GDP per Capita Formula

The \(Gross\ Domestic\ Product\ (GDP)\ per\ capita\) is calculated as follows:

\[ GDP\ per\ Capita = \frac{GDP}{Population} \]

Decomposition of GDP per Capita

GDP per capita can be decomposed into three key components:

\[ \frac{GDP}{Population} = \frac{GDP}{Employment} \times \frac{Employment}{Labor\ Force} \times \frac{Labor\ Force}{Population} \]

Explanation:

• \( \frac{GDP}{Employment} \) = \(Labor_Productivity\) (GDP per worker).
• \( \frac{Employment}{Labor\ Force} \) = \(Employment\ Rate\) (percentage of labor force that is employed).
• \( \frac{Labor\ Force}{Population} \) = \(Labor\ Force\ Participation\ Rate\) (percentage of population in the labor force).

Intuition:

This decomposition helps analyze the sources of economic growth. A country’s GDP per capita can grow due to:

• Increased \(labor\ productivity\) (more output per worker).
• Higher \(employment\ rates\) (more people working in the labor force).
• Greater \(labor\ force\ participation\) (more people actively working or seeking work).

Example Calculation:

Suppose:

• GDP = $10 trillion
• Employment = 200 million workers
• Labor Force = 220 million
• Population = 300 million

The decomposition would be:

\[ \frac{10,000,000,000,000}{300,000,000} = \frac{10,000,000,000,000}{200,000,000} \times \frac{200,000,000}{220,000,000} \times \frac{220,000,000}{300,000,000} \]

By calculating each component, we can see how different factors contribute to GDP per capita.