Problem 1 Consider a consumer whose preferences over (C1, T2) state-contingent consumption bundles are represented by an expected utility function EU(X1, X2 | 71, 72) = 71 . u(X1) + 72 . u(12) where u : R - R is a utility function for monetary payoffs. Consider the following specifications of expected utility functions: (a) EU(X1, X2 | 71, 12) = 71 . (21) 3 + 12 . (12)3, (that is, u(x) = x3 for any x ( R) (b) EU(X1, 12 | 71, 72) = 01 . X1 + 72 . 12, (that is, u(x) = r for any r ER) (c) EU(X1, X2 | 71, 72) = 71 . (21)3 + 72 . (12)3, (that is, u(x) = 23 for any r ( R) Consider the lottery that returns $1 in state 1 and $8 in state 2 with the following probability distribution over states: m1 = = and 2 = 3. For each case (a), (b) and (c), determine the certainty equivalent of the lottery and the consumer's attitude towards risk