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Hyperbolic discounting is an alternative mathematical model that agrees more closely with these findings. [5] According to hyperbolic discounting, valuations fall relatively rapidly for earlier delay periods (as in, from now to one week), but then fall more slowly for longer delay periods (for instance, more than a few days).
In economics, a discount function is used in economic models to describe the weights placed on rewards received at different points in time. For example, if time is discrete and utility is time-separable, with the discount function f(t) having a negative first derivative and with c t (or c(t) in continuous time) defined as consumption at time t, total utility from an infinite stream of ...
The point at which you forego the money is the social discount rate. Generally, this type of discounting resembles a hyperbolic curve as well. Probability discounting takes the same form, but with risk. Say you were offered a certain $50 or a $100 with a 50% chance of winning it. How about a 60% chance? Probability discounting is likewise ...
Therefore, the preferences at t = 1 is preserved at t = 2; thus, the exponential discount function demonstrates dynamically consistent preferences over time. For its simplicity, the exponential discounting assumption is the most commonly used in economics. However, alternatives like hyperbolic discounting have more empirical support.
The theory states an individual's motivation for a task can be derived with the following formula (in its simplest form): = where , the desire for a particular outcome, or self-efficacy is the probability of success, is the reward associated with the outcome, is the individual’s sensitivity to delay and is the time to complete that task.
Some formulations treat β not as a constant, but as a function β(t) that itself varies over time, for example in models which use the concept of hyperbolic discounting. This view is consistent with empirical observations that humans display inconsistent time preferences.
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In other words, people were found to prefer immediate advantages to future advantages in that their discount over a short period of time falls rapidly, while falling less the more the rewards are in the future. Therefore, people are biased towards the present. As a result, Phelps and Pollak introduced the quasi-hyperbolic model in 1968. [7]