Question

Given that your current wealth is $10,000 invested in a cupcake shop at Coldwell’s student cafeteria,...

Given that your current wealth is $10,000 invested in a cupcake shop at Coldwell’s student cafeteria, and assuming that there is a 20% chance of an earthquake destroying the business and reducing your investment to $2,453.

a. What is the expected wealth?

b. What would be an actuarially fair market premium?

c. If the certain utility of the expected wealth you calculated in point a) above, is higher than the expected utility, would you buy the insurance given the premium calculated in point b) above? Explain why.

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Homework Answers

Answer #1

a)

Wealth in case of earthquake=W1=$2453

Probability of earthquake=p=0.20

Wealth in case of no earthquake=W2=$10000

Probability of no earthquake=1-p=1-0.20=0.80

Expected wealth=p*W1+(1-p)*W2=0.2*2453+0.8*10000=$8490.60

b)

Loss in case of earthquake=L=(10000-2453)=$7547

Probability of loss=p=0.20

Actuarially fair premium=p*L=0.2*7547=$1509.40

c)

In this case, certain utility of expected wealth is higher than the expected utility. It means that person is risk averse. His certain utility will be higher than the expected utility if he goes for actuarially fair premium.

He will go for actuarially fair premium to avoid risk.

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