Changes

Consider Holmstrom's 1982 managerial model, except that the manager knows her productivity parameter from the start. The manager lives for two periods <math>(t = 1, 2)\,</math>. Once she is employed by a firm in period <math>t\,</math>, the firm's production cost is <math>C_t = \Beta - e_t\,</math>, where <math>\Beta\,</math> is the her productivity parameter and <math>e_t > 0\,</math> is the effort she exerts at a cost of <math>\phi(e_t)\,</math> (with <math>\phi' > 0\,</math> and <math>\phi'' > O\,</math>). <math>C_t\,</math> is observable but not verifiable, but <math>\Beta\,</math> and <math>e_t\,</math> are not observed by the firms. The manager's utility is <math>\sum_{t=1}^2 \delta^{t-1}[I_t -\phi(e_t)]\,</math>, where <math>I_t\,</math> is her income at time <math>t\,</math> and <math>\delta\,</math> is her discount factor. Firms are competitive (they derive the same benefit from the manager's activity) and the manager cannot commit to staying with the same firm. It is common knowledge that <math>\Beta \in \{\underline{\Beta}, \overline{\BBeta}\}\,</math>, where <math>\overline{\BBeta} > \underline{\Beta} > 0\,</math>, and <math>Pr(\Beta = \overline{\BBeta})=p\,</math>. Let <math>\Delta\Beta \equiv \overline{\BBeta} - \underline{\Beta}\,</math>, and assume that <math>\phi(\Delta\Beta) < \delta\Delta\Beta\,</math>.