Abstract
A mathematical model is proposed to explain leadership effectivess, depending on the performance-maintenance (P-M) theory of leadership. In the modle, effectivess of P (or M) leader behavior is represented as a logistic equation of P behavior (or M behavior) where a so-called carrying capacity coeffcient was nonincreasing (or nondecreasing) function of P (or M) behavior. Effectiveness of combined P and M behaviors is represented as either (1) the sum of effectiveness of the two behaviors, (2) the product of effectiveness of the two behavior, (3) the sum of marginal effectiveness multiplied by the amount of behavior of P and M behaviors. The latter is assumed more necessities for collaboration among members to be effective. The model reproduces empirical findings in the past that more P behavior combined with more M behavior is most effective on the long term basis and Pbehavior combined with few M behavior is the most effective on the short term basis. Furthermore, it is suggested that more M behavior should be required even on the short term basis in the latter among the three types of the formulation of effectiveness in the above.
