## The Value We Place on the Earth

Suppose we can make use of the Earth's resources at the rate of

\[£ A\]

per year. If we assume long term interest rates are \[r %\]

then the present value ofthis years resources is

\[£ A\]

next years resources is

\[£ \frac{ A}{1-1/{(1+ \frac{r}{100}})}\]

the following years resources is

\[£ \frac{ A}{1-1/(1+ \frac{r}{100})^2}\]

and so on. This is a geometric series with first term

\[£A\]

and common ratio \[\frac{1}{1+ \frac{r}{100}}\]

.If we add up the net present value of 75 years use of the Earths resources we obtain the expression

\[S_{75}= \frac{A(1- (1/(1+r/100))^{75})}{1-1/(1+r/100)}\]

.The net present value of all the Earths resources used to eternity is

\[S=\frac{A}{1-1/(1+r/100)}\]

.IN a sense the value we face on the Earth or the value we place on the future is the difference between these two. It is

\[S_{FUTURE} = \frac{A(1/(1+r/100))^{75}}{1-1/(1+r/100)}\]

.If

\[r=5%\]

then \[S_{FUTURE} \simeq 0.026 £A\]

which seems a very low value to put on the Earth, or the future.