uncertainty

Abstract

In this paper, we use the upward power preorder relation on the power sets of ordered sets to construct a mathematical social benefit maximization model in a fiscal year with respect to the initially planned fiscal budgetary policies and the practically implementation of the fiscal budgetary policies. We only consider the uncertainty case for the social benefit functions. By applying the Fan-KKM Theorem, we prove the existence of a generalized optimal complete feasible fiscal budget policy and the existence of a generalized Pareto optimal complete feasible fiscal policy, respectively.