Exercise: GDP growth rate

Exercise:

Assume that country Y has a population of 458 with a constant yearly (population) growth rate of about 2.8%. Find real GDP per capita and the real GDP growth rate for each year from 2015 to 2019. Describe the relationship between the per capita GDP and the GDP growth rate.

Year	Population	Real GDP	p.c GDP	GDP growth rate
2015	458	$23,457	...	n.a
2016	...	$23,943	...	...
2017	...	$24,035.2	...	...
2018	...	$25,431.1	...	...
2019	...	$24,950.6	...	...

Solution:

Year	Population	Real GDP	p.c GDP	GDP growth rate
2015	458	$23,457	$51.1	n.a
2016	471	$23,943	$50.7	2.06%
2017	483	$24,035.2	$49.8	0.39%
2018	498	$25,431.1	$51.1	5.81%
2019	510	$24,950.6	$48.8	-1.89%

General formula for constant population growth:

$\\ \textit{population}_i= 1.028^n \cdot \textit{population}_0 \\\ \\ \textit{where } n= i-2015$

i stands for year (2015, 2016, etc ...). Example:

$\textit{population}_{2018}= 1.028^3 \cdot 458\approx 498$

To find the per capita GDP divide the GDP of year i by its population. Example:

$\textit{Per capita GDP}_{2016}= \frac{\$ 23,943}{471}\approx \$ 50.7$

GDP growth rate is simply the percentage change between this year's GDP and the GDP from the previous year (remember the formula in the previous lesson?). Then, the GDP growth rate for the year 2019 is:

$\textit{GDP growth rate}_{2019}= \frac{\$ 24,950.6- \$25, 431.1}{\$25, 431.1} \cdot 100 \approx -1.89%$

Notice that in the year 2019, the economy of country Y is contracting (i.e getting smaller).

Lastly, by looking at the columns for p.c GDP and GDP growth rate, describe what pattern you see.

If the GDP growth rate is smaller (bigger) than the population growth rate, the GDP per capita decreases (increases) compared to the previous year.

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