Development Economics Workbench
A working study companion for Development Economics (发展经济学), built from the three course slide decks (Chapters 1–3) and rearranged so the models come first. The decks are the Pearson slides for Todaro & Smith, Economic Development, annotated and updated by the course instructor — Chinese glosses, refreshed data, and his own exercises with answers.
How this workbench is organised
the same five blocks in every chapterHow the chapter's ideas build on one another, drawn as a chain rather than a list. Where a theory is answering an earlier one, the arrow says so.
Explanatory prose with the instructor's own worked examples taken apart step by step, plus the data behind each table and figure.
Every formula from the chapter in one place, with the meaning of each symbol. Prints on its own.
The vocabulary, defined in English with the instructor's own Chinese gloss where he supplied one.
Graded multiple choice plus step-by-step calculation problems, including the instructor's own exercises verbatim with his published answers. Your score is stored in this browser and the dashboard below tracks it chapter by chapter, so a week before the exam you can see which chapter is still weak.
Model index
four interactive figures · drag the slidersDevelopment economics is a subject argued in diagrams. Each model below is live: move the parameters and the curves, the steady state, and the areas recompute as you go. They sit inside their chapters, and this index jumps straight to them.
The post-war savings-and-growth arithmetic, g = s/c, with the fixed-coefficient production function it rests on. Chapter 3.
Surplus labour in agriculture, a horizontal labour supply in industry, and the turning point where wages finally start to rise. Chapter 3.
Saving, population growth and depreciation meet at the steady state — and the reason poorer countries grow faster on the way there. Chapter 3.
Why the 2010 reform swapped the arithmetic mean for a geometric one, and what that does to a country that is good at one thing and bad at another. Chapter 2.
Reading the callouts
four kinds of aside, four coloursConnects a concept to another chapter. The four growth theories in Chapter 3 are not a list — each one is a reply to the one before it, and these boxes are where the argument between them shows.
Material the slides leave hanging, and the source data behind each table. Where the instructor updated a figure past the printed textbook — several tables now carry 2022–2026 data — the workbench follows the slides, since that is what will be examined.
Places where two ideas are easy to confuse, or where something on a slide is slightly off. The slides omit the Millennium Development Goal 3 target row, and elsewhere a worked example rounds a figure it should not; both are flagged where they occur rather than quietly fixed.
The instructor's own discussion questions, kept verbatim, with a worked answer below each.
Chapters
three delivered so farProgress dashboard
stored locally in this browserHow to use this before the exam
a suggested orderChapter 3 carries most of the examinable machinery. Work the four models until you can predict what each slider does without touching it — what happens to the steady state when the saving rate rises, why the Lewis wage stays flat until the turning point, what s/c does when c falls. The prose is there to explain the diagrams, not the other way round.
The instructor marked the terms he cares about by writing the Chinese translation into the slide. Those glosses are reproduced here as the Chinese anchor on every key concept — if you can produce the English term from the Chinese one, and say why it matters, that is the concept question answered.
Chapter 3 ends with two exercises the instructor worked in class — a Harrod-Domar calculation and a full Lewis two-sector construction — with his published answers. Both are reproduced verbatim in the self-check block, answers included.
Introducing Economic Development: A Global Perspective
Chapter 1 does three things. It shows you what poverty actually looks like from the inside rather than as a number; it locates development economics as a field — what it shares with neoclassical economics and political economy, and where it breaks away; and it argues that "development" is not the same thing as "income per head", which is the argument the rest of the course is built on. The last section sets out the international goals that framed the field from 2000 to 2015.
The examinable core is section 1.3: Sen's capability approach, and the three core values of development. Both carry a Chinese gloss the instructor wrote into the slide himself — 可行能力 and 奴役 — and those are the terms he expects you to be able to produce.
Concept Map
how the chapter buildsThe capability approach defined here is what Chapter 2's Human Development Index tries to operationalise. Keep the three dimensions Sen argues for in mind — health, knowledge, and a decent standard of living — because the HDI is exactly those three and nothing else. The argument in 1.3 about income having diminishing returns is the same argument behind Figure 1.2 and behind the income index's logarithmic form in Chapter 2.
1.1 How the Other Half Live
slides 2–8 · Todaro 13e §1.2The chapter opens not with a definition but with six testimonies. They are worth reading closely, because the definition of development the chapter eventually gives is assembled out of exactly the things they mention.
Read together, the six say something a single income statistic cannot. The Ugandan woman is describing the loss of voice before she gets to the loss of food. The Moldovan woman is describing shame. The Ethiopian is describing vulnerability. Only the Brazilian mentions income directly, and even there it is bundled with medicine and clothing. The slide draws the conclusion in one line:
That single sentence is the chapter's thesis. If poverty has several dimensions, then a development policy that raises income while leaving the other dimensions untouched has not, by this definition, succeeded.
The slide shows a map of China's urban per capita disposable income in 2022, set against a scale running from Vietnam and Brazil up through Russia, China, Hungary and on to the Czech Republic and Taiwan (China) — the point being that China's national figure conceals provinces sitting at very different rungs of that scale. The instructor then shows four county-level photographs from his own undergraduate fieldwork — Mulei (Xinjiang, 2006), Yan'an (Shaanxi, 2005), Nayong (Guizhou, 2007) and Hulin (Heilongjiang, 2007) — which is the same argument at the scale of a single country: the national average is not a description of anyone's actual life.
1.2 Economics and Development Studies
slides 9–12 · Todaro 13e §1.4Three scopes, not three opinions
Development economics is not a political stance within economics; it is a different scope. The slide sets it beside two neighbours, and the comparison is examinable as a comparison.
| Approach | What it studies | Its working assumptions |
|---|---|---|
| Traditional neoclassical economics | Efficient allocation of scarce resources; optimal growth over time | Perfect markets and a single equilibrium |
| Political economy | How social groups and elites shape resource allocation and distribution | Focus on power and conflict |
| Development economics | Structural transformation of low-income economies, and broad-based improvement in human well-being | Broader scope — includes the two above and asks about institutions |
Key features of developing economies
These four features are the reason the neoclassical apparatus cannot simply be transplanted. Each one is a textbook assumption being switched off.
The slide's summary line: development economics studies the economic, social, and institutional mechanisms that raise living standards at scale.
The important role of values
Development is not value-free — judgements of "improvement" are inherently normative. Policy involves trade-offs between efficiency, equity, growth, stability and sustainability, and the slide is explicit that the focus on poverty and freedom rests on normative commitments to dignity and justice. This is not a disclaimer; it is a claim that the subject matter cannot be described without choosing what counts as better.
Economies as social systems
Four claims, each of which rules out a purely economic answer:
- Economies are embedded in institutions, culture, history, and politics.
- Development policy depends as much on institutional variables as on capital and labour.
- Policies that work in rich countries often fail in developing contexts.
- A holistic, interdisciplinary approach is therefore required.
The "multiple equilibria" point is what later makes the false-paradigm model in Chapter 3 a criticism rather than a curiosity, and it is why the Lewis model's assumption of a single labour market is attacked. Keep the phrase "institutional rigidities" — it appears again in Chapter 3 as the reason capital does not simply flow to where its return is highest.
1.3 What Do We Mean by Development?
slides 13–17 · Todaro 13e §1.5–1.6 · the examinable coreThe traditional economic measure
National development = growth in GNI or income per capita, with income as the main driver of utility. Chapter 2 will show you how this is measured and why the measurement is harder than it looks. The point here is narrower: this is the definition the rest of section 1.3 is arguing against.
The new view: Sen's capability approach 可行能力
Amartya Sen's reformulation replaces income with freedom as the thing to be maximised. Development is the expansion of human capabilities and substantive freedoms. Four terms carry the whole argument:
The distinction examiners reach for is functionings vs capabilities: functionings are what you actually achieve, capabilities are what you could achieve. A person who has plenty to eat has the functioning of being well-nourished; a person who has plenty to eat but lacks access to it has neither. A person fasting by choice has the functioning available as a capability but is not exercising it — and Sen's point is that these two cases are not equivalent, even though both are hungry. Income alone cannot tell them apart.
Some key capabilities
The slide splits them into "beings" (states of existence) and "doings". Each list is a checklist rather than a hierarchy.
| Beings — states of existence | Doings — activities |
|---|---|
| Being able to live a long and healthy life | Being mobile and able to travel freely |
| Being well-nourished and adequately clothed | Being able to take part in the life of the community |
| Being literate and knowledgeable | Working and earning a livelihood |
| Have self-respect and dignity 尊严 | Making autonomous 自主的 life choices |
The slide prints the second column as "Doings (states of existence)", repeating the first column's parenthetical. That is a slip in the deck — doings are activities, not states of existence, and the distinction between the two columns is precisely the point. The table above has been corrected; the slide's wording has not been silently followed.
The three core values of development
This is the most examinable list in the chapter. Three values, each with a short definition and a stated goal.
Notice that only the first of the three is a material condition. A country that eliminated absolute poverty but left its people without voice, dignity or independence would, on this slide's own terms, not yet be developed. That is a strong claim, and it is worth being able to defend it.
Income and happiness: Figure 1.2
The slide plots happiness (vertical) against income per head in US$ per year (horizontal, running to about $35,000), one dot per country, using Layard's data. Three numbered conclusions are printed on it:
The scatter is a steep rise at low income and a near-flat cloud at high income. Ukraine sits at the bottom of the vertical scale, in the low 30s; the high-happiness cluster (roughly 80–100) contains countries spread across a very wide income range, which is the second conclusion made visible — the same happiness level is reached at $10,000 and at $35,000.
Conclusion 1 is the reason the income index inside the HDI takes a logarithmic form, which you will meet in Chapter 2: the index has to be built so that an extra dollar changes it more at $500 than at $30,000. If you can explain why the logarithm is there, you have understood both this figure and that formula.
The central role of women
Women's empowerment is both a core goal and a key driver of development — it improves child health, education, and long-run human capital. The slide states it as a two-way relationship, and the distinction matters: even if you cared nothing about equity between men and women, the growth evidence would still make female education one of the highest-return investments available.
The three objectives of development
- Increase the availability of life-sustaining goods Food, shelter, health, protection
- Raise overall levels of living Higher incomes, more jobs, better education, greater attention to cultural and human values
- Expand the range of economic and social choices By freeing people from servitude and dependence
These three objectives are the three core values restated in operational form — the same three ideas, said once as values and once as aims.
The theory in this section is easier to hold onto with an example, and the textbook supplies the best one in Case Study 1: Pakistan and Bangladesh. The two were a single country until 1971, and the comparison isolates one variable — they share language, religion, colonial history and much else — while their development paths diverged sharply.
Pakistan is still the richer country. On PPP-adjusted estimates its average income was $5,311 in 2017 against $3,677 in Bangladesh. That is the income story, and it has not reversed.
But the human development story ran the other way. In 1970, on the eve of independence, life expectancy in Pakistan was 54 years and in Bangladesh only 44. By 2012 the positions had reversed: 69 in Bangladesh against 65 in Pakistan. Under-5 mortality tells the same story from the other end — Bangladesh started far worse (239 per 1,000 in 1970 against Pakistan's 180) and then fell faster, reaching 139 against 122 by 1990 and continuing to converge.
The growth figures then follow: over 2000–2017 Pakistan's GDP grew about 5.1% a year but with population growth of 2.1%, giving roughly 3% per head. Bangladesh grew about 6% with population growth of only 1.3%, giving about 4.7% per head — and overtaking Pakistan on income per person as well.
This is Chapter 1's whole argument in one pair of countries. If development meant income, the ranking would be settled and Pakistan would win. On Sen's account — and on the evidence of life expectancy and child survival — Bangladesh has been the more successful developer of the two, and the income ranking is now moving to follow the capability gains rather than the other way round.
It also makes concrete what the textbook says about why. Bangladesh's agricultural development proceeded faster and its benefits were less unequally distributed; Pakistan's was held back by social constraints, with the landlord elite capturing the gains from irrigation and the Green Revolution. Same soil, same crop technology, different distribution of power — which is the "institutions and social systems" point from §1.2 showing up as an outcome.
1.4 The Millennium Development Goals
slides 18–21 · Todaro 13e §1.7Eight goals adopted by the United Nations in 2000, with a 2015 deadline. They are worth knowing as a list, because the SDGs that replaced them are an extension of the same structure.
| Goal | Millennium Development Goal |
|---|---|
| 1 | Eradicate extreme poverty and hunger |
| 2 | Achieve universal primary education |
| 3 | Promote gender equality and empower women |
| 4 | Reduce child mortality |
| 5 | Improve maternal health |
| 6 | Combat HIV/AIDS, malaria, and other diseases |
| 7 | Ensure environmental sustainability |
| 8 | Develop a global partnership for development |
Table 1.1 — the goals and their targets
The full table runs to two slides. The targets are the measurable half of each goal:
| Goal | Targets |
|---|---|
| 1 · Extreme poverty and hunger | Reduce by half the proportion of people living on less than $1 a day · Reduce by half the proportion of people who suffer from hunger |
| 2 · Universal primary education | Ensure that all boys and girls complete a full course of primary schooling |
| 3 · Gender equality | No target printed on the slide — see the note below. |
| 4 · Child mortality | Reduce by two-thirds the mortality rate among children under 5 |
| 5 · Maternal health | Reduce by three-quarters the maternal mortality ratio |
| 6 · HIV/AIDS, malaria, other diseases | Halt and begin to reverse the spread of HIV/AIDS · Halt and begin to reverse the incidence of malaria and other major diseases |
| 7 · Environmental sustainability | Integrate the principles of sustainable development into country policies and programmes and reverse the loss of environmental resources · Reduce by half the proportion of people without sustainable access to safe drinking water · Achieve significant improvement in the lives of at least 100 million slum dwellers by 2020 |
| 8 · Global partnership | An open, rule-based, predictable, non-discriminatory trading and financial system · Address the special needs of the least developed countries (tariff- and quota-free access, debt relief for HIPCs, more generous ODA) · Address the special needs of landlocked countries and small island developing states · Deal comprehensively with developing-country debt · Decent and productive work for youth · Access to affordable essential drugs · Make available the benefits of new technologies, especially information and communications |
Goal 3 has no target row on the slide. The printed textbook table carries one — "Eliminate gender disparity in primary and secondary education, preferably by 2005, and in all levels of education no later than 2015" — and the slide's target count is one short of the textbook's, which is how you can tell the row was dropped rather than renumbered. It is flagged here rather than filled in silently, because the omission is visible in the deck you are revising from.
