Abstract
A mathematical model was proposed on the effectiveness of P (performance) and M (maintenance of group itself or human relations) oriented leadership behaviors. It was assumed that P behavior consisted of two sub-categories, i. e., P behavior for improving members' task-related abilities and P behavior for increasing cumulative task achievement, both of which, along with M behavior, were regarded as dynamically determining a dependent variable, the cumulative task achievement. First, it was assumed, in the formulation, that members' abilities and goodness of human relations determined group morale by using production function in economics. Second, it was assumed that group morale was utilized for either improving members' abilities, increasing cumulative task achievement, or improving human relations by the three leadership behaviors respectively. An optimal process that maximized the cumulative task achievement was obtained by using the Pontryagin's maximum principle. Results showed the model could provide plausible interpretation for empirical finding in the past.
