1.10. As chairman of the board of ASP Industries, you estimate that your annual profit is given by the table below. Profit (Π) is conditional upon market demand and the effort of your new CEO. The probabilities of each demand condition occurring are also shown in the table.

You must design a compensation package for the CEO that will maximize the firm’s expected profit. While the firm is risk neutral, the CEO is risk averse. The CEO’s utility function is Utility = W.5 when making low effort Utility = W.5 −100 when making high effort where W is the CEO’s income. (The -100 is the “utility cost” to the CEO of making a high effort.) You know the CEO’s utility function, and both you and the CEO know all of the information in the preceding table. You do not know the level of the CEO’s effort at time of compensation or the exact state of demand. You do see the firm’s profit, however.
Of the three alternative compensation packages below, which do you as chairman of ASP Industries prefer? Why?
Package 1: Pay the CEO a flat salary of $575,000 per year Package 2: Pay the CEO a fixed 6 percent of yearly firm profits Package 3: Pay the CEO a flat salary of $500,000 per year and then 50 percent of any firm profits above $15 million

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Market Demand Low Demand Medium High Demand Demand Market Probabilities .30 .40 .30 Low Effort II-$5 million II-$10 million II-$15 million High Effort =$10 million II-$15 million II-$17 million