The central bank uses the simple monetary rule to set the real interest rate. You observe that the inflation rate is 2 percentage points below the target inflation rate of 3 percent. You also know that the marginal product of capital is 4 percent.

If the central bank sets the real interest rate to
𝑅
𝑡
=
1
%
, you know that the nominal interest rate is
𝑖
𝑡
=
______ percent.

Hint: Calculate the value of
𝑚
¯
first. Then compute the value of
𝑖
𝑡
.

Question

The central bank uses the simple monetary rule to set the real interest rate. You observe that the inflation rate is 2 percentage points below the target inflation rate of 3 percent. You also know that the marginal product of capital is 4 percent.

If the central bank sets the real interest rate to 
𝑅
𝑡
=
1
%
, you know that the nominal interest rate is 
𝑖
𝑡
=
 ______ percent.

Hint: Calculate the value of 
𝑚
¯
 first. Then compute the value of 
𝑖
𝑡
.

BlackTom AI · Accepted Answer

Question restatement: The central bank uses a simple monetary rule to set the real interest rate. You observe that the inflation rate is 2 percentage points below the target inflation rate of 3 percent. You also know that the marginal product of capital is 4 percent.

Step 1: Determine the observed inflation rate. Target is 3%, and inflation is 2 percentage points below target, so π_t = 3% − 2% = 1%.

Step 2: Use the given real interest rate. The bank sets the real interest rate at R_t = 1% (as stated).

Step 3: Translate to the nominal interest rate. The relation between nominal, real, and expected (or current) inflation in a simple rule is i_t = R_t + π_t. Here, R_t = 1% and π_t = 1%.

Step 4: Compute i_t. i_t = 1% + 1% = 2%.

Additional notes: The marginal product of capital (4%) is provided but does not enter the calculation under the simple rule described, which uses the given real rate and current inflation to determine the nominal rate. The hint about calculating m̄ appears to be referencing a broader framework, but with the data given and the standard i_t = R_t + π_t relationship, the resulting nominal rate is 2%.

FA25 ECON 302 002 Final Exam (Chapters 7-9, 11-13, 19-20): Sample Questions

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