Zusammenfassung: Schaefer's model on the exploitation of a single species fish community obeying the logistic law of growth has been modified by adopting an alternative functional form for the harvest rate. The stability of the nontrivial steady state is discussed. The existence of a bionomic equilibrium is proved. The problem for optimal exploitation of the fishery is studied by using variational calculus. Some results are numerically computed to make a comparative study of Schaefer's model and the present one.