Economic growth · Lesson 1 of 14

What is economic growth?

Every growth model is an answer to a question about the numbers: why do incomes per head differ so much, and why do they change at such different speeds? This lesson sets out the numbers. It covers what is measured, why growth compounds, how real countries have grown since 1990, and the regularities Nicholas Kaldor asked every theory to explain.

← Economic growth moduleLesson 1 of 14 · about 40 minutes

The short answer

What is economic growth, and how is it measured?

Economic growth is a sustained rise in the amount an economy produces. The headline number is the percentage change in real GDP, output valued at constant prices so that inflation does not count as growth. For comparing living standards the better number is real GDP per head.

g = \frac{Y _{t} - Y _{t - 1}}{Y _{t - 1}} doubling time = \frac{ln 2}{ln ( 1 + g )} \approx \frac{70}{g ( in % )}

Measure it as a rate, on real output. Growth is the percentage change in real GDP, and living standards follow real GDP per head, which is roughly output growth minus population growth.
Growth compounds. Because each year’s growth is on a bigger base, a steady rate of g% doubles output in about 70 ÷ g years. 2% doubles it in 35 years, 7% in 10.
Small gaps in rates become huge gaps in levels. Over 35 years, 3% a year leaves a country 41% richer than 2% does.
Kaldor’s stylised facts are the long-run regularities every growth model is tested against: steady growth per worker, a stable capital–output ratio and stable factor shares.

A question to hold on to

In how many years will a sum of money triple itself when it is invested at an interest rate of 3% with continuous compounding? Around 40 years, 36, 33 or 30?

JNU 2018Solved at the end ↓

New to this? The few things you need first

Percentage change: The change divided by the starting value. From 200 to 210 is +5%, not +10 per cent.
Real and nominal GDP: Nominal GDP values output at the prices of the year. Real GDP values it at the prices of a fixed base year, so a change in it is a change in quantities.
Logarithms: ln x is the power e must be raised to in order to get x. What matters here: ln(ab) = ln a + ln b, and ln(1 + g) ≈ g when g is small.

The idea

Levels and rates: what is being measured

Two numbers describe an economy’s output over time, and they are easy to confuse. The level is how much is produced: India’s real GDP, or income per head. The growth rate is how fast the level is changing, as a percentage of where it started. A country can have a very low level and a very high growth rate, which is what “catching up” looks like, or the reverse.

The growth rate between two years is

Growth rate

g_{t} = \frac{Y _{t} - Y _{t - 1}}{Y _{t - 1}} = \frac{Y _{t}}{Y _{t - 1}} - 1

Use real GDP. Multiply by 100 to read it as a percentage.

Why per head?

Total output can rise simply because there are more people. What a person can buy depends on output per person. Per-head growth is output growth adjusted for population, and for small rates it is simply the difference:

Growth of a ratio

g_{Y / N} \approx g_{Y} - g_{N}

Exactly, (1 + g_Y)/(1 + g_N) − 1. For rates of a few per cent the shortcut is within a tenth of a point.

Pause and predict

Real GDP grows 6% a year and the population grows 2%. Real GDP per head grows by about

Growth theory usually works with output per worker, $y = Y / L$ , because that is what the models determine. Output per head and output per worker move together unless the share of the population that works changes. The lessons that follow say which one they mean each time.

Interactive

Why growth compounds, and the rule of 70

Growth of 5% this year is 5% of this year’s output; growth of 5% next year is 5% of a bigger number. So growth does not add, it multiplies. After t years at a steady rate g, a level x₀ has become

Compound growth

x_{t} = x_{0} (1 + g)^{t} t_{double} = \frac{ln 2}{ln ( 1 + g )} \approx \frac{70}{100 g}

Doubling needs (1 + g)^t = 2, so t = ln 2 ÷ ln(1 + g). Since ln(1 + g) ≈ g and ln 2 ≈ 0.693, t ≈ 69.3 ÷ (100g). Seventy is used because it divides by more numbers.