From the MDGs to the SDGs
The MDG era ended in 2015. In September of that year UN leaders adopted the 2030 Agenda, launching 17 Sustainable Development Goals to be achieved over the following fifteen years. The SDGs are broader than the MDGs — they apply to all countries rather than only to developing ones, and they add goals on inequality, energy, cities, and climate that the MDGs never covered.
The instructor's update slide carries a number worth remembering: according to the 2025 Sustainable Development Goals Report, only about 35–36% of the targets are progressing well or making moderate progress. The figure is on the slide because it is the honest counterpoint to the 2015 launch language — the goals were adopted, but the scorecard at the ten-year mark is not flattering.
Conclusions
The chapter closes on three points: the importance of development economics; the inclusion of non-economic variables in designing development strategies; and the effort to achieve the MDGs. The slide's closing quotation is "…One future — or none at all." The instructor also assigned the documentary Why Poverty?, Episode 1: Poor Us, which is the same argument as section 1.1 in film form.
Formula Sheet
print-friendlyChapter 1 is almost entirely conceptual, so there is little arithmetic. What follows is the small amount of notation the chapter does define, plus the definitions in the form you would want to write them in an exam.
Key Concepts
21 terms · 8 from the textbookTerms carrying a 中文 anchor are the ones the instructor wrote a Chinese gloss for on the slide — he does that on the terms he treats as examinable, so those are the priority. Definitions marked Todaro are quoted or closely paraphrased from the margin definitions in the 13th edition, so the wording matches what you would be marked against.
Self-Check
16 questions · gradedSection A tests the definitions you would be asked to write out. Section B tests the distinctions that are easy to blur — functionings against capabilities, the three values against the three objectives. Section C asks for the extended answers.
A · Definitions
B · Distinctions
C · Extended answers
- Sustenance — the ability to meet basic needs (food, shelter, health, protection). Goal: to end absolute poverty.
- Self-esteem — a sense of worth and dignity; recognition as an autonomous person. Goal: to be recognised as a person, not a recipient.
- Freedom from servitude — expanded real choices, liberation from dependency and oppression. Goal: expanded real choices.
Only sustenance is a material condition: it can be measured in goods. Self-esteem and freedom from servitude are about a person's standing and range of choice, which can be absent even when basic needs are fully met — which is why the chapter insists a country is not developed merely because its people are fed.
Functionings are actual achievements — the "beings and doings" a person really attains. Capabilities are the real freedom to achieve alternative functionings — the set of lives actually open to them.
Someone starving for lack of food and someone fasting by choice are both failing to achieve the functioning of being well-nourished. But only the second has the capability of being well-nourished: food is available to them and they could choose otherwise. Sen's framework therefore treats their situations as unequal, and argues that any measure built on outcomes alone — income, calorie availability — cannot see the difference. Development, on this view, is about expanding the capability set, not just the level of achievement.
- Diminishing returns of income. Income lifts happiness strongly at low levels; the gains flatten above roughly $20,000 per capita.
- Income is not the only driver. Large happiness gaps exist between countries at similar income levels.
- Development ≠ just GDP growth. Well-being depends on more than income alone.
The implication is that a measure built only on income will misrank countries — in particular it will understate how much well-being a poor country has achieved, and overstate what further income can buy at high levels. That is the motivation for the Human Development Index in Chapter 2, which combines health and education with income, and for the logarithmic form of its income component: the logarithm is what encodes diminishing returns.
- Economies are embedded in institutions, culture, history and politics. Policy cannot be designed from economic theory alone.
- Development policy depends as much on institutional variables as on capital and labour. Two countries with the same endowments can perform very differently.
- Policies that work in rich countries often fail in developing contexts. Transplanting a policy assumes the institutional preconditions came with it.
- A holistic, interdisciplinary approach is required. Development economics has to borrow from outside economics.
Together they explain why the field cannot adopt the neoclassical assumptions wholesale, and they set up the "multiple equilibria" point — if institutions differ, the same endowments need not lead to the same outcome.
Because the goals are the three core values written as measurable commitments. MDG 1 (halve extreme poverty and hunger) is sustenance; MDG 3 (gender equality and empowering women) and MDG 2 (universal primary education) are self-esteem and capability expansion; MDG 8 (a global partnership) is about removing dependency. The framework is the chapter's argument turned into targets with a deadline.
The move to 17 SDGs in 2015 widened the scope further — applying to all countries rather than only developing ones, and adding goals on inequality, energy, cities and climate — which reflects the same underlying claim that development is multidimensional. The 2025 report's finding that only about 35–36% of targets are on track is the honest measure of how far the agenda has actually been implemented.
- Increase the availability of life-sustaining goods — food, shelter, health, protection. Corresponds to sustenance.
- Raise overall levels of living — higher incomes, more jobs, better education, greater attention to cultural and human values. Corresponds to self-esteem.
- Expand the range of economic and social choices — by freeing people from servitude and dependence. Corresponds to freedom from servitude.
The objectives are the core values restated as aims: the same three ideas, said once as what development is and once as what policy should do.
Comparative Economic Development
Chapter 1 argued that development is multidimensional. Chapter 2 is about the consequence: if development is multidimensional, then measuring it is genuinely hard, and every measurement choice is an argument in disguise. The chapter works through the definitions (who counts as developing), the basic indicators (income, health, education), the conversion problem (exchange rates or PPP), and the holistic measures (the HDI and its 2010 rebuild), before listing the ten characteristics developing countries share and the eight ways today's low-income countries differ from the now-developed countries at the same stage.
The examinable core is the Human Development Index — both the old form and the new — because both worked examples are on the slides with every intermediate number, and because the geometric-mean reform is a conceptual argument as much as a formula change. The interactive calculator below shows what that argument looks like when you move it.
Concept Map
how the chapter builds2.1 Defining the Developing World
slides 2–4 · Todaro 13e §2.2 (and §1.3)The World Bank's scheme is the one used in practice: countries are ranked on GNI per capita and sorted into four bands. The thresholds are revised every year, so the slide's 2025 numbers are the ones to quote.
| Group | GNI per capita (2025) | What it means |
|---|---|---|
| Low-income countries (LIC) | < $1,175 | The group the term "developing" most often means, though the World Bank's own "developing" category is LIC + LMC + UMC together. |
| Lower-middle-income (LMC) | < $4,635 | Includes India, Viet Nam, Pakistan, Nigeria. |
| Upper-middle-income (UMC) | < $14,375 | Includes China, Brazil, South Africa, Turkey. |
| High-income countries | > $14,375 | The World Bank's replacement for the older "developed" label. |
The bands are nested in a way that is easy to misread: each threshold is the upper bound of its group, so LMC means "below $4,635 but above $1,175". Note also that the UMC ceiling and the high-income floor are the same number — $14,375 — because together they partition the range.
The slide also shows the alternative grouping the course uses when geography matters more than income: by region. The two groupings disagree on purpose. A country can be upper-middle-income and in Sub-Saharan Africa, or low-income and in East Asia, and which grouping is useful depends on the question — income explains what a government can afford, region explains what its neighbours are doing.
The simplest alternative definition is the one on the instructor's second slide: treat non-OECD countries as developing. The OECD has 38 members, spanning North America, South America, Europe and Asia–Pacific, with members joining in waves from 1961 (Austria, Belgium, Canada, Denmark, France, Germany, Greece, Iceland, Ireland, Luxembourg, the Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, Turkey, the United Kingdom, the United States) through 2021 (Costa Rica). Several countries are in accession talks rather than in the club. The definition is convenient but blunt: it puts Chile and Mexico in the same box as Germany.
The deck gives only the World Bank's income bands. Todaro 13e §2.2.3 lists the other official classifications you would be expected to recognise, and they cut the world up on quite different principles — income, vulnerability, geography, debt:
| Classification | Basis and size |
|---|---|
| G7 and G20 | Geopolitical rather than developmental: the seven largest developed economies, and an expanded group of twenty that brings in the large middle-income countries. |
| Least-developed countries (LDCs) | A UN designation, 47 countries as of end-2018 — 33 in Africa, 9 in Asia, 4 in Oceania, plus Haiti, home to just over a billion people. Entry requires meeting all three of: low income, low human capital, and high economic vulnerability. Countries graduate out: Botswana, Cabo Verde, Equatorial Guinea, Maldives and Samoa already have. |
| Landlocked developing countries (LLDCs) | 30 countries, 15 of them in Africa. A geography-based designation — being landlocked is treated as a distinct development handicap. |
| Small island developing states (SIDS) | 38 countries, recognised for the particular vulnerabilities of small island economies. |
| Heavily indebted poor countries (HIPCs) | 39 countries as of 2019, singled out for debt-relief programmes under international agreements. |
| Newly industrialising countries (NICs) | An informal label for economies at an early stage of export-led manufacturing growth — applied to South Korea and Taiwan in the 1970s–80s, then Thailand and Indonesia. Vietnam is the modern candidate. |
Note the pattern: only the World Bank grouping is strictly income-based. The others exist because income alone does not capture the obstacle — being landlocked, being a small island, or carrying an unsustainable debt overhang each change what a country needs, at the same income level. That is Chapter 1's multidimensionality argument showing up as administrative practice.
2.2 Basic Indicators: Real Income, Health, Education
slides 5–8 · Todaro 13e §2.2.1GNI and GDP
Two accounting identities that get confused constantly. The difference is who is being counted, not what is being counted.
The distinction comes down to one word in each definition. GNI counts what a country's residents earn wherever they earn it, so it adds remittances and subtracts profits repatriated by foreign firms. GDP counts what is produced inside the borders, regardless of who owns it. For a country with large remittance inflows — the Philippines, Bangladesh, Egypt — GNI is meaningfully higher than GDP; for a country hosting a lot of foreign-owned capital, the reverse.
The expenditure approach to GDP
Y = GDP in dollars · C = consumption · I = investment · G = government purchases · NX = net exports = exports − imports
This is the national income accounting identity. It is useful because it breaks GDP into components according to their purpose: goods and services can be consumed, invested by the private sector, bought by the government, or shipped abroad. NX can be positive or negative — a country that exports more than it imports has positive net exports; the United States, which imports more than it exports, has negative net exports and correspondingly a trade deficit.
Measuring changes over time
| Measure | Definition | What makes it move |
|---|---|---|
| Nominal GDP | A measure of GDP when prices and quantities have not been separated | Changes in prices or quantities — you cannot tell which from the number alone |
| Real GDP | The actual quantity of goods and services produced | Changes in quantities only — prices are held fixed |
The slide's own illustration: US nominal GDP was $14.4 trillion in 2008 and only $7.4 trillion in 1995. Did prices change? Did quantities change? Some of both — and the whole point of real GDP is to answer the question that the nominal figure leaves open. The instructor's note frames it as the familiar (total revenue) = price × quantity: nominal GDP is the revenue line, real GDP holds the price term still.
The same price-vs-quantity problem appears in a different form in section 2.3, when comparing across countries rather than across years. There, the exchange rate plays the role of the price term — and the fix is purchasing power parity rather than deflation.
Purchasing Power Parity
slides 9–10 · Todaro 13e §2.2.2Comparing incomes across countries needs a conversion factor, and the obvious one — the market exchange rate — answers the wrong question. It tells you what a dollar buys in currency markets; what you want to know is what it buys in the local market. In poor countries, non-traded goods and services (a haircut, a meal, a bus ride, housing) are far cheaper than they are in rich ones, so converting at the market rate systematically understates real incomes in poor countries.
What the difference looks like in the data
The instructor's table (slide 10) puts the two conversion methods side by side. The pattern is systematic: the poorer the country, the larger the upward revision from switching to PPP.
| Country | Exchange rate (US$) | PPP (US$) | PPP ÷ exchange rate |
|---|---|---|---|
| Niger | 360 | 990 | 2.75× |
| Congo, Dem. Rep. | 460 | 870 | 1.89× |
| Uganda | 600 | 1,820 | 3.03× |
| Haiti | 760 | 1,830 | 2.41× |
| Cambodia | 1,230 | 3,750 | 3.05× |
| Senegal | 1,240 | 3,360 | 2.71× |
| Kenya | 1,460 | 3,250 | 2.23× |
| Bangladesh | 1,470 | 4,040 | 2.75× |
| Pakistan | 1,580 | 5,830 | 3.69× |
| Côte d'Ivoire | 1,580 | 3,820 | 2.42× |
| India | 1,800 | 6,980 | 3.88× |
| Ghana | 1,880 | 4,280 | 2.28× |
| Nigeria | 2,100 | 5,700 | 2.71× |
| Vietnam | 2,160 | 6,450 | 2.99× |
| Egypt, Arab Rep. | 3,010 | 11,360 | 3.77× |
| Bolivia | 3,130 | 7,340 | 2.35× |
| Indonesia | 3,540 | 11,900 | 3.36× |
| Philippines | 3,660 | 10,050 | 2.75× |
| Guatemala | 4,060 | 8,000 | 1.97× |
| Colombia | 5,890 | 14,090 | 2.39× |
| Thailand | 5,950 | 17,040 | 2.86× |
| Peru | 5,960 | 12,880 | 2.16× |
| Dominican Republic | 6,630 | 15,290 | 2.31× |
| Botswana | 6,730 | 16,420 | 2.44× |
| Brazil | 8,600 | 15,200 | 1.77× |
| Mexico | 8,610 | 17,840 | 2.07× |
| China | 8,690 | 16,760 | 1.93× |
| Costa Rica | 11,120 | 16,200 | 1.46× |
| Chile | 13,610 | 23,570 | 1.73× |
| Korea, Rep. | 28,380 | 38,340 | 1.35× |
| United Kingdom | 40,530 | 42,560 | 1.05× |
| Canada | 42,870 | 46,070 | 1.07× |
| United States | 58,270 | 60,200 | 1.03× |
| Low income | 775 | 2,127 | 2.74× |
| Middle income | 4,942 | 11,993 | 2.43× |
| High income | 40,142 | 47,575 | 1.19× |
The ratio column is the story. For high-income countries PPP is barely different from the market rate — the United States is 1.03×, because it is the base. For low-income countries the revision is around two-and-a-half to three times, and the largest ratios in the table belong to India (3.88×), Egypt (3.77×) and Pakistan (3.69×). The low-income group average rises from $775 to $2,127 — a country that looks desperately poor at market rates looks merely poor at PPP.
