Hi,
What is the value of having perfect information? It is only valuable if it improves our decision making process, helping us to earn more money!
If you had perfect information, you would know the state of the environment. If you knew S1 existed, you would make Decision 1 to earn $24; if you knew S2 existed, you would choose Decision 1 to earn $14; likewise, if you know S3 existed, you would choose Decision 3 and earn $15. However, even perfect information doesn't change the fact that there is only a possibility that any one of the three states would exist. The total maximum earnings you could expect with perfect information would be (10% x $24) + (50% x $14) + (40% x $15) = $15.20.
Without this perfect information, you would choose the one decision that yields the highest expected profit. The expected profit for each of the decisions:
Decision 1: (10% x $24) + (50% x $14) + (40% x -$6) = $7.00
Decision 2: (10% x $20) + (50% x $10) + (40% x $5) = $9.00
Decision 3: (10% x -$20) + (50% x $8) + (40% x $15) = $8.00
Without knowing which state, S1, S2 or S3, will exist, you should choose Decision 2 to maximize your expected profits.
With perfect information you would have an expected profit of $15.20, and without it, you would have an expected profit of only $9.00. The 'value' of having the perfect information is only the additional $6.20. You would not pay more than $6.20 to get better information on the state of the environment, because its payoff is only $6.20 more.
Jeanne
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Jeanne David
Academic
Univ of Detroit Mercy
Farmington Hills MI
United States
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Original Message:
Sent: 10-25-2013 03:22 AM
From: Ozge Yagcioglu
Subject: could you please explain the answer?
The solution does not make a sense to me. I could not understand what the logic is, what is trying to be done?
Could you please help me?
Thanks,
Özge
| Question: 23 | The following table contains the profit outcomes for each state of nature and decision combination for a firm:
| States of Nature |
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| S1 | S2 | S3 |
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| | Decision 1 | $ 24 | $14 | $ (6) | | Decision 2 | $ 20 | $10 | $ 5 | | Decision 3 | $(20) | $ 8 | $15 | | Probabilities | 0.10 | 0.50 | 0.40 | The expected value of perfect information for this firm in this case is |
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| Answer (A) is correct.
The first step is to determine the expected value without perfect information by formulating a payoff matrix. For example, the expected payoff for the combination of State of Nature S1 and Decision 1 is $2.40 (10% probability × $24 outcome). The entire payoff matrix is
| S1 | S2 | S3 | Total |
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| | Decision 1 | $ 2.40 | $7.00 | $(2.40) | $7.00 | | Decision 2 | 2.00 | 5.00 | 2.00 | 9.00 | | Decision 3 | (2.00) | 4.00 | 6.00 | 8.00 | Thus, the best decision under conditions of uncertainty is Decision 2 (expected value = $9). If the decision maker knew exactly when each state of nature would occur, the decision would correspond to the maximum profit opportunity for that state of nature. For instance, if S1 is certain, the most profitable decision is Decision 1 ($24). Thus, the expected payoff given perfect information is $15.40. | State of Nature | Profit | Probability | Payoff |
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| | 1 | $24 | 10% | $2.40 | | 2 | 14 | 50 | 7.00 | | 3 | 15 | 40 | 6.00 | The expected value of perfect information is therefore $6.40 ($15.40 - $9.00). | | | | | | | |