A study of the existence of equilibrium in mathematical economics - Xotyeni, Zukisa Gqabi (Rhodes University, Faculty of Science, Department of Mathematics, 2008)
In this thesis we define and study the existence of an equilibrium situation in which producers maximize their profits relative to the production vectors in their production sets, consumers satisfy their preferences in their consumption sets under certain budget constraint, and for every commodity total demand equals total supply. This competitive equilibrium situation is referred to as the Walrasian equilibrium. The existence of this equilibrium is investigated from a various mathematical points of view. These include microeconomic theory, simplicial spaces, global analysis and lattice theory.
Keywords: Equilibrium (Economics) -- Mathematical models; Macroeconomics -- Mathematical models; Economics -- Mathematical models; Welfare economics -- Mathematical models; Lattice theory; Economics, Mathematical