Chapter 20: Economic Growth
Economic growth — the sustained increase in GDP per capita over time — is arguably the most important phenomenon in macroeconomics. Even small differences in annual growth rates, compounded over decades, produce enormous differences in living standards. This chapter traces the relatively recent arrival of modern growth, examines the sources of productivity gains, and explores whether poorer countries can converge with wealthier ones.
Table of Contents
1. The Relatively Recent Arrival of Economic Growth
1.1 Modern Economic Growth
For most of human history, living standards barely changed. The average person in 1700 lived not much better than the average person in 100 CE. Modern economic growth — the period of sustained, rapid increases in per capita output — began only in the late 18th and early 19th centuries with the Industrial Revolution.
Industrial Revolution: The widespread use of power-driven machinery and the resulting economic and social changes in the first half of the 1800s. It began in Great Britain and soon spread to the United States, Germany, and other countries.
Key innovations — the steam engine, the power loom, the steam locomotive — performed tasks that would have required vast numbers of workers. A self-reinforcing cycle emerged:
New inventions → profits → funds for new investment → further inventions → further profits
Since the early 1800s, the average GDP growth rate per capita in the leading industrialized countries has been about 2% per year.
1.2 The World Before Modern Growth
Angus Maddison’s quantitative economic history shows that nations can decline as well as rise. Before the Industrial Revolution, global incomes were remarkably equal — and remarkably low.
| Year | Northern Italy | Spain | England | Byzantium | Iraq | Egypt | Japan |
|---|---|---|---|---|---|---|---|
| 1 CE | $800 | $600 | $600 | $700 | $700 | $700 | — |
| 730 | — | — | — | — | $920 | $730 | $402 |
| 1000 | — | — | — | $600 | $820 | $600 | — |
| 1300 | $1,588 | $864 | $892 | — | — | $610 | — |
| 1348 | $1,486 | $907 | $919 | — | — | — | — |
GDP per capita in current international dollars (Source: Bolt & van Zanden, Maddison Project, 2013)
Key Insight: Institutions — traditions, laws, and governance structures — played a critical role. The Magna Carta (1215) codified due process and reinforced social order, contributing to England’s relatively high GDP per capita by 1348.
1.3 Waves of Catch-Up Growth
The Industrial Revolution led to increasing inequality among nations. By 1870, the 17 most-developed economies had 2.4× the GDP per capita of the poorest. By 1960, this ratio widened to 4.2×.
However, catch-up waves have occurred:
| Country/Region | Period | Annual GDP per Capita Growth |
|---|---|---|
| Japan | 1960s–1970s | ~11% |
| Brazil | 1968–1973 | ~11.1% |
| South Korea, Taiwan, Thailand | 1970s | 11–12% |
| China | 1984–2000s | ~9% |
| India | 2000s–2010s | 7–8% |
Not all countries have caught up. In Niger, Tanzania, and Sudan, GDP per capita at the start of the 2000s was still less than $300.
1.4 Rule of Law and Property Rights
Rule of Law: Laws must be clear, public, fair, enforced, and equally applicable to all members of society.
Property Rights: The rights of individuals and firms to own property and use it as they see fit — including entering into contracts.
Contractual Rights: Based on property rights, these allow individuals to enter into agreements regarding the use of their property, with recourse through the legal system in the event of noncompliance.
The World Bank ranks countries’ legal systems on a scale of 1–6 for effective protection of property rights and rule-based governance. In 2020:
- World average: 2.9
- Lowest ranked: Somalia and Eritrea (1.0), South Sudan (1.5)
- Countries with weak governance — Afghanistan, Central African Republic, Zimbabwe — have lagged far behind in growth
Critical Point: Without enforceable contracts and property rights, people will not enter into agreements for goods or services, transaction costs soar, and economic growth stalls.
2. Labor Productivity and Economic Growth
2.1 What Is Labor Productivity?
Labor Productivity: The value that each employed person creates per unit of their input (typically measured as output per hour worked).
