PART III: A SLEEPY CEO The executive board of ABC&Co. wants to extend the contract for its current CEO for 1 year. However, there is some disappointment with the company's performance over the past year, which some attribute to the CEO's habit of taking naps rather than pushing the company's digital transformation plans. To keep the company on track, the executive board wants to incentivize the CEO to exert more effort on the job. a If the CEO chooses low effort (6 = 0), then the sales for the company are projected to be $60 million a If the CEO chooses high effort (6 = 1), then the sales are projected to be $60 million with probability p and $140 million with probability 1 p. Here, we assume p = .8 0 High effort costs the CEO the equivalent of $400, 000 in additional compensation (a year's valuation of a CEO's afternoon naps). 1. One board member proposes paying the CEO a at wage of W = $2 million, irrespective of the effort level. What effort level would the CEO choose under this at wage? What would be the resulting prots for the company (sales CEO pay)? 2. A different board member proposes to pay the CEO using prot sharing: the CEO receives no wage but is entitled to pay equal to 2% of the company's sales at the end of the year. What effort level would the CEO choose? What would be the net prots (sales - CEO pay)? 3. Suppose that, because of the National Association for the Protection of CEOs' Nap, a company like ABC and Co. cannot offer a wage lower than W = $800,000 to the CEO. The CEO gets to decide between taking this at wage and an alternative compensation package oered by the Board. What is the minimum share of prots r% that the Board needs to offer the CEO in order to incentivize the CEO to undertake high effort? What are the company's prots if the Board oers this package