PPP does not make poor countries rich; it makes the comparison less misleading. And the correction is not uniform — it depends on how much of a country's consumption basket is non-traded, which is why China's ratio (1.93×) is lower than India's (3.88×). If you are asked why, the answer is that China's price level for non-traded goods is closer to international levels than India's is.
Figure 2.2 on the slide ranks 18 countries by GNI per capita at market rates, and the visual point is how compressed the developing world is at the bottom: Congo (Dem. Rep.) $460, Ethiopia ≈$740, Haiti $760, Kenya $1,460, Bangladesh $1,470, Pakistan $1,580, Côte d'Ivoire $1,580, India $1,800, Ghana $1,880, Egypt $3,010, Indonesia $3,540 — and then a jump to the Dominican Republic $6,630, Brazil $8,600, Mexico $8,610, China $8,690, and finally the United Kingdom $40,530, Canada $42,870, United States $58,270. Thirteen of the eighteen countries cluster in the leftmost tenth of the chart.
2.3 Holistic Measures: the Human Development Index
slides 11–21 · Todaro 13e §2.3 + App. 2.1 · the examinable coreThe HDI is Sen's capability approach made operational: three dimensions — health, knowledge, and a decent standard of living — combined into one number between 0 and 1. The classification bands are:
| Band | HDI value |
|---|---|
| Low human development | 0.000 – 0.499 |
| Medium human development | 0.500 – 0.799 |
| High human development | 0.800 – 0.900 |
| Very high human development | 0.900 – 1.000 |
The slide also stresses that the HDI can be calculated for groups and regions within a country, not just for countries — it varies among groups, across regions, and between rural and urban areas. That matters: the whole point of a holistic measure is that a national average can hide the thing you care about.
The old HDI, worked: Bangladesh in 2007
This is the slide's own example, with every intermediate number. The old HDI builds a sub-index for each dimension and then takes the arithmetic mean.
- Income index — logarithmic, because of diminishing returns [ln(1241) − ln(100)] / [ln(40000) − ln(100)] = 0.420
- Life expectancy index (65.7 − 25) / (85 − 25) = 0.678
- Adult literacy index (53.5 − 0) / (100 − 0) = 0.535
- Gross enrolment index (52.1 − 0) / (100 − 0) = 0.521
- Education index — two-thirds literacy, one-third enrolment (2/3)(0.535) + (1/3)(0.521) = 0.530
- HDI — the arithmetic mean of the three (1/3)(0.420) + (1/3)(0.678) + (1/3)(0.530) = 0.543
The goalposts are visible inside the formulas: life expectancy runs from 25 to 85 years, literacy and enrolment from 0 to 100%, and income from ln(100) to ln(40,000). The income index is logarithmic precisely because of the diminishing-returns result from Figure 1.2 in Chapter 1.
What is new in the New HDI
The UNDP rebuilt the index in November 2010. There are two headline changes and several smaller ones.
The smaller changes are just as examinable:
| Change | From → to |
|---|---|
| Income measure | GDP per capita → GNI per capita |
| Education components | Adult literacy + gross enrolment → average actual educational attainment of the whole population, and the expected attainment of today's children |
| Maximum values | Predefined cutoffs → the observed maximum in each dimension |
| Lower goalpost for income | Reduced, on new evidence about how low income levels can go |
The effect of the whole package is that the New HDI can identify not only whether a country is developing, but also whether various significant groups within that country are participating in the development.
The New HDI, worked: China in 2010
- Life expectancy index (73.5 − 20) / (83.2 − 20) = 0.847
- Mean years of schooling index (7.5 − 0) / (13.2 − 0) = 0.568
- Expected years of schooling index (11.4 − 0) / (20.6 − 0) = 0.553
- Education index — a geometric mean of the two, rescaled [√(0.568 × 0.553) − 0] / (0.951 − 0) = 0.589
- Income index [ln(7263) − ln(163)] / [ln(108211) − ln(163)] = 0.584
- New HDI — the cube root of the product ∛(0.847 × 0.589 × 0.584) = 0.663
Compare the two examples carefully. In Bangladesh the three indexes are added and divided by three; in China they are multiplied and cube-rooted. And note that in the Chinese case the education index is itself a geometric mean — of the two schooling sub-indexes — before being fed into a second geometric mean. The old and new formulas cannot be mixed: if you add and divide by three, you have accidentally reverted to the pre-2010 method.
The goalposts changed between the two examples, which is why they are not comparable as scores: life expectancy runs 25–85 in the 2007 calculation but 20–83.2 in the 2010 one, and income now runs from ln(163) to ln(108,211) rather than ln(100) to ln(40,000). The maximum values were deliberately raised to the observed maximum rather than a predefined cutoff — so a country's index can fall even when its actual life expectancy rises.
Discussion of the HDI
Why the geometric mean punishes imbalance
Drag the three component indexes and watch the two means separate. The old HDI is their arithmetic mean; the new one is the cube root of their product. Presets reproduce the two worked examples on the slides.
Table 2.4 — HDI and its components, selected countries (2018)
| Country | HDI rank | Life exp. | Mean yrs | Exp. yrs | GNI/cap | HDI | GNI − HDI rank |
|---|---|---|---|---|---|---|---|
| Canada | 12 | 82.5 | 13.3 | 16.4 | 43,433 | 0.926 | +10 |
| United States | 13 | 79.5 | 13.4 | 16.5 | 54,941 | 0.924 | +13 |
| United Kingdom | 14 | 81.7 | 12.9 | 17.4 | 39,116 | 0.922 | +8 |
| South Korea | 22 | 82.4 | 12.1 | 16.5 | 35,945 | 0.903 | −27 |
| United Arab Emirates | 34 | 77.4 | 10.8 | 13.6 | 67,805 | 0.863 | +13 |
| Chile | 44 | 79.7 | 10.3 | 16.4 | 21,910 | 0.843 | +3 |
| Russian Federation | 49 | 71.2 | 12.0 | 15.5 | 24,233 | 0.816 | +15 |
| Costa Rica | 63 | 80.0 | 8.8 | 15.4 | 14,636 | 0.794 | −14 |
| Turkey | 64 | 76.0 | 8.0 | 15.2 | 24,804 | 0.791 | +43 |
| Cuba | 73 | 79.9 | 11.8 | 14.0 | 7,524 | 0.777 | +19 |
| Mexico | 74 | 77.3 | 8.6 | 14.1 | 16,944 | 0.774 | +2 |
| Sri Lanka | 76 | 76.5 | 10.9 | 13.9 | 11,326 | 0.770 | −26 |
| Brazil | 79 | 75.7 | 7.8 | 15.4 | 13,755 | 0.759 | −40 |
| China | 86 | 76.4 | 7.8 | 13.8 | 15,270 | 0.752 | −23 |
| Botswana | 101 | 67.6 | 9.3 | 12.6 | 15,534 | 0.717 | −15 |
| Gabon | 110 | 66.5 | 9.2 | 12.8 | 16,431 | 0.702 | +9 |
| South Africa | 113 | 63.4 | 10.1 | 13.3 | 11,923 | 0.699 | +3 |
| Egypt | 115 | 71.7 | 7.2 | 13.1 | 10,355 | 0.696 | −80 |
| Guatemala | 127 | 73.7 | 6.5 | 10.8 | 7,278 | 0.650 | +16 |
| India | 130 | 68.8 | 6.4 | 12.3 | 6,353 | 0.640 | −14 |
| Bangladesh | 136 | 72.8 | 5.8 | 11.4 | 3,677 | 0.608 | +20 |
| Ghana | 140 | 63.0 | 7.1 | 11.6 | 4,096 | 0.592 | −22 |
| Equatorial Guinea | 141 | 57.9 | 5.5 | 9.3 | 19,513 | 0.591 | −15 |
| Kenya | 142 | 67.3 | 6.5 | 12.1 | 2,961 | 0.590 | — |
| Pakistan | 150 | 66.6 | 5.2 | 8.6 | 5,311 | 0.562 | — |
| Papua New Guinea | 153 | 65.7 | 4.6 | 10.0 | 3,403 | 0.544 | — |
| Madagascar | 161 | 66.3 | 6.1 | 10.6 | 1,358 | 0.519 | — |
| Côte d'Ivoire | 170 | 54.1 | 5.2 | 9.0 | 3,481 | 0.492 | — |
| Burkina Faso | 183 | 60.8 | 2.3 | 8.5 | 1,650 | 0.423 | — |
| Chad | 186 | 53.2 | 2.0 | 5.4 | 1,750 | 0.404 | — |
| Niger | 189 | 60.4 | 2.0 | 5.4 | 906 | 0.354 | — |
The last column is the most interesting one. It is the country's GNI rank minus its HDI rank, so a positive number means the country does better on human development than its income alone would predict. Turkey is +43 and Bangladesh +20; Egypt is −80 and Brazil −40. The HDI's own advantage statement — "a country can do much better than might be expected at a low level of income" — is exactly what those positive numbers are showing.
The extremes, as of the instructor's 2026 update
The world average in 2023 is 0.72. Burundi and South Sudan are tied at rank 180 as printed on the slide. Note that Norway and Switzerland share 0.970 and are separated only by rounding.
The deck stops at the 2010 rebuild. Todaro 13e §2.3.4 carries the story forward to the index's alternative formulations, which are the natural "so what came next" question:
The textbook also records two criticisms of the New HDI that the deck omits. The first is general: by adding some non-income indicators and omitting others, the index can shift attention away from the things it leaves out — legal rights, for instance — so those may receive less attention than they otherwise would. The second is specific and practical: expected educational attainment is hard to forecast, especially in low- and lower-middle-income countries, which can produce an overly optimistic reading and therefore too little attention to education quality. The deck's own criticism — that gross enrolment overstates schooling — is the same worry in its older form.
2.4 Characteristics of the Developing World
slides 22–31 · Todaro 13e §2.4 · diversity within commonalityThe section's subtitle is the point: there are shared characteristics, but the diversity within them is enormous. The slides develop each characteristic with data, and the data is where the examinable detail lives.
| # | Characteristic | The evidence on the slide |
|---|---|---|
| 1 | Lower levels of living and productivity | Figure 2.4: high-income countries take 58% of global income while Sub-Saharan Africa takes 2%. |
| 2 | Lower levels of human capital — health, education, skills | Under-5 mortality: low-income countries fell from 128 per 1,000 in 1990 to 38 in 2023; high-income countries stand at 4. Figure 2.6 shows under-5 mortality falling steeply as the mother's education rises, across all five countries plotted. |
| 3 | Higher levels of inequality and absolute poverty | Absolute poverty and world poverty measures. |
| 4 | Higher population growth rates | Crude birth rate 粗出生率 — see the table below. |
| 5 | Greater social fractionalisation | Significant ethnic, linguistic and other social divisions within a country. |
| 6 | Larger rural populations, rapid rural-to-urban migration | Table 2.10 — see below. |
| 7 | Lower levels of industrialisation and manufactured exports | Table 2.11 — see below. |
| 8 | Adverse geography | Resource endowments: a nation's supply of usable factors of production, including mineral deposits, raw materials and labour. |
| 9 | Underdeveloped financial and other markets | Imperfect markets; incomplete information. |
| 10 | Quality of institutions and external dependence | Colonial legacy; external dependence and unequal international relations. |
Figure 2.4 — shares of global income, 2024
Nominal GDP, current US dollars. Seven shares, which sum to 100%:
| Group | Share of global income |
|---|---|
| High-income countries | 58% |
| East Asia & Pacific | 17% |
| Latin America & Caribbean | 7% |
| Europe & Central Asia | 7% |
| South Asia | 5% |
| Middle East & North Africa | 4% |
| Sub-Saharan Africa | 2% |
Table 2.6 — the 12 most and least populated countries, 2024
| # | Most populous | Population (m) | GNI per capita (US$) | Least populous | Population (thousands) |
|---|---|---|---|---|---|
| 1 | India | 1,451 | 2,950 | Tuvalu | 12 |
| 2 | China | 1,409 | 13,100 | Nauru | 18 |
| 3 | United States | 340 | 86,000 | Palau | 42 |
| 4 | Indonesia | 283 | 5,200 | Marshall Islands | 53 |
| 5 | Pakistan | 241 | 1,920 | St. Kitts and Nevis | 72 |
| 6 | Nigeria | 223 | 2,280 | Dominica | 100 |
| 7 | Brazil | 216 | 10,300 | Antigua and Barbuda | 105 |
| 8 | Bangladesh | 174 | 2,820 | Micronesia | 108 |
| 9 | Russian Federation | 144 | 11,800 | Grenada | 108 |
| 10 | Mexico | 131 | 11,500 | Tonga | 111 |
| 11 | Ethiopia | 126 | 1,100 | St. Vincent and the Grenadines | 119 |
| 12 | Japan | 124 | 42,500 | Seychelles | ≈128 |
Table 2.10 — the urban population, 2024
| Region | Population (millions, 2024) | Urban share |
|---|---|---|
| World | 8,160 | 58% |
| More developed countries | 1,259 | 81% |
| Less developed countries | 6,901 | 54% |
| Sub-Saharan Africa | 1,217 | 43% |
| Northern Africa | 261 | 53% |
| Latin America and the Caribbean | 662 | 82% |
| Western Asia | 306 | 73% |
| South-central Asia | 2,128 | 37% |
| Southeast Asia | 693 | 54% |
| East Asia | 1,646 | 66% |
| Eastern Europe | 290 | 71% |
The developed/developing split and the regional breakdown are two separate partitions, so the regional rows do not sum to the world total. The check that does hold: 1,259 + 6,901 = 8,160.
