Three 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.

Poor Some Growth Economic Boom

Option a $(10000)1680018500$

Option b $(20000)1200030000$

Option c $900090009000$

Outcomes under different conditions.

$($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?