Suppose you own a company which you expect will earn the following set of state-contingent profits, prior to compensating...

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Suppose you own a company which you expect will earn the following set of state-contingent profits, prior to compensating your company's manager: Pa Low Effort, High Effort Average Economy Profit (average) 33.33% 33.33% $10,000,000 $20,000,000 $12,500,000 $25,000,000 Weak Economy Profit (weak) Good Economy Profit (good) 33.33% $30,000,000 $37,500,000 Expected Profit (E(T)) $20,000,000 $25,000,000 As shown here, state-contingent profits depend jointly on the state of the economy and the manager's effort level. Specifically, if the manager selects a low effort level, then your business is less profitable than when the manager selects a high effort level; specifically, E(low effort) = $20 million compared with E(high effort) = $25 million. The manager's utility U(W) = VW under low effort VW-150 under high effort and her initial wealth is W = $0. Therefore, "minus 50" indicates the manager's disutility associated with expending high rather than low effort. As the risk neutral owner of this company, you wish to maximize expected profit, net of the cost of the manager's compensation. You are considering three mutually exclusive compen- sation schemes: Compensation Scheme #1: a fixed salary of $1,000,000; Compensation Scheme #2: a payment of 7 percent of profits; or Compensation Scheme #3: a salary of $800,000 plus 25% of any profits above $25 million. Calculate the manager's expected utility for each compensation scheme, under low and high effort scenarios. Also calculate expected profit for each compensation scheme, under low and high effort scenarios. As this company's owner, which compensation scheme will you select, and why?