This study employed agency theory and developed a mathematical model to analyze the behavior of managers who smooth earnings when reporting corporate profits. The results revealed that when information asymmetry exists between shareholders and managers, the optimal compensation function proposed by shareholders is influenced by changes in firm performance (Equation 15), and that managers' income smoothing behavior is not a detrimental act but rather an optimal equilibrium behavior that maximizes shareholders' expected utility while satisfying the minimum utility constraint for managers, as it represents a rational response by managers in accordance with shareholders' intentions. Therefore, Pareto optimal equilibrium is achieved when compensation contracts are based on smoothed earnings rather than unsmoothed earnings. Accordingly, this study sought to demonstrate through a mathematical model that managers who possess information about the firm's managerial capabilities engage in income smoothing to reveal the information they hold, and that such income smoothing behavior is also beneficial to shareholders. The difference between this study and the previously developed model of Lambert (1984) lies in the separation of the effect of X₁ into a wealth and risk aversion effect and an information effect for analysis. This model will be of significant assistance to future empirical research and can be utilized as a periodic earnings determination model for professional managers or as a model for resolving conflicts between shareholders and managers.