Optimal Solutions of the Three Species Barents Sea Model

Abstract

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 X_i* (i = 1,2,3) to be found. A simulation program, OPT (see Appendix 11), has been created to find numerical solutions for X_i* (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.