You are an owner of a luxurious sailing boat, worth $10 that you use for recreation on Mansfield lake. Unfortunately, there is a good (50%) chance of a tornado in Storrs (probability is equal to) that completely destroys it. Thus, your boat is in fact a lottery with payment (0, 10). (a) What is the expected value of the "boat lottery"? (Give one number.) (b) Suppose your Bernoulli utility function is given by u(c) = c. Give von Neuman - Morgenstern utility function over lotteries U (C, C) (the formula). (c) Your Bernoulli utility function changes to u(c) Morgenstern utility function. (A formula.) = In c. Give the von Neuman- (d) You can insure your boat by buying insurance policy in which you specify coverage x. The insurance contract costs yx and the premium rate is y=. Find analytically and depict in the graph your budget constraint. Mark the point that corresponds to no insurance. . (e) Find optimal level of coverage x. Are you going to fully insure your boat? (Give one number and yes/no answer.) Depict the optimal consumption plan on the graph. . (f) Propose a premium rate for which you will only partially insure your boat. (Give one number.)