# Notes on discounting

**Notes on discounting**: Rachlin, H. *Journal of the Experimental Analysis of Behavior*, 85, 425-435 (2006).

## Abstract

In general, if a variable can be expressed as a function of its own maximum value, that function may be called a discount function. Delay discounting and probability discounting are commonly studied in psychology, but memory, matching, and economic utility also may be viewed as discounting processes. When they are so viewed, the discount function obtained is hyperbolic in form. In some cases the effective discounting variable is proportional to the physical variable on which it is based. For example, in delay discounting, the physical variable, delay (*D*), may enter into the hyperbolic equation as *kD*. In many cases, however, the discounting data are not well described with a single-parameter discount function. A much better fit is obtained when the effective variable is a power function of the physical variable (*kD ^{s}* in the case of delay discounting). This power-function form fits the data of delay, probability, and memory discounting as well as other two-parameter discount functions and is consistent with both the generalized matching law and maximization of a constant-elasticity-of-substitution utility function.

## Responses

Date"Date" is a type and predefined property provided by Semantic MediaWiki to represent date values. | Author | Lead-in | |
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Behavior-centric versus reinforcer-centric descriptions of behavior | 16 July 2006 | Michael Davison | The paper is a brilliant tour-de-force, but a subtext to the paper is what I will call the behavior-centric view. In this view, stimuli are remembered until a response is emitted, and reinforcers reach back in time to effect this response in the presence of the remembered stimulus... |

*D*), may enter into the hyperbolic equation as

*kD*. In many cases, however, the discounting data are not well described with a single-parameter discount function. A much better fit is obtained when the effective variable is a power function of the physical variable (

*kD<sup>s</sup>*in the case of delay discounting). This power-function form fits the data of delay, probability, and memory discounting as well as other two-parameter discount functions and is consistent with both the generalized matching law and maximization of a constant-elasticity-of-substitution utility function.asticity-of-substitution utility function. +

*Journal of the Experimental Analysis of Behavior*, 85, 425-435 +