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Development Economics 发展经济学 · Nanjing University

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.

Chapters 1–3 delivered · 138 slides Todaro & Smith, Economic Development Four interactive models

How this workbench is organised

the same five blocks in every chapter
1 · Concept Map

How 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.

2 · Core Content

Explanatory prose with the instructor's own worked examples taken apart step by step, plus the data behind each table and figure.

3 · Formula Sheet

Every formula from the chapter in one place, with the meaning of each symbol. Prints on its own.

4 · Key Concepts

The vocabulary, defined in English with the instructor's own Chinese gloss where he supplied one.

5 · Self-Check

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 sliders

Development 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.

Harrod-Domar growth rate

The post-war savings-and-growth arithmetic, g = s/c, with the fixed-coefficient production function it rests on. Chapter 3.

Lewis two-sector model

Surplus labour in agriculture, a horizontal labour supply in industry, and the turning point where wages finally start to rise. Chapter 3.

Solow diagram

Saving, population growth and depreciation meet at the steady state — and the reason poorer countries grow faster on the way there. Chapter 3.

New HDI calculator

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 colours
📖 Beyond the slides

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.

⚠️ Trap

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.

💬 Think

The instructor's own discussion questions, kept verbatim, with a worked answer below each.

Chapters

three delivered so far

Progress dashboard

stored locally in this browser

How to use this before the exam

a suggested order
Start with the diagrams, not the prose

Chapter 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.

Then the definitions, in both languages

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.

Then the instructor's own exercises

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.

Chapter 1

Introducing Economic Development: A Global Perspective

Todaro & Smith, Economic Development, Ch. 1 Source: Chapter1.pptx — 22 slides Instructor's Chinese glosses retained

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.

1

Concept Map

how the chapter builds
What is development? The question the whole course answers. Chapter 1 gives the first answer — income — and then rejects it as incomplete.
first, look at what poverty actually is
1.1 How the other half live Six testimonies. Poverty is not just low income — it is hunger, shame, powerlessness, and vulnerability at once.
Poverty is multidimensional So development must be too. This is the premise everything else rests on.
then, where does the field sit?
1.2 Economics and development studies Neoclassical economics · political economy · development economics. Three scopes, not three opinions.
Development is not value-free Imperfect markets, structural change, multiple equilibria. And normative choices are unavoidable.
which forces the central question
Traditional measure Development = growth in GNI per capita. Income as the driver of utility.
Sen's capability approach 可行能力 Development = expansion of capabilities and substantive freedoms. Functionings vs capabilities.
which yields three criteria and three objectives
Three core values Sustenance · Self-esteem · Freedom from servitude 奴役
Three objectives Life-sustaining goods · higher living levels · wider economic and social choices
Women at the centre Empowerment is both a goal and a driver of development.
and finally, the international agenda
1.4 MDGs (2000–2015) Eight goals. Replaced in 2015 by the 17 SDGs of the 2030 Agenda.
Where this goes next Chapter 2 asks how to measure all this; Chapter 3 asks what makes it grow.
2

1.1 How the Other Half Live

slides 2–8 · Todaro 13e §1.2

The 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.

A poor woman, Uganda
"When one is poor, she has no say in public, she feels inferior. She has no food, so there is famine in her house; no clothing, and no progress in her family."
A blind woman, Tiraspol, Moldova
"For a poor person everything is terrible — illness, humiliation, shame. We are cripples; we are afraid of everything; we depend on everyone. No one needs us. We are like garbage that everyone wants to get rid of."
Discussion group, rural Ethiopia
"Life in the area is so precarious that the youth and every able person have to migrate to the towns or join the army at the war front in order to escape the hazards of hunger escalating over here."
Mbwadzulu Village, Mangochi, Malawi
"We have to line up for hours before it is our turn to draw water."
Discussion group, Brazil
"[Poverty is] … low salaries and lack of jobs. And it's also not having medicine, food, and clothes."
A poor man, Kenya
"Don't ask me what poverty is because you have met it outside my house. Look at the house and count the number of holes. Look at the utensils and the clothes I am wearing. Look at everything and write what you see. What you see is poverty."

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:

Poverty is more than a lack of income — it is inherently multidimensional, as is economic development.

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.

📖 Beyond the slides

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.

3

1.2 Economics and Development Studies

slides 9–12 · Todaro 13e §1.4

Three 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.

ApproachWhat it studiesIts 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.

Highly imperfect markets
Imperfect competition, and limited information — against the perfect-markets assumption.
Large-scale structural change
Whole sectors shift (agriculture → industry → services), so the economy is not a fixed structure being optimised.
Multiple equilibria
Rather than one single equilibrium. The same endowments can support very different outcomes — which is why history and policy matter.
Persistent disequilibrium
And institutional rigidities. The economy is not reliably pulled back to balance.

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.
4

1.3 What Do We Mean by Development?

slides 13–17 · Todaro 13e §1.5–1.6 · the examinable core

The 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:

Functionings
Actual achievements — the "beings and doings" a person really manages. What you actually are and actually do, as opposed to what you could be and could do.
Capabilities
The real freedom to achieve alternative functionings. The set of lives you could actually choose between.
Well-being
Being well plus freedoms of choice. Both halves are required: a well-fed prisoner is not doing well in this framework.
Substantive freedoms
Freedom that is actually available given your circumstances — not freedom on paper.
⚠️ Trap

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 existenceDoings — activities
Being able to live a long and healthy lifeBeing mobile and able to travel freely
Being well-nourished and adequately clothedBeing able to take part in the life of the community
Being literate and knowledgeableWorking and earning a livelihood
Have self-respect and dignity 尊严 Making autonomous 自主的 life choices
⚠️ Trap

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.

1 · Sustenance
The ability to meet basic needs — food, shelter, health, protection. Its goal is to end absolute poverty.
2 · Self-esteem 尊严
A sense of worth and dignity; recognition as an autonomous person. To be a person rather than a recipient.
3 · Freedom from servitude 奴役
Expanded real choices; liberation from dependency and oppression.
💬 Think

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:

1 · Diminishing returns of income
Income lifts happiness strongly at low levels; gains flatten above roughly $20,000 per capita.
2 · Income is not the only driver
Large happiness gaps exist across countries at similar income levels.
3 · Development ≠ just GDP growth
Well-being depends on more than income alone.

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.

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

  1. Increase the availability of life-sustaining goods Food, shelter, health, protection
  2. Raise overall levels of living Higher incomes, more jobs, better education, greater attention to cultural and human values
  3. 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.

📖 Beyond the slides

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.

💬 Think

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.

5

1.4 The Millennium Development Goals

slides 18–21 · Todaro 13e §1.7

Eight 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.

GoalMillennium Development Goal
1Eradicate extreme poverty and hunger
2Achieve universal primary education
3Promote gender equality and empower women
4Reduce child mortality
5Improve maternal health
6Combat HIV/AIDS, malaria, and other diseases
7Ensure environmental sustainability
8Develop 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:

GoalTargets
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
⚠️ Trap

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.

⚠️ Trap

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.

6

Formula Sheet

print-friendly

Chapter 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.

Traditional measure of development
National development = growth in GNI per capita
Income as the main driver of utility. The definition section 1.3 rejects as incomplete — not as wrong.
Capability approach
Development = expansion of capabilities and substantive freedoms
Capabilities are the freedoms; functionings are the achievements.
Well-being
Well-being = being well + freedom of choice
Both terms required. A well-nourished person with no choices does not satisfy this definition.
The three core values
Sustenance · Self-esteem · Freedom from servitude
Each with a stated goal: end absolute poverty · recognition as a person · expanded real choices.
The three objectives
Life-sustaining goods · living levels · economic and social choices
The three values restated as operational aims.
The international framework
8 MDGs (2000–2015) → 17 SDGs (2015–2030)
2025 SDG Report: only ~35–36% of targets on track.
7

Key Concepts

21 terms · 8 from the textbook

Terms 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.

Development economics
The study of the economic, social and institutional mechanisms that raise living standards at scale in low-income economies. Distinguished from neoclassical economics by its assumptions — imperfect markets, structural change, multiple equilibria — and from political economy by including both.
Capability approach 可行能力
Sen's reformulation: development is the expansion of human capabilities and substantive freedoms, not the growth of income. The approach behind the Human Development Index in Chapter 2.
Functionings
Actual achievements — the "beings and doings" a person really attains. Contrast with capabilities, which are what they could attain.
Capabilities
The real freedom to achieve alternative functionings — the set of lives actually available to choose between. Real, not formal: a right you cannot exercise is not a capability.
Substantive freedom
Freedom that is genuinely available given a person's circumstances. The term "substantive" is doing work — it excludes freedoms that exist only on paper.
Sustenance
The first core value: the ability to meet basic needs — food, shelter, health, protection. Its stated goal is to end absolute poverty.
Self-esteem 尊严
The second core value: a sense of worth and dignity, and recognition as an autonomous person rather than as a recipient of assistance.
Freedom from servitude 奴役
The third core value: expanded real choices, and liberation from dependency and oppression. Note that it is freedom from servitude, not simply freedom — the emphasis is on the removal of subordination.
Absolute poverty
Poverty defined against a fixed threshold of subsistence, rather than against the distribution around you. Sustenance's goal is to end it; Chapter 2 puts numbers on it.
Multidimensional poverty
The chapter's opening thesis: poverty is more than low income — it includes hunger, shame, powerlessness, vulnerability and lack of voice at the same time. Chapter 2's HDI is one attempt to measure this.
Political economy
The study of how social groups and elites shape resource allocation and distribution. Focused on power and conflict rather than on efficiency.
Millennium Development Goals (MDGs)
Eight goals adopted by the UN in 2000 with a 2015 deadline, from halving extreme poverty to a global partnership for development. Replaced by the 17 SDGs of the 2030 Agenda.
Sustainable Development Goals (SDGs)
The 17 goals adopted in September 2015 under the 2030 Agenda, applying to all countries rather than only developing ones. The 2025 report puts only about 35–36% of targets on track.
Normative vs positive in development
The slide's claim that development is not value-free: calling something "improvement" already commits you to a view of what is better. Policy trade-offs between efficiency, equity, growth, stability and sustainability are choices, not calculations.
Development Todaro
The process of improving the quality of all human lives and capabilities by raising people's levels of living, self-esteem, and freedom. The textbook's own one-sentence definition — and note that it names all three core values.
Development economics Todaro
The study of how economies are transformed from stagnation to growth and from low-income to high-income status, and overcome problems of extreme poverty. Narrower than the slide's version — it puts the transformation at the centre.
Subsistence economy Todaro
An economy in which production is mainly for personal consumption and the standard of living yields little more than the basic necessities of life — food, shelter, and clothing. The starting point of the growth process, and the setting Lewis's agricultural sector describes.
Institutions Todaro
Constitutions, laws, regulations, social norms, rules of conduct, and generally accepted ways of doing things. Following Douglass North, economic institutions are "humanly devised" constraints that shape human interaction — both the informal and the formal "rules of the game" of economic life. The single most important term in the textbook that the deck never defines.
Social system Todaro
The organisational and institutional structure of a society, including its values, attitudes, power structure, and traditions. This is what §1.2 means by "economies are embedded in institutions, culture, history and politics".
Functionings Todaro
What people do or can do with the commodities of given characteristics that they come to possess or control. Sen's own emphasis: what matters is not the characteristics of the goods consumed but what use the consumer can and does make of them — a book is of little value to an illiterate person.
Capabilities Todaro
The freedoms that people have, given their personal features and their command over commodities. Note that the textbook's phrasing makes the two conditions explicit — capabilities depend on both what you are and what you have.
8

Self-Check

16 questions · graded
0 / 0 correct

Section 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

Single choice. One option is right; the others are near-misses on purpose.
Q1In Sen's capability approach, what is the difference between a functioning and a capability?
Correct.Functionings are the "beings and doings" actually attained; capabilities are the freedom to achieve alternative functionings. Both can be material or non-material, so A is wrong; B and D both smuggle in claims the approach does not make.
Not quite.The distinction is achievement versus freedom to achieve — not material versus non-material, and not individual versus social.
Q2Which of these is not one of the three core values of development?
Correct.The three core values are sustenance, self-esteem and freedom from servitude. Sustainability is a real concern in development policy — it appears in the list of trade-offs in section 1.2 — but it is not one of the three core values.
Not quite.The three are sustenance, self-esteem and freedom from servitude. Sustainability is a policy trade-off, not a core value.
Q3What does the chapter identify as the universal theme in the six testimonies of poor people?
Correct.The slide's own summary line. The six testimonies mention voice, shame, vulnerability, water, medicine and clothing — income appears in only one of them.
Not quite.The theme is multidimensionality. The testimonies deliberately place voice, shame and vulnerability alongside income, and only one of the six mentions income directly.
Q4Which of the following is one of the four key features of developing economies listed in section 1.2?
Correct.The four features are: highly imperfect markets with limited information; large-scale structural change across sectors; multiple equilibria; and persistent disequilibrium with institutional rigidities. A, B and C are each the opposite of one of them.
Not quite.The four features are all the opposite of the neoclassical assumptions: imperfect markets, large-scale structural change, multiple equilibria, and persistent disequilibrium.
Q5How many Sustainable Development Goals replaced the MDGs in 2015?
Correct.17 SDGs, adopted in September 2015 under the 2030 Agenda. The 8 is the number of MDGs they replaced.
Not quite.17 SDGs replaced the 8 MDGs. Option A is the old number.
Q6According to the 2025 Sustainable Development Goals Report cited on the instructor's slide, roughly what share of targets are progressing well or making moderate progress?
Correct.Roughly 35–36% — about a third. This is the instructor's own update to the slide, and it is the counterpoint to the optimism of the 2015 launch.
Not quite.About 35–36%. The figure is deliberately unflattering and is worth remembering as such.

B · Distinctions

Where the near-misses live. Read every option before choosing.
Q7What distinguishes development economics from traditional neoclassical economics on the slide's account?
Correct.The difference is one of scope, not of method or of values. Development economics keeps the neoclassical apparatus but adds structural transformation and broad-based well-being to what it is trying to explain.
Not quite.It is a difference of scope. Development economics does not reject efficient allocation — it studies a setting where the assumptions that make the neoclassical solution work do not hold.
Q8A person has ample food available but is deliberately fasting. Which statement is correct in Sen's framework?
Correct.Both are hungry, so the functioning is absent in both — but only the fasting person has the capability of being well-nourished. This is precisely why income and food availability cannot by themselves tell you whether someone is deprived.
Not quite.Both lack the functioning, but only the fasting person has the capability. The distinction is exactly what lets Sen's framework tell two outwardly identical situations apart.
Q9Which of these best captures the difference between self-esteem and freedom from servitude as core values?
Correct.Self-esteem is about worth and recognition as an autonomous person; freedom from servitude is about the range of real choices and release from dependency and oppression. The slide gives each its own definition.
Not quite.They are distinct: one is about recognition and dignity, the other about the breadth of real choices and the absence of subordination.
Q10What does the slide identify as the central role of women in development?
Correct.The slide states it as a two-way relationship: a goal in its own right, and a driver through improved child health, education and long-run human capital.
Not quite.Both, not one: it is a goal and a driver. The slide also names the channels — child health, education, long-run human capital.

C · Extended answers

Write these out. Compare against the model answer only after you have drafted your own.
Q11State the three core values of development and, for each, the goal the slide attaches to it. Then explain in one sentence why only the first is a material condition.
  1. Sustenance — the ability to meet basic needs (food, shelter, health, protection). Goal: to end absolute poverty.
  2. Self-esteem — a sense of worth and dignity; recognition as an autonomous person. Goal: to be recognised as a person, not a recipient.
  3. 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.

Q12Explain the difference between a functioning and a capability, and use it to explain why two people who are both hungry may not be equally deprived.

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.

Q13Figure 1.2 plots income against happiness. State its three conclusions and explain what the third one implies for how development should be measured.
  1. Diminishing returns of income. Income lifts happiness strongly at low levels; the gains flatten above roughly $20,000 per capita.
  2. Income is not the only driver. Large happiness gaps exist between countries at similar income levels.
  3. 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.

Q14Section 1.2 claims that "economies are social systems". Give the four supporting claims from the slide and explain what each one implies for policy.
  1. Economies are embedded in institutions, culture, history and politics. Policy cannot be designed from economic theory alone.
  2. Development policy depends as much on institutional variables as on capital and labour. Two countries with the same endowments can perform very differently.
  3. Policies that work in rich countries often fail in developing contexts. Transplanting a policy assumes the institutional preconditions came with it.
  4. 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.

Q15Why does the chapter treat the MDGs and the SDGs as part of the definition of development, rather than as a separate policy topic?

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.

Q16Name the three objectives of development and explain how they relate to the three core values.
  1. Increase the availability of life-sustaining goods — food, shelter, health, protection. Corresponds to sustenance.
  2. Raise overall levels of living — higher incomes, more jobs, better education, greater attention to cultural and human values. Corresponds to self-esteem.
  3. 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.

Chapter 2

Comparative Economic Development

Todaro & Smith, Economic Development, Ch. 2 Source: Chapter2.ppt — 35 slides Instructor's Chinese glosses retained

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.

1

Concept Map

how the chapter builds
Measurement is the argument Every way of measuring development encodes a claim about what development is. Chapter 2 is a sequence of those claims, each fixing a problem in the one before.
first: who counts as developing?
2.1 World Bank income groups Rank on GNI per capita. Four bands, thresholds revised every year.
Problem A single cut-off makes "developing" a binary, when the underlying reality is a continuum.
then: what do we measure?
2.2 Real income, health, education GNI vs GDP · the expenditure identity · nominal vs real
PPP 购买力平价 Exchange rates compare currencies, not what money buys. PPP compares what money buys.
which needs a single index
2.3 Old HDI (1990–2009) Three indexes added and divided by three. Arithmetic mean.
New HDI (2010– ) Geometric mean of the three. Refuses perfect substitutability between health, education and income.
then: what is actually true of these countries?
2.4 Ten characteristics What developing countries share — and the diversity within that commonality.
2.5 Eight differences How today's low-income countries differ from today's rich ones at their own start.
2.6 Long-run causes Why the differences exist at all — geography, colonial institutions, inequality. In the book only; the slides never mention it.
Where this goes next Chapter 3 stops measuring and asks what makes these economies grow at all.
2

2.1 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.

GroupGNI 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.
⚠️ Trap

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.

📖 Beyond the slides

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.

📖 Beyond the slides

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:

ClassificationBasis 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.

3

2.2 Basic Indicators: Real Income, Health, Education

slides 5–8 · Todaro 13e §2.2.1

GNI and GDP

Two accounting identities that get confused constantly. The difference is who is being counted, not what is being counted.

Gross National Income (GNI)
The total domestic and foreign value added 附加价值 claimed by a country's residents, without deducting depreciation of the domestic capital stock. Ownership is what matters, not location.
Gross Domestic Product (GDP)
The total value for final use of output produced within an economy, by both residents and non-residents. Location is what matters, not ownership.
⚠️ Trap

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 = C + I + G + NX

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

MeasureDefinitionWhat 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.

4

Purchasing Power Parity

slides 9–10 · Todaro 13e §2.2.2

Comparing 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.

Purchasing power parity (PPP) 购买力平价
Calculated using a common set of international prices for all goods and services.
The PPP conversion factor
The number of units of a foreign country's currency required to purchase the identical quantity of goods and services in the local developing-country market as $1 would buy in the United States.

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.

CountryExchange rate (US$) PPP (US$)PPP ÷ exchange rate
Niger3609902.75×
Congo, Dem. Rep.4608701.89×
Uganda6001,8203.03×
Haiti7601,8302.41×
Cambodia1,2303,7503.05×
Senegal1,2403,3602.71×
Kenya1,4603,2502.23×
Bangladesh1,4704,0402.75×
Pakistan1,5805,8303.69×
Côte d'Ivoire1,5803,8202.42×
India1,8006,9803.88×
Ghana1,8804,2802.28×
Nigeria2,1005,7002.71×
Vietnam2,1606,4502.99×
Egypt, Arab Rep.3,01011,3603.77×
Bolivia3,1307,3402.35×
Indonesia3,54011,9003.36×
Philippines3,66010,0502.75×
Guatemala4,0608,0001.97×
Colombia5,89014,0902.39×
Thailand5,95017,0402.86×
Peru5,96012,8802.16×
Dominican Republic6,63015,2902.31×
Botswana6,73016,4202.44×
Brazil8,60015,2001.77×
Mexico8,61017,8402.07×
China8,69016,7601.93×
Costa Rica11,12016,2001.46×
Chile13,61023,5701.73×
Korea, Rep.28,38038,3401.35×
United Kingdom40,53042,5601.05×
Canada42,87046,0701.07×
United States58,27060,2001.03×
Low income7752,127 2.74×
Middle income4,94211,993 2.43×
High income40,14247,575 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.

