An individual with wealth it: faces a possible loss in which all of his wealth dissappears. This happens with probability p = \"12'. Assume that the individual's utility for wealth function is the square-mot function; 1.:(10) = E. An insurer exists who is willing to insure this risk with an indemnity of .2 dollars of coverage if the loss happens, for which the premium is go. Assume that the insurer is risk neutral, that the only costs it faces are indemnity payments, and that it maximises prot by choosing the unit price of coverage q. Coverage is assumed to be restricted between I] and 11:. At all times in the questions that follow, your answers should be given in as reduced form as possible. 1. \"That is the individual's wealth conditional upon the loss happening, and having purchased 0 units of coverage? What is his wealth conditional upon no loss happening, and having purchased :3 units of coverage? Use that information to write down the individual's expected utility of an amount of coverage C. (5 points) 2. Find the individual's optimal demand for coverage as a function of q and 11:. Find the limit values of q for which coverage is w and for which coverage is 0. Is the demand for coverage strictly decreasing in q for all values of 9' between these two limits? Is the demand for coverage concave, convex or linear? Sketch a graph of the demand for coverage. (7 points) 3. Find, in as reduced form as possible, the indirect utility of the insured individual, v(q) E c(c* ((1)), assuming that some insurance is purchased. Evaluate the rst two derivatives of indirect utility with respect to q. Is the individual risk averse for lotteries on the insurance prim? Explain why, or why not. {5 points} 4. Write down the expected prot of the insurer as a function of q {expected prot is expected revenue less expected costs) when the individual de- mands optimal coverage c*(q}. Find the optimal price 1" for the insurer. When you do this, make sure you consider the second-order condition of the insurer's optimisation problem. {4 points) 5. Find the equilibrium amount of coverage (coverage given (1*), the prot of the insurer in the equilibrium, and the level of indirect utility of the individual. Compare the equilibrium indirect utility of the individual with that which he can obtain if no insurance is purchased. (9 points)