Exercise: inflation and GDP deflator

You have the following table containing information about country Y's GDP deflator, nominal, and real GDP. If the base year is 2015, fill in the blanks and then find the annual inflation rate for each year.

Year	Nominal GDP	GDP Deflator	Real GDP
2015	$23,457	100	$23,457
2016	$25,752	...	$23,943
2017	$25,982	108.1	...
2018	$26,016	...	$25,431.1
2019	$26,323	105.5	...

Solution:

Year	Nominal GDP	GDP Deflator	Real GDP	Inflation rate
2015	$23,457	100	$23,457	n.a
2016	$25,752	107.6	$23,943	7.6%
2017	$25,982	108.1	$24,035.2	0.45%
2018	$26,016	102.3	$25,431.1	-5.37%
2019	$26,323	105.5	$24,950.6	3.13%

GDP deflator for the year 2018:

$\textit{GDP deflator }_{2018}= \frac{ \$26,016}{ \$25,431.1} \cdot 100\approx 102.3$

Real GDP for the year 2017:

$\textit{Real GDP }_{2017}= \frac{ \100}{ \108.1} \cdot \$25,982\approx \$ 24,035.2$

General formula to find real GDP by re-arranging the GDP deflator formula:

$\textit{Real GDP }_{i}= \frac{ \100}{ \textit{GDP deflator}_i} \cdot \textit{Nominal GDP }_i$

Notice that the sub-index i is for the year.

The (annual) inflation rate is simply the growth rate of prices from a year to its previous year:

$\textit{Inflation rate }_{i}= \frac{ \textit{GDP deflator}_i - \textit{GDP deflator}_{i-1}}{\textit{GDP deflator}_{i-1}} \cdot 100$

Inflation rate of the year 2018:

$\textit{Inflation rate }_{2018}= \frac{ 102.3 - 108.1}{108.1} \cdot 100\approx -5.37%$

Notice that in 2018 country Y experienced a negative inflation rate (i.e deflation). This means that from 2017 to 2018 prices dropped by about 5.3%.

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