4.20. The figure in this problem shows a budget set for a consumer over two time periods, with a borrowing rate rB and a lending rate rL, with rL # rB. The consumer purchases C1 units of a composite good in period 1 and C2 units in period 2. The following is a general fact about consumers making consumption decisions over two time periods: Let A denote the basket at which a consumer spends exactly his income each period (the point at the kink of the budget line). Then a consumer with a diminishing will choose to borrow in the first period if at basket A and will choose to lend if at basket A If the MRS lies between these two values, then he will neither borrow nor lend.

(You can try to prove this if you like. Keep in mind that diminishing MRS plays an important role in the proof.)

Using this rule, consider the decision of Meg, who earns $2,000 this month and $2,200 the next with a utility function given by U(C1, C2) ! C1C2, where the C’s denote the value of consumption in each month. For this utility function and . Suppose rL ! 0.05

(the lending rate is 5 percent) and rB ! 0.12 (the borrowing rate is 12 percent). Would Meg borrow, lend, or do neither this month? What if the borrowing rate fell to 8 percent?

MUC1 ! C2 MUC2 ! C1 MRSC1,C2 6 1 " rL.

MRSC1, C2 7 1 " rB MRSC1, C2