A farmer has $3$ decision options. There is a possible storm coming which could freeze his produce.

The probability of a freeze is $0\mathrm{.}2$ and the probability of non freeze is $0\mathrm{.}8.$ He could take $3$ actions; full

protection, light protection, and no protection. Full protection would cost him $20000$ dollars, light

protection would cost $10000$ dollars and no protection $0$ dollars. Furthermore, if he picks full protection

even with the event of a freeze he would not lose any additional money. If he picks light protection, with

the event of a freeze $25000$ dollars worth of produce would be ruined. If he picks no protection $100000$

dollars worth of produce would be ruined.

A$)$ Assume that the payoff is $(-100,0)$

$U_1=5x+100$

$U_2=(x+100{)}^2$

$U_3=1-e^{-\frac{x}{20}}$

Given the above utilities tell which option is risk seeking, which is

risk averse and which one is risk neutral. Explain all.

B$)$ The utility function of the farmer is exponential with the risk tolerance of $R=20$

Find optimal strategy of the farmer

C$)$ Find the risk premium of farmer. $($Compare EMV of optimal strategy under exponential utility$)$

D$)$ Let us define Expected Value of Perfect Information for risk averse decision maker as:

$($CE$($with information$)-($CE$($without information$)$

What is the EVPI? $($Given perfect freeze event$)$