suppose u(W)=ln W for an agent. The agent faces the following gamble with probability 0.5 wealth is 100 and with probability 0.5 a loss occurs so that wealth become 64. the agent can buy any amount of insurance: a coverage of X can be purchased by paying premium r X.

(a) Work out the insurance coverage X that the agent would optimally purchase as a function of r.

(b) plot the optimal X as a function of r.

(c) Calculate the value of r for which full insurance is purchased.

(d) Calculate the value of r for which no insurance is purchased.