3 Precautionary Savings Consider a sample case where agents solve the problem: max u(ct) + Elu(c:+1)] subject to the constraints: Ct + St = yt Ct+1 = St + Ut+1 Here we assume that B = 1, r = 0. The utility function takes the form: u(c) = Inc 1. Let y, = 8, and 10 with prob. 0.6 yt+1 = 5 with prob. 0.4 solve for the optimal c, and st 2. Suppose that yt = 8, and the distribution of yt+1 be 12 with prob. 0.6 #++1= 2 with prob. 0.4 Again solve for the optimal ct and st 3. Suppose the form of utility function instead takes the form: "(c) = c2 repeat (1) and (2) and show your results