Sustained long-term growth comes from increases in worker productivity. The three main determinants are:
| Determinant | Description | Example |
|---|---|---|
| Human Capital | Accumulated knowledge, skills, and expertise from education and experience | College degrees, vocational training |
| Technological Change | Combination of invention (advances in knowledge) and innovation (putting them to use) | Transistor (1947) → smartphones |
| Economies of Scale | Cost advantages from larger-scale production | Industrial oven vs. residential oven |
2.2 Measuring Productivity Growth
U.S. productivity (output per hour) more than doubled between 1977 and 2020 (index: ~50 → 110.5, base year 2012 = 100).
| Period | Annual Productivity Growth |
|---|---|
| 1947–1973 | 2.8% |
| 1973–1979 | 1.2% |
| 1979–1990 | 1.5% |
| 1990–2000 | 2.2% |
| 2000–2007 | 2.7% |
| 2007–2020 | 1.4% |
The productivity slowdown of the 1970s–80s and the subsequent “New Economy” rebound of the late 1990s remain debated. Optimists credit information technology; pessimists caution that a decade of strong growth doesn’t prove a permanent trend.
Productivity → Wages: Over the long run, productivity per hour is the most important determinant of the average wage level. Firms pay workers roughly what those workers produce — otherwise, competing firms would bid wages up or losses would result.
2.3 The Aggregate Production Function
Aggregate Production Function: The process by which an economy as a whole turns economic inputs — human capital, physical capital, and technology — into output measured as GDP per capita.
Two versions:
- Total GDP: GDP = f(workforce, human capital, physical capital, technology)
- Per capita GDP: GDP per capita = f(human capital per person, physical capital per person, technology per person)
The Cobb-Douglas Production Function
The most widely used functional form:
\[Y = A \cdot K^\alpha \cdot L^{1-\alpha}\]Where:
- $Y$ = total output (GDP)
- $A$ = total factor productivity (TFP) — captures technology
- $K$ = physical capital
- $L$ = labor (adjusted for human capital)
- $\alpha$ = capital’s share of income (typically $\approx 0.3$ for the U.S.)
Worked Example: Growth Decomposition with Cobb-Douglas
Taking logarithms and differentiating:
\[\frac{\Delta Y}{Y} = \frac{\Delta A}{A} + \alpha \cdot \frac{\Delta K}{K} + (1-\alpha) \cdot \frac{\Delta L}{L}\]Suppose in a given decade:
- Capital stock grew by 30%: $\frac{\Delta K}{K} = 0.30$
- Labor force grew by 10%: $\frac{\Delta L}{L} = 0.10$
- GDP grew by 25%: $\frac{\Delta Y}{Y} = 0.25$
- $\alpha = 0.3$
Then TFP growth (technology) is the residual:
\[\frac{\Delta A}{A} = 0.25 - (0.3)(0.30) - (0.7)(0.10) = 0.25 - 0.09 - 0.07 = \mathbf{0.09 = 9\%}\]| Source | Contribution | % of Growth |
|---|---|---|
| Physical capital | 0.09 (= 0.3 × 0.30) | 36% |
| Labor | 0.07 (= 0.7 × 0.10) | 28% |
| Technology (TFP residual) | 0.09 | 36% |
| Total GDP growth | 0.25 | 100% |
Technology accounts for 36% of growth even after accounting for capital and labor — and this is likely an underestimate because better technology is often embodied in new capital.
Aggregate Production Function with Diminishing Returns
2.4 The Power of Sustained Growth
The compound growth formula:
\[\text{Future Value} = \text{Present Value} \times (1 + g)^n\]where $g$ = growth rate and $n$ = number of years.
Compound Growth Table (starting from an index of 100):
| Growth Rate | After 10 Years | After 25 Years | After 50 Years |
|---|---|---|---|
| 1% | 110 | 128 | 164 |
| 3% | 134 | 209 | 438 |
| 5% | 163 | 339 | 1,147 |
| 8% | 216 | 685 | 4,690 |
At 1% growth, GDP per capita rises 64% in 50 years. At 5%, the same gain occurs in just 10 years. At 8%, an economy’s living standard more than doubles every decade.
Rule of 70: To estimate how many years it takes for a quantity to double, divide 70 by the growth rate. At 2% growth, doubling takes ~35 years; at 7% growth, only ~10 years.
\(\text{Doubling time} \approx \frac{70}{g}\)
3. Components of Economic Growth
3.1 Physical Capital
Physical Capital: The plant, equipment, and infrastructure (roads, rail systems, utilities) that firms use in production.
