Question

1. Suppose there is a nation which produces and consumes just calculators and notebooks in the following amounts:

	Calculators		Notebooks
	Quantity Produced	Price of each Calculator	Quantity Produced	Price of each Notebook
2018	5	$20	15	$5
2019	6	$30	25	$6

1. Using the CPI, compute the percentage change in the overall price level. Use 2018 as the base year and fix the basket at 2 calculators and 6 notebooks.
2. Using the GDP deflator, compute the percentage change in the overall price level. Also use 2018 as the base year.
3. Is the inflation rate in 2019 the same using the two methods? Explain why or why not.

Answer 1

Answer : 1) Base year is 2018.

CPI = (Market basket at current price level / Market basket at base year price level) * 100

As 2018 is the base year hence the market basket at current price level and base year price level will be same. As a result, the CPI of 2018 is 100.

CPI of 2019 = [{(2 * $30) + (6 * $6)} / {(2 * $20) + (6 * $5)}] * 100 = [96 / 70] * 100 = 1.37 *100

=> CPI of 2019 = 137

% changes in inflation rate = [(CPI of 2019 - CPI of 2018) / CPI of 2018] * 100 = [(137 - 100) / 100] * 100

=> % changes in inflation rate = 37%

Therefore, here the % changes in price level is 37%.

2) Base year is 2018.

GDP deflator = [Nominal GDP / Real GDP] * 100

As 2018 is the base year hence the nominal GDP and real GDP will be same. As a result, the GDP deflator of 2018 is 100.

GDP deflator of 2019 = [{(6 * $30) + (25 * $6)} / {(6 * $20) + (25 * $5)}] * 100 = [330 / 245] * 100 = 1.35 * 100

=> GDP deflator of 2019 = 135

% changes in inflation rate = [(GDP deflator of 2019 - GDP deflator of 2018) / GDP deflator of 2018] * 100 = [(135 - 100) / 100] * 100

=> % changes in inflation rate = 35%

Therefore, here the % changes in price level is 35%.

3) No, the inflation rate of 2019 is different by using two methods.

Because in CPI method the market basket is fixed at 2 calculators and 6 notebooks. But in GDP deflator method the quantity levels are not fixed at 2 calculators and 6 notebooks. Here the GDP deflator is measured based on given table's quantity levels. So, due to differences in quantity levels in two methods the inflation rate is different by using two methods.