l. Solve for the two-period consumer optimization problem when the utility function is given as U (C1, CZ) = Cl\" C21\" and the intertemporal budget constraint is given as 61 + C Y _2 s yl + _2. 1+?" 1+?" (a) Express each period consumption as a function of lifetime income (use Lagrangian and solve for first-order conditions). (b) What is the complementary slackness condition? What is its implication on the budget constraint? (c) What happens to each period consumption when the interest rate rises? Provide economic intuition for the effects. (d) Assume the zero interest rate for simplicity and provide a short cut to your answer in (a) using the property of utility function