Table 2.11 — employment by sector, 2004–2008 (%)
The single most useful table for the structural-change argument in Chapter 3: it shows agriculture absorbing most of the labour force in poor countries while contributing a small share of GDP — the gap between the two columns is the productivity difference Lewis's model is built on.
| Country | Agriculture | Industry | Services | ||||||
|---|---|---|---|---|---|---|---|---|---|
| M | F | GDP | M | F | GDP | M | F | GDP | |
| Africa | |||||||||
| Egypt | 28 | 43 | 13 | 26 | 6 | 38 | 46 | 51 | 49 |
| Ethiopia | 12 | 6 | 44 | 27 | 17 | 13 | 61 | 77 | 42 |
| Madagascar | 82 | 83 | 25 | 5 | 2 | 17 | 13 | 16 | 57 |
| Mauritius | 10 | 8 | 4 | 36 | 26 | 29 | 54 | 66 | 67 |
| South Africa | 11 | 7 | 3 | 35 | 14 | 34 | 54 | 80 | 63 |
| Asia | |||||||||
| Bangladesh | 42 | 68 | 19 | 15 | 13 | 29 | 43 | 19 | 52 |
| Indonesia | 41 | 41 | 14 | 21 | 15 | 48 | 38 | 44 | 37 |
| Malaysia | 18 | 10 | 10 | 32 | 23 | 48 | 51 | 67 | 42 |
| Pakistan | 36 | 72 | 20 | 23 | 13 | 27 | 41 | 15 | 53 |
| Philippines | 44 | 24 | 15 | 18 | 11 | 32 | 39 | 65 | 53 |
| South Korea | 7 | 8 | 3 | 33 | 16 | 37 | 60 | 74 | 60 |
| Thailand | 43 | 40 | 12 | 22 | 19 | 44 | 35 | 41 | 44 |
| Vietnam | 56 | 60 | 22 | 21 | 14 | 40 | 23 | 26 | 38 |
| Latin America | |||||||||
| Colombia | 27 | 6 | 9 | 22 | 16 | 36 | 51 | 78 | 55 |
| Costa Rica | 18 | 5 | 7 | 28 | 13 | 29 | 54 | 82 | 64 |
| Mexico | 19 | 4 | 4 | 31 | 18 | 37 | 50 | 77 | 59 |
| Nicaragua | 42 | 8 | 19 | 20 | 18 | 30 | 38 | 73 | 51 |
| Developed countries | |||||||||
| United Kingdom | 2 | 1 | 1 | 32 | 9 | 24 | 66 | 90 | 76 |
| United States | 2 | 1 | 1 | 30 | 9 | 22 | 68 | 90 | 77 |
M = male, F = female, GDP = share of GDP (2008). Source: World Bank, World Development Indicators 2010, tabs. 2.3 and 4.2. Note on the slide: Ethiopian agricultural employment reflects limited coverage.
In this table, M and F are column shares within each sex — male employment across the three sectors sums to 100, and female employment sums to 100, but the two are separate totals. You cannot compute one from the other. The GDP column is a third, independent split. Compare Madagascar (82% of men in agriculture, but agriculture only 25% of GDP) with South Korea (7% of men in agriculture, 37% of GDP from industry) — that contrast, male employment share against GDP share, is the productivity gap.
Table 2.8 — crude birth rates around the world, 2022
Crude birth rate 粗出生率 = births per 1,000 population per year. The slide lists roughly 150 countries; what matters for revision is the shape of the distribution, and where China and the other large developing countries sit.
| Births per 1,000 | Countries in the band |
|---|---|
| 45 + | Niger |
| 40–44 | Angola, Benin, Burkina Faso, Burundi, Central African Republic, Chad, Dem. Rep. of Congo, Somalia, Uganda |
| 35–39 | Guinea-Bissau, Liberia, Mozambique, Nigeria, South Sudan, Tanzania, Zambia |
| 30–34 | Afghanistan, Cameroon, Côte d'Ivoire, Eritrea, Ethiopia, Ghana, Iraq, Kenya, Mauritania, Rwanda, São Tomé and Príncipe, Senegal, Sierra Leone, Sudan, Tajikistan, Timor-Leste, Togo, Yemen, Zimbabwe |
| 25–29 | Algeria, Egypt, Gabon, Haiti, Kiribati, Kyrgyzstan, Lesotho, Marshall Islands, Namibia, Pakistan, Papua New Guinea, Samoa, Solomon Islands, Turkmenistan, Tuvalu, Vanuatu |
| 20–24 | Belize, Bolivia, Botswana, Cambodia, Djibouti, Dominican Republic, Ecuador, El Salvador, Guatemala, Guyana, Honduras, India, Israel, Jordan, Kazakhstan, Laos, Libya, Maldives, Micronesia, Mongolia, Nepal, Nicaragua, Oman, Paraguay, Philippines, South Africa, Syria, Tonga, Uzbekistan |
| 15–19 | Antigua and Barbuda, Argentina, Azerbaijan, Bangladesh, Bhutan, Brunei, Cape Verde, Colombia, Fiji, Grenada, Indonesia, Iran, Jamaica, Malaysia, Mexico, Morocco, Myanmar, Panama, Peru, Saudi Arabia, Seychelles, Sri Lanka, St. Vincent and the Grenadines, Suriname, Tunisia, Turkey, Venezuela, Vietnam |
| 10–14 | Albania, Armenia, Australia, Austria, Bahamas, Bahrain, Barbados, Belarus, Belgium, Brazil, Canada, Chile, China, Costa Rica, Cuba, Cyprus, Denmark, Dominica, Estonia, France, Georgia, Iceland, Ireland, North Korea, Kosovo, Kuwait, Latvia, Lebanon, Liechtenstein, Lithuania, Luxembourg, Macedonia, Malta, Mauritius, Moldova, Montenegro, Netherlands, New Zealand, Norway, Palau, Poland, Qatar, Romania, Russia, Saint Lucia, Slovakia, Slovenia, St. Kitts-Nevis, Sweden, Switzerland, Thailand, Trinidad and Tobago, United Arab Emirates, United Kingdom, United States, Uruguay |
| < 10 | Bosnia and Herzegovina, Bulgaria, Croatia, Finland, Germany, Greece, Hungary, Italy, Japan, South Korea, Monaco, Portugal, San Marino, Serbia, Singapore, Spain, Taiwan, Ukraine |
The pattern is the demographic transition: the highest rates are concentrated in Sub-Saharan Africa, the lowest in Europe and East Asia. China, Thailand and Brazil now sit in the same band as the United States and the United Kingdom.
Table 2.7 — primary school enrolment and pupil-teacher ratios, 2022
| Region | Net primary enrolment | Pupil-teacher ratio |
|---|---|---|
| Low income | 81% | 37 |
| Lower-middle income | 89% | 28 |
| Upper-middle income | 95% | — |
| High income | 97% | 14 |
| East Asia & Pacific | 96% | — |
| Europe & Central Asia | 96% | — |
| Latin America & Caribbean | 94% | 20 |
| Middle East & North Africa | 92% | 22 |
| South Asia | — | 33 |
| Sub-Saharan Africa | 80% | 36 |
Four cells in the printed table were not legible on the slide render and are marked "—" rather than guessed. The legible ratios run 37 → 28 → 14 for the income groups and 20 → 22 → 33 → 36 for the regions, so the missing values sit inside that band.
Figure 2.4 — under-5 mortality rates, 1990 and 2023
| Income group | 1990 | 2023 |
|---|---|---|
| Low income | 128 | 38 |
| Lower-middle income | 62 | 12 |
| Upper-middle income | — | — |
| High income | — | 4 |
Deaths per 1,000 live births. Two of the eight bar labels and the high-income 1990 value were not legible on the slide. The direction is unambiguous: the largest absolute fall is in low-income countries (128 → 38), which is the same distance travelled as lower-middle-income countries but from a much higher base.
2.5 How Low-Income Countries Differ from the Developed Countries' Earlier Stages
slide 33 · Todaro 13e App. 2.2The comparison is not between rich and poor countries today, but between poor countries today and what today's rich countries looked like when they began industrialising. The eight differences are what make "just do what Britain did" unworkable.
The instructor's own multiple-choice question on this slide asks which of these differences is real: were population growth rates higher in today's developed countries? Was more advanced technology available to them? Were there more opportunities for development assistance? The answer is none of the above — all three statements are false as stated, which is the point. Today's developing countries face higher population growth, have more advanced technology available (the advantage of being a latecomer), and have more development assistance available, not less.
This section is the one place where the deck and the 13th edition disagree most sharply about placement. The deck numbers it §2.5, but in the 13th edition it is not in the chapter body at all — it is Appendix 2.2, "How Low-Income Countries Today Differ from Developed Countries in Their Earlier Stages", at pages 149–156. The chapter's own §2.5 is instead "Are Living Standards of Developing and Developed Nations Converging?", which the deck splits across two chapters: partly here, and partly at the start of its Chapter 3.
The eight differences are unchanged; only their address has moved. If you are reading alongside the book, go to the appendix.
2.6 Long-Run Causes of Comparative Development
Todaro 13e §2.6, pp. 115–122 · not in the slidesThis section asks a harder question than the rest of the chapter. Chapter 2 up to now has described how countries differ and measured the difference. §2.6 asks why the differences exist at all — and in particular why some countries are poor for reasons that go back centuries. It is new in the 13th edition and the slides never mention it, but it is the frame the whole field now uses, and it is what Chapter 3's dependence school was fumbling towards without the evidence to back it up.
The section's organising device is Figure 2.9, a schematic with twenty-two numbered arrows connecting climate, colonial history, inequality and institutions to present-day income. The chain underneath it runs like this:
The four families of explanation
| Cause | The claim | Where it stands |
|---|---|---|
| Physical geography (including climate) | Climate, disease environment and location shape what an economy can do. | Undoubtedly mattered historically. Its direct role today is much less clear: some research finds that once inequality and institutions are accounted for, physical geography adds little. Evidence is mixed — there does appear to be an independent effect of malaria, and in some circumstances landlocked status is an impediment. |
| Institutions | North's "rules of the game": property rights, contract enforcement, restraint on coercive and anti-competitive behaviour, limits on elite power, conflict management — plus social insurance and predictable macroeconomic stability. | The leading explanation. The hard part is that richer countries can afford better institutions, so the direction of causation is not obvious. Acemoglu, Johnson and Robinson's work is the attempt to settle it. |
| Colonial legacies and the reversal of fortune | Geography determined where settlers could survive; settler mortality determined whether colonisers settled or extracted; extraction left institutions that outlived the empire. | Strong supporting evidence, including a striking empirical result — see below. |
| Inequality and factor endowments | Engerman and Sokoloff: what the land was suited to grow determined whether it was worked by slaves, and that determined how unequal the society became. | Tested and supported by Easterly, among others. |
Two claims that sound alike and are not. Geography's direct effect today is weak; geography's indirect effect — through the institutions it caused to be built — is strong. Acemoglu and colleagues show that after accounting for institutional differences, geographic variables such as closeness to the equator have little influence on incomes. That is not an argument that geography does not matter; it is an argument about which link in the chain it operates through.
The reversal of fortune
This is the section's sharpest empirical point, and it is a falsification test rather than a correlation. If geography were fundamental to development prospects, the argument runs, then the areas that were most prosperous before colonisation should still be the most prosperous now.
The explanation is uncomfortable. Where local populations were larger, denser and more organised, it was easier for colonisers to take over the existing structures and collect tribute — so the institutions built there favoured extracting existing wealth over creating new wealth. Where populations were sparse, taking over was harder and colonists had to settle and produce, which required institutions that encouraged investment: constraints on executives, protection from expropriation.
The mechanism for how this persisted is the difference between formal and informal rules. As North stresses, a constitution can be rewritten in a day; the informal norms around it — how people expect contracts to be honoured, whether officials are expected to take bribes — "usually change only ever so gradually". The Congo is the textbook's illustration: the rule of Leopold II is arguably an ultimate cause of the Mobutu regime after independence.
Engerman and Sokoloff: endowments, inequality, and the two Americas
The second strand explains why the New World diverged internally. What the land could grow determined who worked it:
The mechanism connecting inequality to slow development has a name: the social conflict theory of institutions. Where inequality was extreme there was less investment in human capital and in public goods, and less movement toward democratic institutions — with causality running both ways, since education and institutions reinforce each other. The textbook is careful to add that this is not a story about the English being gentler colonisers, given the treatment of Native Americans and of slaves in the southern colonies.
How would you know any of this is true? This is the part of §2.6 with the most to teach methodologically. You cannot randomly assign countries different levels of inequality, so the strategy is to hunt for an instrumental variable — something that shifts inequality without shifting income directly. Settler mortality is offered as exactly that: plausibly unrelated to present-day income except through the institutions it caused.
Easterly's test of the Engerman–Sokoloff hypothesis found that "agricultural endowments predict inequality and inequality predicts development": inequality negatively affects per capita income, and also negatively affects institutional quality and schooling — which are the mechanisms by which it does so. Note the wording. Finding a correlation is the easy half; the hard half is the causal claim, which is why so much effort in the field goes into the search for instruments.
