Production of harvest (H) is a production process involving two essential production factors, fishing effort (E, which itself could be produced in a number of different ways) and stock biomass (X, which in the short run is given).

The figure shows the long term relationships in terms of long term catch (red curve on top) and long term stock-effort relationship (red line below). The green curve gives the natural stock biomass growth as a function of stock biomass (F(X)), while the blue lines represent short term catches of different constant fishing effort values (H(E=const.,X)).

The conversion from the short term catch equation to the long term catch equation is obtained by implementing the long term effect on the stock biomass from fishing effort:

Open and free access to a fishery implies that one of the production factors (X, the stock biomass) is freely available even if this is a scarce resource. This is a basic market failure. Another characteristic with a fishery, including an open access fishery, is the long term consequences of previous fishing activities, which implies a relationship between the two input factors. In the long run the stock biomass may be determined by previous use of fishing effort.

"Surplus Production Models and Equilibrium Harvest" from the Wolfram Demonstrations Project

Explore the relation between short term and long term harvest functions in the demonstration to the left.

More on the production function in fishery could be found here: