supposes that a borrower and a lender agree on the nominal interest rate to be paid on a loan. Then inflation turns out to be higher than they both expected. Using a method similar to the GDP deflator, compute the percentage change of the overall price level. Also use 2009 as the base year.Is the inflation rate in 2010 the same using the two methods? Explain why or why not.
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To compute the percentage change of the overall price level using a method similar to the GDP deflator, we need to compare the nominal interest rate agreed upon to the real interest rate, which adjusts for inflation.
1. Calculate the real interest rate:
- Subtract the expected inflation rate from the nominal interest rate.
- For example, if the agreed nominal interest rate is 7% and the expected inflation rate is 3%, the real interest rate would be 7% - 3% = 4%.
2. Calculate the GDP deflator:
- The GDP deflator measures the overall price level in an economy.
- Divide the nominal GDP by the real GDP and multiply by 100. This gives the GDP deflator.
- For example, if the nominal GDP is $2 trillion and the real GDP is $1.8 trillion, the GDP deflator is (2 / 1.8) * 100 = 111.11.
3. Calculate the percentage change of the overall price level:
- Take the GDP deflator for the current year and subtract the GDP deflator for the base year. Divide this difference by the GDP deflator of the base year and multiply by 100.
- If the GDP deflator for 2010 is 115 and the GDP deflator for 2009 (base year) is 100, the percentage change of the overall price level would be ((115 - 100) / 100) * 100 = 15%.
Now, to answer the question whether the inflation rate in 2010 is the same using the two methods (nominal interest rate and GDP deflator), we need to understand that the nominal interest rate reflects the inflation expectation at the time the loan was agreed upon, while the GDP deflator measures the actual inflation rate.
In this case, if the inflation turns out to be higher than expected by both the borrower and the lender, it means the actual inflation rate would be higher than the expected inflation rate used to calculate the real interest rate. Therefore, the inflation rate calculated using the nominal interest rate method would likely be lower than the inflation rate calculated using the GDP deflator method.
So, the inflation rate in 2010 would not be the same using these two methods because they utilize different factors. The nominal interest rate method relies on the expected inflation rate, while the GDP deflator method examines the actual changes in the overall price level.