Read this straight against Chapter 3's international-dependence revolution. The dependence school made the same broad claim — that poor countries are poor because of their historical relationship with rich ones — and it was dismissed for two decades partly because it offered assertion rather than evidence, and partly because its prescription was autarky. §2.6 is the same intuition rebuilt on instruments and natural experiments, with a different implication: the legacy is real, but what has to change is institutions and inequality, which is not something you can achieve by cutting ties.
Formula Sheet
print-friendlyKey Concepts
26 terms · 13 from the textbookThe terms carrying a 中文 anchor are the ones the instructor glossed on the slide.
Self-Check
21 questions · gradedSection B is the calculation section — the two HDI worked examples and the PPP conversion. Section C reproduces the instructor's own multiple-choice questions.
A · Definitions and distinctions
B · Calculation
This is the slide's own Bangladesh 2007 example. Each sub-index is min-max normalised between its goalposts.
- Income index — goalposts ln(100) and ln(40,000) [ln(1241) − ln(100)] / [ln(40000) − ln(100)] = 2.5185 / 5.9915 = 0.4204
- Life expectancy index — goalposts 25 and 85 (65.7 − 25) / (85 − 25) = 40.7 / 60 = 0.6783
- Adult literacy index — goalposts 0 and 100 (53.5 − 0) / (100 − 0) = 0.5350
- Gross enrolment index — goalposts 0 and 100 (52.1 − 0) / (100 − 0) = 0.5210
- Education index — two-thirds literacy, one-third enrolment (2/3)(0.5350) + (1/3)(0.5210) = 0.3567 + 0.1737 = 0.5303
- HDI — the arithmetic mean of the three dimension indexes (0.4204 + 0.6783 + 0.5303) / 3 = 1.6290 / 3 = 0.5430
This is the slide's own China 2010 example. Note that the aggregation at the end is a geometric mean, not a sum.
- Life expectancy index (73.5 − 20) / (83.2 − 20) = 53.5 / 63.2 = 0.8465
- Mean years of schooling index (7.5 − 0) / (13.2 − 0) = 0.5682
- Expected years of schooling index (11.4 − 0) / (20.6 − 0) = 0.5534
- Education index — a geometric mean of the two, then rescaled √(0.5682 × 0.5534) = √0.31445 = 0.5608; 0.5608 / 0.951 = 0.5897
- Income index [ln(7263) − ln(163)] / [ln(108211) − ln(163)] = 3.7966 / 6.4982 = 0.5843
- New HDI — the cube root of the product 0.8465 × 0.5897 × 0.5843 = 0.29175; ∛0.29175 = 0.6631
- The ratio 6,980 / 1,800 = 3.88×
The market exchange rate only reconciles the prices of traded goods, because those are what currencies are actually demanded for. A large share of what an Indian household consumes — housing, food prepared at home, local transport, personal services — is never traded internationally, and those prices are far lower in India than in the United States.
Converting at the market rate therefore values those goods at US prices, which is the wrong price. PPP revalues the whole consumption basket at a common set of international prices, which is why it corrects India's income upward by nearly a factor of four while barely touching the United States — the US is the base against which the common prices are set.
Thresholds: LIC < $1,175 · LMC < $4,635 · UMC < $14,375 · High > $14,375.
| Country | GNI per capita | Group |
|---|---|---|
| Bangladesh | $1,470 | Lower-middle income — above $1,175, below $4,635 |
| China | $8,690 | Upper-middle income — above $4,635, below $14,375 |
| Brazil | $8,600 | Upper-middle income — same band as China, and only $90 below it |
| United States | $58,270 | High income — far above $14,375 |
Two things to notice. First, China and Brazil are almost indistinguishable on this measure yet are usually treated as very different development stories — a reminder that the income group is a classification, not an explanation. Second, none of the four is in the low-income group, which is now small.
C · The instructor's own questions
D · Extended answers
The old HDI added the three component indexes and divided by three. An arithmetic mean treats the dimensions as perfect substitutes: a sufficiently high income index could compensate entirely for a poor health index, and the total would be unchanged. That is a very strong assumption, and in the context of human development it is implausible — a country where people are rich but die young is not equivalent to one where they are poorer but healthy.
The New HDI takes the cube root of the product instead. Because it is a product, a low value in any one dimension drags the whole index down in a way that strength elsewhere cannot fully offset. This is imperfect substitutability: the dimensions can be traded off against one another to a degree, but not without limit.
The implication is that the New HDI is more sensitive to imbalance. Two countries with the same arithmetic mean of the three components will not have the same New HDI — the more unequal one scores lower. Use the calculator above to see this: move one slider down and watch the gap between the two means widen.
The same logic was applied one level down: the education index is itself the geometric mean of the mean-years and expected-years sub-indexes, before being fed into the outer geometric mean.
A market exchange rate equates the prices of goods that are traded internationally, because those are the goods currencies are demanded to buy. But a large part of what households consume is non-traded — housing, local transport, personal services, food prepared at home. These cannot be shipped, so their prices are set by local supply and demand, and they are far cheaper where wages are low.
Converting a poor country's income at the market rate implicitly values all of its consumption at rich-country prices. The result is a systematic understatement of real income in poor countries. PPP corrects this by using a common set of international prices for all goods and services, so that the comparison measures what income actually buys rather than what it converts into.
The PPP conversion factor is defined as the units of foreign currency required to buy, in the local developing-country market, the identical quantity of goods and services that $1 buys in the United States. In the instructor's table this raises low-income countries from $775 to $2,127 — a factor of 2.74 — while leaving the United States at 1.03×, since it is the base.
- Lower levels of living and productivity
- Lower levels of human capital — health, education, skills
- Higher levels of inequality and absolute poverty
- Higher population growth rates
- Greater social fractionalisation
- Larger rural populations, but rapid rural-to-urban migration
- Lower levels of industrialisation and manufactured exports
- Adverse geography
- Underdeveloped financial and other markets
- Quality of institutions and external dependence
Evidence, for example:
- Characteristic 1 — Figure 2.4: high-income countries take 58% of global income; Sub-Saharan Africa takes 2%.
- Characteristic 2 — Figure 2.4 (mortality): under-5 mortality in low-income countries was 128 per 1,000 in 1990 and 38 in 2023, against 4 in high-income countries.
- Characteristic 4 — Table 2.8: crude birth rates above 40 per 1,000 are concentrated in Sub-Saharan Africa, while most of Europe and East Asia now sits below 15.
- Characteristic 7 — Table 2.11: Madagascar has 82% of men in agriculture against 25% of GDP from it, whereas South Korea has 7% of men in agriculture and 37% of GDP from industry.
- Physical and human resource endowments
- Per capita incomes and levels of GDP relative to the rest of the world
- Climate
- Population size, distribution and growth
- Historic role of international migration
- International trade benefits
- Basic scientific and technological research and development capabilities
- Efficacy of domestic institutions
It matters because it rules out the naive reading of the growth record — that today's poor countries should simply repeat what Britain or Germany did. The conditions are not the same. Two of the differences work in the latecomer's favour (advanced technology is available to import; development assistance exists), and several work against it (climate and disease burden, far higher population growth, an existing industrial world setting the terms of trade).
The instructor's own question on this slide tests exactly this: three plausible-sounding statements about the pioneers are all false, and the correct answer is "none of the above".
The final column, GNI per capita rank minus HDI rank. A positive value means the country ranks higher on human development than its income alone would predict.
| Positive — better than income predicts | Negative — worse than income predicts |
|---|---|
| Turkey +43 | Egypt −80 |
| Bangladesh +20 | Brazil −40 |
| Cuba +19, Guatemala +16, Russian Federation +15 | South Korea −27, Sri Lanka −26, China −23, Ghana −22 |
Turkey and Bangladesh achieve levels of health and education well above what their income would suggest; Egypt and Brazil achieve well below. The same table shows the converse case too — Equatorial Guinea has a GNI per capita of $19,513 (higher than Turkey's $24,804 band suggests for its region) but an HDI of only 0.591, because that income is not being converted into health or education. Growth is not the same thing as development, and this column is the arithmetic of that claim.
GDP is the total value for final use of output produced within an economy, by residents and non-residents alike. GNI is the total domestic and foreign value added claimed by a country's residents, without deducting depreciation of the domestic capital stock.
The difference is ownership versus location. A country with large remittance inflows — the Philippines, Bangladesh, Egypt — has residents earning income abroad that counts in GNI but not in GDP, so GNI exceeds GDP. A country hosting large amounts of foreign-owned capital has the opposite pattern.
The 2010 reform switched the HDI's income component from GDP per capita to GNI per capita because the index is meant to measure the command over resources available to people, not the output produced on a territory. Remittances genuinely raise a household's ability to buy health and education, which is what the other two dimensions measure — so an income measure that excluded them was understating the resources actually available to the population. The same logic runs through the other 2010 changes: each one moves the index closer to what people actually have.
E · The long-run causes
The argument runs from what the land could grow to who worked it.
- Where climate suited plantation agriculture Particularly sugar, which had large scale economies — slavery and other mass exploitation of labour were introduced
- Where indigenous populations survived contact and minerals were present Vast land grants were issued that included claims to the labour of the people living on them (by Spain)
- Different endowments, same outcome Both produced high economic and political inequality
- North America differed because of its endowments Grain lacked the scale economies of tropical agriculture and mineral extraction; scarce labour with abundant land inhibited the concentration of power; and attracting settlers required more egalitarian institutions
- Which is why the poorer starting societies overtook the richer ones Egalitarian access facilitated broad-based innovation, entrepreneurship and investment — the US and Canada surpassed societies whose populations were mostly illiterate, disenfranchised and lacking collateral
The persistence mechanism is the social conflict theory of institutions. Extreme inequality meant less investment in human capital and in public goods, and less movement toward democratic institutions — because elites blocked both, since each would erode their position. Causality runs in both directions, since education and institutions reinforce one another.
The textbook is explicit that this is not a story about gentler colonisers. The treatment of Native Americans and of slaves in the southern colonies shows that. The difference was in what the land was suited to and how much labour it took to work it — not in who was doing the colonising.
Classic Theories of Economic Growth and Development
This is the model chapter, and the one that carries the most examinable machinery. It opens with the stylised facts of growth — the Great Divergence, catch-up, and the awkward fact that convergence shows up in growth rates but not in income levels — and then works through four families of theory that each tried to explain those facts: the linear stages, the structural-change models, the international-dependence school, and the neoclassical counterrevolution whose centrepiece, the Solow model, is still the starting point for growth economics.
The theories are not a list. Each one is a reply to the one before it, and the replies are what the exam asks about. The three interactive models below — Harrod-Domar, Lewis, and Solow — are the ones you should be able to draw from memory and reason about when a parameter moves.
Concept Map
how the chapter buildsGrowth over the Very Long Run
slides 3–13 · Todaro 13e §2.5, not Ch. 3Sustained growth is recent
Sustained increases in standards of living are a recent phenomenon. Modern economic growth emerged only in the most recent two or three centuries. Until about 12,000 years ago humans were hunters and gatherers; the agricultural revolution around 10,000 BC brought settlements and eventually cities, but even the sporadic peaks of achievement that followed were characterised by low average living standards — wages in ancient Greece and Rome were roughly equal to wages in fifteenth-century Britain or seventeenth-century France, all of them well before modern growth began.
The instructor's figure plots average world GDP per capita from 1 to 2010 (Maddison's data). It is flat for most of its length and then turns up sharply. His framing of the timescale is worth remembering: compress the 130,000 years since modern humans appeared into a single day, and the era of modern growth would have begun only in the last three minutes.
The Great Divergence 分化
The magnitudes are the thing to remember:
| When | How much per capita GDP differed across countries |
|---|---|
| Before 1700 | By a factor of only two or three |
| Today | By a factor of 50 for several countries |
Since 1700, living standards in the richest countries have risen from roughly $500 per person to approaching $45,000 — a factor of 90 in a period that is a flash in human history.
Modern growth around the world
After the Second World War, growth in Germany and Japan accelerated sharply — Japan averaging nearly 6% per year between 1950 and 1990 — and both settled at roughly three-quarters of the US level. The United Kingdom was the richest country in the late nineteenth century, then slipped because it grew substantially slower than the United States; since 1950 the two have grown at more or less the same rate, with UK income staying at about three-quarters of the US level. Brazil accelerated until 1980 and then stagnated; China and India have had the reverse pattern.
In per capita terms the ratios are: Japan and the United Kingdom about 3/4 of the United States, Brazil and China about 1/5, and Ethiopia only about 1/40.
Reasons to expect convergence
- Technology transfer Enables developing countries to leapfrog earlier stages — no need to rediscover the steam engine
- Diminishing returns to factor accumulation An extra machine adds more output where machines are scarce — so the poor should grow faster
The slide's own caution: divergence occurred for two centuries from the start of the industrial revolution, but the most recent data demonstrate that, on average, (re-)convergence is now underway. "Expect convergence if conditions are similar" is the qualification that later becomes conditional convergence.
Four periods of the convergence record
| Period | What happened |
|---|---|
| 1952–1965 | No global convergence pattern emerged; Japan achieved rapid catch-up growth, while China and India stagnated at very low income levels. |
| 1965–1978 | Japan sustained strong growth and narrowed its income gap with the US, but China and India remained slow-growing low-income economies. |
| 1991–2004 | China's growth took off, and clear global relative convergence appeared for the first time, driven by large developing economies. |
| 2004–2017 | Global convergence deepened further, with China and India both maintaining rapid catch-up while advanced economies grew modestly. |
Growth convergence ≠ absolute income convergence
This is the chapter's sharpest empirical point, and it is easy to get wrong. Over 1990–2017:
| Country or group | Income growth, 1990–2017 |
|---|---|
| China | +412% |
| India | +389% |
| Sub-Saharan Africa | +67% |
| High-income OECD countries | +68% |
China and India grew far faster than the high-income OECD countries. But because they started from such a low base, the absolute gap in per capita income between them and the advanced economies still widened substantially. Relative convergence — closing the ratio — is not the same thing as absolute convergence, which would mean closing the difference.
