3. A consumer's income in the current period is y = 25C! and her income in the future period is y" = 3130. The real interest rate r is [1.05, or 5%, per period. Assume there are no taxes. Suppose that the utilit},r function is Hit... E!) : VJE + ,'g/E and let = [1.9. {a} Determine the consumer's lifetime wealth we {present discounted value of life time income]. Write down the lifetime budget constraint. {b} Derive the Marginal Rate of Substitution between c and c". {c} Write down the consumer maximization problem. What is the objective func- tion? \"That are exogenous variables? \"that are endogenous {choice} variables? {d} Solve for c" as a flmction of s using the lifetime budget constraint. Replace it into the objective flmction so that the problem only depends on c. {e} Take the rst order condition with respect to c and use it to nd c\" and c\". {f} Is this agent a borrower or a saver? Compute her optimal savingsfborrowings using the computations above and her budget constraint