The initial wealth is M with the probability of 50% incurring a loss P < M. Buy up to P perfectly divisible units of insurance is allowed, Q, at a price of 0.5 per unit (so Q units of insurance cost Q/50). Their utility function over wealth levels is differentiable and strictly increasing.

(1) Consider the problem of choosing M [0, P] in order to maximisation the expected utility. Describe the economic meaning of this condition when the objective function is concave in Q . Assume this condition holds in what follows.

(2) When the decision maker would be fully insured? Without doing any computations, explain why the decision maker will not fully insure if the price of insurance increases to 0.11 per unit.