Data source on the slide: Penn World Table.
This is the single most confusable pair of ideas in the chapter. A poor country growing at 7% while a rich one grows at 2% is converging in relative terms — the ratio of incomes is falling. But if the poor country started at $1,000 and the rich at $40,000, the absolute gap grows: 7% of $1,000 is $70, while 2% of $40,000 is $800. Convergence in the growth-rate sense is compatible with divergence in the income-level sense, and both were happening at once over 1990–2017.
A broad sample of countries
Over 1960–2007, growth rates across countries ranged from −23% to +16% per year. Some countries exhibited a negative growth rate; others sustained nearly 6%; most sustained about 2%. Per capita GDP in 2007 varied by a factor of about 64. The lesson the slide draws is the familiar one: small differences in growth rates result in large differences in standards of living over a few decades.
Everything in this section — the Great Divergence, the two reasons to expect convergence, the four periods — belongs to Chapter 2 of the 13th edition, §2.5 "Are Living Standards of Developing and Developed Nations Converging?" (pages 108–115), not to Chapter 3. The deck moves it to the front of its Chapter 3 because it is the evidence the growth theories have to explain, which is a defensible way to teach it but makes the book's contents page misleading if you are trying to follow along.
The mapping in full, for reference:
| What this deck calls it | Where the 13th edition puts it |
|---|---|
| Ch3, growth facts (this section) | Chapter 2, §2.5, pp. 108–115 |
| Ch4 §4.1 "How Low-Income Countries Differ…" (deck Ch2 §2.5) | Appendix 2.2, pp. 149–156 |
| Old arithmetic HDI (deck Ch2 §2.3) | Appendix 2.1, pp. 143–148 |
| Solow model (deck Ch3, main text) | Appendix 3.2, pp. 194–198 |
| Endogenous growth theory | Appendix 3.3, pp. 199–204 — not in the deck at all |
| Components of economic growth | Appendix 3.1, pp. 188–193 — not in the deck at all |
The pattern is worth noting: the 13th edition has pushed much of what the deck teaches as core into appendices, and added §2.6 "Long-Run Causes of Comparative Development" (institutions, geography, colonial legacies) to the Chapter 2 body in its place. The deck is built on an earlier edition — its footers read Copyright © 2012 Pearson Addison-Wesley — so the mismatch is expected rather than a sign you have the wrong book.
3.1 Classic Theories: Four Approaches
slide 14 · Todaro 13e §3.1The chapter organises the field into four families. Each is a claim about what causes underdevelopment, and therefore about what should be done.
| Approach | Core claim | The prescription |
|---|---|---|
| Linear stages of growth 阶段增长模型 | Development is a series of successive stages through which all countries must pass. | Get the savings and investment to the level that moves you to the next stage. |
| Theories and patterns of structural change 结构变革 | Use modern economic theory and statistical analysis to portray the internal process of structural change. | Manage the reallocation of labour and output from agriculture to industry. |
| International-dependence revolution 国际依附革命理论 | External and internal institutional and political constraints on economic development. | Remove the structural dependence; reform the international order and domestic elites. |
| Neoclassical free-market counterrevolution | Emphasise free markets, open economies, and the privatisation of inefficient public enterprises. | Get the state out of the way. |
Notice that the four are roughly chronological and that each is a reaction to the previous one's failure. The stages models dominated the 1950s and 1960s; structural change grew out of their disappointment; dependence theory grew out of the observation that structural change was not happening where it was expected; and the neoclassical counterrevolution is a direct attack on both the dependence school's conclusions and the interventionist policies that followed from the stages models.
3.2 Development as Growth: Rostow and Harrod-Domar
slides 15–24 · Todaro 13e §3.2 · model 1Rostow's stages of growth
The classic statement of the linear-stages view: the transition from underdevelopment to development can be described in terms of a series of steps or stages through which all countries must proceed. The sequence is what gives the family its name, and the assumption that the sequence is universal is what the later critiques attack.
The Harrod-Domar growth model
The model the stages view needed to make its arithmetic work. Its appeal to scholars and politicians is that it is very simple — and its origin is the Marshall Plan of 1948–51, where the question was precisely how much investment a country needed to hit a growth target. Two economists developed it independently in the 1940s: Roy Harrod (England) and Evsey Domar (MIT).
The derivation
Start from the identity between saving and investment. If the saving rate is s and the capital-output ratio is c — the amount of capital needed for one unit of increase in GDP — then:
Saving equals the saving rate times income; that saving finances investment; investment adds to the capital stock; and the capital required is c times the increase in output.
Rearranging (3.6) gives the model's central result — the rate of growth of GDP:
The slide also writes it the other way up, Y = ΔK / s, with the annotation "GDP depends on K". That is the same equation read right-to-left, and it states the model's underlying claim: to get more output you need more capital, and how much capital you can get depends on how much you save.
In the absence of government, the growth rate of national income will be directly related to the savings ratio and inversely related to the economy's capital-output ratio. That is the whole policy content of the model: to grow faster, save more or make capital more productive.
What determines c?
The slide pushes on the capital-output ratio, since it is the more interesting of the two parameters.
Empirically, over 1970–2019 capital-output ratios followed clearly divergent patterns across economies (Penn World Table): Japan and South Korea saw a steady long-term increase driven by sustained capital deepening; the US ratio remained relatively stable; most Latin American and African economies spiked sharply in the 1980s amid economic distress and then declined; India and Indonesia dipped in the 1980s before returning to a gradual upward trend.
Harrod-Domar: the growth rate and the production function behind it
Drag the sliders to move g = s/c. Switch to the second mode to run it backwards — what savings rate does a target growth rate require?
The fixed-coefficient production function
The model's assumptions are easiest to see in the production function. Capital (K) and labour (L) are always used in a fixed proportion; there are constant returns to scale, so doubling both doubles output. The slide's example: to produce 100 tons of cement a year a country needs $10 million of capital and 100 workers.
- How many tons when K = $20 m and L = 200? Both inputs doubled → constant returns to scale → 200 tons
- How many tons when K = $15 m and L = 200? 200 workers could produce 200 tons, but $15 m of capital supports only 150 tons → output is 150 tons, and 50 workers are redundant
With that functional form, the isoquants are right-angled rather than smooth: to produce a given level of output you need at least a certain amount of both inputs, and extra quantities of one alone do nothing. The kink of each isoquant lies on the ray K/L = 1/10, which is why the model implies capital and labour must grow at the same rate.
Compare this L-shaped isoquant with the smooth, convex isoquants of the neoclassical production function in section 3.5. The change from one to the other is the single change that makes the Solow model work: with smooth isoquants, capital and labour can be substituted, so K/L is free to adjust, so diminishing returns can operate, and so a steady state can exist.
Criticisms of the stages model
The instructor's note adds the practical objection: in reality, more saving and investment is not a necessary condition for economic growth.
The knife-edge is the term the instructor bolded on the slide, and it is worth being able to explain. Because K and L must be used in exactly the fixed proportion, an economy that accumulates capital faster than it grows its labour force ends up with idle machines; one that grows labour faster ends up with unemployed workers. There is no price mechanism in the model to bring the two back together — the economy balances on a knife edge, and any deviation is permanent.
The full account of what actually drives growth sits in Todaro 13e Appendix 3.1, which the deck skips entirely. It names three components, and the third is the one every classic model in this chapter leaves outside itself.
- Capital accumulation — new investment in land, physical equipment and human resources. Its defining feature is a trade-off between present and future consumption. Note the extension the deck never makes: directly productive investment is supplemented by social and economic infrastructure — roads, electricity, water, sanitation, communications. A farmer who buys a tractor gains nothing if there is no transport to get the extra crop to market. Investment also works by raising the quality of what already exists: irrigation that lets 100 hectares produce what 200 did is equivalent to doubling the land.
- Population and labour force growth — traditionally counted as positive, since more workers and larger domestic markets both help. But the text is careful: whether it helps or hurts depends on the economy's ability to absorb and productively employ the added workers, which depends in turn on the rate and kind of capital accumulation.
- Technological progress — classified three ways: neutral (more output from the same inputs, equivalent to doubling every input), labour-saving, and capital-saving.
That last distinction carries a point worth remembering. Progress since the late nineteenth century has been overwhelmingly labour-saving, because most of the world's research is done in developed countries, where labour is the scarce factor. But in labour-abundant, capital-scarce developing countries it is capital-saving progress that is needed most — cheaper, more labour-intensive methods. That mismatch between what the world's research produces and what poor countries actually need is the same problem the Lewis model's "antidevelopment growth" describes from the other direction.
3.3 Structural-Change Models: the Lewis Two-Sector Model
slides 25–40 · Todaro 13e §3.3 · model 2The structural-change family studies the transformation of an agricultural economy into a more industrialised one, using the tools of neoclassical price and resource-allocation theory and econometrics. Two landmarks: W. Arthur Lewis's "two-sector surplus labour" theory, and Hollis B. Chenery and coauthors' "patterns of development" empirical analysis. Lewis — Saint Lucian, Nobel Memorial Prize 1979 — is the one the chapter develops in detail.
The agricultural sector
Fixed capital KA and unchanging technology tA, so production varies only with labour input LA. Four properties:
- Decreasing returns in terms of labour Adding workers to fixed land adds less and less output
- Zero return to labour after a certain point This is surplus labour: production does not increase with extra labour
- All workers share the production equally So the wage equals the average product, not the marginal product
Mechanically, the story runs: draw a production function that becomes flat at a certain point; from it derive the MP curve, which is also the labour demand curve and which turns zero at the same point where the TP curve becomes flat. There is no labour supply curve — employment is up to the point where MP becomes zero, and the wage is determined by the average product, because there is no labour market in the conventional sense. It is a subsistence economy, and WA = TPA / LA.
The industrial (modern) sector
The same construction, with two changes. Draw a production function; derive the MP curve, which is again the labour demand curve. But the labour supply is horizontal — perfectly elastic — and the wage in the modern sector is higher than the agricultural wage. Labour supply and labour demand together determine the wage level and employment in the industrial sector.
The reason the supply is horizontal is the whole point: while surplus labour exists in agriculture, the modern sector can hire as many workers as it wants at the going wage, because those workers are producing nothing where they are. The wage only has to be slightly above the agricultural wage to attract them.
The two sectors together: migration and industrialisation
Put the panels side by side and the model becomes a theory of development. Modern-sector growth raises the demand for labour; the higher wage pulls workers out of agriculture; the modern sector expands and the economy grows. This self-sustaining growth will not last forever, though:
- Surplus labour is eventually absorbed Once the modern sector has hired everyone who was producing nothing
- Further withdrawal reduces agricultural output Because the next workers to leave were producing something
- The marginal product of agricultural labour rises above zero More land per person remaining
- Cheap labour is gone; the industrial wage must rise Which means an upward-sloping labour supply curve
The Lewis two-sector model, after Figure 3.1
Push the industrial capital stock up and watch labour demand shift from D1(KM1) to D3(KM3). While the intersection stays on the flat part of the supply curve, output and profit rise but the wage does not — which is exactly the result in the instructor's exercise answers.
Criticisms of the Lewis model
The third criticism is the one the chapter develops graphically, and it is the sharpest. Suppose KM2 technology requires much less labour per unit of output than KM1 technology does. Even though total output grows substantially — 0D2EL1 is significantly greater than 0D1EL1 — total wages (0WMEL1) and employment (L1) remain unchanged. All the extra income and output growth is distributed to the few owners of capital, while income and employment for the mass of workers stay where they were.
That is why the instructor bolded the term: growth has occurred by every national-accounts measure, and nothing has happened to the workers it was supposed to benefit. The labour productivity of the L1th worker is still WM.
"Antidevelopment growth" is the counterexample that the dependence school will later use against the structural-change models, and that the Solow model's technology parameter will leave entirely unexplained. Keep the phrase — it names a phenomenon none of the four approaches handles cleanly.
3.4 The International-Dependence Revolution
slides 41–42 · Todaro 13e §3.4The dependence school denies the premise of both families above: that development is a matter of getting the quantities right. It argues that developing countries are held where they are by external and internal institutional and political constraints — and that the obstacles are therefore structural, not technical.
The neocolonial dependence model 新殖民主义
An indirect outgrowth of Marxist thinking. Its elements:
The dualistic-development thesis 二元发展论
The second strand, which is about structure rather than power. Four propositions:
- Superior and inferior elements can coexist A modern sector and a traditional one can exist side by side in the same economy
- The coexistence is chronic It does not resolve itself over time; it is a stable state, not a transition
- The degrees of superiority or inferiority tend to increase The gap widens rather than narrowing
- The superior element does little or nothing to pull up the inferior Which is the direct contradiction of the Lewis model's prediction
Proposition 4 is the one to notice, because it is a direct empirical denial of Lewis. Lewis's model says the modern sector absorbs the traditional one through labour migration; the dualism thesis says the modern sector coexists with, and even deepens, the traditional one. Both are describing the same two sectors — they disagree about whether the relationship between them is convergent or self-reinforcing.
Criticisms and limitations
| Criticism | What it says |
|---|---|
| It does little to show how to achieve development in a positive sense | The school is strong on diagnosis and weak on prescription. Knowing what is blocking development is not the same as knowing what would start it. |
| Accumulating counterexamples | China and India, above all. Both were peripheral by any definition, both were subject to the constraints the theory describes, and both grew rapidly anyway. |
The instructor's note records the school's own prescription in one word: autarky is best — cutting the ties to the core rather than negotiating better terms within them.
