question 2

( 10pts) Consider the following utility function: U(W)=lnW, where W is wealth. This function belongs to an individual who has a wealth of $90,000. He faces the possibility of a catastrophic loss of $40,000 of his wealth with probability q. a. What is the value of q, if he can purchase a fair insurance policy that fully compensates him for his loss at a premium of $8,000 ? b. Using your answer in (a), explain with math and graphically whether U[E(W)]>E[U(W)]. c. Using your answer from (a), what is the most this individual would be willing to pay for an insurance policy that fully compensates him for loss