Question Ce: t 100 and a utility function of the form u(W) = W05 where W represents the payoff from a particular outcome. Suppose that this individual faces a loss of L with probability 0.5. To reduce her risk, she would like to purchase an insurance policy that gives her a payment of B if she suffers the loss. Suppose that the cost of the policy is equal to the the premium, M policy is actuarially fair, what is the premium that insurance companies will charge? (b) [2 marks] Use all of the information above to write down an expression for this indi- vidual's expected utility with the actuarially fair insurance. (c) |6 marks] Let the individual's objective be to choose the optimal insurance payment, B. What is the optimal B? (d) [7 marks] Suppose that for each dollar of benefit paid out, an insurance company incurs an additional fraction > 0 as an administrative cost. The insurance company passes this cost on to the buyer by reducing the benefit paid by a fraction . What is the individual's optimal B in this case? How does it compare to your answer in part (c)? You can assume that the the insurance industry is competitive and the premium will be actuarially fair. (e) [3 marks] Now let L = 40, will this individual prefer having an insurance policy where is greater than zero to not having insurance at all? Explain