Question

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?

Short answer

Yes, it is possible for GDP to rise while per capita GDP falls, and for GDP to fall while per capita GDP rises. This can occur when the changes in population and GDP have an inverse relationship. In the first scenario, if the increase in GDP is less than the increase in population, per capita GDP will decrease. In the second scenario, if the decrease in GDP is less than the decrease in population, per capita GDP will increase.

Step-by-step solution

GDP and Per Capita GDP Definitions

GDP (Gross Domestic Product) is the total market value of all goods and services produced within a country in a given period of time. It is usually measured annually. Per Capita GDP is the GDP divided by the population of the country. It is a measure of average individual income and a key indicator of the standard of living in a country. The formula to calculate per capita GDP is: Per Capita GDP = \( \frac{GDP}{Population} \) Now we will analyze the two scenarios.

Scenario 1: GDP rising and per capita GDP falling

For GDP to rise while per capita GDP to fall, we need to examine the relationship between GDP and population in the per capita GDP formula. If the increase in GDP is less than the increase in population, this could cause per capita GDP to decrease. Example: - GDP increases from 100 to 110 (10% increase) - Population increases from 10 to 15 (50% increase) Initial per Capita GDP: \( \frac{100}{10} = 10 \) New per Capita GDP: \( \frac{110}{15} \approx 7.33 \) In this example, GDP increased, while per capita GDP decreased. Therefore, it is possible for the GDP to rise while the per capita GDP falls.

Scenario 2: GDP falling and per capita GDP rising

For GDP to fall while per capita GDP to rise, we need to examine the relationship between GDP and population in the per capita GDP formula. If the decrease in GDP is less than the decrease in population, this could cause per capita GDP to increase. Example: - GDP decreases from 100 to 90 (10% decrease) - Population decreases from 10 to 4 (60% decrease) Initial per Capita GDP: \( \frac{100}{10} = 10 \) New per Capita GDP: \( \frac{90}{4} = 22.5 \) In this example, GDP decreased, while per capita GDP increased. Therefore, it is possible for the GDP to fall while the per capita GDP rises.