Welcome to your study space
Understand economics at your own pace: step-by-step guided courses, and exercises to practice.
GDP per capita
Bringing a country's wealth down to one person.
GDP per capita = GDP / populationProblem / motivation
China produces nearly twenty times more than Switzerland. Yet the average Swiss lives far better than the average Chinese. How can one and the same figure, GDP, say both?
Two words to set down before we go in. GDP is the value of everything a country produces new and that goes through a price — final goods and services — over a year: the size of the “cake” (the course “GDP” builds it step by step). The STANDARD OF LIVING is what inhabitants can actually consume and do, on average — a flow, what passes through in the year, not wealth accumulated over time.
Now, a big cake says nothing about the size of the slices: a very populous country produces a lot simply because it has a lot of people. Hence the tool of this course: dividing GDP by the number of inhabitants — GDP PER CAPITA, the average share of output per person. Why would that share tell us anything about the standard of living? Because output is distributed as income — wages, profits, taxes: more output per head means more income to distribute per head (the course “The three approaches to GDP” shows this circuit). Distributed does not mean distributed equally, nor all of it to households — we shall come back to this.
One last tool, the most important in the course: BIG NUMBERS. One billion = 1,000 million. So BILLIONS divided by MILLIONS give THOUSANDS: 600 €bn shared between 30 million people is 600 ÷ 30 = 20… THOUSAND euros each, that is €20,000. Keep that reflex to hand — the poll turns on it.
Assumptions
In your view, which assumptions are needed for this model to hold? Jot down your ideas — no lead is wrong, this is your worksheet.
Your worksheet is still empty. Go for it: propose at least one idea.
0 idea(s) proposedFormalization
The formula fits into a division — but a division has to be READ. The cake (GDP, in euros) shared between the guests (population, in inhabitants) gives everyone's share: euros divided by inhabitants reads “euros PER inhabitant” — the unit follows the division, just as kilometres divided by hours give km/h. And note what this division manufactures: an “average” inhabitant who does not exist — a convenient fiction, not a real person.
GDP is counted in BILLIONS, population in MILLIONS. Since 1 billion = 1,000 million, write 600 €bn = €600,000 million; divide by 30 million inhabitants: the “millions” on top and bottom cancel out, leaving 600,000 ÷ 30 = 20,000 — plain euros. Hence the shortcut that avoids all the zeros: bn ÷ millions = THOUSANDS. 600 ÷ 30 = 20, answer €20,000.
Like any division, the formula turns over: GDP = GDP per capita × population (and population = GDP ÷ GDP per capita). The big-numbers reflex has its return direction too, worth remembering as a mirror image: THOUSANDS multiplied by MILLIONS give BILLIONS. Check it: €20,000 × 30 million inhabitants → 20 × 30 = 600, thousands times millions → 600 €bn. It closes the loop — the exercises will have you handle the formula in both directions.
Output per head ≈ average standard of living, because output is distributed as income. But an AVERAGE rises as soon as the top rises, even if the person in the middle — the MEDIAN — earns not one euro more. And a territory's output does not all land in the pockets of its inhabitants: a share stays with firms and the government, and in some small countries profits go back abroad (gross national income — GNI — per capita corrects for this). Click each term:
Solving / calculation
France, INSEE's 2024 accounts (INSEE being France's national statistics institute): GDP of 2,919.9 €bn — say 2,920 — for an average population of 68.5 million. Get the calculator out if you need it: your job is the units, not the division. Work through it, then go and check the promise made at the start: China and Switzerland.
- The cake (1 bn = 1,000 million)
GDP = 2,920 €bn = €2,920,000 million - The slices: the average population of the year
population = 68.5 million - Divide — the “millions” cancel out
2,920,000 / 68.5 ≈ 42,600, in plain euros. Shortcut: 2,920 ÷ 68.5 ≈ 42.6 → THOUSANDS of €≈ €42,600 per inhabitant (official 2024 figure: €42,630) - The opening promise, finally in figures — in dollars, the common currency of comparisons (€1 ≈ $1.08 in 2024; source World Bank)
China: $18,730bn / 1,409 m ≈ $13,300 — Switzerland: $970bn / 9 m ≈ $108,000Total: 18,730 ÷ 970 ≈ 19 → China ~19 times Switzerland. Per head: 108,000 ÷ 13,300 ≈ 8 → Switzerland ~8 times China.
The same figure really does say both: total GDP measures size, GDP per capita approximates the average standard of living — and the division reverses the ranking. It is the second, never the first, that we compare between countries.
GDP per capita = GDP / populationVary GDP and population: the average share recomputes itself. Try the orders of magnitude of a giant economy — 18,700 billion (whatever the currency, the mechanism is the same) for 1,400 million inhabitants: the share falls towards 13,400.
Economic interpretation
Dividing by population radically changes how international comparisons read — provided you know what the average says, and what it leaves unsaid.
The 2024 orders of magnitude (in dollars): Switzerland ≈ $108,000 per inhabitant, United States ≈ $86,000, France ≈ $46,000, China ≈ $13,300. The world's 2nd largest economy is far down the PER CAPITA ranking: its output is spread over 1.4 billion people.
Growth in GDP per capita ≈ GDP growth − population growth. +1% of GDP with +2% more inhabitants: the average share falls by about 1%. (The exact computation gives −0.98%: percentages multiply instead of adding up — for small rates, the subtraction is plenty, keep it.) Every country has to grow faster than its population, otherwise everyone grows poorer on average.
The average rises as soon as the highest incomes rise — even if the person in the MIDDLE (the median) earns nothing more. Two tools, two questions: the average tells you the size of theoretical slices, the median tells you what the person “in the middle” actually lives on.
A share of output stays with firms (investment) and with the government (public services); and in some small countries, multinationals' profits inflate GDP and then leave again for abroad — Ireland is the textbook case, and gross national income (GNI) per capita corrects for that effect. Nobody collects “their” GDP per capita as a wage.
Limits / critiques
Exercises
The reflex first: BILLIONS of euros divided by MILLIONS of inhabitants give…
A and B have the same total GDP, but A has twice as many inhabitants as B. A's GDP per capita is…
A country's GDP per capita is €25,000 for 40 million inhabitants. What is its total GDP (in €bn)?
Over the year, a country's GDP rises by 1% and its population by 2%. Its GDP per capita…
Close the opening promise (World Bank, 2024): China ≈ $18,700bn for ≈ 1,400 million inhabitants; Switzerland ≈ $970bn for ≈ 9 million. Who has the higher GDP per capita, and by roughly how many times?
A country has GDP of 600 €bn and 30 million inhabitants. What is its GDP per capita (in €)?
True or false: a country with a larger total GDP necessarily has a higher GDP per capita.
INSEE's 2024 accounts: France's GDP 2,920 €bn, average population 68.5 million. What GDP per capita (in €, to the nearest €100)?
Two countries show the same GDP per capita converted into euros, but prices are markedly lower in country A. Where is the real average standard of living higher?