Model Description
A social-ecological model of a fishing ground open to eco-tourism is presented here. To assess the impact of introducing eco-tourism on the welfare of the fishing association and on the resource level, Lee and Iwasa (2011) constructs a model in which the fishing association charges an entrance fee to tourists. The level of the fee is chosen to regulate tourist number as well as maximing benefits accrued to the fishing association (combined revenue from tourism and conventional fishing by traditional fishers).
Reference
Lee, J.-H., & Iwasa, Y. (2011). Tourists and traditional divers in a common fishing ground. Ecological Economics, 70(12), 2350-2360. Elsevier B.V. doi:10.1016/j.ecolecon.2011.07.013
Scenarios
One interesting case is explored here. Under certain parameter choices, there could be a conflict of interest between traditonal fishers and the fishing association because the total benefit to the fishing association (revenue from tourism and fishing) and the benefits to traditional fishers (revenue from fishing only) are maximized at different parameter values. To see this, set F=1, to=10, alpha=1, p=1, a=0.1, b=1, beta=0.5, r=2, K=100, and q=1. View the change of auxiliary variable 'total benefit' in the y-axis as q (entrance fee) is varied from 0 to 25. Clearly, the total benefit to the fishing association is maximized when q=11. Now, view the change of auxilary variable 'divers' benefit' in the y-axis as q (entrance fee) is varied from 0 to 25. The benefit to traditional fishers is maximized when q=25. Therefore, there occurs a conflict of interest between traditional divers and the fishing association.
$\Large \frac{dX}{dt}=rX \left (1-\frac{X}{K} \right )-aFX-bTX$ |
| Rate of change in fish stock |
$\Large T=t_{o}X^{\alpha}e^{-\beta q}$ |
| Number of tourists visiting the common fishing ground (note: tourists potentially pollute the fishing ground and do some recreational fishing) |
$\Large \phi = paFX+qT$ |
| Total benefit accrued to the community by introducing eco-tourism (collected by their fishing association) |
$\Large \phi_{divers}=paFX$ |
| Benefit accrued to the traditional divers from catching fish in the common ground co-shared with tourists |
#=====define parameters par F=1, txo=10, alpha=1, p=1, a=0.1, b=1, beta=0.5, r=2, K=100 par q=1 #=====define some hidden variables===== #============economic functions #==================demographicfunctions #=====auxiliary quantities================= aux totben=phi aux bendiver=p*a*F*X aux tourist=Tx #======right hand sides #q=p*(K/r)*a*F*b+1/beta Tx=txo*X^alpha*exp(-beta*q) phi=p*a*F*X+q*Tx dX/dt=r*X*(1-X/K)-a*F*X-b*Tx*X #=============initial data init X=1 @ meth=qualrk @ bounds=1000 @ total=25 @ dt=0.1 @ yp=X @ ylo=0,yhi=50 done
Yu JHD, Arizona State University.
Bozicevic M, Arizona State University.
