1. Solve for the two-period consumer optimization problem when the utility function is given as U (C1, C2) = CfC21_\" and the intertemporal budget constraint is given as C1 + C Y 2 S Y1 + 2. 1+?" 1+?\" (a) Express each period consumption as a function of lifetime income (use Lagrangian and solve for rst-order conditions). (b) What is the complementary slackness condition? What is its implication on the budget constraint? (c) What happens to each period of consumption when the interest rate rises? Provide economic intuition for the e'ects. (d) Assume the zero inlcrcst rate for simplicity and provide a shortcut to your answer in (a) using the property of utility function. 2. Consider an economy with the following Cobb-Douglas production function: Y =KU3L2'3. (a) Derive the equation describing labor demand as a mction of the real wage and the capital stock. (b) The economy has 1,000 units of capital and a labor force of 8,000 workers. Assuming that factor prices adjust to equate supply and demand, calculate the real wage, total output, and the total income earned by workers. (c) Now, suppose that the new president, concerned about the welfare of the working class, passes a law setting a minimum wage that is 10 percent above the equilibrium wage you derived in part (b). What happens to the real wage, employment, output, and the total income earned by workers in this scenario? (no need to derive the numerical values) ((1) Does the president succeed in her goal of helping the working class? Explain why