Fact 1: for most of history, living standards barely changed
Over the last 2,000 years, when did GDP per person start to rise, and was it the same everywhere?
Ask the room to sketch, on paper, GDP per person in the United Kingdom from the year 1 to today. Most students draw a gently rising line. Collect two or three sketches before showing the data.
The measure: GDP per person as a multiple of 500 dollars a year (2011 prices), roughly the level at which people can barely survive.
Growth began only two or three centuries ago, and at different times
Until about 1700, GDP per person stayed between 1 and 3 times subsistence in every country.
U.K. GDP per person in 2022 was 33 times its level in the year 1, and almost all of the rise came after 1800.
The take-off came first in the U.K. and the U.S., later in Japan and Argentina, and in China only in recent decades. Ghana’s rise is much smaller.
Sustained growth is a recent event in human history, and it did not start everywhere at once.
The 33 times is the title of the notebook’s figure. The 1 to 3 times subsistence is the “What to notice” of Fig. 1: only the United Kingdom had pulled a little higher by 1500 to 1700.
A way to make the timing vivid: if all of human history were squeezed into one calendar year, modern growth would start only on December 31.
Why growth was absent for so long, and why it started when it did, is still debated (more people versus more ideas per person, institutions, coal, trade). Chapter 6 returns to it with the economics of ideas.
The Great Divergence: gaps of 2 to 3 times became gaps of 14 times
United Kingdom
0.66
Japan
0.65
China
0.33
Argentina
0.31
Ghana
0.07, about 1/14
Before 1700, incomes across countries probably differed by a factor of 2 or 3 at most. Different start dates turned small gaps into huge ones.
The table is the notebook’s Key numbers for Fig. 1 (relative GDP per person in 2022). Italy, the richest country of the year 1 in these data, today has about 62 percent of U.S. GDP per person, and Egypt about 23 percent.
Economic historians call this widening “the Great Divergence”. Ask: what would the table have looked like in 1700? (All entries between roughly 0.3 and 1.)
The textbook reports Japan and the U.K. at about 3/4 of the U.S. level; with the 2023 Maddison release it is about 2/3.
Fact 2: U.S. income since 1870
How has U.S. GDP per person grown since 1870: in a straight line, faster and faster, or in fits and starts?
Ask students to guess a number first: how much richer is the average American today than in 1870? Then the shape. Most will remember the hook (almost 17 times), but few have thought about the shape of the path.
A steeper curve, but a steady percentage rise
1870 to 2022: $4,634 → $77,942, a factor of 16.8 . From 1870 to 2025, the chart’s title: about 18-fold.
1970 to 2000: $30,595 → $58,913, almost double in 30 years.
Each year’s increase is roughly proportional to the level: \(y_{t+1} - y_t \approx \bar{g}\,y_t\) , with \(\bar{g}\) about 2 percent.
The curve steepens because a steady percentage applies to a growing base.
The numbers are the notebook’s key numbers for Fig. 2. The textbook gives about 4,200 dollars for 1870; our value is about 10 percent higher because we use the newer Maddison estimates before 1929.
A parents-and-children comparison works well: a student born in 2000 grew up in an economy almost twice as rich, per person, as the one their parents were born into around 1970.
The equation on the slide is the key observation of the chapter: the change is proportional to the level. That is what a constant growth rate means, and it leads to Act II.
An upward-bending curve does not mean growth is speeding up
U.S. income rises more each decade on the chart, so U.S. growth must be accelerating.
A constant 2 percent adds more dollars every year, because it applies to a larger base. On a linear scale, constant growth always bends upward. To see whether growth speeds up, look at a ratio scale (Act II).
This is the most common misreading of Fig. 2, and also of charts of stock prices, house prices and the price level.
Ask: what would a line with a constant slope on this chart mean? (The same dollar increase every year, so a falling growth rate: 1,000 dollars is 10 percent of 10,000 but only 2 percent of 50,000.)
Transition: Act II builds the tools to read growth correctly.