Growth a year	Exact doubling time	Rule of 70
1%	69.66 years	70.0 years
2%	35.00 years	35.0 years
3%	23.45 years	23.3 years
4%	17.67 years	17.5 years
5%	14.21 years	14.0 years
6%	11.90 years	11.7 years
7%	10.24 years	10.0 years
8%	9.01 years	8.8 years
10%	7.27 years	7.0 years

The shortcut is within about a year at any rate you will meet in the exam. Now set two economies growing at different rates and watch the gap open. The preset One point of growth compares 3% and 4%.

A starts at 100 and B at 25. After 30 years A is at 181 and B at 144; after 60 years, 328 and 825. B overtakes A after about 36 years.

Two things to take away. First, switch to the log axis: each curve turns into a straight line, and a steeper line means a faster rate. That is why growth is plotted on log scales. Second, try Fast, but too far behind. Growing twice as fast as the leader is not enough if you start at a tenth of its income, because the leader is also compounding. The catch-up time is

t^{*} = \frac{ln ( y _{A} / y _{B} )}{ln ( 1 + g _{B} ) - ln ( 1 + g _{A} )}

Real data

What the data say: twelve countries since 1990

Here is real GDP per head for twelve countries from the World Bank, in dollars of constant purchasing power (2021 international dollars, which adjusts for price differences between countries). Switch on and off the countries you want, and between levels and an index that starts every country at 100 in 1990.

Country	1990	2025	Multiple	Growth a year	Doubles every
India	2,140	10,039	4.7×	4.5%	16 years
China	1,667	25,067	15×	8.1%	9 years
United States	44,384	76,931	1.7×	1.6%	44 years
Korea, Rep.	14,378	55,697	3.9×	3.9%	18 years

Source: World Bank, World Development Indicators, series NY.GDP.PCAP.PP.KD (GDP per capita, PPP (constant 2021 international $)), read from the World Bank API on 2026-10-06; the series was last updated 2026-07-13. The latest years are the World Bank’s own estimates and get revised. “Growth a year” is the compound annual rate between the first and last year shown.

Read the table under the chart, not just the lines. Between 1990 and 2025, income per head multiplied by 4.7 in India (about 4.5% a year) and 15.0 in China (8.1% a year), against 1.7 in the United States (1.6%). South Korea, already in the middle of its rise in 1990, went from $14,378 to $55,697, a multiple of 3.9. Nigeria grew slowly (1.2% a year), and Ethiopia (3.7%) grew faster, but from a very low base.

Three facts stand out, and each is a question for a theory:

Levels differ enormously. In 2025 income per head in the United States was about 25 times Ethiopia’s. Why? (Lessons 5, 6 and 8.)
Growth rates differ and persist. China and South Korea grew at about 4% to 8% a year over these 35 years, while Nigeria managed about 1%. Why? (Lessons 3, 10 and 11.)
Rich countries do not stop growing. The United States, already the richest of the twelve in 1990, still grew about 1.6% a year rather than levelling off. Why? (Lessons 5 and 10.)

What a theory must explain

Kaldor's stylised facts

In 1961 the Cambridge economist Nicholas Kaldor argued that growth theorists should not start with elegant assumptions. They should start from the broad, stable patterns in the data, which he called stylised facts, and ask whether a model reproduces them. His list, as it is usually summarised:

#	The fact (for the long run, in industrial economies)	What a model has to deliver
1	Output per worker grows at a steady rate	Sustained growth of y = Y/L, not a one-off rise
2	Capital per worker grows at a steady rate	k = K/L rising in step with output per worker
3	The rate of return on capital is roughly constant	No fall in the return, so no running out of investment
4	The capital–output ratio is roughly constant	K/Y steady while both K and Y grow
5	Labour and capital keep roughly constant shares of income	Shares that do not drift, as in Cobb–Douglas
6	Growth rates of output per worker differ widely between countries	A reason why, rather than one rate for all

Facts 1 to 5 together describe balanced growth: output, capital and wages grow at the same rate, so ratios such as K/Y stay put. The Solow model in Lesson 5 is built to produce exactly this in the long run, and the Harrod–Domar model in Lesson 4 cannot. Fact 6 is what the endogenous growth models of Lessons 10 and 11 were built to explain.

