Assume the following:

The price level in 2020 = $100

People expect the price level in 2021 to be = $106

Actual price level in 2021 turns out to be $105

One-year nominal interest rate in 2020 = 5%

Which of the following calculations is correct?

Question

Assume the following:

The price level in 2020 = $100

People expect the price level in 2021 to be = $106

Actual price level in 2021 turns out to be $105

One-year nominal interest rate in 2020 = 5%

Which of the following calculations is correct?

BlackTom AI · Accepted Answer

We start by identifying the key bits of information: the nominal interest rate in 2020 is 5%, and the expected price level in 2021 implies expected inflation of 6% (since 100 -> 106 is a 6% rise). The real interest rate is the nominal rate adjusted for inflation.

Option by option:

Option 1: The real interest rate in 2020 equals +1%. If we subtract expected inflation (6%) from the nominal rate (5%), we get 5% - 6% = -1%, not +1%. This option misapplies the relationship and yields the wrong sign.

Option 2: The real interest rate in 2020 equals -1%. Using the approximation r ≈ i − π^e with i = 5% and π^e = 6% gives r ≈ 5% − 6% = −1%. Even with the exact Fisher approach (r = (1+i)/(1+π^e) − 1 = (1.05/1.06) − 1 ≈ −0.00943, about −0.94%), the result is still negative and close to −1%, so this option correctly captures the direction and magnitude in typical rounding.

Option 3: The real interest rate in 2020 equals +2%. This would require either a higher nominal rate or lower inflation than given. With i = 5% and π^e = 6%, a +2% real rate would contradict the basic relation r ≈ i − π^e, making this option inconsistent with the data.

Option 4: The real interest rate in 2020 equals −2%. While negative real rates are possible, achieving −2% would require i − π^e ≈ −2%, i.e., 5% − 6% ≈ −1%, not −2%. This option moves away from the calculated approximate result based on the provided figures.

Option 5: None of the above. Since Option 2 provides a plausible and commonly accepted calculation given the data (i = 5%, π^e = 6%), this choice would be inaccurate if we accept that calculation as correct.

In summary, applying the standard real-interest calculation with the given nominal rate and expected inflation yields a real rate around −1%, making Option 2 the most consistent choice with the provided information.

Assume the following: The price level in 2020 = $100 People expect the price level in 2021 to be = $106 Actual price level in 2021 turns out to be $105 One-year nominal interest rate in 2020 = 5% Which of the following calculations is correct?单项选择题

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