The mathematics of growth
Act II
A growth rate is a percentage change; constant growth multiplies
\[g_t \equiv \frac{y_{t+1} - y_t}{y_t} \qquad\Longrightarrow\qquad y_{t+1} = y_t\,(1+\bar{g})\]
Apply it year after year: \(y_1 = y_0(1+\bar{g})\) , \(y_2 = y_0(1+\bar{g})^2\) , …
\[y_t = y_0\,(1+\bar{g})^t\]
The constant growth rule: each year adds one more factor \((1+\bar{g})\) .
Derivation, compressed: multiply the definition by y_t and add y_t to both sides. Next year’s value is this year’s value times the growth factor 1 + ḡ: the 1 carries over what is there, the ḡ adds the new part, proportional to the level. For a population, everyone alive is still counted next year and n̄ L_t newcomers join.
Substituting year after year gives one more factor each year, and after t years there are t of them. The book chapter’s Model overview also shows why the pattern holds for every t.
Two properties of a growth rate: it has no units (dollars or euros, people or billions give the same rate), and it is relative to the starting level.
Experiment: 2 percent a year for a century
Start with 6 billion people and let the population grow by 2 percent a year. How many people are there after 100 years? Write down your guess.
Ask for guesses before revealing anything. Typical answers: 18 billion (“2 percent of 6 billion is 0.12 billion, times 100 years is 12 billion more”) or something like 20. Write two or three on the board; we come back to them on the interpretation slide.
The example is the textbook’s: 6 billion was roughly the world population in 2000. It is only an illustration: demographers expect population growth to fall toward zero this century.
43.5 billion, not 18: compounding makes growth grow
35
12.0 billion10.2 billion
70
24.0 billion14.4 billion
100
43.5 billion18.0 billion
\[(1+\bar{g})^2 = 1 + 2\bar{g} + \bar{g}^2\]
Each year’s growth becomes part of the base for next year’s growth.
Reveal the predictions: the guess of 18 billion is exactly simple growth, which adds 2 percent of the starting value every year. Compound growth adds 2 percent of the current value.
The table is the notebook’s Check 1. After 35 years compound growth has doubled the population, after 70 years quadrupled it; simple growth reaches only 1.7 and 2.4 times the start.
The squared factor shows where they part: 1 + 2ḡ is simple growth over two years, and ḡ² is growth in the second year on the growth of the first. Over many years these extra terms pile up.
One percentage point of growth, over a century, is a factor of 2.7
1%
2.7 ×
2%
7.2 ×
3%
19.2 ×
the starting level \(y_0\) , up 1%
1% in every year, forever
the growth rate \(\bar{g}\) , up one point
an effect that grows with \(t\)
A higher level shifts the whole path once; a higher growth rate keeps widening the gap.
The factors are 1.01^100, 1.02^100 and 1.03^100 (the book chapter’s Model overview). Two economies starting at the same level: after a century, one growing at 3 percent is 2.65 times richer than one growing at 2 percent (exactly 1.03^100 / 1.02^100).
Comparative statics in logs: ln y_t = ln y_0 + t ln(1 + ḡ). The starting level enters with coefficient 1, the growth factor with coefficient t, so the longer the horizon, the more the growth rate matters relative to the level.
For the policy students: a reform that raises the level of output by 1 percent once is worth much less than one that raises the growth rate by 0.1 points forever. This is why growth economists study growth rates so intensely.
Experiment: relabel the vertical axis
Keep the same population path, but space the labels 6, 12, 24, 48 billion equally up the vertical axis. What shape does the curve take now?
Draw the axis on the board: 6, 12, 24, 48 equally spaced, each tick double the one before. Ask the students to plot the four doubling points (years 0, 35, 70, 105). Most will see the answer on paper before the chart appears.
The slope is the growth rate, and the doubling time is about 70/g
\[\ln y_t = \ln y_0 + t\,\ln(1+\bar{g}) \qquad\quad t_{\text{double}} = \frac{\ln 2}{\ln(1+\bar{g})} \approx \frac{70}{g}\]
1%
69.7 years
70.0 years
2%
35.0 years 35.0 years
3%
23.4 years
23.3 years
7%
10.2 years
10.0 years
Doubling depends only on the growth rate, not on the starting level.
Logs turn multiplying into adding: taking logs of the constant growth rule gives a straight line in t with slope ln(1 + ḡ), which is very close to ḡ for small rates (ln 1.02 = 0.0198). A ratio scale plots the log, so it draws that line.
