Simon(1952) examined Homan's idea(1950) about the interaction in a soc
ial group and proposed a mathematical model.In this study we tried to
rewrite this Simon-Homans model to take into the results of PM leaders
hip studies. This theory was considered qualitatively in our discussio
n and it was tried mathematically to clarify the questions as follows:
(1) Why is the productivity under PM leadership style including M beh
avior, which doesn't directly connect with the productivity, greater t
han that under P leadership style? (2) Why is M leadership style usual
ly superior than P leadership style on the long term basis! When the t
heoretical model about social behavior is discussed, it is at least ne
cessary to show the existence of the stable solution of the model sati
sfying the results of the field researches. We developed an argument t
o answer these problems.