16. (Symmetric probability o) Suppose the wealth that is to be received at a time 7 in the future has the form W = a+hr+cx where a is a constant and x is a random variable The value of the variable can be selected by the investor. Suppose that the investor has a utility function that is increasing and strictly concave Suppose also that the probability distribution of x is symmetric; that is, x and x have the same distribution. It follows that E(x) = 0 and that the investor cannot influence the expected value of wealth

(a) Show that the optimal choice is h = 0.

(b) Apply this result to the corn farm problem to show that the optimal futures position is +4,000.