Table 1.

Discounting equations, parameters, and ED50 values for the functions under consideration.

Model Name	Equation	parameters	ED50	Citation
Mazur	E(Y) = 1/(1 + kD)	k	$\frac{1}{k}$	(Mazur, 1987)
Samuelson	E(Y) = e−kD	k	$\frac{\text{ln}\left(2\right)}{k}$	(Samuelson, 1937)
Myerson & Green	E (Y) = 1/(1+kD)s	k, s	$\frac{\left(2^{1/s}-1\right)}{k}$	(Myerson & Green, 1995)
Rachlin	E (Y) = 1/(1+kDs)	k, s	${\left(\frac{1}{k}\right)}^{1/s}$	(Rachlin, 2006)
Laibson*	E (Y) = βδD	β,δ	$lo{g}_{\delta }\left(\frac{1}{2\beta }\right)$	(Laibson, 1997)
Random Noise	E(Y) = c	c	–	–

Note. E(Y) represents the expected indifference point at delay D. Model residuals are assumed Gaussian with constant variance.

^*The Equation for the Laibson model is assumed to hold for D > 0, and E(Y) = 1 when D = 1.