Physical capital affects productivity through:
- Quantity increases — more computers, more machines
- Quality improvements — faster computers, more efficient machines
The average U.S. worker in the late 2000s worked with physical capital worth almost 3× as much as that of the average worker in the early 1950s.
3.2 Human Capital
Human Capital: The accumulated knowledge, skills, and expertise of workers — built through education and experience.
Capital deepening occurs when society increases the level of capital per person:
| Year | % of U.S. Adults with High School Diploma | % with College Degree |
|---|---|---|
| 1970 | ~50% | ~11% |
| 2000+ | 80%+ | ~30% |
Girls’ Education in Low-Income Countries: Each additional year of schooling for girls leads to fewer and healthier children, lower maternal mortality (1–2 fewer deaths per 1,000 women), and an extra half-year of schooling for each of their children. Wages typically increase 10–20% per additional year of education.
3.3 Technology
Technology (in economics): All the ways in which existing inputs produce more or higher-quality output, as well as entirely new products. It includes:
- Invention — advances in knowledge
- Innovation — putting those advances to use in new products or services
- Also new management methods, organizational forms, and institutional arrangements
The U.S. Patent and Trademark Office has issued more than 150,000 patents annually in recent years.
3.4 Growth Accounting: What Matters Most?
Growth accounting studies decompose economic growth into contributions from physical capital deepening, human capital deepening, and technology (measured as the residual — the unexplained portion).
Three Key Lessons from Growth Accounting:
- Technology is the most important contributor — often explaining more than half of U.S. growth
- Human capital is at least as important as physical capital — Europe rebuilt after WWII in less than two decades thanks to skilled workers and technological knowledge
- All three factors work together — educated workers generate innovations; innovations require investment in physical capital; new machines require additional training
3.5 A Healthy Climate for Growth
A market-oriented economy with supportive government policies provides the best environment for growth:
| Policy Area | Example |
|---|---|
| Education | Denmark: free public school (Folkeskole), gov’t vouchers for private schools |
| Savings & Investment | U.S.: low capital gains taxes encourage investment |
| Infrastructure | Japan: major road and public works projects in mid-1990s |
| Special Economic Zones | Mauritius: government-supported SEZs with no trade taxes |
| Scientific Research | EU: strong R&D programs; Austrian firms with gov’t support increased research intensity |
Special Economic Zone (SEZ): An area within a country, usually with port access, where the government does not tax trade, encouraging international commerce and investment.
4. Economic Convergence
4.1 What Is Convergence?
Convergence: A pattern in which economies with low per capita incomes grow faster than economies with high per capita incomes, potentially narrowing the gap over time.
| Category | Countries | Avg Growth 1990–2000 | Avg Growth 2010–2019 |
|---|---|---|---|
| Fast Growth Club (≥5%) | Cambodia, China, India, Ireland, Laos, Mozambique, Uganda, Vietnam | 6.0–10.6% | 5.4–7.3% |
| Slow Growth Club (≤2%) | Central African Rep., France, Germany, Haiti, Italy, Jamaica, Japan, Switzerland | −1.5–2.0% | −0.2–2.0% |
| U.S. (reference) | United States | 3.2% | 2.3% |
Overall pattern: Low-income countries averaged 3.8–4.5% growth; middle-income 4.0–4.7%; high-income only 1.7–2.7%.
4.2 Arguments Favoring Convergence
- Diminishing Marginal Returns to Capital Deepening
- In low-income countries, each additional unit of human or physical capital has a larger marginal effect
- A $5,000 increase in capital per worker matters more when the starting point is $2,000 than when it’s $50,000
- “Advantages of Backwardness” (Alexander Gerschenkron)
- Low-income countries can adopt already-invented technologies rather than inventing from scratch
- Adapting proven technology is cheaper and lower-risk than pioneering new technology
- Learning from Others
- Countries observe successful growth strategies and replicate market-friendly institutions
4.3 Arguments Against Convergence
- Technology Can Offset Diminishing Returns
- If an economy invests in both capital deepening and better technology, it can shift to a higher production function and avoid flattening out
- High-income countries continuously innovate, maintaining growth despite high capital levels
- Institutional Requirements
- Copying technology is only “easy” if the country has supportive economic, educational, and legal institutions
- Many low-income countries lack the infrastructure to absorb and deploy new technologies effectively
Capital Deepening + Technology: Escaping Diminishing Returns
Imagine an economy at point R on production function Technology 1, with capital level $C_1$ and output $G_1$. Capital deepening alone (moving from $C_1$ → $C_2$ → $C_3$ along Technology 1) yields diminishing returns: R → U → W.