Treat the list with care. It is a stylisation, not a law. Jones and Romer (2010) offer an updated set of facts that emphasise population, ideas and institutions, and Karabarbounis and Neiman (2014) document a fall in the share of income going to labour in many countries since the 1980s, which strains fact 5.

A distinction the exams like

Growth is not development

Growth is a rise in output per head. Development is wider: whether people live longer, are educated, are free of poverty, and can choose how to live. Growth is usually a means to development, since a richer country can afford more schools and clinics, but the link is loose. Two countries with the same GDP per head can differ greatly in life expectancy or in how widely income is shared. That is why the Human Development Index combines income with health and education, and why exam papers ask students to separate the two ideas. The development module that follows this one takes up the measures.

The short test

If the question is about how much output, or how fast it is rising, it is growth. If it is about whether lives are going well, it is development.

Solving the opening question

The opening question, solved

JNU 2018 · foundation

In how many years will a sum of money triple itself when invested at 3% with continuous compounding?

Write the growth law.
With continuous compounding at rate r, the sum after t years is x₀e^rt.
Set it equal to three times the start.
$e^{0.03 t} = 3$
Take logs.
$t = \frac{l n 3}{0.03} = \frac{1.0986}{0.03} \approx 36.6$

Answer

About 36 years. The doubling-time rule gives the same method: ln 2 ÷ 0.03 ≈ 23 years to double, and tripling takes ln 3 ÷ ln 2 ≈ 1.58 times as long.

A neighbour of this question appears often. “A lily pad doubles every day and covers the lake on day 48; when did it cover half?” (JNU 2012) is not 24 but day 47, because doubling means the day before was exactly half. And “a person’s wealth doubles every two years and is ₹10 lakh fifty years after the start; when was it ₹5 lakh?” (JNU 2017) is two years earlier, at year 48. Neither 24 nor 25 is an option, so both are “none of the above”.

Watch out for

The mistakes examiners are fishing for

Adding rates instead of multiplying factors. A 20% rise then a 20% fall is ×1.2 × 0.8 = 0.96, a 4% fall, not zero.
Using nominal GDP. Growth in nominal GDP includes inflation. Growth means real GDP.
Reading a straight line on a linear axis as steady growth. On a linear axis steady growth curves upward. A straight line there means steady addition and a slowing growth rate.
Rule of 70 with the rate as a decimal. Use 70 ÷ 3, not 70 ÷ 0.03, when the rate is 3%.
Continuous against annual compounding. Doubling at r continuous is ln 2 ÷ r; at annual rate g it is ln 2 ÷ ln(1 + g). They differ slightly, since r = ln(1 + g).

Revise

The lesson on one screen

Growth: The percentage change in real GDP, (Y_t − Y_t−1) ÷ Y_t−1. Per head: growth of output minus growth of population, approximately.
Compounding: x_t = x₀(1 + g)^t. Doubling time = ln 2 ÷ ln(1 + g) ≈ 70 ÷ g.
Why it matters: 1 point more growth for 35 years makes income about 40% higher: 2% gives ×2.00, 3% gives ×2.81.
Log scale: Equal distances are equal percentages; a straight line is steady growth; a steeper line is faster growth.
Kaldor's facts: Steady growth of output and capital per worker, a stable capital–output ratio and return on capital, stable factor shares, and large differences in growth between countries.
Growth against development: Output per head against health, education, poverty and freedom. Related, not the same.

Practice

Check yourself

0 of 8 correct so far

A. Numbers

Problem 1

An economy grows at a steady 6% a year. Find its exact doubling time, and the rule-of-70 estimate.

Exact (years)Rule of 70 (years)

Problem 2

Real GDP rises from 2,000 to 2,880 over five years. What is the compound annual growth rate, in per cent?

CAGR (%)

Problem 3

Real GDP grows 6% and population 2%. Find the exact growth of GDP per head, in per cent.

Per head (%)

B. Concepts

1On a log-scale chart, a straight upward line for a country's GDP per head means that it is

2Country A has twice the income per head of B and grows at 2%; B grows at 4%. Which statement is correct?

