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


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,






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.



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