A small Pacific island holds the entire world stock K of a natural fertilizer. The market price p of the fertilizer varies inversely with the rate at which it is sold, that is,
p = p(x); pʹ(x) where x denotes the number of tons of fertilizer mined and sold per year. Giving equal regard to present and future generations, the island government wishes to choose a rate of exploitation of their natural resource x which maximizes total revenue f(x) from the resource where

What is the optimal exploitation rate?

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f(x)=kp(x), x > 0