The following is a payoff table giving revenues for various situations.

State 1 State 2 State 3
Probability 0.25 0.4 0.35
Alternative 1 25 50 65
Alternative 2 20 60 45
Alternative 3 40 85 50
Alternative 4 30 50 70
If a person were to use the expected monetary value criterion, what decision would be made?

Question

The following is a payoff table giving revenues for various situations.

​	State 1	State 2	State 3
Probability	0.25	0.4	0.35
Alternative 1	25	50	65
Alternative 2	20	60	45
Alternative 3	40	85	50
Alternative 4	30	50	70
If a person were to use the expected monetary value criterion, what decision would be made?

BlackTom AI · Accepted Answer

To determine the decision under the expected monetary value (EMV) criterion, we must compute the probability-weighted average payoff for each alternative across all states.

Option 1: Calculate EMV for Alternative 1 by weighting each state's payoff by its probability. 25 at State 1 with prob 0.25 contributes 25 × 0.25 = 6.25; 50 at State 2 with prob 0.40 contributes 50 × 0.40 = 20; 65 at State 3 with prob 0.35 contributes 65 × 0.35 = 22.75. Summing these gives EMV = 6.25 + 20 + 22.75 = 49.00.

Option 2: For Alternative 2, compute 20 × 0.25 = 5; 60 × 0.40 = 24; 45 × 0.35 = 15.75. The total EMV is 5 + 24 + 15.75 = 44.75.

Option 3: For Alternative 3, compute 40 × 0.25 = 10; 85 × 0.40 = 34; 50 × 0.35 = 17.5. The total EMV is 10 + 34 + 17.5 = 61.50.

Option 4: For Alternative 4, compute 30 × 0.25 = 7.5; 50 × 0.40 = 20; 70 × 0.35 = 24.5. The total EMV is 7.5 + 20 + 24.5 = 52.00.

Now compare the EMVs across all alternatives. Alternative 1 yields 49.00, Alternative 2 yields 44.75, Alternative 3 yields 61.50, and Alternative 4 yields 52.00. The largest EMV is 61.50 for Alternative 3, making it the preferred choice under the EMV criterion.

In contrast, you can see why the other options are not optimal: Alternative 2 has the lowest EMV among the four, misaligning with a decision framework that weights outcomes by their probabilities; Alternative 1 is better than 2 but still falls short of 3; Alternative 4, while second-best to 3, does not reach the EMV of Alternative 3 due to its state-by-state payoffs and probabilities.

Overall, the decision that maximizes expected monetary value is Alternative 3, given its highest probability-weighted payoff across all states.

类似问题

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