Jessica will live for two periods. She is only able to work in the first period, when she earns $100. The interest rate between the first and second period is r, meaning that if she saves X in the first period she can consume X(1+r) in the second. Her utility function is U(C1,C2)=C1^Alfa*C2^1-Alfa a. Draw Jessica’s budget constraint. Be as precise and complete as possible. b. How do you expect the amount of Jessica's savings to be related with ?? c. Solve for Jessica's optimal levels of C1 and C2. A social security system is introduced. This system takes an amount Z < W from Jessica in the first period via a payroll tax, sets it aside where it earns an interest rate of r, and returns the proceeds to her in retirement. d. Assume that Jessica can save (at rate r) but cannot borrow. How much will she save, as a function of the size of the Social Security system?