Metropolitan Cablevision Has the Choice of Using One of Three

Metropolitan Cablevision has the choice of using one of three DVR systems.Profits are believed to be a function of customer acceptance.The payoff to Metropolitan for the three systems is: $$\begin{array} { c c c c } &&System\\\underline {\text { Acceptance Level }} & \underline { \mathrm { I } } & \underline { \mathrm { II } } & \underline { \text { III } } \\\text { High } & \$ 150,000 & \$ 200,000 & \$ 200,000 \\\text { Medium } & \$ 80,000 & \$ 20,000 & \$ 80,000 \\\text { Low } & \$ 20,000 & - \$ 50,000 & - \$ 100,000\end{array}$$ The probabilities of customer acceptance for each system are: $$\begin{array} { c c c c } &&System\\\underline {\text { Acceptance Level }} & \underline { \mathrm { I } } & \underline { \mathrm { II } } & \underline { \mathrm { III } } \\ \text { High } & .4 & .3 & .3 \\\text { Medium } & .3 & .4 & .5 \\\text { Low } & .3 & .3 & .2\end{array}$$ The first vice president believes that the indifference probabilities for Metropolitan should be: $$\begin{array} { c c } \text { Amount } & \text { Probability } \\\$ 150,000 & .90 \\\$ 80,000 & .70 \\\$ 20,000 & .50 \\- \$ 50,000 & .25\end{array}$$ The second vice president believes Metropolitan should assign the following utility values: $$\begin{array} { c c } \text { Amount } & \text { Utility } \\\$ 200,000 & 125 \\\$ 150,000 & 95 \\\$ 80,000 & 55 \\\$ 20,000 & 30 \\- \$ 50,000 & 10 \\- \$ 100,000 & 0\end{array}$$
a. Which vice president is a risk taker? Which one is risk averse?
b. Which system will each vice president recommend?
c. What system would a risk neutral vice president recommend?