ECON7074 Chap.4 Long-Run Growth Facts and Growth Arithmetic
Long-Run Growth Facts and Growth Arithmetic
This chapter sets out the facts any theory of growth must explain and the arithmetic needed to read them. It adopts real GDP per person as the working measure of living standards, then shows that sustained improvement is a recent event: modern growth began only in the last two or three centuries, in different countries at different times.
Uneven take-off produced the Great Divergence, widening gaps between rich and poor nations from a factor of two or three to dozens.
The chapter explains why long income series are drawn on ratio scales, where constant growth appears as a straight line, and summarises cross-country evidence on growth rates, convergence, the contrast between counting countries and counting people, the benefits and costs of growth, and its link with happiness. It closes with compound-growth algebra, doubling times and how small rate gaps become large income gaps.
Worked numbers throughout are original, so you can rebuild every step by hand.
What this chapter covers
- 01
Real GDP per person as a living-standard measure
- 02
Modern growth and the Great Divergence
- 03
Ratio scales and straight-line growth
- 04
Cross-country growth rates and convergence
- 05
Benefits, costs and happiness
- 06
Compound growth and doubling times
Worked example · free
Ratio-scale growth paths: income per person at 2% and 1% a year over 140 years
- +1Use y_t = y_0(1 + g)^t with g = 0.02: 1,000 times 1.02 to the power 140 is about 1,000 times 16.0, or roughly 16,000.
- +1With g = 0.01: 1,000 times 1.01 to the power 140 is about 1,000 times 4.03, or roughly 4,030.
- +1Divide the levels: 16,000 / 4,030 is about 3.97, so the faster economy ends nearly four times richer per person.
- +1At 2% income doubles every ln 2 / ln 1.02, about 35 years, so it rises one doubling tick per 35 years; constant growth adds equal steps on a ratio axis and draws a straight line.
Key terms
- Great Divergence
- The historical widening of income gaps between countries as modern growth began in some places centuries before others.
- Ratio scale
- A vertical axis on which equal distances represent equal proportional changes, such as each tick doubling the value below it.
- Compound growth
- Growth in which each period's percentage increase applies to a base that already includes earlier gains, so levels rise exponentially.
- Doubling time
- How many periods a variable needs to double at a constant growth rate, found from ln 2 divided by ln(1 + g).
- Modern economic growth
- Sustained, long-lasting rises in income per person that began only in the last two or three centuries.
Long-Run Growth Facts and Growth Arithmetic FAQ
Why does the course measure living standards with real GDP per person?
It is a single number that can be measured for most countries across long periods. The lecture surveys several development indicators, such as life expectancy, and then adopts real GDP per person as a simple working measure. It leaves out leisure, the environment and distribution, so treat it as a practical yardstick for comparison rather than a complete measure of wellbeing.
What is the Great Divergence?
It is the widening of income gaps between countries that followed the uneven start of modern growth. Before 1700 rich and poor nations differed by a factor of roughly two or three; today the lecture reports gaps of over fifty, and its summary slide more than sixty, between the richest and poorest economies.
Why do economists plot income on a ratio scale?
On a ratio scale equal vertical distances mean equal percentage changes, so a variable growing at a constant rate appears as a straight line and its slope shows the growth rate. On an ordinary axis the same series curves upward, which makes steady growth look like acceleration and hides changes in the rate.
Do poorer countries always grow faster and catch up?
No. Across a broad sample of countries over forty years, some economies shrank, a few grew close to six percent a year and most grew near two percent. A low starting income on its own does not guarantee catch-up, which is why later chapters ask what conditions convergence requires.
How do I find the time needed for income to double?
Set the compound-growth formula equal to twice the starting value, so (1 + g) raised to the power t equals 2, and take natural logarithms to get t equal to ln 2 divided by ln(1 + g). As a quick check, seventy divided by the growth rate in percent gives a close approximation.
Exam move
Learn this chapter as facts plus one formula. Memorise the stylised facts as short claims you can defend: recent take-off, uneven start dates, the Great Divergence, a typical growth rate near two percent, and the difference between counting countries and counting people. Then drill compound growth until solving for the level, the rate or the time is automatic, always using logarithms when the unknown sits in the exponent.
Sketch one series on an ordinary axis and again on a ratio axis to see why constant growth becomes a straight line. Finally, practise answering a chart question in three sentences: what the line shows, what the slope means, and what the comparison implies.
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