#1. A firm has three investment alternatives. Pay offs are in thousands of dollars.U(100)=10 and U(0)=0Economic ConditionsDecision Alternatives Up, s1 Stable, s2 Down, S3Investment A, d1 100 25 0Investment B, d2 75 50 25Investment C, d3 50 50 50Probabilities 0.40 0.30 0.30                                                     Indifference Probability (p)Profit                        Decision Maker A                       Decision Maker B$75,000                          0.80                                              0.60$50,000                          0.60                                              0.30$25,000                          0.30                                              0.15j. What is the expected utility of d1 for decision maker B?k. What is the expected utility of d2 for decision maker B?l. What is the expected utility of d3 for decision maker B?

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Asked Nov 9, 2019
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#1. A firm has three investment alternatives. Pay offs are in thousands of dollars.
U(100)=10 and U(0)=0
Economic Conditions
Decision Alternatives Up, s1 Stable, s2 Down, S3
Investment A, d1 100 25 0
Investment B, d2 75 50 25
Investment C, d3 50 50 50
Probabilities 0.40 0.30 0.30
                                                     Indifference Probability (p)
Profit                        Decision Maker A                       Decision Maker B
$75,000                          0.80                                              0.60
$50,000                          0.60                                              0.30
$25,000                          0.30                                              0.15
j. What is the expected utility of d1 for decision maker B?
k. What is the expected utility of d2 for decision maker B?
l. What is the expected utility of d3 for decision maker B?

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Expert Answer

Step 1

i.

 

The expected utility of d1 for decision maker B is 0.445 and it is obtained below:

 

From the given information, U(100)=10 and U(0)=0. The probabilities are 0.4, 0.3 and 0.3.

For decision maker B, the indifference probabilities are 0.60, 0.30 and 0.15.

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E(d) (0.4)+0.15 (0.3)+0 (0.3) 0.445

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Step 2

j.

 

The expected utility of d2 for decision maker B is 0.3...

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E(d,) 0.60 (0.4)+0.30 (0.3)+ 0.15 (0.3) =0.375

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