Figure 6.9. (a) The condition g'(N) - SN maximizes the present value of harvest as long as g'(0) is sufficiently big. If it is not (as for S2 in panel (b), drawn for a g(N) that may not be logistic) then the optimal behavior, in terms of maximizing present value, is to drive the stock to extinction.

We integrate by parts according to oo

SN (t)e dt from which we conclude that the present value is dN e-S' dt = N (i)e-SiĀ° + dt lo

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