Three Decision Makers Have Assessed Payoffs for the Following Decision

Essay

Three decision makers have assessed payoffs for the following decision problem (payoff in dollars).
​ $$\begin{array} { | c | c | c | c | } \hline { \text { Decision Alternative } } & { \text { State of Nature } } \\\hline & s 1 & s 2 & s 3 \\\hline d 1 & 15 & 40 & - 20 \\\hline d 2 & 60 & 80 & - 80 \\\hline\end{array}$$ ​
The indifference probabilities are as follows:
$\begin{array}{cccc}\text { Indifference Probability }(p)\\\text {payoff}& \text { Decision Maker A } & \text { Decision Maker B } & \text { Decision Maker C } \\\hline 80 & \text { Does not apply } & \text { Does not apply } & \text { Does not apply } \\60 & 0.7 & 0.95 & 0.87 \\40 & 0.5 & 0.9 & 0.74 \\15 & 0.3 & 0.8 & 0.59 \\-20 & 0.15 & 0.6 & 0.37 \\-80 & \text { Does not apply } & \text { Does not apply } & \text { Does not apply } \\\hline\end{array}$
a. Plot the utility function for money for each decision maker.
b. Classify each decision maker as a risk avoider, a risk taker, or risk neutral.
c. For the payoff of 40, what is the premium that the risk avoider will pay to avoid risk? What is the premium that the risk taker will pay to have the opportunity of the high payoff?