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.
Linda Chen, Associate Professor, Department of Mathematics and Statistics, Swarthmore College
"On the Mathematics of Utility Theory,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 16
, Article 10.
Available at: https://scholar.rose-hulman.edu/rhumj/vol16/iss1/10