But if capital deepening is combined with technological improvement:
- $C_1$ → $C_2$ with Technology 1 → Technology 2: economy moves R → S
- $C_2$ → $C_3$ with Technology 2 → Technology 3: economy moves S → T
With continuous technological progress, there is no reason growth must slow down.
4.4 The Slowness of Convergence
Convergence Example:
- Rich country: starts at $40,000 GDP per capita, grows at 2%/year
- Poor country: starts at $4,000, grows at 7%/year
After 30 years:
- Rich: $40{,}000 \times (1.02)^{30} = $72{,}450$
- Poor: $4{,}000 \times (1.07)^{30} = $30{,}450$
The income ratio narrowed from 10:1 to 2.4:1 — real progress, but people in the poorer country still feel quite poor relative to the richer one. And as the gap shrinks, catch-up growth opportunities diminish.
Convergence Trajectories
Takeaway: High-income countries have built their advantages over 100+ years. Even with highly optimistic growth differentials, convergence takes decades. Small annual differences compound into enormous gaps.
5. Key Takeaways
- Modern economic growth is a recent phenomenon — essentially the last 200 years, beginning with the Industrial Revolution
- Labor productivity (output per hour) is the ultimate driver of long-run growth and wages
- Three sources of growth: physical capital deepening, human capital deepening, and technological change — technology is the most important
- The aggregate production function links inputs (labor, capital, technology) to output (GDP)
- Compound growth makes even small rate differences enormous over time — the Rule of 70 helps estimate doubling times
- Rule of law, property rights, and contractual rights are essential preconditions for sustained growth
- Convergence is possible — low-income countries can grow faster via diminishing returns and technology adoption — but it is slow and not guaranteed
- Government policies (education, infrastructure, R&D, trade openness) can create a healthy climate for growth
6. Practice Questions
Q1. What was the approximate average annual GDP per capita growth rate for leading industrialized countries over the last two centuries?
Answer
About 2% per year. While this seems modest, compound growth over 200 years has transformed living standards dramatically.Q2. An economy starts with GDP per capita of $10,000. If it grows at 4% per year, what will GDP per capita be after 20 years? What about a country growing at 1%?
Answer
At 4%: $10{,}000 \times (1.04)^{20} = \$21{,}911$ At 1%: $10{,}000 \times (1.01)^{20} = \$12{,}202$ The 4%-growth country's GDP per capita is nearly 80% higher than the 1%-growth country after just 20 years — illustrating the power of compound growth.Q3. Name the three main determinants of labor productivity and give an example of each.
Answer
1. **Human capital** — a worker with a college degree and 10 years of experience is more productive than an untrained worker 2. **Technological change** — the invention of the transistor (1947) led to smartphones and computers that make workers vastly more efficient 3. **Economies of scale** — a bakery with industrial ovens produces more per worker-hour than one with residential ovensQ4. Explain the difference between property rights and contractual rights. Why do they matter for economic growth?
Answer
**Property rights** are the rights to own and use property as one sees fit. **Contractual rights** build upon property rights — they allow individuals to enter agreements regarding property use, with legal recourse for noncompliance. Without them, people won't engage in transactions (risk of non-payment), businesses won't invest (risk of expropriation), and economic growth stalls. The World Bank finds that countries with the weakest legal protections have the lowest GDP per capita.Q5. What is capital deepening? Distinguish between human capital deepening and physical capital deepening with U.S. examples.
Answer
**Capital deepening** is an increase in the average level of capital per person. **Human capital deepening** in the U.S.: the share of adults with a high school diploma rose from ~50% in 1970 to 80%+ by 2000. **Physical capital deepening:** the average U.S. worker in the late 2000s worked with equipment worth nearly 3× what workers had in the early 1950s. Both contribute to higher labor productivity.Q6. What are the three key lessons from growth accounting studies?
