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DanielleElmas
11 days ago
8

Suppose a family has saved enough for a 10 day vacation (the only one they will be able to take for 10 years) and has a utility

function U = V1/2 (where V is the number of healthy vacation days they experience). Suppose they are not a particularly healthy family and the probability that someone will have a vacation-ruining illness (V = 0) is 20%. What is the expected value of V?
Business
1 answer:
stepan [3K]11 days ago
5 0

Answer:

2 Days

Explanation:

To clarify, we need to restate the utility function for clarity

U=V^{1/2}

1. Probability of an illness occurring in the family is 20%

2. If an illness occurs, the total number of days impacted is calculated as:

Total vacation days = 10 days x Probability of illness = 20%

= 10 x 0.2 = 2 days

This indicates that should an illness occur based on this probability, 2 out of the 10 vacation days will be affected

3. The number of remaining vacation days to enjoy would thus be 10-2 = 8 days

This indicates that even after accounting for 2 days of potential illness, the family can still enjoy their vacation period.

V= 2 days

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