As chairman of the board of ASP Industries, you estimate that your annual
profit is given by the table below. Profit (\Pi) 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.
$$\begin{array}{|lccc|}
\hline \begin{array}{c}
\text { MARKET } \\
\text { DEMAND }
\end{array} & \begin{array}{c}
\text { LOW } \\
\text { DEMAND }
\end{array} & \begin{array}{c}
\text { MEDIUM } \\
\text { DEMAND }
\end{array} & \begin{array}{c}
\text { HIGH } \\
\text { DEMAND }
\end{array} \\
\hline \begin{array}{l}
\text { Market } \\
\text { Probabilities }
\end{array} & .30 & .40 & .30 \\
\hline \text { Low Effort } & \Pi=\$ 5 \text { million } & \Pi=\$ 10 \text {
million } \Pi=\$ 15 \text { million } \\
\hline \text { High Effort } & \Pi=\$ 10 \text { million } & \Pi=\$ 15 \text {
million } \Pi=\$ 17 \text { million } \\
\hline
\end{array}$$
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 yearr Package
2: Pay the CEO a fixed 6 percent of yearly firm profits Package 3
3: Pay the CEO a flat salary of \(\$ 500,000\) per year and then 50 percent of
any firm profits above \(\$ 15\) million