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A small business owner has a log utility function,?(?) = ln(?). She faces a 10% chance...

A small business owner has a log utility function,?(?) = ln(?). She faces a 10% chance of having a fire that will reduce her net worth to $1.00, a 10% chance that a fire will reduce her net worth to $50,000, and an 80% chance that her business will retain its value of $100,000.

a. What is the business owner’s expected wealth?

b. What is the utility of expected wealth in this scenario?

c. What is the expected utility of wealth in this scenario?

d. Is this person risk averse? Explain.

e. What is the certainty equivalent of wealth in this scenario and what does this mean?

f. What are the risk premium and cost associated with this gamble?

g. What is the maximum amount she would pay for insurance that ensures her wealth is not affected?

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