A simple model of bioeconomic (that is, biological and economic) equilibrium in an open-access fishery in which resource growth is logistic is given by and B − C = PeES − wE = 0 with all variables and parameters defined as in the text of the chapter.

(i) Demonstrate that the equilibrium fishing effort and equilibrium stock can be written as

(ii) Using these expressions, show what happens to fishing effort and the stock size as the

‘cost-price ratio’ w/P changes. In particular, what happens to effort as this ratio becomes very large? Explain your results intuitively.

E g e

w PeS S w Pe = − ⎛

⎝

⎜ ⎞

⎠ 1 ⎟ = MAX and GS g S S ( ) = − S eES ⎛

⎝

⎜ ⎞

⎠ 1 ⎟ − MAX G S gS S S ( ) ln = ⎛

⎝

⎞

⎠

MAX SMAX 1 + ke−gt