Doubling time: set y_t = 2 y_0. The starting level cancels, leaving 2 = (1 + ḡ)^t; take logs. With ln 2 ≈ 0.693 and ln(1 + ḡ) ≈ ḡ, the doubling time is about 69.3/g with g in percent. Rounding up to 70 corrects for ln(1 + ḡ) being slightly smaller than ḡ, and 70 divides nicely.
The table is the notebook’s Check 3 (the exact values are 69.66, 35.00, 23.45 and 10.24). At 7 percent the rule is off by more than 2 percent, so for fast growth use the exact formula.
After k doublings, a variable is 2^k times its start: two doublings at 2 percent (70 years) make 6 billion into 24 billion.
Reading a ratio-scale chart
a straight line
constant growth
a steeper straight line
faster growth
a line that bends up (flattens)
growth that speeds up (slows down)
two parallel lines
equal growth, a constant ratio of levels
equal vertical steps
equal percentage changes
Read the slope, not the height: on a ratio scale the slope is the growth rate.
Every row follows from ln y_t = ln y_0 + t ln(1 + ḡ). Parallel lines: the vertical gap is ln y^A − ln y^B = ln(y^A / y^B), so a constant gap means a constant ratio.
Practice: point at a ratio-scale chart from the news (a stock index, COVID cases in 2020) and ask which row applies.
Fact 3: the U.S. growth rate over 150 years
On a ratio scale, does U.S. GDP per person since 1870 look like a curve or a straight line? If a line, what is its slope?
Recall Fig. 2: a curve that bends upward on a linear scale. Now ask what we would see on a ratio scale if the growth rate had been roughly constant (a straight line), rising (a curve bending up) or falling (a curve flattening).
Close to a straight line, with a few small bends
1870–2022, textbook’s numbers
1.92%
1870–2025, our data
1.88%
1870–1929
1.56%
1950–2005
2.21%
Steady growth of about 2 percent a year is one of the most remarkable regularities in macroeconomics.
The numbers are the notebook’s key numbers for Fig. 5, computed with the formula on the next slide. The textbook’s 1.92 percent uses 4,200 dollars in 1870 and 76,000 dollars in 2022.
The slightly slower growth before 1929 and slightly faster growth in 1950–2005 are exactly the bends you see on the ratio scale; on the linear scale of Fig. 2 they are invisible.
Ask: why should growth be so steady in a country that went through a civil-war aftermath, two world wars, the Great Depression and huge technological change? Chapters 5 and 6 offer an answer: growth in the long run is driven by ideas, and the flow of new ideas changes slowly.
The average growth rate is the one steady pace that links the end points
\[\frac{y_t}{y_0} = (1+\bar{g})^t \qquad\Longrightarrow\qquad \bar{g} = \left(\frac{y_t}{y_0}\right)^{1/t} - 1\]
Check: 6 billion at 2% for 100 years gives 43.47 billion, and the formula gives back 0.0200 .
With yearly rates \(g_1, \dots, g_t\) : \((1+\bar{g})^t = (1+g_1)\cdots(1+g_t)\) . So \(1+\bar{g}\) is a geometric mean .
Over 100 years, a 1% error in the final value moves \(\bar{g}\) by only 0.01 points.
Derivation: the constant growth rule turned around. Divide by y_0, raise both sides to the power 1/t, subtract 1. For t = 1 it gives back the ordinary percentage change. In logs, ln(1 + ḡ) is the slope of the straight line joining the first and the last point on a ratio scale.
The checks are the notebook’s Check 4. Only the end points matter: booms and slumps in between count only through where they leave the level at the end.
Robustness: over a century, a 1 percent measurement error in the final level changes the average growth rate by 0.0101 percentage points; over one year, by a full point. Long-run growth rates are more reliable than any single year’s number.
Up 10 percent, then down 10 percent, is not zero growth
A variable rose 10% one year and fell 10% the next, so its average growth rate was zero.
It ends at \(1.10 \times 0.90 = 0.99\) of its start: the average growth rate is \(0.99^{1/2} - 1 \approx\) −0.5% a year. Average the growth factors (a geometric mean), not the rates.
