Here are the formulas and explanations for Expected Monetary Value (EMV), Expected Profit with Perfect Information (EPPI), and Expected Value of Perfect Information (EVPI):

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1. Expected Monetary Value (EMV):

$EMV = \sum_{i=1}^{n} P_i \cdot V_i$ Where:

• $P_i$ = Probability of outcome $i$.
• $V_i$ = Value (monetary payoff) associated with outcome $i$.
• $n$ = Number of possible outcomes.

Explanation: The EMV is the weighted average of possible outcomes based on their probabilities. It represents the best estimate of monetary returns under uncertainty.

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2. Expected Profit with Perfect Information (EPPI):

$EPPI = \sum_{i=1}^{n} P_i \cdot \max(V_i)$ Where:

• $\max(V_i)$ = Maximum payoff (profit) for each outcome $i$, assuming perfect knowledge of the state of nature.
• $P_i$ = Probability of outcome $i$.

Explanation: The EPPI calculates the expected profit if you had perfect foresight about which outcome will occur.

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3. Expected Value of Perfect Information (EVPI):

$EVPI = EPPI - EMV$

Explanation: EVPI is the difference between the expected value with perfect information and the expected monetary value. It quantifies the value of eliminating uncertainty by acquiring perfect information.

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Example Calculation

Given Data:

• Outcomes: $V_1 = 100, V_2 = 50, V_3 = -30$
• Probabilities: $P_1 = 0.4, P_2 = 0.3, P_3 = 0.3$

Step 1: Calculate EMV

$EMV = (0.4 \cdot 100) + (0.3 \cdot 50) + (0.3 \cdot -30) = 40 + 15 - 9 = 46$

Step 2: Calculate EPPI

Assume perfect knowledge: $EPPI = (0.4 \cdot 100) + (0.3 \cdot 50) + (0.3 \cdot 0) = 40 + 15 + 0 = 55$

Step 3: Calculate EVPI

$EVPI = EPPI - EMV = 55 - 46 = 9$

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Key Insights:

• EMV gives an average outcome under uncertainty.
• EPPI assumes ideal conditions where uncertainty is eliminated.
• EVPI measures the monetary value of reducing uncertainty.

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Do you want to explore detailed examples or solve a specific problem?

Here are some related questions:

1. How can EMV guide decision-making under uncertainty?
2. What industries use EVPI for strategic planning?
3. How does risk-aversion impact the interpretation of EMV?
4. Can EVPI be greater than EPPI? Why or why not?
5. How does sensitivity analysis affect these calculations?

Tip: Always compare EVPI to the cost of obtaining perfect information. If the cost is higher, it's not worth pursuing!