Investment analysis
Assume an equilibrium fishery where ? = ?A.Consider the two alternatives:

A: Continue the equilibrium situation, where the present value (the discounted flow of profits over all future) with discount rate i is:

B: Stop fishing one period and invest the stock growth in the fish stock. Next period a new equilibrium fishery is established, exactly harvesting the new stock growth, giving a per period profit equal ?B. The present value of case B is:

The two alternatives represents an investment problem: Should the fisher invest in the stock or continue the first equilibrium situation (A)? The investment is

while the benefit of the investment is the difference of the two presents value from next year and throughout all time

which by applying the formula of an infinite geometric series gives

The fisher is indifferent between investing in the stock or continue the equilibrium fishery when the investment equals the gain:

The corresponding continuous time relation is

with a continuous time discount rate

considering the investment of one unit of harvest (for example one kilo). ?(X) is defined by

when total revenue (TR) and total cost (TC) are



Inserting the profit expression into the equilibrium relation above, the golden rule of maximising present value in the fishery is obtained:

In Norwegian: