# ECON 400 Suppose there is a 50-50 chance that a risk averse

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## ECON 400 Suppose there is a 50-50 chance that a risk averse

1. Suppose there is a 50-50 chance that a risk averse individual with a current wealth of

\$20,000 and a utility function of

U(W) = W 1/3

will contract a debilitating disease and suffer a loss of \$10,000.

1. Calculate this individual’s Risk Aversion and Relative Risk Aversion coefficient.Does the measurement mean the person is risk averse, neutral or seeking?
2. Calculate the cost of actuarially fair insurance in this situation and use a general utility of wealth graph to show that the individual will prefer fair insurance against this loss to accepting the gamble uninsured.
3. Suppose two types of policies were available:
1. A fair policy covering the complete loss, meaning \$20,000 minus the cost of a fair insurance policy
2. A fair policy covering only half of any loss incurred, meaning a policy that will cover only \$5,000 in losses, so the cost of this actuarially fair policy will be half of the full coverage policy

Which policy is preferred?  To make this comparison consider the utility of each policy not the expected value.