Answer
1. **Technology is the most important contributor** to U.S. growth — often explaining more than half of growth 2. **Human capital is at least as important as physical capital** — Europe's post-WWII recovery demonstrates this 3. **All three factors are complementary** — educated workers invent new technologies, which require physical capital investment, which in turn demands new trainingQ7. Explain Alexander Gerschenkron’s “advantages of backwardness.” Under what conditions might this advantage fail to materialize?
Answer
Gerschenkron argued that low-income countries have extra potential for catching up because they can adopt and adapt already-invented technologies rather than pioneering new ones. However, this advantage fails when a country lacks supportive institutions — a functioning legal system, educated workforce, market infrastructure, and stable governance. Without these, the theoretical possibility of technology adoption has little practical relevance.Q8. Using the compound growth formula, calculate how long it takes an economy growing at 5% per year to double its GDP per capita (use the Rule of 70).
Answer
Using the Rule of 70: $\frac{70}{5} = 14$ years. Exact calculation: $(1.05)^{14} = 1.98$ — nearly exactly double. The Rule of 70 provides a quick and accurate approximation for estimating doubling times.Q9. Why doesn’t capital deepening alone lead to sustained economic growth?
Answer
Because of **diminishing marginal returns**. As an economy adds more capital per worker (holding technology constant), each additional unit of capital produces a smaller increase in output. The aggregate production function flattens out. Only by combining capital deepening with technological improvement can an economy shift to a higher production function and sustain growth indefinitely.Q10. Compare the “fast growth club” and “slow growth club” from the convergence data. What pattern emerges?
Answer
The **fast growth club** (Cambodia, China, India, Vietnam, etc.) averaged 5%+ GDP growth in both 1990–2000 and 2010–2019. The **slow growth club** (France, Germany, Italy, Japan, etc.) averaged 2% or less. The pattern: low- and middle-income countries grow faster than high-income countries, consistent with convergence theory. Low-income countries averaged 3.8–4.5% growth vs. 1.7–2.7% for high-income countries.Q11. A Canadian worker produces 10 loaves of bread per hour while a U.S. worker produces 2. If Canadian productivity grows at 1% per year and U.S. productivity grows at 3% per year, who is more productive after 5 years?
Answer
Canada: $10 \times (1.01)^5 = 10.51$ loaves/hour U.S.: $2 \times (1.03)^5 = 2.32$ loaves/hour **Canada is still far more productive** (10.51 vs. 2.32). Even though the U.S. grows faster, the starting gap is so large that convergence takes much longer than 5 years. This illustrates the **slowness of convergence**.Q12. List four government policies that can promote economic growth and explain how each contributes.
Answer
1. **Education investment** — deepens human capital, raising worker productivity (e.g., Denmark's free public schooling) 2. **Low capital gains taxes** — encourages private savings and investment in physical capital 3. **Infrastructure spending** — increases physical capital stock and reduces transaction costs (e.g., Japan's 1990s public works) 4. **Special Economic Zones** — encourage international trade and foreign investment by removing trade taxes (e.g., Mauritius, which enjoyed above-average growth since the 1980s)Q13. Using the Cobb-Douglas production function $Y = A \cdot K^{0.3} \cdot L^{0.7}$, an economy has GDP growth of 4.5%, capital growth of 6%, and labor growth of 1.5%. Calculate TFP growth and interpret what it means.
Answer
Growth decomposition: $$\frac{\Delta Y}{Y} = \frac{\Delta A}{A} + \alpha \cdot \frac{\Delta K}{K} + (1-\alpha) \cdot \frac{\Delta L}{L}$$ $$4.5\% = \frac{\Delta A}{A} + (0.3)(6\%) + (0.7)(1.5\%)$$ $$4.5\% = \frac{\Delta A}{A} + 1.8\% + 1.05\%$$ $$\frac{\Delta A}{A} = 4.5\% - 2.85\% = \mathbf{1.65\%}$$ | Source | Contribution | Share | |---|---|---| | Capital deepening | 1.80% | 40% | | Labor growth | 1.05% | 23% | | TFP / Technology | **1.65%** | **37%** | TFP growth of 1.65% means the economy became 1.65% more efficient at converting inputs into output — through better technology, management, or institutional improvements — independent of simply adding more capital or labor.Q14. Country A starts at $2,000 GDP per capita and grows at 8%. Country B starts at $50,000 and grows at 1%. (a) Using the Rule of 70, how many years for A to double? For B? (b) Using logarithms, when will A’s GDP per capita equal B’s?
