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Suppose a small business investor has a certain amount of money available to invest now. Four alternative investments are available. Th estimated profits of each investment under each economic condition are indicated in the following table.Alternatives States of NatureS1 S2 S3 S4A1 $170 $45 -$60 $100A2 $30 $190 $175 -$65A3 $145 -$50 $120 $110A4 -$40 $80 $10 $70Based on the above information, what would be the amount of regret, if alternative A3 is selected by the investor and suppose that the state of nature turns out to be S1? Note: don't insert the dollar sign ($) when answering the question.

Question

Suppose a small business investor has a certain amount of money available to invest now. Four alternative investments are available. Th estimated profits of each investment under each economic condition are indicated in the following table.Alternatives States of NatureS1 S2 S3 S4A1 170170 45 -6060 100A2 3030 190 175175 -65A3 145145 -50 120120 110A4 -4040 80 1010 70Based on the above information, what would be the amount of regret, if alternative A3 is selected by the investor and suppose that the state of nature turns out to be S1? Note: don't insert the dollar sign ($) when answering the question.

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Solution

To calculate the regret, we first need to identify the best outcome in state of nature S1. Looking at the table, we can see that the best outcome in S1 is $170 (from alternative A1).

The regret is calculated as the difference between the best outcome and the actual outcome. If the investor chooses alternative A3 and the state of nature turns out to be S1, the actual outcome is $145.

So, the regret would be 170(bestoutcome)170 (best outcome) - 145 (actual outcome) = $25.

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