When analyzing how borrowing and lending affect the consumer's budget constraint, we measure spending in the current time period on the horizontal axis and spending in the future time period on the vertical axis. Assume that the interest rate at which the consumer can lend and borrow is 10%, income in period 1 is $1000 and income in period 2 is $1200. The point of maximum current consumption can be expressed as
A) 1000+ 1200/1.1.
B) 1000(1.1) + 1200.
C) 1000+ 1200 + .1
D) 1000/1.1 + 1200/1.1 + 1.

Question

Quizplus · Accepted Answer

The point of maximum current consumption is the one where the budget constraint is tangent to the highest indifference curve. Given that the interest rate is 10%, we can use the formula for present value of future income to calculate the amount of future income that equals $1 of present income: 1/1.1 = 0.909. Therefore, the budget constraint equation is:
C1 + 0.909C2 = 1000 + 0.909×1200 = 2181.8
The point of maximum current consumption is where this equation intersects the highest indifference curve, which is at C1 = $1636.36 and C2 = $1399.09. To check, we can calculate the present value of this consumption bundle: PV = 1636.36 + 0.909×1399.09 = $3000, which equals total income in both periods.

When Analyzing How Borrowing and Lending Affect the Consumer's Budget