Fishery Model

Model Description

This is a standard Gordon-Schaefer model that simulates a simple open-access fishery in discrete time. A fishery stock grows logistically and is harvested by humans. Fishers always exert too much effort and harvest fish at a level that is socially NOT optimal. This happens because fishers are driven to harvest until their net profit drops down to zero. A socially optimal level of harvesting effort is attained when marginal cost of harvesting effort and marginal revenue from harvesting become equal.

Reference

Clark, C. W. (1990). Mathematical bioeconomics: the optimal management of renewable resources (second edi.). New York: Wiley Interscience.

Default Dynamics

(Please describe default dynamics for this model.)

$S_{t+1} = S_t + r S_t (1-S_t) - q S_t E_t$
Fish stock change: fish stock grows logistically and is harvested at a rate $q S_t E_t$.
$E_{t+1} = E_t + E_t ( p q S_t - c )$
Change in harvesting effort: harvesting effort increases when the net profit from harvesting is greater than zero. Otherwise, effort is reduced. 
# simple fishery model

# difference equations
S(t+1) = S + r*S*(1-S) - q*S*E
E(t+1) = E + E*(p*q*S - c)

# parameters: p = price, q = catchability, r = growth rate, c = opportunity cost
init S=1, E=0.1
par p=1, q=1, r=2.5, c=.1

@ xp=S,yp=E
@ total=200
done

Bozicevic M,  Arizona State University. 

You can adjust total time of simulation below.
This model has two state variables. You can set their initial values below.
This model has four parameters. You can set their values below.
Enter the axes to be plotted for this model.