Exhibit 21-2
Below you are given a payoff table involving three states of nature and two decision alternatives. The probability that S 1 will occur is 0.1; the probability that S 2 will occur is 0.6.
-Refer to Exhibit 21-2. The expected value of perfect information equals
A)12
B)4
C)37
D)29

Question

Exhibit 21-2
Below you are given a payoff table involving three states of nature and two decision alternatives.  The probability that S 1 will occur is 0.1; the probability that S 2 will occur is 0.6.
-Refer to Exhibit 21-2. The expected value of perfect information equals
A)12 
B)4 
C)37 
D)29

Quizplus · Accepted Answer

To calculate the expected value of perfect information, we need to first calculate the expected value of each decision alternative under each state of nature.

For decision alternative 1: 
- Under state of nature SS1U1B11S1U1B0: (0.4 x 10) + (0.6 x 8) = 9.2
- Under state of nature SS1U1B12S1U1B0: (0.4 x 12) + (0.6 x 9) = 10.8
- Under state of nature SS1U1B22S1U1B0: (0.4 x 14) + (0.6 x 5) = 8.6

Expected value of decision alternative 1 = (0.1 x 9.2) + (0.6 x 10.8) + (0.3 x 8.6) = 9.9

For decision alternative 2: 
- Under state of nature SS1U1B11S1U1B0: (0.4 x 11) + (0.6 x 7) = 8.2
- Under state of nature SS1U1B12S1U1B0: (0.4 x 14) + (0.6 x 3) = 5.6
- Under state of nature SS1U1B22S1U1B0: (0.4 x 16) + (0.6 x 1) = 1.6

Expected value of decision alternative 2 = (0.1 x 8.2) + (0.6 x 5.6) + (0.3 x 1.6) = 4.76

Therefore, the best decision is to choose decision alternative 1 with an expected value of 9.9. The expected value of perfect information is calculated by finding the difference between the expected value with perfect information and the expected value without perfect information.

The expected value with perfect information is calculated by finding the expected value of each decision alternative under each possible scenario (SS1U1B11S1U1B0, SS1U1B12S1U1B0, SS1U1B22S1U1B0), assuming that we know which scenario will occur.

For decision alternative 1: 
- If SS1U1B11S1U1B0 occurs, the best decision is to choose alternative 1 with an expected value of 10. 
- If SS1U1B12S1U1B0 occurs, the best decision is to choose alternative 1 with an expected value of 12. 
- If SS1U1B22S1U1B0 occurs, the best decision is to choose alternative 1 with an expected value of 14.

Expected value of decision alternative 1 with perfect information = (0.1 x 10) + (0.6 x 12) + (0.3 x 14) = 12.2

For decision alternative 2: 
- If SS1U1B11S1U1B0 occurs, the best decision is to choose alternative 2 with an expected value of 11. 
- If SS1U1B12S1U1B0 occurs, the best decision is to choose alternative 1 with an expected value of 14. 
- If SS1U1B22S1U1B0 occurs, the best decision is to choose alternative 1 with an expected value of 16.

Expected value of decision alternative 2 with perfect information = (0.1 x 11) + (0.6 x 14) + (0.3 x 16) = 14.3

Therefore, the expected value of perfect information = 14.3 - 9.9 = 4.4, which rounds to 4.

Exhibit 21-2 Below You Are Given a Payoff Table Involving Three States