2
$\begingroup$

I'm trying to determine my hyperbolic discount function for a given set of my own time preferences. I have determined that I am indifferent between {$}1000 today and {$}1004 tomorrow; {$}1000 today and {$}1020 in a weeks time; {$}1000 today and {$}1040 in a months time and {$}1000 today and {$}1050 in 2 months time. I want to determine if this discount rate is hyperbolic.

Hyperbolic discount functions can be described mathematically as

$$g(D)=\frac{1}{1+kD}$$

where D is the delay and $k$ is the parameter governing the degree of discounting.

Am I right in saying that $k$ can there be found by calculating the percentage difference of the dollar amounts?

I would therefore have 0.004 corresponding ot 1 day; 0.02 corresponding to 7 days; 0.04 corresponding to 30 days and; 0.05 corresponding to 60 days.

Plugging these into the hyperbolic discount function, I get,

$$g_1(D)=\frac{1}{1+0.004(1)}=0.996$$

similarly,

$$g_{7}(D)=\frac{1}{1+0.02(7)}=0.877$$

$$g_{30}(D)=\frac{1}{1+0.04(30)}=0.455$$

$$g_{60}(D)=\frac{1}{1+0.05(60)}=0.25$$

Is this approach correct? Looking at my results, it seems that my hyperbolic discount function declines very quickly in later the later period (30 - 60 days), and I'm not 100% sure if I have interpreted $k$ correctly.

$\endgroup$

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.