A Hyperbolic Discounting Utility Function

Abstract

In 1960, an economist named Tjalling C. Koopmans set out to define the postulates necessary and sufficient to assume a discounting model which was already commonly in use in economic theory. This discounting model describes the choices an individual makes as discounted exponentially as time increases. However, there exists empirical research in psychology and behavioral economics which would indicate that the discounting rate people use to make choices is not exponential but instead hyperbolic. That is, that the average discount rate over long intervals is lower than the average discount rate over shorter intervals. Thus, I examine a functional form which includes a declining discount rate. I attempt to define the postulates necessary to assume the hyperbolic model. I begin with a brief digression into the economic history of interest rates to emphasize that discounting is a behavioral norm, discuss the dialog between theorists on the impact and origins of interest rates, and then define my assumptions for the theoretical model