User:A-tron/maximum economic yield

In biology and economics, maximum economic yield or MEY is the yield (catch) at which a renewable resource is sustainably harvested providing the greatest economic benefit.

Calculating MEY

For a theoretical resource exhibiting logistic growth, we describe population dynamics using the Verhulst population growth model:

${\frac {dN}{dt}}=rX\left(1-{\frac {X}{K}}\right)$

where E is a measure of harvest effort, X is the population biomass, r is the population's intrinsic growth rate, and K is the carrying capacity of the environment.

We then use the Schaeffer catch equation:

$H(E,X)=qEX\$

where H is the annual harvest to define harvest of the resource. The constant q measures the ability to harvest and is similar to the technological progress paramter A in the Cobb-Douglas production function.

Combining the two equations above we have:

$rX-{\frac {rX^{2}}{K}}=qEX$