The number is the notebook’s Check 4 (−0.0050). The plain average of growth rates overstates the true average whenever rates vary, because a fall applies to a larger base than the rise that preceded it.
Where it matters: investment returns (“the fund averaged 5 percent a year”), inflation over several years, and growth averages across volatile periods. Ask the students: a stock falls 50 percent and then rises 50 percent. Where does it end? (At 75 percent of its start.)
Growth rules: products add, ratios subtract, powers multiply
\[z = x \times y \Rightarrow g_z = g_x + g_y \qquad z = \frac{x}{y} \Rightarrow g_z = g_x - g_y \qquad z = x^a \Rightarrow g_z = a\,g_x\]
Rule
0.130
0.070
−0.070
0.200
0.015
0.0425
Exact, one year
0.133
0.068
−0.064
0.210
0.015
0.0411
Logs turn each operation into a simpler one; the rules are close when growth rates are small.
Derivation: the change in the log of a variable is approximately its growth rate. Taking logs of z = x × y gives ln z = ln x + ln y; subtracting this year from next year gives Δln z = Δln x + Δln y. The same steps give the ratio and power rules.
The table is the notebook’s version of the textbook’s Table 3.1, with an extra row that checks each rule by computing the exact one-year growth. The rules are approximate with yearly data: for the product, 1 + g_z = (1 + g_x)(1 + g_y), so the exact answer has the extra term g_x g_y = 0.003. They hold exactly in logs or in continuous time.
With the U.S. rates of the next figure (1.9 and 1.4 percent) the gaps are tiny: rule 3.300 vs exact 3.327 percent.
Fact 4: GDP, population and GDP per person
Since 1870, U.S. population grew about 1.4 percent a year and GDP per person about 1.9 percent. How fast did total GDP grow?
Let students apply the product rule in their heads: total GDP = GDP per person × population, so its growth rate is about the sum. Ask for the answer before showing the figure.
Slower population growth means GDP per person carries more of GDP growth
1870–2025
3.29%
≈
1.88%
+
1.39%
1950–2025
3.08%
≈
1.97%
+
1.09%
2000–2025
2.14%
≈
1.36%
+
0.77%
\(g_Y \approx g_y + g_L\) : the sum is not exact because a year’s growth compounds, \((1+g_Y) = (1+g_y)(1+g_L)\) .
The rows are the slider steps of the figure. The cross term g_y × g_L is tiny for small rates (0.019 × 0.014 ≈ 0.0003).
Since 1980, U.S. population growth has been below 1 percent a year, so growth in GDP per person is a larger part of GDP growth than in the nineteenth century. Note also that growth per person since 2000 (1.36 percent) is below the long-run average.
For the policy students: aging and slower population growth lower GDP growth even if each person’s productivity grows as before. That matters for tax revenue and public pensions, which depend on total GDP, while living standards depend on GDP per person.
Fast GDP growth can hide stagnant living standards
GDP grew fast, so people must be getting richer.
Niger, 1950–2022: GDP grew 2.9% a year, but population grew 2.8%, so GDP per person barely changed. Living standards follow \(g_y = g_Y - g_L\) .
The Niger numbers are from the notebook’s “What to notice” for Fig. 9 (the website version for other countries, Maddison data). The ratio rule is the reason: GDP per person = GDP / population.
The opposite case: Japan’s population has been shrinking since about 2010, so its GDP per person grows faster than its total GDP.
Headlines usually report total GDP growth. For living standards, always subtract population growth.
The growth rules split output growth into its sources
\[Y = A\,K^{1/3}L^{2/3} \quad\Longrightarrow\quad g_Y = g_A + \tfrac{1}{3}g_K + \tfrac{2}{3}g_L \quad\Longrightarrow\quad g_y = g_A + \tfrac{1}{3}g_k\]
productivity \(A\)
1
1
capital \(K\)
1/3
1/3
labor \(L\)
2/3
−1/3
capital and labor together
1
0
Per person, only productivity growth and capital per person remain, and capital counts one third.
This is the textbook’s case study with the production function of Chapter 4. The product rule used twice gives g_Y = g_A + g_(K^1/3) + g_(L^2/3); the power rule turns the last two into multiples. Dividing by L (the ratio rule) subtracts g_L, leaving g_y = g_A + (1/3)(g_K − g_L) = g_A + (1/3) g_k, where k = K/L.
