8. Consider the following decision table under risk, in which the consequences a

Question

8. Consider the following decision table under risk, in which the consequences are monetary payoffs. Consequences Xij States a $100 $110 $120 a2$90$100$120 3 $100 110 $100 Actions Probabilit 1/2 1/4 1/4 Convert this problem into one of choosing between lotteries (a). The decision maker holds the following indifferences with reference lotteries: $100 $120 (0.5) $90 (0.5); $110 $120 (0.8) $90 (0.2) Which action should the decision maker choose Hint: To solve the problem, we need to find u(a1), u(a2) and u(a3) first, and then pick up u(aj) _ that is max We set (assume) utility of money u($120)= 1 and u($90)=0 And find u($100), u($110) from given conditions, i.e., $ 100 $ 120 (0.5): $90 (05) $ 110 $ 120 (0.8): $90 (02) Then u(a1),u(a2) and u(a3)

Explanation / Answer

Ans:

We will make the comparisons of respective actions using Expected monetary payoffs.

Expected monetary payoff of action 1, a1=100*0.25+110*0.5+120*0.25=25+55+30=110

Expected monetary payoff of action 2, a2=90*0.25+100*0.5+120*0.25=22.5+50+30=102.5

Expected monetary payoff of action 3, a3=100*0.25+110*0.5+100*0.25=25+55+25=105

Best monetary payoff is from action a1 i.e. 100, so choose action 1, a1.

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