# Growth and Convergence

Business I · Economic History · https://tryals.app/learn/business-i/growth-and-convergence

Why are some countries rich while others remain poor? The **Solow model** predicts that countries with lower capital per worker should grow faster due to diminishing returns to capital, leading to **convergence**.

**Conditional convergence** holds only among peer groups with similar institutions and savings rates—such as OECD countries or US states. However, **unconditional divergence** occurs globally; the rich-poor gap widened from 3:1 in 1820 to over 20:1 today, proving catch-up is not automatic.

$$\text{Conditional convergence} \neq \text{Unconditional convergence}$$

**Growth Failures** explain why some nations miss out:
- **Institutions**: Extractive systems block investment; inclusive property rights foster growth.
- **Geography**: Tropical barriers, disease, and being landlocked impose penalties.
- **Human capital**: Health and skills limit labour quality.
- **State capacity**: Weak or predatory governance strangles enterprise.

## Why Convergence Fails

**Total factor productivity (TFP)** explains most cross-country income gaps. Rich nations are not just capital-heavy; they use all inputs more productively through better technology, management, and trust.

Since 1990, **The Great Convergence** has been driven by China and India, shifting global distribution as Asia rapidly catches up.

| Scope | Result |
| --- | --- |
| Similar institutions (OECD) | Poor members grow faster, convergence |
| Full world sample | No automatic catch-up, divergence common |
| The difference | Institutions, human capital, savings, stability |

> **Pitfall:** The **Lucas paradox**—capital failing to flow to capital-poor regions—proves that institutional barriers bind development far more than mere capital scarcity.

## Practice questions

9 of this lesson's 14 practice questions, with answers. The full set is in the app.

### 1. Unconditional convergence, all poor countries growing faster than rich ones regardless of institutions, is strongly supported by the data.

**Answer:** False

**Why:** Unconditional convergence fails the data test. Only conditional convergence (among similar-institution peers) holds. Without good institutions, being poor does not guarantee fast growth.

Page: https://tryals.app/practice/business-i/growth-and-convergence/unconditional-convergence-all-poor-countries-growing-faster-than

### 2. A country's GDP per capita is **2,000 dollars** (constant 2011 PPP). The US level is **60,000 dollars**. Express this country's income as a **percentage of the US level**.

**Answer:** 3.33 (within ±0.1)

**Why:** $2{,}000 / 60{,}000 \approx 3.33\%$ of US income, a 30:1 gap that summarises the divergence problem in one number.

Page: https://tryals.app/practice/business-i/growth-and-convergence/a-countrys-gdp-per-capita-is-2-000-dollars-constant-2011-ppp-the

### 3. China's GDP per capita grew at roughly what annual rate between 1990 and 2020 (in %)?

**Answer:** 8 (within ±1)

**Why:** About 8% annually, the fastest sustained per-capita growth in history. At 8%, income doubles every 9 years.

Page: https://tryals.app/practice/business-i/growth-and-convergence/chinas-gdp-per-capita-grew-at-roughly-what-annual-rate-between-1990

### 4. Sort each factor into its school of thought.

**Answer:**

- Institutions (Acemoglu): Property rights and rule of law, Extractive vs inclusive political systems
- Geography (Sachs): Malaria burden in the tropics, Landlocked location and distance from markets
- Human capital: Years of schooling and literacy rates

**Why:** Three schools, overlapping but distinct: institutions create incentives, geography imposes constraints, and human capital determines what labour can do.

Page: https://tryals.app/practice/business-i/growth-and-convergence/sort-each-factor-into-its-school-of-thought

### 5. Match each growth concept to its meaning.

**Answer:**

- Convergence → Poorer countries growing faster and catching up
- Divergence → The gap between rich and poor countries widening
- TFP → Productivity not explained by capital or labour alone
- Extractive institutions → Systems concentrating wealth in a few hands

**Why:** Four concepts that frame the biggest question in economics, why some nations are rich and others poor.

Page: https://tryals.app/practice/business-i/growth-and-convergence/match-each-growth-concept-to-its-meaning

### 6. Growth accounting finds that most of the income gap between rich and poor countries is not explained by capital or education. What does that residual tell us?

A. That total factor productivity is a mathematical artefact with no real content
B. That poor countries lack natural resources, which growth accounting omits
C. That the measurements of capital and education are too imprecise to be useful
D. That how inputs are combined matters more than how many

**Answer:** D. That how inputs are combined matters more than how many

**Why:** TFP is a measure of our ignorance and also a finding: give a poor country identical capital and schooling and it still produces less, so the binding constraint is organisational rather than physical. It is why development economics turned toward institutions after decades of financing machines.

Page: https://tryals.app/practice/business-i/growth-and-convergence/growth-accounting-finds-that-most-of-the-income-gap-between-rich-and

### 7. Why does TFP explain most of the income gap between rich and poor countries?

A. Poor countries have higher TFP but less capital
B. Rich countries simply have more natural resources
C. Rich countries use all inputs more productively
D. TFP is the same everywhere, only capital differs

**Answer:** C. Rich countries use all inputs more productively

**Why:** TFP captures everything beyond raw inputs: institutions, technology, management, trust. Giving a poorly governed country more capital doesn't close the gap, the deep determinants need to change.

Page: https://tryals.app/practice/business-i/growth-and-convergence/why-does-tfp-explain-most-of-the-income-gap-between-rich-and-poor

### 8. Which regions have shown strong convergence growth since 1990?

A. Sub-Saharan Africa (broadly)
B. East Asia (China, South Korea, Vietnam)
C. Southeast Asia (Thailand, Indonesia)
D. South Asia (India)

**Answer:** B. East Asia (China, South Korea, Vietnam); C. Southeast Asia (Thailand, Indonesia); D. South Asia (India)

**Why:** Asia broadly has converged. Sub-Saharan Africa has had mixed results, some countries have grown, but many have not converged, and the gap with the rich world remains large.

Page: https://tryals.app/practice/business-i/growth-and-convergence/which-regions-have-shown-strong-convergence-growth-since-1990

### 9. Order the historical arc of global income divergence and convergence.

**Answer:**

1. Pre-industrial world: income roughly similar everywhere (~3:1)
2. Industrial Revolution: Europe and US pull ahead
3. Colonial era: extractive institutions cement divergence
4. Postwar: Japan and Europe converge toward the US
5. Post-1990: China and India begin rapid catch-up

**Why:** Similarity, divergence, institutional lock-in, selective convergence, and the Asian surge, the global income story in five acts.

Page: https://tryals.app/practice/business-i/growth-and-convergence/order-the-historical-arc-of-global-income-divergence-and-convergence