Read the table: more workers with the same capital raise output but spread the capital thinner, so output per person falls by a third of a point. Scaling both inputs together raises output one for one but leaves output per person unchanged: constant returns to scale.
The notebook’s Your turn: with A growing at 1, K at 3 and L at 1 percent, the rules give 2.67 percent for Y. Chapters 4 to 6 build on this decomposition.
Across countries and people
Act III
Fact 5: can a poor country catch up?
Since 1870, has any country that started poorer than the U.S. closed the gap? Has any rich country fallen behind?
Ask students to name candidates before revealing the chart. Usual answers: Japan, South Korea, China for catching up; Argentina for falling behind. Remind them how to read the coming chart: ratio scale, so parallel lines mean equal growth rates.
Catching up takes decades of growth well above 2 percent
Japan: 5.9% a year from 1950 to 1990; from 33% of U.S. GDP per person in 1870 to 65% in 2022.
South Korea: from 7% of the U.S. level in 1950 to 71% in 2022.
China grew 5.6% a year after 1978, India 4.4% after 1990. In 2019: China 30% of the U.S. level, India 13%.
Argentina: 32% of the U.S. level in 2019, after slow growth since about 1980.
Catch-up, or convergence , happens, but not automatically, and not everywhere.
Numbers: the chart title (Japan, 33 to 65 percent), the notebook’s key numbers for Fig. 6 (growth spurts and the 2019 ratios) and its “What to notice” (Korea).
The textbook reports faster growth for China and India; the Maddison Project has since revised both series down. Note the slowdown once a country gets close: Japan’s growth fell sharply after 1990, near the frontier.
Ask: why would a poor country be able to grow faster than the leader? (It can adopt ideas and technologies that already exist; capital is scarce and so its return is high.) Chapter 5 turns this into a model.
On a ratio scale, a gap that looks small can be large
China’s line in 2019 sits not far below the U.S. line, so China must be close to the U.S. level.
China had about 30% of U.S. GDP per person in 2019. On a ratio scale, equal distances are equal ratios : the gap is \(1/0.30 \approx 3.3\) times, almost two doublings.
The 30 percent is the notebook’s key number for Fig. 6 (2019). On a ratio scale the vertical distance between two lines is the log of their ratio: ln(3.3) ≈ 1.2, which is 1.74 doublings (2^1.74 ≈ 3.3).
Always read the tick labels. On a ratio scale, the distance from 10,000 to 20,000 is the same as from 40,000 to 80,000.
The same caution applies to Fig. 7 and Fig. 8, which put income on a ratio scale along the horizontal axis.
Fact 6: growth across 110 countries
Since 1960, did poor countries grow faster than rich ones, slower, or about the same?
Ask for a show of hands. Then explain the chart to come: one dot per country; horizontal axis, GDP per person in 2023 relative to the U.S. (ratio scale); vertical axis, the average growth rate from a starting year to 2023.
Sample: the 111 countries of the Penn World Table with data since 1960 (the textbook’s sample), minus Venezuela (see the notes of the next slide).
Small differences in growth rates become enormous gaps
Most countries grew 1 to 3 percent a year from 1960 to 2023.
Singapore grew 5.9% a year: income doubles every 12 years, and it rose 36-fold in 63 years.
Madagascar: −0.2% a year; Nicaragua: 0.5% a year.
The upward tilt is partly built in: fast growth is what made a country rich today .
Over a lifetime, the difference between 1 and 6 percent a year is the difference between stagnation and transformation.
The Singapore, Madagascar and Nicaragua numbers are the notebook’s key numbers for Fig. 7. With the Rule of 70, 70 / 5.9 ≈ 12 years per doubling; 63 years are about five doublings, 2^5 = 32, close to the exact factor of 36.
Make it personal: in Singapore, young adults today are many times richer than their grandparents were at the same age; in Madagascar, slightly poorer.
The tilt caveat matters for policy discussion: you cannot conclude from the 1960 picture that being rich causes fast growth. The horizontal axis is the outcome of the growth on the vertical axis. With later starting years, there is no sign that poor countries are left behind on average.
