Total GDP tells you how much an economy produces (GDP = C + I + G + NX). To compare living standards, divide by the number of people. With GDP in trillions and population in millions, scientific notation keeps the powers of ten straight.
Key idea
$$\text{GDP per person} = \dfrac{\text{GDP}}{\text{population}}$$ It is the most common single measure of average living standards. But GDP leaves out some things that matter for well-being, so it is a useful measure, not a complete one.
Why it works
A country with many people can have a huge total GDP even if each person produces little, and a small country can have a modest total with high output per person. Dividing by population puts countries of different sizes on the same footing. As a growth rate, GDP per person grows by about the growth of GDP minus the growth of population.
Worked examples
Worked example: Dividing with powers of ten
A country's GDP is \$1.8 trillion and its population is 45 million. Find GDP per person.
- $\$1.8 \text{ trillion} = 1.8 \times 10^{12}$ dollars; $45 \text{ million} = 4.5 \times 10^{7}$ people.
- $\dfrac{1.8}{4.5} \times 10^{12 - 7} = 0.4 \times 10^{5} = 40{,}000$.
Answer: \$40,000 per person
Worked example: Growth per person
Real GDP grows 3% in a year and population grows 1%. About how fast does real GDP per person grow?
- Growth of a ratio $\approx$ growth of the top − growth of the bottom.
- $3\% - 1\% = 2\%$.
Answer: About 2%
What GDP leaves out
- Work at home and volunteering: cooking, child care and caring for relatives have no market price.
- Leisure: producing the same output in fewer hours is a gain GDP does not show.
- The environment: pollution and the using up of natural resources are not subtracted.
- How income is shared: an average says nothing about how it is spread across people.
- The underground economy: unreported work is missed.
- Quality and new goods: better products at the same price are hard to measure.
Even so, GDP per person moves closely with many things people care about, such as life expectancy, health and education, which is why economists still use it, alongside other measures.
Common mistake
Treating GDP as a complete measure of well-being, or comparing total GDP across countries with very different populations. Check: before you compare living standards, divide by population; then ask what the number leaves out.