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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 $70Suppose that the small business investor assigns prior probabilities of 0.10 to S1, 0.20 to S2, 0.30 to S3 and 0.40 to S4.Based on the above information, what is the expected opportunity loss (EOL) for alternative A1? Note: don't insert the dollar sign ($) 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 190 175−175 -65A3 145−145 -50 120120 110A4 -4040 80 1010 70Suppose that the small business investor assigns prior probabilities of 0.10 to S1, 0.20 to S2, 0.30 to S3 and 0.40 to S4.Based on the above information, what is the expected opportunity loss (EOL) for alternative A1? Note: don't insert the dollar sign ($) when answering the question.

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Solution

To calculate the Expected Opportunity Loss (EOL) for alternative A1, we first need to calculate the opportunity loss for each state of nature for each alternative. The opportunity loss is the difference between the best payoff in a state of nature and the payoff of the alternative in question.

  1. Calculate the best payoff for each state of nature (S1, S2, S3, S4). This is done by selecting the highest profit from all alternatives for each state.

    Best payoff for S1: max(170,170, 30, 145,−145, -40) = 170BestpayoffforS2:max(170 Best payoff for S2: max(45, 190,−190, -50, 80)=80) = 190 Best payoff for S3: max(-60,60, 175, 120,120, 10) = 175BestpayoffforS4:max(175 Best payoff for S4: max(100, -65,65, 110, 70)=70) = 110

  2. Calculate the opportunity loss for A1 in each state of nature. This is done by subtracting the profit of A1 from the best payoff in each state.

    Opportunity loss for A1 in S1: 170−170 - 170 = 0OpportunitylossforA1inS2:0 Opportunity loss for A1 in S2: 190 - 45=45 = 145 Opportunity loss for A1 in S3: 175−(−175 - (-60) = 235OpportunitylossforA1inS4:235 Opportunity loss for A1 in S4: 110 - 100=100 = 10

  3. Calculate the Expected Opportunity Loss (EOL) for A1. This is done by multiplying the opportunity loss in each state by the probability of that state, and then summing these values.

    EOL for A1 = (0.10 * 0)+(0.20∗0) + (0.20 * 145) + (0.30 * 235)+(0.40∗235) + (0.40 * 10) = 0+0 + 29 + 70.5+70.5 + 4 = $103.5

So, the Expected Opportunity Loss (EOL) for alternative A1 is $103.5.

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