Specific Electric Co. asks you to implement a pay-for-performance incentive contract for its new CEO. The CEO can either work hard with a personal cost of $200,000 or reduce her effort, thereby avoiding the personal cost. The CEO faces three possible outcomes: her company experiences good luck with probability 0.3, medium luck with probability 0.4, or bad luck with probability 0.3. Although the management team can distinguish the three "states" of luck as the quarter unfolds, the compensation committee of the board of directors (and the shareholders) cannot do so. Sometime thereafter, the CEO decides to expend high or low work effort, and one of the observable shareholder values then results.
Shareholder Value
Good Luck (30%) Medium Luck (40%) Bad Luck (30%)
High CEO Effort $1 billion $800 million $500 million
Low CEO Effort $800 million $500 million $300 million
Assume 10 million shares and a $65 initial share price, implying a $650,000,000 initial shareholder value. Since the CEO's effort and the company's luck are unobservable to the owners and company directors, it is not possible upon observing a reduction to $50 share prices and $500,000,000 value to distinguish whether the company experienced low CEO effort and medium luck, or high CEO effort and bad luck. Answer the following problems from the perspective of a member of the compensation committee who is aligned with shareholder interests and is deciding on bonus plans for the CEO
Answer the following problems:

1. What is the maximum amount it would be worth to shareholders to elicit high CEO effort all the time rather low CEO effort all the time?

2. If you decide to pay 1% of this amount (in problem 1) as a cash bonus, what performance level (what share price or shareholder value) in the table should trigger the bonus? Suppose you decide to elicit high CEO effort when and if medium luck occurs by paying the bonus for $800 million outcomes. What criticism can you see with this incentive contract plan?

3. Suppose you decide to elicit high CEO effort when and if good luck occurs by paying the bonus for $1 billion outcomes only. What criticism can you see with this incentive contract plan?

4. Suppose you decide to elicit high CEO effort when and if bad luck occurs by paying the bonus for $500 million outcomes. What criticism can you see with this incentive contract plan?