Answer
**(a) Doubling times:** - Country A: $70/8 = \mathbf{8.75}$ years - Country B: $70/1 = \mathbf{70}$ years A doubles every ~9 years; B doubles every ~70 years. **(b) Convergence time:** $$2{,}000 \times (1.08)^t = 50{,}000 \times (1.01)^t$$ $$\left(\frac{1.08}{1.01}\right)^t = \frac{50{,}000}{2{,}000} = 25$$ $$(1.0693)^t = 25$$ $$t = \frac{\ln(25)}{\ln(1.0693)} = \frac{3.2189}{0.06698} \approx \mathbf{48.1 \text{ years}}$$ Despite a massive 7-percentage-point growth advantage, it takes nearly **half a century** for A to catch up — illustrating the slowness of convergence when starting gaps are large.Q15. Somalia scores 1.0 (lowest) on the World Bank’s rule-of-law index, while Denmark scores 5.0 (near highest). Somalia has GDP per capita of ~$500 and Denmark ~$60,000. (a) Explain using the aggregate production function why this gap exists. (b) If Somalia improved its rule-of-law score to 3.0 (world average), estimate what would happen to growth rates, citing the three channels.
Answer
**(a)** The aggregate production function says GDP per capita depends on physical capital, human capital, and technology per person. Somalia's weak rule of law undermines all three: - **Physical capital:** Investors won't build factories where property can be seized → low K/L - **Human capital:** Instability disrupts education → low H/L - **Technology adoption:** No incentive to innovate or adopt technology when contracts aren't enforced → low A The 120:1 GDP per capita ratio ($60,000 vs. $500) reflects the compound effect of institutional failure on all three inputs. **(b)** Improving rule of law to world average (3.0) would accelerate growth through three channels: 1. **Investment channel:** Enforceable property rights → foreign and domestic investment rises → physical capital deepening 2. **Human capital channel:** Stable institutions → schools function, returns to education are realizable → human capital deepening 3. **Technology channel:** Contractual rights enable technology licensing, joint ventures, and importing proven methods → TFP growth Countries that improved governance (e.g., Botswana, South Korea, Mauritius) typically saw growth rates jump from 1-2% to 5-8%. But institutional reform itself is the hardest part.7. Glossary
| Term | Definition |
|---|---|
| Aggregate Production Function | The process by which an economy turns inputs (human capital, physical capital, technology) into output (GDP per capita) |
| Capital Deepening | An increase in the average level of physical and/or human capital per person |
| Compound Growth Rate | The rate of growth multiplied by a base that includes past GDP growth, producing exponential effects over time |
| Contractual Rights | Rights of individuals to enter agreements regarding property use, with legal recourse for noncompliance |
| Convergence | Pattern in which economies with low per capita incomes grow faster than those with high per capita incomes |
| Human Capital | The accumulated knowledge, skills, and expertise of workers |
| Industrial Revolution | The widespread use of power-driven machinery and resulting economic/social changes in the first half of the 1800s |
| Infrastructure | A component of physical capital such as roads, rail systems, and utilities |
| Innovation | Putting advances in knowledge to use in a new product or service |
| Invention | Advances in knowledge |
| Labor Productivity | The value of what is produced per worker, or per hour worked |
| Modern Economic Growth | The period of rapid economic growth from approximately 1870 onward |
| Physical Capital | The plant, equipment, and infrastructure that firms use in production |
| Production Function | The process by which a firm turns inputs (labor, machinery, raw materials) into outputs (goods and services) |
| Rule of Law | A system where laws are clear, public, fair, enforced, and equally applicable to all |
| Special Economic Zone (SEZ) | An area where the government does not tax trade, usually with port access, to encourage commerce |
| Technological Change | A combination of invention (advances in knowledge) and innovation (applying those advances) |
| Technology | All the ways existing inputs produce more or higher-quality output, plus entirely new products |