# Hyperbolic Discount function

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.