3Which of these is NOT one of Kaldor's stylised facts?

4A rise in real GDP per head with no change in life expectancy or schooling is best described as

Real questions

Past papers, by level

Questions from CUET, JNU and UGC NET on compounding, doubling time and the history of growth theory.

Foundation

Definitions, one-step arithmetic and which-model questions. Most CUET and Hyderabad questions sit here.

3 questionsPractise →

Standard

Growth accounting, steady-state algebra, statement questions and matching, up to JNU, IIT JAM and UGC NET level.

6 questionsPractise →

All 9 past-paper questions for this lesson, easiest first: practise the full set →

These are questions from the TestStop bank. A free account answers 10 a day, each with its worked solution; All-Access opens every set with no daily limit.

Quick answers

Frequently asked questions

What is economic growth?

Economic growth is a sustained increase in the quantity of goods and services an economy produces. It is measured as the percentage change in real GDP, the value of output at constant prices, from one period to the next. What matters most for living standards is the growth of real GDP per head, which is output growth minus population growth, approximately.

How is the economic growth rate calculated?

Growth rate = (real GDP this year − real GDP last year) ÷ real GDP last year, multiplied by 100 to give a percentage. Use real GDP, which strips out price changes, not nominal GDP. For the average growth rate over several years, use the compound annual growth rate: (end value ÷ start value)^(1 ÷ years) − 1.

What is the rule of 70?

The rule of 70 says that something growing at g per cent a year doubles in about 70 ÷ g years. At 2% a year income doubles in about 35 years, at 7% in about 10. It comes from the exact doubling time, ln 2 ÷ ln(1 + g), because ln 2 is about 0.693. The rule is accurate for growth rates up to roughly 10%.

What is the difference between GDP growth and GDP per capita growth?

GDP growth is the growth of total output. GDP per capita growth is the growth of output per person, which is approximately GDP growth minus population growth (exactly, (1 + g_Y) ÷ (1 + g_N) − 1). A country can have fast GDP growth and little improvement in income per head if its population grows almost as fast.

What are Kaldor's stylised facts of economic growth?

In 1961 Nicholas Kaldor summarised the long-run regularities that a growth theory should explain: output per worker grows at a steady rate; capital per worker grows at a steady rate; the rate of return on capital is stable; the capital–output ratio is stable; labour and capital keep roughly constant shares of national income; and growth rates of output per worker differ substantially between countries. Later work, such as Jones and Romer (2010), updates the list, and the stability of factor shares has been questioned.

Why do economists plot GDP on a log scale?

Because growth is a percentage change. On a log scale equal distances mean equal percentage changes, so a straight line is steady growth and a steeper line is faster growth, whatever the starting level. On an ordinary scale a rich country's steady 2% looks steeper than a poor country's steady 6% simply because 2% of a large number is a large number.

Is economic growth the same as economic development?

No. Growth is a rise in output, usually measured by GDP per head. Development is wider: health, education, freedom to choose, poverty and inequality. Growth is usually necessary for development and does not guarantee it. Measures such as the Human Development Index combine income with life expectancy and schooling to capture the difference.

← The moduleOverview and diagnostic Lesson 2 →The production function: returns to scale, Cobb–Douglas and technical change

What is economic growth?

Levels and rates: what is being measured

Why per head?

Why growth compounds, and the rule of 70

What the data say: twelve countries since 1990

Kaldor's stylised facts

Growth is not development

The opening question, solved

The mistakes examiners are fishing for

The lesson on one screen

Check yourself

A. Numbers

B. Concepts

Past papers, by level

Foundation

Standard

Frequently asked questions

Read next

What is economic growth?

Levels and rates: what is being measured

Why per head?

Why growth compounds, and the rule of 70

What the data say: twelve countries since 1990

Kaldor's stylised facts

Growth is not development

The opening question, solved

The mistakes examiners are fishing for

The lesson on one screen

Check yourself

A. Numbers

B. Concepts

Past papers, by level

Foundation

Standard

Frequently asked questions

Read next