Let's solve the problem step by step:

Given Data:

• Investment Cost: $50,000.
• Success Payoff: $200,000 (including investment).
• Failure Payoff: $0.
• Probability of Success: $P(\text{Success}) = 0.50$.
• Probability of Failure: $P(\text{Failure}) = 1 - 0.50 = 0.50$.

(i) Expected Monetary Value (EMV):

The formula for EMV is: $\text{EMV} = \left( P(\text{Success}) \times \text{Payoff in Success} \right) + \left( P(\text{Failure}) \times \text{Payoff in Failure} \right)$

Substitute the values: $\text{EMV} = (0.50 \times 200,000) + (0.50 \times 0) = 100,000 + 0 = 100,000$

Since the cost of investment is $50,000, the net EMV becomes: $\text{Net EMV} = \text{EMV} - \text{Investment Cost} = 100,000 - 50,000 = 50,000$

Answer: The expected monetary value is $50,000.

(ii) Classification of Risk Attitude:

If the person decides not to undertake the investment, despite a positive expected monetary value ($50,000 > 0$), this indicates risk aversion.

• Risk Aversion: The person prefers to avoid potential losses, even when the expected value suggests a favorable outcome.
• EMVer: Refers to someone who bases decisions on the expected monetary value.
• Risk-Taker: Someone who chooses higher-risk options for potentially higher rewards.

Answer: The person is a risk avoider, as they opt out despite a positive EMV.

(iii) EMV with Perfect Information:

If the person has perfect information, they will know in advance whether the venture will succeed or fail. This means:

• If Success is guaranteed, they gain the net payoff: $200,000 - 50,000 = 150,000$.
• If Failure is guaranteed, they will avoid the investment and gain: $0$.

The expected payoff with perfect information is calculated as: $\text{Payoff with Perfect Information} = \left( P(\text{Success}) \times \text{Success Payoff} \right) + \left( P(\text{Failure}) \times \text{Failure Payoff} \right)$

Substitute values: $\text{Payoff with Perfect Information} = (0.50 \times 150,000) + (0.50 \times 0) = 75,000 + 0 = 75,000$

Expected Value of Perfect Information (EVPI):

The EVPI is the difference between the payoff with perfect information and the EMV:

$\text{EVPI} = \text{Payoff with Perfect Information} - \text{EMV}$ $\text{EVPI} = 75,000 - 50,000 = 25,000$

Answer:

• EMV with Perfect Information: $75,000.
• Expected Value of Perfect Information (EVPI): $25,000.

Do you want details on any of the steps? Here are 5 related questions for further exploration:

1. How does probability impact the EMV calculation in decision-making scenarios?
2. What are other examples of risk-averse behavior in real-life investments?
3. Can you explain the difference between "Expected Value of Perfect Information" and "Expected Value of Sample Information"?
4. How can sensitivity analysis help in evaluating risky investments?
5. What role does utility theory play in determining whether a person is risk-averse?

Tip: Always compare EMV with alternative options to make the most informed decision in uncertain scenarios!