⚠️ Trap

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.

📖 Beyond the slides

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.

5

2.3 Holistic Measures: the Human Development Index

slides 11–21 · Todaro 13e §2.3 + App. 2.1 · the examinable core

The 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:

BandHDI value
Low human development0.000 – 0.499
Medium human development0.500 – 0.799
High human development0.800 – 0.900
Very high human development0.900 – 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.

Worked Bangladesh, 2007 — old (arithmetic) HDI
PPP GDP per capita $1,241 · life expectancy 65.7 years · adult literacy 53.5% · gross enrolment 52.1%
  1. Income index — logarithmic, because of diminishing returns [ln(1241) − ln(100)] / [ln(40000) − ln(100)] = 0.420
  2. Life expectancy index (65.7 − 25) / (85 − 25) = 0.678
  3. Adult literacy index (53.5 − 0) / (100 − 0) = 0.535
  4. Gross enrolment index (52.1 − 0) / (100 − 0) = 0.521
  5. Education index — two-thirds literacy, one-third enrolment (2/3)(0.535) + (1/3)(0.521) = 0.530
  6. 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.

1 · A geometric mean, not an arithmetic one
The traditional HDI added the three components and divided by three. The New HDI takes the cube root of the product of the three component indexes. A geometric mean is also used to build the overall education index from its two components.
Why it matters
The arithmetic mean silently assumed one component could be traded off against another as perfect substitutes — a very strong assumption. The geometric mean allows only imperfect substitutability: a very low score in any one dimension drags the whole index down.

The smaller changes are just as examinable:

ChangeFrom → 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

Worked China, 2010 — New (geometric) HDI
Life expectancy 73.5 years · mean years of schooling 7.5 · expected years of schooling 11.4 · GNI per capita $7,263
  1. Life expectancy index (73.5 − 20) / (83.2 − 20) = 0.847
  2. Mean years of schooling index (7.5 − 0) / (13.2 − 0) = 0.568
  3. Expected years of schooling index (11.4 − 0) / (20.6 − 0) = 0.553
  4. Education index — a geometric mean of the two, rescaled [√(0.568 × 0.553) − 0] / (0.951 − 0) = 0.589
  5. Income index [ln(7263) − ln(163)] / [ln(108211) − ln(163)] = 0.584
  6. New HDI — the cube root of the product ∛(0.847 × 0.589 × 0.584) = 0.663
⚠️ Trap

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.

⚠️ Trap

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

Advantage
A country can do much better than might be expected at a low level of income — and substantial income gains can still accomplish relatively little in human development. The HDI is built to make both facts visible.
Drawback · gross enrolment overstates schooling
Enrolment counts who is registered, not who is learning or who finishes.
Drawback · equal weight
The three dimensions are weighted equally, which is a choice rather than a finding.
Drawback · no attention to quality
A year of schooling is a year of schooling, regardless of what was taught.
Model

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)

CountryHDI rankLife exp. Mean yrsExp. yrsGNI/cap HDIGNI − HDI rank
Canada1282.513.3 16.443,4330.926+10
United States1379.513.4 16.554,9410.924+13
United Kingdom1481.712.9 17.439,1160.922+8
South Korea2282.412.1 16.535,9450.903−27
United Arab Emirates3477.4 10.813.667,805 0.863+13
Chile4479.710.3 16.421,9100.843+3
Russian Federation4971.2 12.015.524,233 0.816+15
Costa Rica6380.08.8 15.414,6360.794−14
Turkey6476.08.0 15.224,8040.791+43
Cuba7379.911.8 14.07,5240.777+19
Mexico7477.38.6 14.116,9440.774+2
Sri Lanka7676.510.9 13.911,3260.770−26
Brazil7975.77.8 15.413,7550.759−40
China8676.47.8 13.815,2700.752−23
Botswana10167.69.3 12.615,5340.717−15
Gabon11066.59.2 12.816,4310.702+9
South Africa11363.410.1 13.311,9230.699+3
Egypt11571.77.2 13.110,3550.696−80
Guatemala12773.76.5 10.87,2780.650+16
India13068.86.4 12.36,3530.640−14
Bangladesh13672.85.8 11.43,6770.608+20
Ghana14063.07.1 11.64,0960.592−22
Equatorial Guinea14157.9 5.59.319,513 0.591−15
Kenya14267.36.5 12.12,9610.590
Pakistan15066.65.2 8.65,3110.562
Papua New Guinea15365.7 4.610.03,403 0.544
Madagascar16166.36.1 10.61,3580.519
Côte d'Ivoire17054.15.2 9.03,4810.492
Burkina Faso18360.82.3 8.51,6500.423
Chad18653.22.0 5.41,7500.404
Niger18960.42.0 5.49060.354

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

Top 5
1 Iceland 0.972 · 2 Norway 0.970 · 3 Switzerland 0.970 · 4 Denmark 0.962 · 5 Germany 0.959
Bottom 5
184 Niger 0.394 · 183 Central African Rep. 0.397 · 182 Chad 0.398 · 180 Burundi 0.433 · 180 South Sudan 0.433

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.

📖 Beyond the slides

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:

Inequality-Adjusted HDI (IHDI)
Imposes a penalty on the HDI that grows with inequality across people. This is the natural extension of the geometric-mean argument: the mean already punishes imbalance between dimensions, and the IHDI punishes imbalance within them.
Gender Inequality Index (GII)
A separate index focused on gender-based disadvantage — the operational counterpart of Chapter 1's "central role of women".
Multidimensional Poverty Index (MPI)
The UNDP's measure of overlapping deprivations in health, education and living standards. The direct heir of Chapter 1's opening claim that poverty is multidimensional; covered in Chapter 5 of the book.

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.

6

2.4 Characteristics of the Developing World

slides 22–31 · Todaro 13e §2.4 · diversity within commonality

The 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.

#CharacteristicThe evidence on the slide
1Lower levels of living and productivity Figure 2.4: high-income countries take 58% of global income while Sub-Saharan Africa takes 2%.
2Lower 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.
3Higher levels of inequality and absolute poverty Absolute poverty and world poverty measures.
4Higher population growth rates Crude birth rate 粗出生率 — see the table below.
5Greater social fractionalisation Significant ethnic, linguistic and other social divisions within a country.
6Larger rural populations, rapid rural-to-urban migration Table 2.10 — see below.
7Lower levels of industrialisation and manufactured exports Table 2.11 — see below.
8Adverse geography Resource endowments: a nation's supply of usable factors of production, including mineral deposits, raw materials and labour.
9Underdeveloped financial and other markets Imperfect markets; incomplete information.
10Quality 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%:

GroupShare of global income
High-income countries58%
East Asia & Pacific17%
Latin America & Caribbean7%
Europe & Central Asia7%
South Asia5%
Middle East & North Africa4%
Sub-Saharan Africa2%

Table 2.6 — the 12 most and least populated countries, 2024

#Most populousPopulation (m) GNI per capita (US$)Least populous Population (thousands)
1India1,4512,950 Tuvalu12
2China1,40913,100 Nauru18
3United States34086,000 Palau42
4Indonesia2835,200 Marshall Islands53
5Pakistan2411,920 St. Kitts and Nevis72
6Nigeria2232,280 Dominica100
7Brazil21610,300 Antigua and Barbuda105
8Bangladesh1742,820 Micronesia108
9Russian Federation14411,800 Grenada108
10Mexico13111,500 Tonga111
11Ethiopia1261,100 St. Vincent and the Grenadines119
12Japan12442,500 Seychelles≈128

Table 2.10 — the urban population, 2024

RegionPopulation (millions, 2024) Urban share
World8,16058%
More developed countries1,25981%
Less developed countries6,90154%
Sub-Saharan Africa1,21743%
Northern Africa26153%
Latin America and the Caribbean66282%
Western Asia30673%
South-central Asia2,12837%
Southeast Asia69354%
East Asia1,64666%
Eastern Europe29071%

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
MFGDP MFGDP MFGDP
Africa
Egypt284313 26638 465149
Ethiopia12644 271713 617742
Madagascar828325 5217 131657
Mauritius1084 362629 546667
South Africa1173 351434 548063
Asia
Bangladesh426819 151329 431952
Indonesia414114 211548 384437
Malaysia181010 322348 516742
Pakistan367220 231327 411553
Philippines442415 181132 396553
South Korea783 331637 607460
Thailand434012 221944 354144
Vietnam566022 211440 232638
Latin America
Colombia2769 221636 517855
Costa Rica1857 281329 548264
Mexico1944 311837 507759
Nicaragua42819 201830 387351
Developed countries
United Kingdom211 32924 669076
United States211 30922 689077

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.

⚠️ Trap

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 1,000Countries in the band
45 +Niger
40–44Angola, Benin, Burkina Faso, Burundi, Central African Republic, Chad, Dem. Rep. of Congo, Somalia, Uganda
35–39Guinea-Bissau, Liberia, Mozambique, Nigeria, South Sudan, Tanzania, Zambia
30–34Afghanistan, 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
25–29Algeria, Egypt, Gabon, Haiti, Kiribati, Kyrgyzstan, Lesotho, Marshall Islands, Namibia, Pakistan, Papua New Guinea, Samoa, Solomon Islands, Turkmenistan, Tuvalu, Vanuatu
20–24Belize, 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
15–19Antigua 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
10–14Albania, 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
< 10Bosnia 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

RegionNet primary enrolment Pupil-teacher ratio
Low income81%37
Lower-middle income89%28
Upper-middle income95%
High income97%14
East Asia & Pacific96%
Europe & Central Asia96%
Latin America & Caribbean94%20
Middle East & North Africa92%22
South Asia33
Sub-Saharan Africa80%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 group19902023
Low income12838
Lower-middle income6212
Upper-middle income
High income4

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.

7

2.5 How Low-Income Countries Differ from the Developed Countries' Earlier Stages

slide 33 · Todaro 13e App. 2.2

The 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.

