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Right now, the market's discounting function is at work.
Unless you project that the economic contraction is forever, the discounting function of the market sooner or later takes over.
Although hyperbolic discounting will arise from a uniform (and infinite) distribution of exponential functions [37, 73, see also Supporting Information Appendix S1], as the number of exponential functions included in the sum decreases, the discounting function deviates from true hyperbolicity.
The independent variable of the subjective-probability discounting function is SP at delay D, not delay D per se.
Several authors utilized a simpler form of hyperbolic probability discounting function by setting s = 1 (simple hyperbolic function, [ 11]): V = A/(1 + kO ).
Several studies found that hyperbolic probability discounting function (Equation 6) fits the behavioral data better than the exponential discount function (Equation 5).
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Indeed, visual comparison of the delay discounting functions for HMMs and LMMs in Fig. 2 bears a striking similarity to previous findings showing reduced delay of gratification for those with various addictions (for example, see the discounting functions for problem gamblers and controls in Alessi & Petry, 2003).
Model fits of how well subjects' discounting functions fit Mazur's [85] nonlinear equation used to derive k values are calculated as R2 values.
Whether the experimental data is sufficiently explained by two exponential discounting functions will require additional experiments on very large data sets capable of determing such differences [45, see discussion in Predictions, below].
In addition to the suggestion that hyperbolic discounting could arise from multiple exponentials proposed here, three explanations for the observed behavioral hyperbolic discounting have been proposed [37]: (1) maximizing average reward over time [5], [71], [74], (2) an interaction between two discounting functions [75] [77], and (3) effects of errors in temporal perception [8], [37].
Model fits of how well subjects discounting functions fit Mazur's equation were calculated as R2 values.
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