Different Interest Rates for Borrowing and Lending: You first analyzed inter temporal budget constraints with different interest rates for borrowing and saving (or lending) in end of- chapter exercise 3.8.
A. Suppose that you have an income of $100,000 now and you expect to have an income of $300,000 10 years from now, and suppose that the interest rate for borrowing from the bank is twice as high as the interest rate the bank offers for savings.
(a) Begin by drawing your budget constraint with €œconsumption now€ and €œconsumption in 10 years€ on the horizontal and vertical axes. (Assume for purposes of this problem that your consumption in the intervening years is covered and not part of the analysis.)
(b) Can you explain why, for a wide class of tastes, it is rational for someone in this position not to save or borrow?
(c) Now suppose that the interest rate for borrowing was half the interest rate for saving. Draw this new budget constraint.
(d) Illustrate a case where it might be rational for a consumer to flip a coin to determine whether to borrow a lot or to save a lot.
B. Suppose that your incomes are as described in part A and that the annual interest rate for borrowing is 20% and the annual interest rate for saving is 10%. Also, suppose that your tastes over current consumption c1 and consumption 10 years from now c2 can be captured by the utility function u(c1,c2) = cα1 c2(1ˆ’α) .
(a) Assuming that interest compounds annually, what are the slopes of the different segments of the budget constraint that you drew in A(a)? What are the intercepts?

Graph 6.15: Different Interest Rates for Borrowing and Lending
(b) For what ranges of α is it rational to neither borrow nor save?

Cb) t0 5) -(It3) (0