1 · Physical and human resource endowments
What each country starts with — minerals, fertile land, and the health and skills of its people.
2 · Per capita incomes relative to the rest of the world
Today's developing countries start far below the frontier; the now-developed countries were near it.
3 · Climate
Tropical disease burdens and agricultural conditions that temperate-zone pioneers did not face.
4 · Population size, distribution and growth
Today's poor countries carry far higher population growth rates than the pioneers ever did.
5 · Historic role of international migration
The now-developed countries exported surplus labour; today's are more likely to receive or lose it under different rules.
6 · International trade benefits
The terms on which a latecomer can trade, with an existing industrial world already in place.
7 · Scientific and technological R&D capabilities
Today's latecomers can import technology — but the capability to develop it is concentrated elsewhere.
8 · Efficacy of domestic institutions
Institutions were built before or after independence, under very different conditions.
💬 Think

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.

📖 Where to find this in the book

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.

8

2.6 Long-Run Causes of Comparative Development

Todaro 13e §2.6, pp. 115–122 · not in the slides

This 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:

Physical geography Including climate. Once genuinely exogenous — human activity can now alter it, but it did not choose itself.
shapes what kind of colony gets established, and what can be grown
Precolonial institutions Existing social organisation, and how easy it was to take over.
Precolonial labour abundance and comparative advantage Dense populations to coerce; crops like sugar with large scale economies.
Type of colonial regime Extraction or settlement — decided by settler mortality and by what the land was good for.
which determined how unequal the new society would be
Inequality Whether land, labour and political power concentrated in few hands.
Postcolonial institutional quality Property rights, contract enforcement, constraints on elites — inherited, not chosen.
which feeds through to the things development is actually made of
Human capital Where inequality is extreme, less is invested in educating the non-elite.
Public goods quality The same.
Effective civil society And the same.
Well-functioning markets Which need the institutions above to exist at all.
and finally,
Income and human development The outcome Chapter 2 has been measuring all along — here explained rather than described.

The four families of explanation

CauseThe claimWhere 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.
⚠️ Trap

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.

They are not. Past population density and past urbanisation — both positively correlated with past income — are negatively correlated with current income.

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:

Where climate suited plantation agriculture
Particularly sugar, with large scale economies. Slavery and other forms of 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).
Both roads led to the same place
High economic and political inequality, which then persisted — the early inequities were perpetuated by limiting non-elite access to land, education, finance, property protection, voting rights and labour markets.
Why North America diverged
Its emerging comparative advantage in grain lacked the scale economies of tropical agriculture and mineral extraction. Scarce labour with abundant land inhibited the concentration of power, and the need to attract settlers pushed institutions toward greater egalitarianism. That environment "facilitated broad-based innovation, entrepreneurship and investment" — which is how the United States and Canada came to surpass societies that had started out much richer.

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.

💬 Think

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.

9

Formula Sheet

print-friendly
Expenditure approach to GDP
Y = C + I + G + NX
NX = exports − imports, and may be negative.
GNI per capita (PPP)
GNI ÷ population, converted at the PPP factor
The conversion factor is the currency needed to buy, locally, what $1 buys in the US.
Old HDI (1990–2009)
HDI = ⅓·Ihealth + ⅓·Iedu + ⅓·Iincome
Arithmetic mean — assumes perfect substitutability. Bangladesh 2007 = 0.543.
New HDI (2010– )
HDI = ∛(Ihealth × Iedu × Iincome)
Geometric mean — allows only imperfect substitutability. China 2010 = 0.663.
Health index
(LE − 20) ÷ (83.2 − 20)
New-HDI goalposts. The old HDI used 25 and 85.
Education index (New HDI)
[√(Imean yrs × Iexp yrs)] ÷ 0.951
Itself a geometric mean, then rescaled.
Education index (old HDI)
⅔·Iliteracy + ⅓·Ienrolment
A weighted arithmetic mean — the two versions are not interchangeable.
Income index
[ln(GNI) − ln(163)] ÷ [ln(108,211) − ln(163)]
New-HDI goalposts. The logarithm encodes diminishing returns, per Figure 1.2.
Crude birth rate
(births ÷ mid-year population) × 1,000
"Crude" because it is per head of total population, not per woman of childbearing age.
World Bank income groups (2025)
LIC < 1,175 · LMC < 4,635 · UMC < 14,375 · High > 14,375
Thresholds are upper bounds of each group.
10

Key Concepts

26 terms · 13 from the textbook

The terms carrying a 中文 anchor are the ones the instructor glossed on the slide.

GNI 国民总收入
Total domestic and foreign value added claimed by a country's residents, without deducting depreciation of the domestic capital stock. Ownership, not location.
GDP 国内生产总值
Total value for final use of output produced within an economy, by residents and non-residents alike. Location, not ownership.
Value added 附加价值
The value a producer adds to the inputs it buys — the term the instructor glossed inside the GNI definition, and the reason the two aggregates are measured the way they are rather than as raw turnover.
Purchasing power parity (PPP) 购买力平价
A conversion factor calculated from a common set of international prices: the units of foreign currency required to buy locally the identical basket that $1 buys in the United States. Corrects the systematic understatement of poor-country incomes by market exchange rates.
Human Development Index (HDI)
A composite of three dimensions — health, education, income — scaled 0 to 1. Sen's capability approach made operational. Bands: low <0.5, medium <0.8, high <0.9, very high up to 1.0.
New HDI (2010 reform)
The same three dimensions combined by geometric rather than arithmetic mean, plus GNI replacing GDP per capita, attainment-based education components, observed rather than predefined maxima, and a reduced lower income goalpost.
Perfect vs imperfect substitutability
The conceptual difference between the two HDIs. An arithmetic mean lets a high score in one dimension fully offset a low score in another; a geometric mean does not, which is what "imperfect substitutability" means here.
Crude birth rate 粗出生率
The annual number of live births per 1,000 population. Called "crude" because the denominator is the whole population rather than the number of women of childbearing age.
Absolute poverty
Poverty measured against a fixed subsistence threshold — the MDG line was $1 a day, later revised. Contrasted with relative poverty, which is defined against the distribution around you.
Social fractionalisation
Significant ethnic, linguistic and other social divisions within a country. Characteristic 5 of the developing world, and a recurring explanation for weak public goods provision.
Resource endowments
A nation's supply of usable factors of production — mineral deposits, raw materials and labour. Characteristic 8's supporting term, under the heading of adverse geography.
External dependence
Characteristic 10, in two parts: the colonial legacy, and dependence in international relations. Both reappear in Chapter 3 as the core of the dependence school.
Demographic transition
The movement from high to low birth and death rates that accompanies development. Visible in Table 2.8: the highest crude birth rates are in Sub-Saharan Africa, the lowest in Europe and East Asia.
Human capital Todaro
Productive investments in people — skills, values and health — resulting from expenditure on education, on-the-job training programmes, and medical care. The term the deck uses without ever defining.
Value added Todaro
The portion of a product's final value that is added at each stage of production. The textbook's definition is terser than the slide's, and worth having: it is value added at each stage, which is why summing it across an economy cannot double-count intermediate goods.
Capital stock Todaro
The total amount of physical goods existing at a particular time that have been produced for use in the production of other goods and services. Note the definition is about what the goods are for, not what they are — a car is capital or consumption depending on its use.
Depreciation Todaro
The wearing out of equipment, buildings, infrastructure and other forms of capital, reflected in write-offs to the value of the capital stock. The d in the Solow equation Δk = sy − (n+d)k.
Diminishing marginal utility Todaro
The concept that the subjective value of additional consumption (or income) lessens as total consumption becomes higher. The assumption sitting behind the logarithmic income index in the HDI, and behind Figure 1.2 in Chapter 1.
Dependency burden Todaro
The proportion of the total population aged 0–15 and 65+, considered economically unproductive and therefore not counted in the labour force. The mechanism connecting high fertility to low income per head — a young population carries a heavy dependency burden.
Fractionalisation Todaro
Significant ethnic, linguistic, and other social divisions within a country. The slide's own gloss was 种族、语言 — the two dimensions the textbook names.
Resource endowment Todaro
A nation's supply of usable factors of production, including mineral deposits, raw materials, and labour. Part of characteristic 8, adverse geography.
Imperfect market Todaro
A market in which the theoretical assumptions of perfect competition are violated — by a small number of buyers or sellers, barriers to entry, or incomplete information. Development economics' first key feature (§1.2) stated precisely.
Incomplete information Todaro
The absence of the information producers and consumers need to make efficient decisions, resulting in underperforming markets. Note it is defined by its consequence, not merely as ignorance.
Brain drain Todaro
The emigration of highly trained or qualified people from a country — an outflow of exactly the human capital the previous entry describes as an investment. Relevant to the deck's characteristic 10, external dependence.
Terms of trade Todaro
The ratio of a country's average export price to its average import price. A deteriorating ratio means a country must export more to buy the same imports — the central mechanism of the dependence school's argument in Chapter 3.
Very high-income country Todaro
An informal category for a per capita income standard indicative of economies that master frontier technologies, skills and productivity — around $40,000 at 2018 prices. Not a World Bank band; a way of naming the frontier itself.
Reversal of fortune
Acemoglu, Johnson and Robinson's finding that among formerly colonised countries, past population density and past urbanisation — both proxies for past prosperity — are negatively correlated with income today. The areas richest before colonisation are often poorest now. It is a falsification test of the geography explanation: if geography were fundamental, the old prosperous areas would still be prosperous.
Extractive vs settler institutions
The two colonial regimes settler mortality is said to have selected. Where mortality was high, colonisers ruled at arm's length — "steal fast and get out" — and built institutions that extracted surplus from the local population. Where it was low and populations sparse, they settled and produced, which required constraints on executives and protection from expropriation. The institutions outlived the empire.
Social conflict theory of institutions
The claim that the degree of inequality itself shapes how institutions evolve: where inequality is extreme, elites block the extension of democratic rights and under-invest in human capital and public goods, because both would erode their position. Causality runs both ways, since education and institutions reinforce one another.
Instrumental variable
A variable used to identify the causal effect of c on d by affecting c without affecting d except through c. Settler mortality is the standard example: plausibly unrelated to present-day income except via the institutions it caused. You cannot randomly assign countries different levels of inequality, so this is how §2.6 makes causal claims.
11