3.5 The Neoclassical Counterrevolution: Market Fundamentalism
slides 43–44 · Todaro 13e §3.5The counterrevolution challenges the statist 计划经济 model — the assumption, shared by the stages models and the dependence school alike, that the state is the agent of development. It comes in three flavours, which the slide distinguishes carefully.
| Approach | Its claim | How far it goes |
|---|---|---|
| Free market approach 自由市场分析 | Markets alone are efficient. | The strongest claim — no market failure worth correcting. |
| Public choice approach 公共选择理论 | Government does nothing right. | A claim about incentives: officials pursue their own interests, not the public's. |
| Market-friendly approach 亲善市场理论 | Admits market failure. | The weakest claim — markets are best but not perfect, so selective intervention can be justified. |
Main arguments
- Denies the efficiency of intervention Planning does not improve on the market outcome
- Points up state-owned enterprise failures Public firms are inefficient — the case for privatisation
- Stresses government failures Rent-seeking, capture, and the political economy of policy
And one theoretical point, which is the bridge to the Solow model: traditional neoclassical growth theory — with diminishing returns — cannot sustain growth by capital accumulation alone.
Do not merge the three approaches. They are ordered by how much they concede: the free-market approach concedes nothing, the public-choice approach concedes that markets exist but attacks government motive, and the market-friendly approach concedes that markets can fail. The slide introduces all three under the single heading of "challenging the statist model", which makes them look interchangeable — they are not.
The Solow Growth Model
slides 44–72 · Todaro 13e App. 3.2 · model 3 · the centrepieceDeveloped in the mid-1950s by Robert Solow of MIT, and the basis for the Nobel Prize he received in 1987. The slide's framing of the question it answers is worth keeping: in 1960 South Korea and the Philippines were similar in many respects — per capita GDP about $1,800 and $2,200 respectively, less than 15% of the US level; populations of about 25 million, half of working age; similar fractions working in industry and agriculture. Between 1960 and 2007 their paths diverged dramatically: the Philippines grew at about 1.7% per year, South Korea at just under 6%, reaching nearly $24,000 against the Philippines' $5,000. The Solow model is the starting point for understanding that difference.
What it adds to the production model
Assumptions: the neoclassical production function
The Cobb-Douglas production function
Most popular function form for production. Assume A is determined exogenously; it has decreasing returns to capital.
Note that the slides use the square-root case specifically: both exponents are 0.5, so α = 0.5 throughout. That matters for the steady state below.
- Find Y Y = 1 × 100.5 × 1000.5 = √10 × 10 = 31.62
- Double K. What is Y now? Y = 1 × 200.5 × 1000.5 = √20 × 10 = 44.72
- Is Y doubled? No. 2 × 31.62 = 63.25 ≠ 44.72. Output rose by a factor of 1.414 = √2
Dividing through by L: the per-worker form
The model is solved in per-worker terms. Divide both sides by L:
And in general form: y = Af(k).
The slide asks the question directly: although Y has constant returns to scale with respect to K and L, y has decreasing returns with respect to k. Why? Because k is the number of machines per worker: when k is small, adding machines raises productivity a lot; when k is already large, adding machines raises productivity less. The doubling of K in the example above doubled k but did not double y — that is DRTS in action, and it is the mechanism the whole model rests on.
The capital accumulation equation
This is the second equation of the Solow model:
s = saving rate · y = output per worker · n = population growth rate · d = depreciation rate
The growth of the capital-labour ratio relies on three things: savings, population growth and depreciation. The two equations — y = Af(k) and Δk = sy − (n+d)k — together determine the equilibrium.
The Solow diagram
Three lines on axes of k (horizontal) and y (vertical): the production function y = Af(k), the saving curve sy below it, and the straight line (n+d)k from the origin.
The Solow diagram and the transition to the steady state
Move any parameter and the steady state recomputes. The arrows show which way the economy is travelling at each level of k. Switch to the two-country mode to see the catch-up argument — and why it is the model's weakest prediction.
At the steady state
k and y are constant. Are K and Y also constant? No. Remember that Y = yL and K = kL, and L is growing at a rate of n. Therefore Y and K grow at a rate of n. The instructor's example: if y = 10 and L is growing at 2%, then Y is growing at 2%.
The closed form is worth knowing, because it makes the comparative statics immediate. Setting sy = (n+d)k and substituting y = Akα:
Different initial conditions: the catch-up argument
Suppose two countries X and Z have the same A, f, s, n and d, but country X has larger k and y than country Z. Which country grows faster?
- Country Z grows faster Because f(k) has decreasing returns, at a lower level of k the slope of f(k) is larger — the same change in k produces a larger change in y
- This is the famous catch-up theory Poorer countries grow faster
- And the prediction Poor and rich countries reach the same level of per capita GDP eventually
Can a country grow in the long run?
Short-run versus long-run is the whole content of this question. In the short run the economy may not be at the steady state, and k and y may grow. In the long run the economy reaches the steady state, and k and y are stable. So capital accumulation cannot sustain growth — and the chapter is explicit that this is a drawback, because empirically economies appear to continue growing over time.
Strengths and weaknesses of the Solow model
| Strengths | Weaknesses |
|---|---|
| It provides a theory that determines how rich a country is in the long run — long run = steady state. | It focuses on investment and capital, while the much more important factor of TFP is still unexplained. |
| The principle of transition dynamics allows an understanding of differences in growth rates across countries: a country further from the steady state will grow faster. | It does not explain why different countries have different investment and productivity rates. A more complicated model could endogenise the investment rate. |
| Its key elements lie at the heart of virtually every model in modern macroeconomics: a production function in capital and labour, and an accumulation equation showing how forgoing consumption today raises the capital stock tomorrow. | It does not provide a theory of sustained long-run economic growth. |
Countries will be rich to the extent that they have a high rate of investment, a high TFP level, and a low rate of depreciation. The model's own verdict on capital accumulation is blunt: because of diminishing returns, an economy accumulating capital sees the marginal product of capital decline, until eventually the additional output produced by investment is only just enough to offset wear and tear. At that point growth stops.
This is the bridge to everything that comes after the course's Chapter 3. If capital accumulation cannot sustain growth, and technology is exogenous, then the interesting question — what actually drives sustained growth? — has been pushed outside the model. Endogenous growth theory, and the economics of innovation and institutions, exist because of this gap.
The gap the deck flags at the end of this section is answered in Todaro 13e Appendix 3.3. Endogenous growth theory exists precisely to close it, and the argument is examinable as a contrast with Solow.
The problem it attacks. In the Solow model, the growth of income per head that is not explained by labour or capital accumulation is dumped into a residual — the Solow residual — and that residual accounts for roughly 50% of historical growth in the industrialised nations. Calling half of all growth "exogenous technological progress" has two drawbacks: you cannot analyse what determines technological advance, because it is independent of any economic agent's decisions; and the theory cannot explain why residuals differ so much between countries using similar technologies. There was a third puzzle — developing countries have low capital-labour ratios and so should offer high returns, yet capital kept flowing from poor countries to rich ones.
The reformulation. Drop the assumption of diminishing returns to capital, allow increasing returns to scale, and let investment in physical and human capital generate externalities that exceed the private gain. Many such models collapse to the same simple form as the Harrod-Domar equation:
A represents anything affecting technology; K covers both physical and human capital. There are no diminishing returns in this form, which is the whole point — capital accumulation can now sustain growth indefinitely.
Note what that does to the chapter's structure: the AK form is Harrod-Domar's equation, the very thing Solow's model was built to replace. Endogenous growth theory puts it back, with the no-diminishing-returns assumption made explicit rather than assumed away.
The sharpest consequence, and the likeliest thing to be examined as a contrast: endogenous growth theory predicts no convergence at all. Growth rates remain constant and differ across countries according to national savings rates and technology levels, and there is no tendency for capital-poor countries to catch up with rich ones that share their savings and population growth rates. A recession in one country can cause a permanent widening of the income gap.
Set that against Solow's conditional convergence and against Barro's two figures below. The field is arguing with itself, and the disagreement is exactly what a compare-and-contrast question would ask for.
The Solow Model: Empirical Evidence
slides 68–72 · Todaro 13e §3.5The test case is Robert Barro, 1991, "Economic growth in a cross section of countries," Quarterly Journal of Economics — a paper using regression techniques, on 98 countries over 1960–1985, asking whether incomes converge.
| Figure | What it shows |
|---|---|
| Barro Figure 1 | No sign of convergence. The raw scatter of growth against initial per capita GDP has no negative slope — poor countries were not systematically growing faster. |
| Barro Figure 2 | Conditional convergence. Holding constant a set of variables that includes proxies for starting human capital, higher initial per capita GDP is substantially negatively related to subsequent per capita growth. The negative relationship appears once other variables are controlled for. |
Why no unconditional convergence?
- The Solow model assumes the same steady state for every country If countries differ in s, n, d or A, they have different steady states and there is no reason for them to converge to each other
- Many other variables affect growth Such as initial human capital — which is why Barro's second regression controls for them
- A causality problem in the statistics Is it that saving causes growth of GDP, or growth of GDP causes saving?
The distinction between the two figures is the examinable point. Unconditional (or absolute) convergence says poor countries grow faster than rich ones, full stop — and the data reject it. Conditional convergence says a country grows faster the further it is below its own steady state — and that survives, once you control for the determinants of the steady state. The Solow model actually predicts the conditional version, which is why the failure of the unconditional version is not as damaging as it first appears.
The instructor's closing slide on this section shows the growth rate of labour productivity in constant 2017 USD for China, Germany, Japan and the USA — the same comparison at the productivity level rather than the income level, and with the same pattern of faster growth in the catch-up economies.
3.6 Reconciling 协调 the Differences
slides 67, 73 · Todaro 13e §3.6The chapter closes by refusing to pick a winner. The conclusions the slides draw:
Relevance of growth theories to today's developing countries
The slide is candid about the limits of everything in the chapter:
The textbook closes the chapter with Case Study 3: South Korea and Argentina, which runs all four theories against two countries that were well matched in 1960 and then swapped places. It is the best worked example in the book of what "each theory has some strengths and some weaknesses" actually means in practice.
The reversal. In 2017 South Korea's per capita income was about $38,340 at PPP and Argentina's about $20,270 — but forty years earlier the position was exactly reversed, with Argentina's real income double South Korea's. Both are midsize and both were long classified as middle-income, which is what makes the comparison fair.
| Approach | South Korea | Argentina |
|---|---|---|
| Stages | Partly confirmed. Investment ran at only 15% of GNI in 1965 — below takeoff levels — then rose to 37% by 1990 and near 40% over 2000–2007. But Rostow's 1960 book never mentioned South Korea; he picked India. Few of the "preconditions for takeoff" were in place. | Strongly contradicted. Argentina ranked 11th in the world on per capita income in 1870, ahead of Germany; it is not in the top 60 today. Rostow judged its takeoff "successful" in 1960, and growth was negative over 1965–1990. |
| Structural change | Broadly confirmed, and closely follows Lewis — rising agricultural productivity, labour shifting from agriculture to industry, a growing capital stock, more education and skills, and the demographic transition. Income grew over 7% a year through 1965–1990. | Little explanatory power. The transformation happened but did not deliver the growth the patterns models predict. |
| Dependence | Seriously challenged. South Korea was a Japanese colony until 1945 and thereafter wholly dependent on the United States, and received enormous aid — yet graduated to OECD membership. Dependence theorists call it an exception. | Contributes real insight — one of the two theories that does illuminate Argentina's history. |
| Neoclassical | Also challenged. Far from a free-market story: development planning, tax breaks, export targets set for individual firms, orchestrated technology licensing, deliberate building of indigenous industry. | Contributes insight, alongside the dependence reading. |
The case study's verdict is §3.6's verdict in miniature: no single approach explains either country, and the pair is chosen precisely because the two theories that fail on South Korea are the two that work on Argentina. It is also worth holding onto the two policies the text singles out in South Korea as "of exceptional importance" — the most ambitious land reform programme in the developing world, and a strong emphasis on primary rather than university education.
The Instructor's Exercises
slides 76–80 · with his published answersTwo exercises were worked in class and appear at the end of the deck with full answers. They are the closest thing available to a worked exam question, and both are reproduced here verbatim.
- What will be the initial GDP growth rate? g = s / c = 12% / 5 = 2.4%
- Technological advance causes c to fall to 4. How does this affect the growth rate? g = 12% / 4 = 3%
- Starting again from the initial situation, s rises to 15%. How does this affect the growth rate? g = 15% / 5 = 3%
- What does the Harrod-Domar model tell us about the sources of economic growth? The growth rate is directly related to the saving ratio, and inversely related to the capital-output ratio
Parts (b) and (c) both give 3% by different routes — halving c and raising s by a quarter. That is the model's practical content: growth can be raised either by saving more or by making capital more productive, and the two are substitutes on a one-for-one basis in this arithmetic. Whether a real economy can actually deliver either is the question the criticisms section takes up.
- Draw a labour supply curve that is initially perfectly elastic — horizontal — but becomes steeply and positively sloped at a certain point. Then draw a single downward-sloping labour demand curve that intersects the perfectly elastic portion of the supply curve.
- What area represents total modern-sector output? What areas represent the share paid to labourers as wages, and the share paid to capitalists? Answer (a) below
- Reinvestment of profits raises labour demand. Draw the new demand curve to the right of the original, still intersecting the elastic portion. What happens to total output and to the returns paid to labourers and capitalists? Answer (b) below
- Now suppose further reinvestment, but all surplus labour has already migrated, so the new demand curve intersects the steep portion of the supply curve. What happens now? Answer (c) below
The point of part (b) is that the wage is unchanged while output and profit both rise. That is the labour-surplus phase, and it is counter-intuitive enough to be worth stating plainly: employment goes up, total wages go up, output goes up, profit goes up — and every worker is paid exactly what they were paid before. Part (c) is where that finally breaks, and it is only then that the model delivers a rising standard of living for workers.
Formula Sheet
print-friendlyKey Concepts
53 terms · 25 from the textbookThis chapter carries far more Chinese glosses than the other two — the theories are exactly what the instructor expects you to be able to name. Every term below with a 中文 anchor is one he glossed himself.
