Is it possible for GDP to rise while at the same time per capita GDP is falling? Is it possible for GDP to fall while per capita GDP is rising?

To assess this possibility, we can consider the following equation for per capita GDP: Per capita GDP = \(\frac{GDP}{Population}\) If GDP increases while per capita GDP decreases, it means that population change must have a greater impact on the equation. Therefore, the population must increase at a higher rate than the GDP increase. For example, let's take two scenarios: Scenario A (Initial): GDP = 100 Population = 10 Per capita GDP = \(10\) Scenario B (Subsequent): GDP = 120 (20% increase) Population = 15 (50% increase) Per capita GDP = \(8\) In this example, GDP has increased by 20%, while the population increased by 50%. Consequently, per capita GDP has decreased from 10 to 8, showing that it is possible for GDP to rise while per capita GDP is falling.

Now let's consider a case where the GDP falls, and per capita GDP rises. We can use the same per capita GDP equation: Per capita GDP = \(\frac{GDP}{Population}\) In this situation, if GDP decreases while per capita GDP increases, it means that the population change has a more significant impact on the equation than the GDP change. Therefore, the population must decrease at a higher rate than the GDP decrease. Let's consider two scenarios to illustrate this: Scenario C (Initial): GDP = 100 Population = 10 Per capita GDP = \(10\) Scenario D (Subsequent): GDP = 90 (10% decrease) Population = 8 (20% decrease) Per capita GDP = \(11.25\) In this example, GDP has decreased by 10%, while the population has decreased by 20%. Consequently, per capita GDP has increased from 10 to 11.25, demonstrating that it is possible for GDP to fall while per capita GDP is rising.