Public Finance and Public Policy There are three kinds of individuals in a community: a low risk type (L) whose probabil

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Public Finance and Public Policy
There are three kinds of individuals in a community: a low risk type (L) whose probability of getting
disabled is 5%, a medium risk type (M) whose probability of getting disabled is 10% and a high risk
type whose probability of getting disabled is 60%. If they are not disabled, they can earn an income
of 500/ and in the case they are disabled they will have an income of just 10/
All individuals are risk averse and have a utility function given by In w, where w is the income.
a. What is the actuarially fair premium for types L, M and H respectively?
b. What is the maximum premium that the insurance company can charge so that all types
choose to buy the insurance, given that the insurance company has no means to tell which
individual is of which type?
c. Suppose the community has equal number of citizens belonging to each type. If the insurer
charges the premium amount you calculated in part b above, what will be its profits?