13. The following profit payoff table was presented in Problem 1: State of Natur

Question

13. The following profit payoff table was presented in Problem 1: State of Nature Decision Alternative 250 100 S. 100 100 25 75 d, The probabilities for the states of nature are PCs) = 0.65, P(s) = 0.15, and P(s) = 0.20. a. What is the optimal decision strategy if perfect information were available? b. What is the expected value for the decision strategy developed in part (a)? c. Using the expected value approach, what is the recommended decision without perfect information? What is its expected value? d. What is the expected value of perfect information?

Explanation / Answer

Ans:

a)If perfect information weer available,we will choose maximum in each state:

here

s1,250 (max) is given by d1

s2,we can choose either d1 or d2

s3,75(max) is given by d2

b)

Expected value when perfect information is available

=250*0.65+100*0.15+75*0.20

=162.5+15+15

=192.5

c)Without perfect information:

Expected value(d1)=250*0.65+100*0.15+25*0.20=182.5 (maximum)

Expected value(d2)=100*0.65+100*0.15+75*0.20=95

As,expected pay off from d1 aternative is maximum i.e 182.5,so choose d1

d)

Expected value of perfect information=192.5-182.5=10

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