Consider the utility function of an individual given by u(x) - ln(x - 10, 000). His...

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Answer 1

Answer #1

Answer:

Utility function U=ln(X-10000)

A)

Marginal utility of wealth=dU/dX=1/(X-10000)

Since as the wealth increases the marginal utility decreases because marginal utility and wealth has inverse relationship. So the person is risk averse.

B)

Total Wealth T= $2,70,000

Worth of House H=$ 1,70,000

If there is no Fire

Total wealth = X=$2,70,000

If there is Fire

Total Wealth = X=T-H=2,70,000-1,70,000=$1,00,000

So expected utility E(U)=(1-Probability of fire)*U(2,70,000)+ Probability of Fire*U(1,00,000)

E(U)=90%*ln(270000-10000)+10%*ln(100000-10000)=11.22+1.14=12.36

Wealth for Expected Utility = e^(12.36)+10000=$243281.23

Insurance premium=270000-243281.23=$26718.77

fair Premium =10%*1,70,000=$17000

So risk Premium =Insurance Premium - Fair Premium =26718.77-17000=$9718.77

C)

Risk Premium =Insurance Premium - Fair Premium

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Consider the utility function of an individual given by u(x) - ln(x - 10, 000). His...

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Consider the utility function of an individual given by u(x) - ln(x - 10, 000). His...

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