Question

Let \(\pi^e\) be the expected inflation rate, \(i\) be the nominal interest rate and \(r\) be the real interest rate. Which of the following statements is/are correct?

• A. For small values of \(r\) and \(\pi^e\), \(r \approx i - \pi^e\).
• B. When real interest rate is low, there are greater incentives to borrow and fewer incentives to lend.
• C. Real interest rate reflects the real cost of borrowing.
• D. If \(i = 8%\) and \(\pi^e = 10%\), then \(r\) is approximately (+) 2%.

Hint:

The Fisher equation \(r \approx i - \pi^e\) is a good approximation when inflation is moderate, and it highlights why high inflation reduces real returns.

Answer 1

The Correct Option is A, B, C

Step 1: Recall Fisher equation.
The real interest rate is given by: \[ 1 + r = \frac{1+i}{1+\pi^e} \Rightarrow r \approx i - \pi^e \text{(for small values)}. \] Thus, (A) is correct.
Step 2: Incentives at low real interest rates.
When \(r\) is low, borrowing becomes cheaper in real terms, so people are encouraged to borrow. Lenders, however, earn less in real terms, reducing their incentive to lend. Thus, (B) is correct.
Step 3: Meaning of real interest rate.
The real interest rate accounts for inflation and therefore measures the actual (real) cost of borrowing. Thus, (C) is correct.
Step 4: Check option (D).
If \(i = 8%\) and \(\pi^e = 10%\): \[ r \approx i - \pi^e = 8 - 10 = -2%, \] not \(+2%\). So, (D) is incorrect.
Therefore, the correct answers are (A), (B), and (C).