Maximizing the Present Value of Resource Rent in a Gordon-Schaefer Model

unit cost of effort

0.4

unit price of harvest

1.5

discount rate δ

0.1

The classical Gordon–Schaefer model presents equilibrium revenue (

TR

) and cost (

TC)

, including opportunity costs of labor and capital, in a fishery where the fish population growth follows a logistic function. Unit price of harvest and unit cost of fishing effort are assumed to be constants. In this case, the open access solution without restrictions (

OA

) is found when

TR=TC

and no rent (abnormal profit,

Π=TR-TC

) is obtained. Abnormal profit (here resource rent) is maximized when

TR'(X)=TC'(X)

(maximum economic yield,

MEY

). Discounted future flow of equilibrium rent is maximized when

Π'(X)/δ=π

, where

π

is the unit rent of harvest and

δ

is the discount rate. This situation is referred to as the optimal solution (

OPT

), maximizing the present value of all future resource rent. The open access solution and

MEY

equilibriums are found to be special cases of the optimal solution, when

δ=∞

and

δ=0

, respectively.