Suppose that a person can borrow and lend at an interest rate of 10%. But there is a 5% rate of inflation and the person has to pay an income tax of 30% on all interest income. If the person borrows money, he can deduct interest as an expense. Where current consumption is on the horizontal axis and future consumption is on the vertical axis, the budget line will
A) have a kink at the point of no saving or lending.
B) be a straight line with a slope of about -1.02.
C) be a straight line with a slope of about -1.05.
D) be a straight line with a slope of about -1.35.
E) None of the above.

Question

Quizplus · Accepted Answer

Since there is inflation, the effective interest rate becomes 10% - 5% = 5%. The income tax reduces the effective interest rate to 5% × (1 - 0.3) = 3.5%. Therefore, if the person borrows money at 3.5% interest rate, he needs to pay back 1.035 dollars for every dollar he borrows. This means that the budget constraint can be represented by the equation:

Future Consumption = 1.035 × (Current Consumption - Interest Paid)

or

Current Consumption = (1/1.035) × Future Consumption + (1/1.035) × Interest Paid

which is the equation of a straight line with a slope of -1.035/1.035 = -1.02. Hence, the answer is B.

Suppose That a Person Can Borrow and Lend at an Interest