On the Mathematics of Utility Theory

Utility theory is a field of economics which hopes to model the innate preferences humans have toward different objects. Though it is most obviously economic in spirit and application, the ever-growing discipline finds its theoretical roots in mathematics. This paper will explore the mathematical underpinnings of basic utility theory by following, divulging, and extending the work of Ok [Real Analysis with Economics Applications, 2007]. We will develop necessary analytic and algebraic concepts, and use this mathematical framework to support hypotheses in theoretical economics. Specifically, we establish classical existence theorems (Rader, Debreu, and von-Neumann Morgenstern) in both utility and expected utility contexts. The paper will require only a firm grasp of real analysis in Rn, elementary group theory and linear algebra, and will proceed assuming no prior knowledge of economic theory