Fact 7: counting people, not countries
In 1960, what share of the world’s people lived in countries with GDP per person below 5 percent of the 2019 U.S. level? And in 2019?
Write down two numbers: your guess for 1960 and for 2019.
In Fig. 7, China and Luxembourg each count as one dot. Now every person counts equally. The poverty line is GDP per person at 5 percent of the 2019 U.S. level, about the textbook’s “7 dollars a day”.
Collect guesses. Many students expect poverty to have changed little, or even risen, because news coverage of poverty has not faded.
Poverty fell from 69 percent of the world’s people to 8.5 percent
Below the line: 68.7% of the world’s people in 1960, 8.5% in 2019.
In 2019, about 0.6 billion people were below the line; with the 1960 distribution it would have been 4.7 billion .
The fall was slow until 1990 and very fast after it, driven above all by growth in China and India.
Counting people, the last 60 years saw the largest fall in poverty in history.
Reveal the predictions. The numbers are the notebook’s key numbers for Fig. 8, with our 110 countries; the textbook reports “2 out of 3” in 1960 and “less than 1 out of 12” in 2019.
Caveat: this measure uses each country’s average income, so it ignores inequality within countries. Household-survey measures (such as the World Bank’s poverty counts, Ch2) tell the same broad story of a large fall since 1990.
Ask: why does the curve jump? Because a whole country, all at the same average income, crosses the line at once. China crossing the line is hundreds of millions of people moving at once.
Can policy start a growth take-off?
What can a government do to turn slow growth into decades of catch-up, like South Korea, and avoid stalling, like Argentina?
What the evidence suggests
Take-offs are common; sustaining them for decades is rare.
Fast growers invested heavily, opened to trade and stayed stable.
Institutions that protect property and contracts matter in the long run.
Why it is contested
Most take-offs follow no obvious reform, so luck plays a role.
Growth rates jump around far more than policies do.
What works in one country often fails in another.
The left column: Hausmann, Pritchett and Rodrik (2005, Journal of Economic Growth) find that growth accelerations of at least two points for eight years are frequent, but mostly not preceded by major reforms, and that many fade. The Commission on Growth and Development (2008, “The Growth Report”, World Bank) studied the 13 economies that grew at 7 percent or more for 25 years and lists common features: openness to the world economy, macroeconomic stability, high saving and investment, markets to allocate resources, and committed governments. Acemoglu, Johnson and Robinson (2001, American Economic Review) argue that institutions explain much of the long-run income gaps.
The right column: Easterly, Kremer, Pritchett and Summers (1993, Journal of Monetary Economics) show that growth rates are much less persistent across decades than country characteristics, which points to shocks and luck.
Lucas (1988, Journal of Monetary Economics) framed the question the textbook closes with: is there something a government could do to make its economy grow like the fastest growers, and if so, what? Ask the students for their answer, and come back to it after Chapters 4 to 6.
Growth has costs: pollution, depletion and climate
Should countries slow growth to protect the environment, or grow first and clean up later?
Why growth can help
Local pollution often worsens early in development, then improves as incomes rise.
Richer countries can afford cleaner technology and rules.
In the poorest countries, the bigger health threat is too little growth.
Why it is contested
The improvement is not automatic: it follows regulation.
Carbon emissions do not fall with income in the same way; their damage is global.
GDP does not subtract resource depletion.
The left column is the “environmental Kuznets curve”: Grossman and Krueger (1995, Quarterly Journal of Economics) find that several local pollutants first rise and then fall with income per person. The textbook’s example is London, whose smog was deadly in the nineteenth and twentieth centuries and is far lower today.
The right column: Stern (2004, World Development) reviews the evidence and concludes that the inverse-U is weak or absent for many pollutants, and that declines reflect policy and technology rather than income itself. For greenhouse gases the costs fall on other countries and future generations, so markets alone do not correct them; Nordhaus (2019, American Economic Review, Nobel lecture) sets out the economics of climate policy.
Link to Ch2: GDP leaves out environmental damage, so “growth” as measured can overstate gains in welfare. Ask: which policy tools let a country grow while cutting emissions? (Carbon prices, standards, support for clean technology.)
