decision mThree different investment options are available to a decision maker. The payoff for each option under each of three different market conditions is given in the table. Negative values are given in brackets.

Option a Option b Option c

Poor Some Growth $(10000)16800(20000)12000$

$90009000$

Outcomes under different conditions.

Economic Boom $18500$

$30000$

$9000$

$($a$)$ Using three different decision making criteria, advise on which option would be suitable. Explain the criteria you use.

$($b$)$ If there is a $20\%$ chance of poor conditions, $60\%$ chance of some growth and $20\%$ of boom, calculate the maximum expected gain.

$($c$)$ If it is possible to get a perfect forecast for the market, how much should you pay for this forecast? That is$,$ what is the value of perfect information?