1. (40 points} Consider two consumers, A and B. A and B both want perfect consumption smoothing {c = er) and both have no current wealth. However, the two consumers have different income streams. Person A's current income, YA: = 121}, and iture income, y'x, = 1.56. Person B's current income, ya, is 140, and future income, vrB, = is 132. The real interest rate is 20%- {a}. Calculate the present value of lifetime resources (PVLR) for consumer A and consumer B, respectively. {b}. Draw consumer A's budget constraint- How does the budget constraint of consumer A compare to the budget constraint of consumer B? Explain. {c}. Find consumer A's optimal lifetime consumption plan, (ca, cfx}. How does consumer B's optimal lifetime consumption plan, (ca, era}, compare to consumer A's lifetime consumption plan? Explain. {d}. Is consumer A a current saver or a current borrower? Explain. Is consumer B a current saver or a current borrower? Explain. (e). Draw a graph that illustrates how an increase in the interest rate {above 0.10) will affect the budget constraints of consumer A and consumer B. How does the budget constraint of consumer A. compare to the budget constraint of consumer B