Suppose that an investor has the utility function U(X) = l-e 'a" Where a > 0 and the outcome of an investment is a random variable X with mean u, finite variance, and finite moment-generating function (Ma) = E(e'ax), for a > O. Show that the compensatory risk premium and the insurance risk premium have the same value, (1 say, and express (1 in terms of u and the moment-generating function (41. In this case both the Arrow-Pratt and global risk aversions are a. Confirm directly that as aiO, (1 = a Var (X)/2 + 0(a). Under what circumstances is it true that (1 = a Var (X)/2 for all a > 0? Prove that w " w - (141')2 Z 0, and hence that (1 is an increasing function of a. This shows that the more risk-averse the investor is, the higher the value of the premium required