Consider two consumers, A and B. A and B both want perfect consumption smoothing (c = cf) and both have no current wealth. However, the two consumers have different income streams. Person A's current income, yA, = 100, and future income, yfA, = 121. Person B's current income, yB, is 120, and future income, yfB, = is 99. The real interest rate is 10%.
(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, cfA). How does consumer B's optimal lifetime consumption plan, (cB, cfB), 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?