Self-Check

21 questions · graded
0 / 0 correct

Section 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

Single choice.
Q1Country A hosts a large number of foreign-owned factories and has few citizens working abroad. Which is larger, its GDP or its GNI?
Correct.GDP counts output produced inside the borders regardless of ownership; GNI counts income claimed by residents. Foreign-owned factories inflate GDP above GNI, and with few citizens abroad there is no offsetting inflow.
Not quite.GDP counts what is produced inside the borders, including foreign-owned production; GNI counts what residents claim. With much foreign-owned capital and little income from abroad, GDP exceeds GNI.
Q2Why does converting incomes at PPP raise poor countries' measured income so much more than rich countries'?
Correct.Haircuts, meals, bus rides and housing cost far less where wages are low, and those are exactly the goods excluded from trade. The market exchange rate only reconciles traded goods, so it understates the purchasing power of a poor-country income.
Not quite.The reason is the price of non-traded goods. They are cheap in poor countries because they cannot be traded, and the market rate ignores this entirely.
Q3What single change to the HDI did the UNDP describe as "probably most consequential" in 2010?
Correct.The geometric mean. It is the change that alters the index's meaning — from perfect to imperfect substitutability between the three dimensions — rather than just its inputs.
Not quite.It is the switch to the geometric mean. The others are real changes but they alter the inputs, not the logic of the aggregation.
Q4What does the geometric mean in the New HDI assume about the three dimensions?
Correct.That is precisely what the reform was for. A product under a cube root cannot be rescued by strength elsewhere in the way a sum can.
Not quite.Perfect substitutability was the old assumption. The geometric mean deliberately weakens it to imperfect substitutability.
Q5Which of these is not one of the drawbacks of the HDI listed on the slide?
Correct.B is false — the slide explicitly says the HDI can be calculated for groups and regions within a country, and that it varies between rural and urban areas. That is presented as a strength, not a drawback.
Not quite.The HDI can be and is calculated for sub-national groups — the slide treats this as one of its advantages. The three real drawbacks are gross enrolment, equal weighting, and indifference to quality.
Q6Table 2.11 shows Madagascar with 82% of men in agriculture but agriculture only 25% of GDP, while South Korea has 7% of men in agriculture and 37% of GDP from industry. What does this contrast illustrate?
Correct.That gap is the empirical basis for the Lewis model in Chapter 3: labour can be moved out of agriculture and into industry while raising total output, because its marginal product in agriculture is near zero.
Not quite.It illustrates the sectoral productivity gap. Agriculture is not inherently unproductive — the point is that labour is concentrated where output per worker is low.

B · Calculation

Work these on paper first. The reveal shows the full step-by-step.
Q7Compute the old (arithmetic) HDI for a country with PPP GDP per capita $1,241, life expectancy 65.7 years, adult literacy 53.5% and gross enrolment 52.1%. Show every sub-index.

This is the slide's own Bangladesh 2007 example. Each sub-index is min-max normalised between its goalposts.

  1. Income index — goalposts ln(100) and ln(40,000) [ln(1241) − ln(100)] / [ln(40000) − ln(100)] = 2.5185 / 5.9915 = 0.4204
  2. Life expectancy index — goalposts 25 and 85 (65.7 − 25) / (85 − 25) = 40.7 / 60 = 0.6783
  3. Adult literacy index — goalposts 0 and 100 (53.5 − 0) / (100 − 0) = 0.5350
  4. Gross enrolment index — goalposts 0 and 100 (52.1 − 0) / (100 − 0) = 0.5210
  5. Education index — two-thirds literacy, one-third enrolment (2/3)(0.5350) + (1/3)(0.5210) = 0.3567 + 0.1737 = 0.5303
  6. HDI — the arithmetic mean of the three dimension indexes (0.4204 + 0.6783 + 0.5303) / 3 = 1.6290 / 3 = 0.5430
HDI = 0.543 — medium human development.
Q8Now the New HDI. Life expectancy 73.5 years, mean years of schooling 7.5, expected years 11.4, GNI per capita $7,263. Use the 2010 goalposts: life 20–83.2, schooling 0–13.2 and 0–20.6, education rescale divisor 0.951, income ln(163)–ln(108,211).

This is the slide's own China 2010 example. Note that the aggregation at the end is a geometric mean, not a sum.

  1. Life expectancy index (73.5 − 20) / (83.2 − 20) = 53.5 / 63.2 = 0.8465
  2. Mean years of schooling index (7.5 − 0) / (13.2 − 0) = 0.5682
  3. Expected years of schooling index (11.4 − 0) / (20.6 − 0) = 0.5534
  4. Education index — a geometric mean of the two, then rescaled √(0.5682 × 0.5534) = √0.31445 = 0.5608; 0.5608 / 0.951 = 0.5897
  5. Income index [ln(7263) − ln(163)] / [ln(108211) − ln(163)] = 3.7966 / 6.4982 = 0.5843
  6. New HDI — the cube root of the product 0.8465 × 0.5897 × 0.5843 = 0.29175; ∛0.29175 = 0.6631
New HDI = 0.663 — high human development.
Q9India's GNI per capita is $1,800 at market exchange rates and $6,980 at PPP. Compute the ratio, and explain in two sentences why the ratio is so much larger than the United States' 1.03×.
  1. 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.

Q10Using the World Bank's 2025 thresholds, classify these countries and say which group each falls in: Bangladesh (GNI/cap $1,470), China ($8,690), Brazil ($8,600), the United States ($58,270).

Thresholds: LIC < $1,175 · LMC < $4,635 · UMC < $14,375 · High > $14,375.

CountryGNI per capitaGroup
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

These two are on the last slides of the deck, with the answers in the speaker notes.
Q11Which of the following is not an indicator used to compute the Human Development Index?
Correct.The instructor's answer is C. Infant mortality rate is not one of the three dimensions — health enters through life expectancy, education through literacy and enrolment (or, in the New HDI, through years of schooling), and living standards through income. Infant mortality is a development indicator but not an HDI component, which is exactly the distinction the question is testing.
Not quite.The instructor's answer is C — infant mortality rate. It is a development indicator, but the HDI's health dimension uses life expectancy at birth instead.
Q12Conditions of today's developed countries at the start of their industrialisation differ from conditions in the developing world in that:
Correct.The instructor's answer is D. All three statements are false as written: today's developing countries have higher population growth rates, have more advanced technology available to them (the latecomer's advantage), and have more development assistance available, not less.
Not quite.The instructor's answer is D — none of the above. Each statement is the reverse of the truth: population growth is higher now in developing countries, and both advanced technology and development assistance are more available to them than they were to the pioneers.

D · Extended answers

Write these out in full.
Q13Explain why the UNDP replaced the arithmetic mean with a geometric mean in 2010, and what the change implies about how the three dimensions of human development relate to one another.

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.

Q14Why is a market exchange rate the wrong conversion factor for comparing incomes across countries, and what does PPP do instead?

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.

Q15List the ten characteristics of the developing world. For any three of them, give the evidence from the chapter's tables.
  1. Lower levels of living and productivity
  2. Lower levels of human capital — health, education, skills
  3. Higher levels of inequality and absolute poverty
  4. Higher population growth rates
  5. Greater social fractionalisation
  6. Larger rural populations, but rapid rural-to-urban migration
  7. Lower levels of industrialisation and manufactured exports
  8. Adverse geography
  9. Underdeveloped financial and other markets
  10. 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.
Q16Give the eight ways today's low-income countries differ from today's developed countries at the start of their industrialisation, and explain why the comparison matters.
  1. Physical and human resource endowments
  2. Per capita incomes and levels of GDP relative to the rest of the world
  3. Climate
  4. Population size, distribution and growth
  5. Historic role of international migration
  6. International trade benefits
  7. Basic scientific and technological research and development capabilities
  8. 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".

Q17The HDI's stated advantage is that "a country can do much better than might be expected at a low level of income". Which column of Table 2.4 shows this, and give two examples at each extreme.

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 predictsNegative — worse than income predicts
Turkey +43Egypt −80
Bangladesh +20Brazil −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.

Q18Distinguish GNI from GDP, and explain why the choice between them matters for a country with large remittance inflows. Why did the 2010 HDI reform switch from one to the other?

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

From §2.6, which the slides do not cover. This is the textbook's own framing rather than the instructor's, so treat it as background rather than as a likely exam question.
Q19What is the "reversal of fortune" that Acemoglu, Johnson and Robinson document?
Correct.The areas richest before colonisation — dense, urbanised, well organised — are often the poorest now. It is a falsification test of the geography explanation: if geography were fundamental, they would still be rich.
Not quite.It is the finding that pre-colonial prosperity predicts present-day poverty. Dense, organised populations were easier for colonisers to take over for tribute, so they got extractive institutions rather than settlement.
Q20Why is settler mortality offered as an instrumental variable rather than just another cause?
Correct.That is what makes it an instrument rather than a control: it has to affect the outcome only through the causal channel you are testing. Countries cannot be randomly assigned different levels of inequality, so this is how the causal claim gets made.
Not quite.An instrument must affect the outcome only through the variable of interest. Settler mortality is claimed to shape institutions without directly shaping income today — that exclusion is the whole argument, and it is contestable.
Q21Engerman and Sokoloff explain why North America and Latin America diverged. Set out the argument, and name the mechanism by which the resulting inequality persisted.

The argument runs from what the land could grow to who worked it.

  1. Where climate suited plantation agriculture Particularly sugar, which had large scale economies — slavery and other mass exploitation of labour were introduced
  2. 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)
  3. Different endowments, same outcome Both produced high economic and political inequality
  4. 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
  5. 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.

Chapter 3

Classic Theories of Economic Growth and Development

Todaro & Smith, Economic Development, Ch. 3 Source: Chapter3.pptx — 81 slides Three interactive models · instructor's exercises with answers

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.

1

Concept Map

how the chapter builds
The facts to be explained Growth is recent, it diverged, and it sometimes converges. Every theory in the chapter is an attempt to account for that pattern.
four families of explanation, in historical order
3.2 Linear stages 阶段增长模型 Rostow's stages. Development as a sequence every country must pass through. The Harrod-Domar model supplies the arithmetic: g = s/c.
3.3 Structural change 结构变革 Lewis's two-sector surplus-labour model. Development as labour moving from agriculture to industry.
both assume the process works if you get the quantities right — so the next two attack that
3.4 International dependence 国际依附革命理论 Neocolonial dependence, core–periphery, the false-paradigm model, the dualistic-development thesis. Development is blocked from outside.
3.5 Neoclassical counterrevolution 新古典主义革命 The reply: free markets, public choice, market-friendly approaches. Government failure is the problem, not the solution.
which brings the field to its dominant model
The Solow model 索洛 Diminishing returns, capital accumulation made endogenous, and a steady state. Explains catch-up — and predicts its own limits.
Its verdict Capital accumulation cannot sustain long-run growth. The engine must be technical progress, which the model leaves unexplained.
and finally, back to the data
3.6 Reconciling 协调 Governments fail, but so do markets. No universally accepted paradigm.
Where this goes next Later chapters take up what Solow leaves out — technology, institutions, and the microeconomics of poverty.
2

Growth over the Very Long Run

slides 3–13 · Todaro 13e §2.5, not Ch. 3

Sustained 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

Divergence 分化
A tendency for per capita income (or output) to grow faster in higher-income countries than in lower-income ones, so that the income gap widens across countries over time.
The Great Divergence
The recent era of increased difference in standards of living across countries.

