# Behavioral Finance Hyperbolic Discounting

Hyperbolic discounting is a model based method of quantifying human and even animal propensities for valuing deferred gratification or reward at a lowed level than immediate or faster gratification or reward. “Sooner” has more value than “later”, in hyperbolic discounting.

Another way of describing it is that “…people penalize various options for having a delayed payoff.” 1 It is roughly proportional to the inverse of the delay, as represented by this chart.

There is also exponential discounting, where a set unit of devaluation is assigned to each increment of delay. Hyperbolic discounting has accelerated discounting for the shorter increments of delay, with slower discounting for the longer increments of delay, or a variable quantification of discount based on the length of delay.

Having less of something if it comes a day early, as opposed to waiting a year for and a day for more of it, for example, would make the one day delay less important after a year than it is in the immediate future.

The term “dynamic inconsistency” is used to differentiate hyperbolic discounting from exponential discounting. It refers to inconsistencies in relation to time. People make decisions today, when a different choice would have been preferred by the future self, even though the same reasoning is used both today and in the future.  Future reward is valued more in hyperbolic discounting than in exponential discounting, but decisions are made in the present that favor immediate reward.

The hyperbolic, rather than exponential shape of plotted decisions that are made for less/sooner, more later choices is the basis for the term. (Chung and Herrnstein, 1967).  There is also a hyperbolic shape to spontaneous choices in humans and animals. (Green et al., 1994; Kirby, 1997).

To summarize hyperbolic discounting: If someone offered 10 dollars now and 50 dollars a year from now, most would choose the 10 dollars. But if offered 10 dollars now and 50 dollars a year from now, most would choose the 50 dollars even though the profit in both cases is the same!

It lies in humans problems with understanding logarithmic concepts and a “lens” of distortion of concepts of benefits over time. A benefit that comes 10 years from now is conceptually easier to digest than a benefit that comes 10 years after 30 years from now.

Given a choice between a photo machine that prints out photos in 5 minutes for a dollar each and a photo machine that prints out photos the next day for 50 cents each, most would choose to pay the dollar and get the photos in 5 minutes. In the future, the person would agree that waiting for a day would have been the better option.

There are, however decision making influences that are based on age, the amount of time involved, the reward in relation to the delay, whether money is involved, whether some other form or intensity of gratification or need is involved, and other factors.

One interesting question involves the increasing number of people who will wait for an on line purchase to be delivered, rather than getting immediate gratification from bringing the item home from the store on the same day.

1. Greg Muller, “Hyperbolic Discounting”, The Everything Seminar

Wikipedia, “Hyperbolic Discounting”