Self-Check
22 questions · gradedThe calculation sections reproduce the instructor's two exercises with his own answers. Work them before revealing.
A · Growth facts
B · The four approaches
C · The models · calculation
This is the instructor's Exercise 1, with his published answers.
- (a) Initial growth rate g = s / c = 12% / 5 = 2.4%
- (b) c falls to 4 g = 12% / 4 = 3%
- (c) s rises to 15% g = 15% / 5 = 3%
- (d) The sources of growth The growth rate is directly related to the saving ratio, and inversely related to the capital-output ratio
- Rearrange g = s/c for s s = g × c = 7% × 3 = 21%
A 21% saving rate is high — it means forgoing a fifth of national income — and whether it is feasible is left open because the model treats s as a parameter that policy can set. The criticisms section attacks exactly this: the model assumes a country can determine its own savings and investment, and it assumes the institutional structures needed to convert saving into productive investment already exist.
The historical reference point is the Marshall Plan, where this equation was used in precisely this direction: to compute how much capital a war-damaged economy needed to hit a growth target.
- (a) Both inputs doubled Constant returns to scale → output doubles → 200 tons
- (b) Capital limits output $15 m supports 150 tons; 200 workers could produce 200, but the capital is not there → 150 tons, with 50 workers redundant
- (c) The production function Y = min{10K, L}
- (a) Initial output Y = 1 × 100.5 × 1000.5 = 3.1623 × 10 = 31.62
- (b) K doubled to 20 Y = 1 × 200.5 × 1000.5 = 4.4721 × 10 = 44.72
- (c) Not doubled 2 × 31.62 = 63.25 ≠ 44.72. The ratio is 44.72 / 31.62 = 1.414 = √2
Why: the exponents sum to 1, so the function has constant returns to scale in K and L together — double both and output doubles. But each exponent individually is below 1, so each input on its own has diminishing returns. Doubling only K raises output by 20.5 = √2, not by 2.
This is the property the whole Solow model runs on: because capital alone has diminishing returns, accumulation cannot raise output per worker indefinitely.
- Steady-state condition sy = (n+d)k, and y = A k0.5, so 0.20 k0.5 = 0.065 k
- Solve for k* k0.5 = 0.20 / 0.065 = 3.0769, so k* = 3.0769² = 9.47
- And y* y* = A √k* = √9.47 = 3.08
- Closed form check k* = (sA/(n+d))² = (0.20/0.065)² = 3.0769² = 9.47 ✓
- Now s rises to 30% k* = (0.30/0.065)² = 4.6154² = 21.30
That asymmetry is the model's central lesson. A large rise in the saving rate produces a much smaller proportional rise in output per worker.
No. K and Y are not constant at the steady state. The steady state fixes the per-worker quantities, not the totals.
- Recall the definitions Y = yL and K = kL
- At the steady state, y and k are constant So anything that happens to Y and K comes entirely from L
- L grows at rate n Therefore Y and K grow at rate n as well
- The instructor's example y = 10, L growing at 2% → Y is growing at 2%
Country Z grows faster.
- The reason f(k) has decreasing returns, so at a lower level of k the slope of f(k) is larger — the same change in k produces a larger change in y
- The name of the principle Transition dynamics — a country further below its steady state grows faster
- The prediction it yields Poorer countries grow faster, and poor and rich countries reach the same level of per capita GDP eventually — the famous catch-up theory
D · Lewis · the turning point
The instructor's answer (a):
- Total output — the area 0D1FL1, i.e. the whole area under the demand curve up to employment L1.
- Returns to labour (the wage bill) — the rectangle 0WM1FL1, wage times employment.
- Returns to capital (profit) — the remainder, WM1D1F, the area between the demand curve and the wage line.
The accounting is the same as any factor-share decomposition: output is the area under the marginal product curve, the wage bill is the rectangle at the market wage, and profit is what is left. The interest of the Lewis case is entirely in what happens to those three areas as demand shifts.
The instructor's answer (b):
- Total output grows to area 0D2GL2.
- Returns to labour rise to 0WM1GL2 — but note that the wage for each worker does not rise. The rectangle is wider, not taller.
- Returns to capital increase to area WM1D2G.
The instructor's answer (c):
- Total output grows to area 0D3HL3.
- Returns to labour rise to the area 0WM2HL3. Not only does total employment rise, the wage per worker also rises — to WM2.
- Returns to capital increase to area WM2D3H. It is not clear whether returns to capitalists have increased, decreased, or stayed the same as compared with part (b). In any case, returns to capitalists are now growing more slowly than before.
E · Extended answers
Why accumulation cannot sustain growth. The production function y = Af(k) has diminishing returns in k — each additional machine per worker adds less output than the one before. As an economy accumulates capital, the marginal product of capital falls. Eventually the additional output produced by investment is only just enough to offset depreciation and to equip new workers, and the economy reaches the steady state where sy = (n+d)k. At that point k and y are constant: growth in the standard of living stops.
Total output Y and the capital stock K do keep growing, but only at rate n, the rate of population growth — because Y = yL and L is growing at n. Output per worker is what stops growing, and that is the measure that matters for living standards.
The two weaknesses that follow.
- Missing long-run growth The model predicts that growth stops, but empirically economies continue to grow over time. Something is missing, and that something is technology.
- Technology is exogenous, and TFP unexplained A is determined outside the model. The model does not explain why countries differ in TFP or in investment rates, and TFP matters more than capital for explaining income differences.
These two weaknesses are precisely what later growth theory exists to address.
Unconditional (absolute) convergence is the claim that poor countries grow faster than rich ones, full stop — so that income levels converge. The raw scatter of growth against initial per capita GDP (Barro's Figure 1) shows no negative slope, so this version is rejected.
Conditional convergence is the claim that a country grows faster the further it is below its own steady state. Once Barro controls for a set of variables including proxies for starting human capital, higher initial per capita GDP is substantially negatively related to subsequent per capita growth (Figure 2). So this version is supported.
Why the first result is not fatal. The Solow model actually predicts the conditional version. It says a country converges to its own steady state, and the steady state depends on s, n, d and A. Countries with different saving rates, population growth rates or productivity levels have different steady states, so there is no reason for them to converge on each other. The slide gives this as the first of three explanations: "the Solow model assumes the same steady state for every country."
The statistical problem: causality. Saving and growth are jointly determined — it is not obvious whether a high saving rate causes fast growth, or whether fast growth generates the income that permits high saving. A simple regression cannot separate the two directions.
The other explanation the slide gives is that many other variables affect growth, which is exactly why the conditional regression has to include them.
Where the Course Goes Next
Three chapters have been delivered so far, covering the material through the classic growth theories. This page holds the placeholder for what comes next, the two papers the instructor put on the slides as extension reading, and a short revision checklist that cross-references the three chapters.
Delivered So Far
138 slides across three chaptersEach chapter is built from the instructor's own deck, slide by slide. Where a slide carried only an image — a figure, a table, or a formula stored as a picture — the content was read off the rendered slide rather than guessed at, and where a cell could not be read it is marked as illegible rather than filled in.
Next Chapters
placeholders — awaiting slidesThese are the topics that follow in a standard development-economics sequence. They are listed so the shape of the rest of the course is visible, and each will be built out to the same five-block structure as the three chapters above when the decks arrive.
Contemporary Models of Development and Underdevelopment
Poverty, Inequality, and Development
Population Growth and Economic Development
Urbanisation and Rural-Urban Migration
The order is not arbitrary. Chapter 3's criticisms section names three questions the classic models leave unanswered — how to make people save and firms invest, how to make investment more efficient, and whether agricultural workers automatically move to the cities and find work. Chapters 4, 5 and 7 are where those three questions are taken up.
Extension Reading
shown at the end of the Chapter 3 deckThe instructor closed the Chapter 3 slides with the title pages of two research papers. They are not examinable material, but they mark the direction of his own interest and both are about China, which is where the course's examples keep landing.
Both papers are worth reading against Chapter 3, because each takes one of its loose ends and makes it the centre of the analysis. The first questions the saving-versus-consumption trade-off that the Harrod-Domar model takes for granted. The second is a direct empirical study of unconditional convergence — within a single country, which is a cleaner test than Barro's across countries, and it finds the convergence that Barro could not.
The instructor also assigned the documentary Why Poverty?, Episode 1: Poor Us, at the end of Chapter 1 — an animated history of attempts to end poverty, and the same argument as section 1.1 in another medium.
Reading Alongside the Textbook
Todaro & Smith, 13th editionThe course slides were built on an earlier edition — their footers read Copyright © 2012 Pearson Addison-Wesley — so if you are working from the 13th edition the chapter numbers match but the section numbers often do not. Nothing is missing; some of it has moved into appendices, and some of it has moved into a different chapter.
| What the slides call it | Where the 13th edition puts it |
|---|---|
| Ch. 1 — poverty, the field, capability, MDGs | §1.2, §1.4, §1.5–1.6, §1.7 (pp. 42–64) |
| Ch. 1 — country classification | Moved to §1.3 and again to §2.2 (pp. 48, 78–86) |
| Ch. 2 — defining and measuring development | §2.1–2.3 (pp. 76–94) |
| Ch. 2 — the traditional (arithmetic) HDI | Appendix 2.1 (pp. 143–148) |
| Ch. 2 — ten characteristics | §2.4 (pp. 95–107) |
| not in the slides at all | §2.6 Long-Run Causes of Comparative Development (pp. 115–122) |
| Ch. 2 — how low-income countries differ | Appendix 2.2 (pp. 149–156) |
| Ch. 3 — the growth facts (divergence, convergence) | Chapter 2, §2.5 (pp. 108–115) |
| Ch. 3 — four approaches, linear stages, Lewis, dependence, counterrevolution | §3.1–3.5 (pp. 157–178) |
| Ch. 3 — the Solow model | Appendix 3.2 (pp. 194–198) |
| Ch. 3 — reconciling the differences | §3.6 (p. 179) |
| not in the slides at all | Appendix 3.1 Components of Economic Growth (pp. 188–193) |
| not in the slides at all | Appendix 3.3 Endogenous Growth Theory (pp. 199–204) |
Three things in the 13th edition are worth reading even though the slides never mention them, and all three are written up in the chapters above with the argument set out in full:
- Appendix 3.1, Components of Economic Growth — capital accumulation, population and labour force growth, and technological progress, with the three-way classification of technology into neutral, labour-saving and capital-saving.
- Appendix 3.3, Endogenous Growth Theory — the answer to the gap the slides themselves flag: if capital accumulation cannot sustain growth and technology is outside the model, what does explain sustained growth? The answer is the AK model, and its prediction is the opposite of Solow's.
- §2.6, Long-Run Causes of Comparative Development — the chapter's hardest question: why do the differences exist at all? Geography, colonial regime type, inequality and institutional quality, built around the Acemoglu–Johnson–Robinson "reversal of fortune" result and the Engerman–Sokoloff factor-endowment argument. It also contains the clearest introduction to instrumental variables you will meet in this course — worth reading for the method as much as the conclusion.
Three case studies also fill gaps: Pakistan and Bangladesh (Ch. 1, on whether income or capability is the better measure of development), Ghana (Ch. 2, on colonial legacies and institutions), and South Korea and Argentina (Ch. 3, which runs all four theories against two countries that swapped places). The first and third are summarised in the relevant chapters here.
Do not be thrown by page numbers quoted in the slides' images — several tables were re-sourced when the instructor updated the data to 2022–2026, so a figure captioned "2018" may carry later numbers here than in your printed copy. Where the two disagree, the slides win, because the slides are what will be examined.
Revision Checklist
what to be able to do, chapter by chapterEach item below is something you should be able to do from memory, on paper, without the slides. They are ordered by how likely they are to appear as an exam question, based on what the instructor chose to gloss, bold, or work through in class.
A · Things you must be able to draw
| Diagram | What you must be able to do with it |
|---|---|
| The Solow diagram | Draw y = Af(k), sy and (n+d)k; mark the steady state S; show which way the economy moves when k is below or above k*. Then show what happens when s rises, when n rises, and when A rises. |
| The Lewis two-sector diagram | Draw both panels. On the modern side, show the horizontal labour supply, the downward-sloping demand curves, and label the areas for output, wages and profit. Show what changes at the turning point. |
| The fixed-coefficient isoquant | Draw Y = min{10K, L} with right-angled isoquants, and contrast it with the smooth isoquants of the Cobb-Douglas function. |
B · Calculations you must be able to do
| Calculation | Where |
|---|---|
| g = s/c, and running it backwards for a growth target | Chapter 3 · Harrod-Domar |
| The old HDI: five sub-indexes then an arithmetic mean | Chapter 2 · Bangladesh 2007 |
| The New HDI: the same sub-indexes then a geometric mean | Chapter 2 · China 2010 |
| k* = (sA/(n+d))² for α = 0.5, then y* = A√k* | Chapter 3 · Solow |
| Cobb-Douglas with α = 0.5, and why doubling K does not double Y | Chapter 3 · production function |
| Reading Table 2.11's three-way split, and the PPP ratio column | Chapter 2 · data sections |
C · Terms to be able to define in both languages
D · Distinctions that are easy to blur
| Do not confuse | with |
|---|---|
| Functionings | Capabilities — achievement versus freedom to achieve |
| GNI | GDP — who owns it versus where it is produced |
| Old HDI (arithmetic) | New HDI (geometric) — the formulas are not interchangeable |
| Growth convergence | Absolute income convergence — relative gaps can narrow while absolute gaps widen |
| Unconditional convergence | Conditional convergence — Barro's two figures give opposite answers |
| Free market approach | Market-friendly approach — the third one admits market failure |
| Exogenous | Endogenous — Solow's single change is making capital endogenous |
| CRTS in K and L | DRTS in k — the same function has both |
| The wage not rising (Lewis phase 1) | The wage bill not rising — the bill rises with employment while the wage stays flat |
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