The magnitudes are the thing to remember:

WhenHow much per capita GDP differed across countries
Before 1700By a factor of only two or three
TodayBy 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.

Convergence 趋同
Poorer countries will grow faster to "catch up" to the level of income in richer countries.
Technology transfer 技术转移
The mechanism that makes convergence plausible: developing countries can leapfrog over some of the earlier stages of technological development rather than inventing each one themselves.

Reasons to expect convergence

  1. Technology transfer Enables developing countries to leapfrog earlier stages — no need to rediscover the steam engine
  2. 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

PeriodWhat 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 groupIncome 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.

⚠️ Trap

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.

📖 Where to find this in the book

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 itWhere 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

3.1 Classic Theories: Four Approaches

slide 14 · Todaro 13e §3.1

The chapter organises the field into four families. Each is a claim about what causes underdevelopment, and therefore about what should be done.

ApproachCore claimThe 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.
4

3.2 Development as Growth: Rostow and Harrod-Domar

slides 15–24 · Todaro 13e §3.2 · model 1

Rostow'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:

S = sY = cΔY = ΔK = I (3.5)

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.

sY = cΔY (3.6)

Rearranging (3.6) gives the model's central result — the rate of growth of GDP:

ΔY Y = s c (3.7)
💬 Think

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.

Capital intensity
Steel production needs far more capital per unit of output than apparel does, so a country's sectoral mix moves c.
Efficiency
Idle machines still count in K but produce nothing, which raises the measured c. c is therefore partly a measure of how badly the capital stock is used.

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.

Model 1

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.

Worked The slide's two questions
100 tons of cement per year requires $10 m of capital and 100 workers
  1. How many tons when K = $20 m and L = 200? Both inputs doubled → constant returns to scale → 200 tons
  2. 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
The production function is Y = min{10K, L} — a Leontief, or fixed-coefficient, form. Output is set by whichever input is scarcer.

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.

Criticisms of the stages model

Not suitable for long-term prediction
Because c changes over time, so g = s/c is not stable.
No technological change
The K/Y ratio is assumed constant — technology is outside the model.
Fixed K/L ratio, no substitution
Hiring one more worker cannot increase production without buying one more machine. This is the assumption the Solow model removes.
K and L must grow at the same rate
Otherwise there will be unemployment of one resource or the other — the economy falls off the knife-edge.
Assumes the institutions exist
The social and institutional structures necessary for production and growth are assumed rather than explained.
Assumes the state can set s and I
A country is assumed able to determine its own savings and investment — which is precisely what the dependence school denies.

The instructor's note adds the practical objection: in reality, more saving and investment is not a necessary condition for economic growth.

⚠️ Trap

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.

📖 Beyond the slides

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.

5

3.3 Structural-Change Models: the Lewis Two-Sector Model

slides 25–40 · Todaro 13e §3.3 · model 2

The 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 model's setting
Applies to surplus-labour developing nations around the 1970s, and to China today. Two sectors: agriculture (with surplus labour) and industry.
The mechanism
Labour transfers to the modern sector. The modern sector grows, which drives economic growth. The urban wage rate is constant — a little higher than the subsistence wage in rural areas.

The agricultural sector

Fixed capital KA and unchanging technology tA, so production varies only with labour input LA. Four properties:

  1. Decreasing returns in terms of labour Adding workers to fixed land adds less and less output
  2. Zero return to labour after a certain point This is surplus labour: production does not increase with extra labour
  3. 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:

  1. Surplus labour is eventually absorbed Once the modern sector has hired everyone who was producing nothing
  2. Further withdrawal reduces agricultural output Because the next workers to leave were producing something
  3. The marginal product of agricultural labour rises above zero More land per person remaining
  4. Cheap labour is gone; the industrial wage must rise Which means an upward-sloping labour supply curve
Model 2

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

Surplus labour rural, full employment urban
The model assumes surplus labour in rural areas but full employment in urban areas. This is not true in reality — the instructor's own question is "China?"
Constant urban wage
The model assumes a constant wage in the urban sector until all surplus labour is absorbed. Not true either: unions and multinational corporations tend to raise urban salaries substantially.
Capitalists only duplicate production
The model assumes that when capitalists make money they reinvest in the same technology. They could instead invest in labour-saving technology — which produces antidevelopment growth.
💬 Think

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.

6

3.4 The International-Dependence Revolution

slides 41–42 · Todaro 13e §3.4

The 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:

Legacy of colonialism
The economic structures left behind when formal empire ended — export orientation, dependence on a few commodities, institutions built for extraction.
Unequal power
Relations between rich and poor countries are not bargains between equals, and the terms reflect that.
Core (the developed) – periphery (外围) (the developing)
The world economy as a system in which the core extracts surplus from the periphery, and the periphery's condition is a consequence of the core's prosperity rather than an independent fact.
The false-paradigm model 虚假范例模型
The pitfalls of using "expert" foreign advisors who misapply developed-country models. Advice built on the wrong model produces policies that fail, and the failure is then blamed on the country.

The dualistic-development thesis 二元发展论

The second strand, which is about structure rather than power. Four propositions:

  1. Superior and inferior elements can coexist A modern sector and a traditional one can exist side by side in the same economy
  2. The coexistence is chronic It does not resolve itself over time; it is a stable state, not a transition
  3. The degrees of superiority or inferiority tend to increase The gap widens rather than narrowing
  4. The superior element does little or nothing to pull up the inferior Which is the direct contradiction of the Lewis model's prediction
⚠️ Trap

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

CriticismWhat 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.

7

3.5 The Neoclassical Counterrevolution: Market Fundamentalism

slides 43–44 · Todaro 13e §3.5

The 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.

ApproachIts claimHow 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

  1. Denies the efficiency of intervention Planning does not improve on the market outcome
  2. Points up state-owned enterprise failures Public firms are inefficient — the case for privatisation
  3. 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.

⚠️ Trap

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.

8

The Solow Growth Model

slides 44–72 · Todaro 13e App. 3.2 · model 3 · the centrepiece

Developed 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

Capital stock is no longer exogenous 外生
Rather than being given at some fixed level outside the model, agents accumulate tools, machines, computers and buildings over time.
Capital stock is now "endogenised" 内生
Converted from an exogenous variable into an endogenous one. This one change is the whole difference from the production model.
Accumulation as a possible engine of growth
The model allows us to consider whether capital accumulation can sustain long-run growth — and, as it turns out, answers no.

Assumptions: the neoclassical production function

K/L and K/Y are not fixed
They vary, depending on the endowment of the economy. This is the assumption the Harrod-Domar model refused.
Decreasing returns to capital
Each extra machine adds less output than the one before.
Substitution between labour and capital
The isoquants are smooth and convex, not right-angled.

The Cobb-Douglas production function

Most popular function form for production. Assume A is determined exogenously; it has decreasing returns to capital.

Y = AK0.5L0.5

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.

Worked The slide's own example
A = 1, K = 10, L = 100
  1. Find Y Y = 1 × 100.5 × 1000.5 = √10 × 10 = 31.62
  2. Double K. What is Y now? Y = 1 × 200.5 × 1000.5 = √20 × 10 = 44.72
  3. Is Y doubled? No. 2 × 31.62 = 63.25 ≠ 44.72. Output rose by a factor of 1.414 = √2
Doubling capital alone raises output by only √2 ≈ 1.41, because the exponents sum to 1 (constant returns to scale in K and L together) but each exponent individually is less than 1 (diminishing returns to each alone).

Dividing through by L: the per-worker form

The model is solved in per-worker terms. Divide both sides by L:

yYL = AK0.5L0.5 L = Ak0.5    where k = K/L

And in general form: y = Af(k).

⚠️ Trap

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:

Δk = sy − (n + d)k

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.

When k is small
sy > (n+d)k. Saving per person is larger than the amount needed to compensate for new workers and depreciation, so k increases and the economy shifts right.
When k is large
sy < (n+d)k. k decreases and the economy shifts left.
Steady state
When k is at point S, sy = (n+d)k. The amount saved per person exactly equals the amount needed to compensate for new workers and depreciation, so k does not change and the economy stays at S.
Model 3

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:

k* = ( sA n + d )1/(1−α)    which for α = 0.5 is simply    k* = ( sA n + d )2

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?

Worked Which country grows faster?
  1. 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
  2. This is the famous catch-up theory Poorer countries grow faster
  3. And the prediction Poor and rich countries reach the same level of per capita GDP eventually
This is the principle of transition dynamics: a country further from its steady state grows faster.

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

StrengthsWeaknesses
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.

📖 Beyond the slides

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:

Y = A K

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.

⚠️ Trap

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.

9

The Solow Model: Empirical Evidence

slides 68–72 · Todaro 13e §3.5

The 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.

FigureWhat 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?

  1. 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
  2. Many other variables affect growth Such as initial human capital — which is why Barro's second regression controls for them
  3. A causality problem in the statistics Is it that saving causes growth of GDP, or growth of GDP causes saving?
⚠️ Trap

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.

10

3.6 Reconciling 协调 the Differences

slides 67, 73 · Todaro 13e §3.6

The chapter closes by refusing to pick a winner. The conclusions the slides draw:

Governments do fail, but so do markets
A balance is needed. This is the one sentence that summarises the whole chapter's argument between the four approaches.
Institutional and political realities matter
Any theory must attend to them in the developing world.
No universally accepted paradigm
Development economics has none, and the chapter does not pretend otherwise.
Insights are continually evolving
Each theory has some strengths and some weaknesses.

Relevance of growth theories to today's developing countries

The slide is candid about the limits of everything in the chapter:

They are elegant models that explain certain aspects of growth
Not nothing — the mechanism in each is real.
The biggest problem of all: the production process is a black box
Every model here takes technology and institutions as given rather than explaining them.
Practical questions the models do not answer
How to make people save and firms invest · how to make investment more efficient · whether agricultural workers automatically move to the cities and easily find a job — and if not, how to make the structural change happen.
Each country has its unique problem
Which is the strongest argument against any linear-stages view.
📖 Beyond the slides

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.