“Growth can’t go on forever”
A skeptic says: “A planet with finite resources cannot sustain 2 percent growth forever. At that rate we would be 7 times richer in a century. Rich countries should aim for zero growth.”
Reply: growth in GDP per person is mostly better ideas, not more materials: new goods, better quality and more output from the same inputs. The environmental costs are real, but they depend on what we produce and how, which policy can change. Ending growth would also end the fall in poverty.
Take the objection seriously. The 7.2 is 1.02^100 from Act II. The objection goes back at least to “The Limits to Growth” (Meadows et al. 1972), and is renewed today in the “degrowth” literature.
The reply rests on what growth is. U.S. GDP per person has grown about 2 percent a year for 150 years, while the energy and materials used per dollar of GDP have fallen. Much of what we buy today is services and information. Whether ideas can keep growth going is the subject of Chapter 6.
But the skeptic has a point: some resources, like a stable climate, are not priced, so growth can use them up. The answer is to price them (see the previous slide), not necessarily to stop growth. For the poorest countries, where the poverty count of Fig. 8 is concentrated, zero growth would mean no further escape from poverty.
Ask the policy students: what would you need to measure to know whether growth is sustainable?
What to remember from this chapter
Sustained growth is recent and spread unevenly, which caused the Great Divergence.
Constant growth multiplies: \(y_t = y_0(1+\bar{g})^t\) . Small rates compound into large gaps.
On a ratio scale, constant growth is a straight line; a variable doubles in about \(70/g\) years.
Average growth is \((y_t/y_0)^{1/t} - 1\) . Products add growth rates, ratios subtract them, powers multiply them.
U.S. GDP per person has grown about 2% a year since 1870; some countries caught up, and world poverty fell sharply.
Ask each student to write down one growth rate from today they will remember, and its doubling time. Good questions to seed for the next lectures: why did the U.K. take off first? Why did Korea catch up but not Argentina? Can 2 percent go on?
Walk the three branches of the mind map in about a minute each: the long-run facts (cyan), the mathematics of growth (lavender), across countries and people (green). Click the image to zoom in.
Sustained growth is recent and uneven, and it compounds: a few points a year, kept up for decades, separate rich from poor
Next: Chapter 4, A Model of Production
Chapter 4 asks why some countries are so much richer than others at a point in time, with the production function Y = A K^(1/3) L^(2/3) we just used for the growth rules.
Sources
Fig. 1, growth over the very long run. Maddison Project Database 2023 (gdppc; Bolt, J. and J. L. van Zanden 2024, doi:10.34894/INZBF2 ); earliest years: Maddison Database 2010 . Inspired by Fig. 3.1 in Jones (2024).Figs. 2, 5 and 9, the United States. BEA via FRED: GDPCAB230RC0A052NBEAA191RD3A086NBEAFigs. 3 and 4, constant growth. Model figures adapted from Figs. 3.3 and 3.4 in Jones (2024).Fig. 6, per capita GDP since 1870. Maddison Project Database 2023, in 2022 dollars with the BEA GDP deflator . Inspired by Fig. 3.6 in Jones (2024).Figs. 7 and 8, growth and the world distribution. Penn World Table 11.0 (rgdpe, pop; Feenstra, R., R. Inklaar and M. Timmer 2015, doi:10.34894/FABVLR ). Inspired by Figs. 3.7 and 3.8 in Jones (2024).Growth take-offs. Hausmann, R., L. Pritchett and D. Rodrik (2005), Journal of Economic Growth 10(4); Easterly, W., M. Kremer, L. Pritchett and L. Summers (1993), Journal of Monetary Economics 32(3); Acemoglu, D., S. Johnson and J. Robinson (2001), American Economic Review 91(5); Commission on Growth and Development (2008), The Growth Report , World Bank; Lucas, R. E. (1988), Journal of Monetary Economics 22(1).The costs of growth. Grossman, G. and A. Krueger (1995), Quarterly Journal of Economics 110(2); Stern, D. (2004), World Development 32(8); Nordhaus, W. (2019), American Economic Review 109(6); Meadows, D. et al. (1972), The Limits to Growth .Textbook. Jones, C. I. (2024). Macroeconomics , 6th ed.Book chapter, with the data, code and every figure. Data Science and Macroeconomic Models, Chapter 3 .