The board of directors of a major corporation is trying to determine how to structure the salary of the new CEO. One option is for the board to offer the new CEO a flat salary of $1 million per year. A second option is to offer a profit-sharing plan with a base salary of $200,000 plus 10% of the firm's profit. If the CEO puts a lot of effort into the job, she will generate a $10 million profit for the firm. If the CEO exerts modest effort, the corporation will earn $7 million in profit. Expending a lot of effort costs the CEO $500,000; expending modest effort costs her $300,000.
a. Draw the extensive-form game tree for the game played between the board and the CEO. Assume that the board moves first, choosing the type of salary offer. Assume that the CEO moves second, choosing her effort level. Be sure to enumerate payoffs to the board (and the shareholders they represent) and the CEO.
b. What is the equilibrium outcome for this game? What kind of contract should the board offer? What level of effort should the CEO choose?