ApproachSouth KoreaArgentina
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.

11

The Instructor's Exercises

slides 76–80 · with his published answers

Two 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.

Exercise 1 Harrod-Domar
A developing country's capital-output ratio c = 5, savings rate s = 12%
  1. What will be the initial GDP growth rate? g = s / c = 12% / 5 = 2.4%
  2. Technological advance causes c to fall to 4. How does this affect the growth rate? g = 12% / 4 = 3%
  3. Starting again from the initial situation, s rises to 15%. How does this affect the growth rate? g = 15% / 5 = 3%
  4. 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
Running it backwards is the way the model was actually used: to hit a 7% growth target with c = 3, the required saving rate is s = g × c = 7% × 3 = 21% — and the slide's own question is whether that is feasible in reality.
💬 Think

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.

Exercise 2 Lewis two-sector model
Refer to Figure 3.1 in Todaro & Smith. Draw a single graph with the real wage in the modern sector (MPLM) on the vertical axis and the quantity of modern-sector labour (QLM) on the horizontal.
  1. 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.
  2. 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
  3. 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
  4. 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
(a) Initial position
Total output is represented by area 0D1FL1. Returns to labour are represented by 0WM1FL1, and returns to capital by WM1D1F.
(b) Demand shifts right, still on the elastic portion
Total output grows to area 0D2GL2. Returns to labour rise to 0WM1GL2, but note that the wage for each worker does not rise. Returns to capital increase to area WM1D2G.
(c) Demand shifts right again, now past the turning point
Total output grows to area 0D3HL3. Returns to labour rise to the area 0WM2HL3. Notice that not only does total employment rise, the wage per worker also rises. 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.
⚠️ Trap

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.

12

Formula Sheet

print-friendly
Harrod-Domar: saving-investment identity
S = sY = cΔY = ΔK = I
Equations (3.5) in the slides. Saving finances investment, which adds to the capital stock.
Harrod-Domar growth rate
ΔY / Y = s / c
Equation (3.7). Directly related to the saving ratio, inversely related to the capital-output ratio.
Harrod-Domar, run backwards
s = g × c
The required saving rate for a target growth rate — the form the model was used in for the Marshall Plan.
Fixed-coefficient production function
Y = min{10K, L}
Leontief form. Right-angled isoquants; K/L fixed; no substitution.
Cobb-Douglas production function
Y = A K0.5 L0.5
The slides use α = 0.5 specifically. CRTS in K and L together.
Per-worker production function
y = Y/L = A k0.5  where k = K/L
General form y = Af(k). DRTS in k, because k is machines per worker.
Solow capital accumulation
Δk = sy − (n + d)k
The second equation of the Solow model. s = saving rate, n = population growth, d = depreciation.
Steady state condition
sy = (n + d)k
Point S. k stops changing, but Y and K still grow at rate n.
Steady-state capital, closed form
k* = (sA / (n+d))1/(1−α)
For α = 0.5, this collapses to k* = (sA / (n+d))².
Steady-state output
y* = A (k*)α
Since the slides set α = 0.5, y* = A √k*.
Lewis: agricultural wage
WA = TPA / LA
Wage equals the average product, because there is no labour market — all workers share output equally.
Lewis: modern-sector areas
Output 0D1FL1 = Wages 0WM1FL1 + Profit WM1D1F
Total output is the area under the demand curve; wages are the rectangle; profit is the remainder.
Growth rate spread, 1960–2007
−23% to +16% per year across countries
Most countries about 2%. Per capita GDP in 2007 varied by a factor of about 64.
Divergence, before and after
Before 1700: factor of 2–3 · Today: factor of 50
The Great Divergence. Richest countries rose from ~$500 to ~$45,000 per person.
13

Key Concepts

53 terms · 25 from the textbook

This 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.

Divergence 分化
A tendency for per capita income to grow faster in higher-income countries than in lower-income ones, so the income gap widens over time.
Convergence 趋同
The opposite: poorer countries grow faster and catch up to richer ones. Distinguished from absolute income convergence, which the 1990–2017 data reject — China and India converged in growth rates while the absolute income gap widened.
Technology transfer 技术转移
The ability of developing countries to "leapfrog" earlier stages of technological development. A reason to expect convergence, provided conditions are similar.
Linear stages of growth 阶段增长模型
The view that development is a series of successive stages through which all countries must pass. Rostow's stages of growth are its classic statement.
Structural change 结构变革
The transformation of an agricultural economy into a more industrialised one, studied with neoclassical price theory and econometrics. Lewis's two-sector model and Chenery's patterns of development are its landmarks.
Harrod-Domar model
Growth as g = s/c. Its appeal is simplicity; its origin is the Marshall Plan. Assumes a fixed-coefficient production function, so K and L must grow together or the economy falls off the knife-edge.
Capital-output ratio (c)
The amount of capital needed for one unit of increase in GDP. Determined by capital intensity and by efficiency — idle machines raise measured c.
Knife-edge
The Harrod-Domar instability: because K and L must be used in a fixed proportion, any divergence in their growth rates leaves one of them unemployed with no mechanism to correct it.
Surplus labour
Labour whose marginal product in agriculture is zero — output does not increase if these workers leave. The condition that makes the Lewis model's horizontal labour supply possible.
Self-sustaining growth
In Lewis, the phase in which modern-sector expansion continuously absorbs surplus labour. It ends at the turning point, when the supply of labour stops being perfectly elastic.
Antidevelopment growth
Growth achieved by labour-saving technology that leaves wages and employment unchanged, distributing all the gain to capital owners. The instructor bolded this term.
Neocolonial dependence model 新殖民主义
The dependence school's core theory: an outgrowth of Marxist thinking in which the legacy of colonialism leaves the periphery structurally subordinate to the core.
Core and periphery 外围
The developed core and the developing periphery, in a relationship of unequal power in which the periphery's condition is a consequence of the core's prosperity.
False-paradigm model 虚假范例模型
The pitfalls of using "expert" foreign advisors who misapply developed-country models to developing-country conditions.
Dualistic-development thesis 二元发展论
Superior and inferior elements coexist; the coexistence is chronic; the degrees of superiority and inferiority tend to increase; and the superior element does little to pull up the inferior. A direct empirical denial of Lewis's convergence prediction.
Neoclassical counterrevolution 新古典主义革命
Market fundamentalism: the free market, public choice and market-friendly approaches that challenge the statist model. Denies the efficiency of intervention, points up state-owned enterprise failures, stresses government failures.
Statist model 计划经济
The assumption that the state is the agent of development — the target of the counterrevolution.
Free market approach 自由市场分析
Markets alone are efficient. The strongest of the three counterrevolution positions.
Public choice approach 公共选择理论
Government does nothing right — a claim about incentives rather than about markets. Officials pursue their own interests.
Market-friendly approach 亲善市场理论
The weakest counterrevolution position: it admits market failure, and so leaves room for selective intervention. Do not merge it with the free-market approach.
Solow model 索洛
Capital accumulation made endogenous, with diminishing returns. Predicts a steady state and conditional convergence — and concludes that capital accumulation cannot sustain long-run growth.
Exogenous 外生
Determined outside the model. In Solow, A — technology — remains exogenous, which is the model's central weakness.
Endogenous 内生
Determined inside the model. Solow's one change to the production model is to make the capital stock endogenous.
Steady state
The point S where sy = (n+d)k. k and y constant; Y and K still growing at rate n.
Transition dynamics
The principle that a country further below its steady state grows faster — the Solow model's explanation of growth-rate differences, and the basis of the catch-up argument.
Conditional vs unconditional convergence
Unconditional: poor countries grow faster, period — rejected by Barro Figure 1. Conditional: a country grows faster the further below its own steady state it is — supported by Figure 2 once other variables are controlled for.
TFP (total factor productivity)
The residual productivity term. Solow's second weakness: it is "still unexplained", and it matters more than capital for explaining income differences.
Reconciling 协调
The chapter's closing position: governments fail, but so do markets; a balance is needed; development economics has no universally accepted paradigm.
Necessary condition Todaro
A condition that must be present, though it need not be sufficient in itself, for an event to occur. Capital formation may be a necessary condition for sustained growth — there must be tools before output can grow — but social, institutional and attitudinal changes may also be needed for growth to continue.
Sufficient condition Todaro
A condition that, when present, causes or guarantees that an event will occur. The pair with the previous entry is the cleanest way to state the Harrod-Domar criticisms: high saving is necessary for growth but not sufficient for it.
Capital–labour ratio Todaro
The number of units of capital per unit of labour — the k of the Solow model. The Harrod-Domar model fixes it; Solow's single change is to let it vary.
Structural transformation Todaro
The process of transforming an economy so that manufacturing's contribution to national income eventually surpasses agriculture's. More generally, a major alteration in the industrial composition of any economy.
Patterns-of-development analysis Todaro
An attempt to identify the characteristic features of the internal process of structural transformation that a "typical" developing economy undergoes as it generates and sustains modern growth. Chenery's empirical counterpart to Lewis's theory.
Dependence Todaro
The reliance of developing countries on developed-country economic policies to stimulate their own growth — and, in a second sense, the situation in which developing countries are dependent on the developed world in a way that can be either beneficial or a constraint on development.
Dominance Todaro
In international affairs, a situation in which developed countries have much greater power than less-developed ones in decisions affecting important international economic issues — the prices of agricultural commodities, for instance. The power asymmetry behind the dependence argument.
Centre Todaro
In dependence theory, the economically developed world. The counterpart of periphery — note that the deck's Chinese gloss was on 外围, the periphery, which is the half of the pair being described.
Comprador groups Todaro
In dependence theory, local elites who act as fronts for foreign investors. The internal half of the dependence argument — the reason the school treats the obstacle as both external and internal.
Dualism Todaro
The coexistence of two situations or phenomena — one desirable and the other not — that are mutually exclusive to different groups of society: extreme poverty alongside affluence, modern and traditional economic sectors, growth and stagnation.
Autarky Todaro
A closed economy that attempts to be completely self-reliant. The dependence school's prescription, recorded in the instructor's note as "autarky is best".
Closed economy Todaro
An economy with no foreign trade transactions or other economic contact with the rest of the world. The Solow model's setting — and the reason its convergence prediction is stated for closed economies.
Open economy Todaro
An economy that practises foreign trade and has extensive financial and non-financial contact with the rest of the world.
Market failure Todaro
A market's inability to deliver its theoretical benefits, due to imperfections such as monopoly power, lack of factor mobility, significant externalities, or lack of knowledge. The term that separates the market-friendly approach from the free-market one.
Capital accumulation Todaro
Increasing a country's stock of real capital — net investment in fixed assets. To increase the production of capital goods necessitates a reduction in the production of consumer goods, which is the trade-off that makes it a cost now and a benefit later.
Economic infrastructure Todaro
The physical and financial capital embodied in roads, railways, waterways, airways and other transport and communications, plus water supplies, financial institutions, electricity, and public services such as health and education. What makes private investment productive.
Production possibility curve Todaro
A curve showing the alternative combinations of two commodities that can be produced when all available factors are efficiently employed. Given resources and technology, it sets the boundary between the attainable and the unobtainable — Appendix 3.1's device for showing what growth is.
Technological progress Todaro
The increased application of new scientific knowledge in the form of inventions and innovations, with regard to both physical and human capital. Classified two ways by the textbook: by direction (neutral, labour-saving, capital-saving) and by effect on a factor (labour-augmenting, capital-augmenting).
Neutral technological progress Todaro
Higher output levels achieved with the same quantity or combination of all factor inputs — conceptually equivalent to doubling every input, and therefore also representable as an outward shift of the production possibility curve.
Labour-saving technological progress Todaro
Achieving higher output using an unchanged quantity of labour inputs. Computers, automated looms, tractors and mechanical ploughs are all examples. Progress since the late nineteenth century has been overwhelmingly of this kind — which is precisely why it is unsuited to labour-abundant developing countries.
Capital-saving technological progress Todaro
The same, using an unchanged quantity of capital inputs. A much rarer phenomenon, because most of the world's research is conducted in developed countries, where the mandate is to save labour. In capital-scarce developing countries it is what is needed most.
Solow residual Todaro
The proportion of long-term economic growth not explained by growth in labour or capital, and therefore assigned primarily to exogenous technological change. Responsible for roughly 50% of historical growth in the industrialised nations — the quantity endogenous growth theory sets out to explain.
Endogenous growth theory Todaro
Economic growth generated by factors within the production process — increasing returns, induced technological change — studied as part of the growth model rather than assumed from outside it. Also called the new growth theory. Its central move is to drop diminishing returns to capital, and its central prediction is that there is no convergence.
Complementary investments Todaro
Investments that complement and facilitate other productive factors. The idea behind the "big push" in Chapter 4: one investment is unprofitable unless others are made at the same time.
Public good Todaro
An entity that provides benefits to all individuals simultaneously, and whose enjoyment by one person in no way diminishes that of anyone else. The standard justification for the state producing something the market will not.
14

