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The phenomenon of hyperbolic discounting is implicit in Richard Herrnstein's "matching law", which states that when dividing their time or effort between two non-exclusive, ongoing sources of reward, most subjects allocate in direct proportion to the rate and size of rewards from the two sources, and in inverse proportion to their delays. [8]
In behavioral economics, time preference (or time discounting, [1] delay discounting, temporal discounting, [2] long-term orientation [3]) is the current relative valuation placed on receiving a good at an earlier date compared with receiving it at a later date. [1] Applications for these preferences include finance, health, climate change.
The theory emphasizes time as a critical and motivational factor. The argument for a broad, integrative theory stems from the absence of a single theory that can address motivation in its entirety. Thus, it incorporates primary aspects of multiple major theories, including expectancy theory , hyperbolic discounting , need theory and cumulative ...
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 ...
It is calculated as the present discounted value of future utility, and for people with time preference for sooner rather than later gratification, it is less than the future utility. The utility of an event x occurring at future time t under utility function u, discounted back to the present (time 0) using discount factor β, is
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When considering longer time periods, a fixed "pure time preference" discount rate becomes extremely counterintuitive; a 1% rate implies that Tutankhamun should ethically value a single day of his life over the sum total entire lives of everyone living today. Over long periods, peoples' stated preferences become extremely hyperbolic. [4]
Following the classical finite volume method framework, we seek to track a finite set of discrete unknowns, = / + / (,) where the / = + (/) and = form a discrete set of points for the hyperbolic problem: + (()) =, where the indices and indicate the derivatives in time and space, respectively.