Problem 1: Decision under uncertainty. Consider a riskaverse decision maker with a VNM utility function 1;.(112) over wealth levels to e [0.00). The utility function is increasing and differentiable as many times as required. The decision maker lives for two periods, and does not discount the future. In period 1, the decision maker's income is y > 0 with certainty. In period 2, the income is y 6 with probability 1/2 and y + 6 with probability 1/2, where 6 E (053;). In period 1, the decision maker chooses its savings 3; E [0,y], which means that it consumes y a: in period 1 and y + a: :l: 6 in period 2. a) Provide simple conditions on it such that the decision optimally chooses a positive level of savings in period 1. Explain. b) Assume now that the uncertainty about second period income 3} is more general insofar as it is allowed to have any non-degenerate distribution with a positive lower bound of support and an expected value of lE[g'}] = 1; while maintaining all the other assumptions. Is the condition you provided in a) still sufcient for a positive level of optimal savings? Explain