Suppose that the shareholders can hire a board of directors to monitor the CEO. The board of directors cannot perfectly monitor the effort level of the CEO, but hiring the board of directors increases the chance that they observe the true effort level of the CEO. The cost of hiring the board of directors to the shareholders is z. If hired, the board of directors will observe the effort level of the CEO with probability ½. Assume that the CEO can choose from two effort levels: high (e=1) and low (e=0). The cost of each unit of effort is c. Assume that the shareholders will pay a wage of w to the shareholder. However, if the board of directors observes low effort by the agent, then the shareholders will pay a wage of zero to the CEO. If the CEO chooses high effort the shareholders receive a payoff of Y and if the CEO chooses low effort the shareholders receive a payoff of zero. The shareholders first choose to hire the board of directors or not, then the CEO chooses the effort level.
a) Draw the game tree (Hint: only the shareholders and CEO should be in the game tree. The board of directors only influences the payoffs at the end of the tree).
b) If the shareholders hire the board of directors, then what condition must hold for the CEO to choose high effort? (Hint: The payoff for high must be greater than choosing low.)
c) If the shareholders do not hire the board of directors, then what condition must hold for the CEO to choose high effort? (Hint: The payoff for high must be greater than choosing low.)
d) Suppose that the CEO will choose low effort if the shareholders do not hire a board of directors, but will choose high effort if the shareholders do hire a board of directors. What condition must hold for the shareholders to hire a board of directors? (Hint: The payoff for hire given what the CEO will do must be greater than the payoff of not hiring given what the CEO will do).