Optimal Solutions of the Three Species Barents Sea Model
Equations (7.42)–(7.44) give the necessary conditions for an interior solution to the maximization problem in Equation (7.6). If such a solution exists, it can be found by solving the three equations for the three state variables, the fish stocks. Unfortunately the non-linearities of Equations (7.42)–(7.44) are too complex for an analytical solution for Xi* (i = 1,2,3) to be found. A simulation program, OPT (see Appendix 11), has been created to find numerical solutions for Xi* (i = 1,2,3) from the three golden rule equations. The partial derivatives of the growth functions with respect to stocks are needed in this computation, and they are shown in Appendix 10.
KeywordsPrice Increase Interior Solution Stock Level Catch Rate Economic Parameter
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