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.

Author Bio

Harshil Sahai graduated from Swarthmore College in 2015 with majors in Mathematics and Economics. Harshil’s paper “On the Mathematics of Utility Theory” was completed as a part of his senior mathematics thesis at Swarthmore. Harshil enjoyed playing as the captain of the Swarthmore squash team, and partakes regularly in philosophical debates and critiquing society with fellow students. Harshil plans to pursue research in Economics at the University of Chicago, before applying to Ph.D. programs in Economics and related disciplines.