Consider two economies: Barylia and Lithasia. The GDP per capita in Li

Consider two economies: Barylia and Lithasia. The GDP per capita in Lithasia is $6,000 while the GDP per capita in Barylia is $12,000. Both countries grow exponentially at an annual rate of 10%.

How will their GDPs vary over the next year? Is there any limitation of comparing the absolute levels of GDP per capita of both countries over the next years? If yes, what is a plausible solution?

ANSWER

The GDP per capita of Lithasia after one year will be $6,000 + $600 = $6,600.
The GDP per capita of Barylia after one year will be $12,000 + $1,200 = $13,200.
Initially, the gap between the GDP per capita of both countries was $12,000 – $6,000 = $6,000.
A year hence, the gap between the GDP per capita of both countries is $13,200 – $6,600 = $6,600.
Hence, over one year, the gap between the GDP per capita of both countries has increased by $600.
Ratio of GDP per capita of Barylia and Lithasia after one year = $13,200/$6,600 = 2 times.
Hence, even after a year, the GDP per capita of Barylia is twice that of Lithasia.
This implies that the relative GDPs of both nations have remained stable although the absolute gap has increased. Thus, comparing absolute levels of GDP per capita does not lead us to an accurate conclusion. In the presence of exponential growth, even though relative GDPs remain stable, the absolute gaps in the GDPs of both countries will increase. For this reason, a better statistic to be considered is the ratio of the GDP per capita rather than comparing the absolute levels of GDP per capita of both countries over time.