Suppose a CEO is hired to manage a large car company. The shareholders for the company agree to pay the CEO a wage of w. After receiving the wage, the CEO can choose an effort level e. There is a cost, c, per unit of effort expended by the CEO. For each unit of effort expended by the CEO the shareholders receive a payoff of Y. Since the company is so large, it is difficult for the shareholders to know whether the CEO is expending high effort or not. Assume that both the shareholders and CEO only care about their own payoffs
a) Write the utility functions for the shareholders and the CEO
b) Find the equilibrium predictions for the wage, w, offered by the shareholders and the effort level, e, chosen by the CEO using backward induction.