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Understand economics at your own pace: step-by-step guided courses, and exercises to practice.
GDP growth
How fast does an economy grow richer?
g = (GDP₂ − GDP₁) / GDP₁ × 100Problem / motivation
“2% growth” — you hear it all the time. But is 2% a lot, a little, and over what stretch of time does it really add up?
A small percentage repeated every year has a spectacular effect: each increase applies to a total that has already grown, like a snowball getting bigger as it rolls. Mathematicians say growth is “exponential” — it multiplies from year to year — rather than “linear” — it does not merely stack the same amount on top every year.
Three words before we go on. GDP — the value of everything newly produced in the country over a period (the subject of the course “GDP”) — serves here as the measure of output. We take it REAL, that is, corrected for inflation — the general rise in prices — so as to keep only the quantities produced, “in volume”: raw, at today's prices, GDP is called “nominal”, and that nominal → real step is the subject of the previous course, “Nominal vs real GDP”.
GROWTH, finally, is the change in real GDP from one period to the next, expressed as a percentage: it is the rate, written g, that this course teaches you to compute and to read.
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
First, put a name on the letter: g (for growth) is the growth rate. The formula states a simple sentence: take the change in real GDP — the finish minus the start —, relate it to the starting point — that is, DIVIDE it by that starting point —, and multiply by 100 to express it as a percentage. It is a rate of change, the same tool that measures the rise in a rent or a wage.
Second tool, the multiplying coefficient: “+4%” means “× 1.04”, “−4%” means “× 0.96”. You go from the rate to the coefficient by adding it to 1 (4% = 0.04; 1 + 0.04 = 1.04). As a result, the formula also reads the other way round: GDP₂ / GDP₁ gives the coefficient directly — 2,828 / 2,800 = 1.01 — and the rate follows: +1%.
That detour pays off straight away: successive growth rates MULTIPLY (through their coefficients), they do not add up (through their percentages). +4% then +5% is × 1.04 × 1.05 = × 1.092, that is +9.2% — not +9% — because the second increase applies to an amount already increased. This is the snowball effect announced at the start.
And the famous 70? Doubling means reaching a coefficient of 2. Multiplying by 1.02 year after year, you get there in about 35 years; the mathematics (the natural logarithm of 2 is 0.693…) shows that, roughly, doubling time ≈ 70 / rate. It is an approximation, a very good one for small rates — and 70 was preferred to 69.3 because you can divide by it in your head. Click each term:
Solving / calculation
Real GDP goes from 2,800 to 2,828 €bn (billions of euros, written “€bn”). What growth is that? Then try other values.
- Change
2,828 − 2,800+28 €bn - Related to the start
28 / 2,8000.01 - As a percentage
0.01 × 100g = 1% - Check in coefficient form
2,828 / 2,800 = 1.01× 1.01: indeed +1%
1% real growth: modest, but compounded over 70 years it would still double GDP (rule of 70: 70 ÷ 1 = 70).
g = (GDP₂ − GDP₁) / GDP₁ × 100Choose the starting and finishing year: the growth rate adjusts.
Economic interpretation
A rate cannot be read on its own: you have to think about compounding, about duration — and about population. A few keys to reading it:
1% then 2% then 3%… each year applies to the total already increased: coefficients multiply, as seen in the formalisation (+4% then +5% = × 1.092, that is +9.2%).
Going from 1% to 2% growth halves — very nearly, that being the approximation in the rule of 70 — the doubling time: ≈ 70 years at 1%, ≈ 35 years at 2%.
“Growing richer” is judged by dividing by population: growth in GDP per capita ≈ GDP growth − population growth. +2% of GDP with +2% more inhabitants makes nobody richer on average — the final exercise has you build this.
The average annual growth rate (in finance, CAGR) is the constant rate which, repeated every year, would lead to the same finishing point. You do not average the percentages: you look for the annual coefficient which, multiplied by itself as many times as there are years, gives back the total coefficient — exercise 7 has you do it.
France has been growing at about 1% a year in recent years (+1.1% in 2024 according to INSEE, the national statistics institute). The “Trente Glorieuses” (1946-1975, the post-war reconstruction decades) ran at around 5% a year — a doubling every ~14 years — and China in the 2000s at around 10%: a doubling every ~7 years (70 ÷ 10).
Limits / critiques
Exercises
Real GDP goes from 2,000 to 2,060 €bn. What is the growth rate (in %)?
True or false: growth of +4% followed by −4% brings GDP back to its initial level.
GDP grows by +0.5% in each of the four quarters of the year. Over the whole year, growth is…
Over two years, real GDP goes from 2,000 to 2,205 €bn. What is the AVERAGE annual growth rate (in %)? (Hint: look for the coefficient which, applied twice in a row, leads from 2,000 to 2,205 — try round coefficients: × 1.04? × 1.05? — and check by multiplying.)
At 5% growth a year, GDP doubles in about… (rule of 70)
A recession — a period in which GDP falls, in practice often two consecutive quarters of decline — cuts GDP by 20%. What growth rate (in %) does it then take to get back exactly to the initial level?
GDP goes from 1,000 to 1,050, then from 1,050 to 1,102.5 €bn. Growth in the second year is…
Build GDP per capita. An economy produces real GDP of 2,000 €bn for 50 million inhabitants. One year later: real GDP 2,040 €bn (+2%), population 51 million (+2%). By how much has GDP PER CAPITA changed (in %)?