Self-Check

22 questions · graded
0 / 0 correct

The calculation sections reproduce the instructor's two exercises with his own answers. Work them before revealing.

A · Growth facts

The empirical record in section 3.1.
Q1How much did per capita GDP differ across countries before 1700, and how much does it differ today?
Correct.A factor of two or three before 1700; a factor of 50 for several countries today. That widening is the Great Divergence.
Not quite.The slide's numbers are 2–3 before 1700 and 50 today. The factor of 90 is the rise in living standards within the richest countries since 1700, which is a different statistic.
Q2Over 1990–2017, China grew 412% and India 389%, while high-income OECD countries grew 68%. What happened to the absolute income gap between them?
Correct.Growth convergence is not absolute income convergence. Faster growth in percentage terms does not close an absolute gap when the starting levels are very far apart.
Not quite.The gap widened. 412% of a small number is still a small number — the slide's whole point is that relative convergence and absolute convergence are different things.
Q3Which of these is a reason to expect convergence, according to the slide?
Correct.Both reasons are on the slide: technology transfer lets countries leapfrog earlier stages, and diminishing returns mean an extra machine adds more output where machines are scarce.
Not quite.The two reasons are technology transfer and diminishing returns to factor accumulation — not increasing returns.

B · The four approaches

Which theory claims what, and to which earlier theory it is a reply.
Q4What does the linear-stages approach claim about development?
Correct.Rostow's classic statement. The universality of the sequence — that all countries must pass through the same steps — is both its defining claim and the thing later critiques attack.
Not quite.The stages view holds that development is a succession of steps all countries must pass through. Options A, C and D are the dependence, neoclassical and structural-change positions respectively.
Q5Which of the three neoclassical counterrevolution approaches concedes that markets can fail?
Correct.Only the market-friendly approach admits market failure. The free market approach says markets alone are efficient; the public choice approach attacks government motive, not market outcomes.
Not quite.It is the market-friendly approach — the weakest of the three, and the only one that leaves room for intervention.
Q6Which proposition of the dualistic-development thesis directly contradicts the Lewis model?
Correct.Lewis predicts the modern sector absorbs the traditional one through labour migration. The dualism thesis denies precisely that — the modern sector coexists with, and may deepen, the traditional one.
Not quite.It is the fourth proposition — the superior element does not pull up the inferior. That is the direct denial of Lewis's absorption story.
Q7What does the dependence school prescribe, according to the instructor's note?
Correct.The instructor's note records the position in one word: autarky is best. If the relationship with the core is what blocks development, the remedy is to leave it, not to negotiate better terms within it.
Not quite.The note says "autarky is best". Options A and C are the neoclassical counterrevolution's prescriptions; B is Harrod-Domar's.

C · The models · calculation

These are the instructor's own exercises. Work them before revealing.
Q8Harrod-Domar. c = 5, s = 12%. (a) Find g. (b) Technology lowers c to 4 — find g. (c) Instead, s rises to 15% — find g. (d) What does the model tell us about the sources of growth?

This is the instructor's Exercise 1, with his published answers.

  1. (a) Initial growth rate g = s / c = 12% / 5 = 2.4%
  2. (b) c falls to 4 g = 12% / 4 = 3%
  3. (c) s rises to 15% g = 15% / 5 = 3%
  4. (d) The sources of growth The growth rate is directly related to the saving ratio, and inversely related to the capital-output ratio
Notice (b) and (c) both reach 3% by different routes — a 20% fall in c, or a 25% rise in s. Formally, a proportional change in s and an equal proportional change in c have opposite and equal effects on g.
Q9What saving rate does a 7% growth target require if c = 3? Is that feasible in reality, and why is the question left open on the slide?
  1. 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.

Q10The fixed-coefficient production function. To make 100 tons of cement a year a country needs $10 m of capital and 100 workers. (a) K = $20 m, L = 200 — how much output? (b) K = $15 m, L = 200 — how much output? (c) Write the production function.
  1. (a) Both inputs doubled Constant returns to scale → output doubles → 200 tons
  2. (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
  3. (c) The production function Y = min{10K, L}
This is a Leontief, or fixed-coefficient, form. Output is set by whichever input is scarcer — which is why the isoquants are right-angled and why the model has no way to substitute one input for the other.
Q11Cobb-Douglas. A = 1, K = 10, L = 100. (a) Find Y. (b) K doubles — find Y. (c) Is Y doubled? Explain why or why not.
  1. (a) Initial output Y = 1 × 100.5 × 1000.5 = 3.1623 × 10 = 31.62
  2. (b) K doubled to 20 Y = 1 × 200.5 × 1000.5 = 4.4721 × 10 = 44.72
  3. (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.

Q12Solow. s = 20%, n = 1.5%, d = 5%, A = 1, α = 0.5. Find k* and y*. Then say what happens to k* if s rises to 30%.
  1. Steady-state condition sy = (n+d)k, and y = A k0.5, so 0.20 k0.5 = 0.065 k
  2. Solve for k* k0.5 = 0.20 / 0.065 = 3.0769, so k* = 3.0769² = 9.47
  3. And y* y* = A √k* = √9.47 = 3.08
  4. Closed form check k* = (sA/(n+d))² = (0.20/0.065)² = 3.0769² = 9.47 ✓
  5. Now s rises to 30% k* = (0.30/0.065)² = 4.6154² = 21.30
k* more than doubles — from 9.47 to 21.30 — because with α = 0.5 the exponent 1/(1−α) is exactly 2, so k* goes as the square of the saving rate. y* rises only by √2, to 4.62, because of diminishing returns.

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.

Q13At the steady state, k and y are constant. Are K and Y also constant? If y = 10 and L is growing at 2%, how fast is Y growing?

No. K and Y are not constant at the steady state. The steady state fixes the per-worker quantities, not the totals.

  1. Recall the definitions Y = yL and K = kL
  2. At the steady state, y and k are constant So anything that happens to Y and K comes entirely from L
  3. L grows at rate n Therefore Y and K grow at rate n as well
  4. The instructor's example y = 10, L growing at 2% → Y is growing at 2%
Output per worker is constant; total output grows at the rate of population growth. This is why the Solow model is often described as explaining why countries are rich rather than why they grow — in the steady state, the growth rate of the standard of living is zero.
Q14Two countries X and Z have the same A, f, s, n and d, but X has larger k and y than Z. Which grows faster, and why? What is this principle called?

Country Z grows faster.

  1. 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
  2. The name of the principle Transition dynamics — a country further below its steady state grows faster
  3. 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
This is the Solow model's strongest empirical claim and its most conspicuous failure. The mechanism is real — as the diagram shows, the gap sy − (n+d)k is larger at low k — but the prediction that all countries converge on the same level has been rejected by the data, which is why the model is tested in its conditional form instead.
Q15A country's saving rate rises permanently. In the Solow model, what happens to its long-run growth rate of output per worker?
Correct.The level of y* rises, but the long-run growth rate of y returns to zero — capital accumulation cannot sustain growth because of diminishing returns. Only the transition period shows faster growth.
Not quite.The level rises, but not the long-run growth rate. Once the new steady state is reached, output per worker stops growing — this is the model's central and most disappointing result.

D · Lewis · the turning point

The instructor's Exercise 2, in order.
Q16In the Lewis model's initial position, which areas represent total modern-sector output, the wage bill, and the return to capital?

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.

Q17Reinvestment raises labour demand, but the new demand curve still intersects the horizontal portion of the supply curve. What happens to total output, wages, and profit?

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.
This is the labour-surplus phase, and the counter-intuitive step is the middle one: total wages rise because more people are employed, not because anyone is paid more. Every worker earns exactly WM1, before and after.
Q18Further reinvestment now pushes the demand curve past the turning point, so it intersects the steep portion of the supply curve. What happens now?

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.
This is the turning point, and it is what the whole model has been building towards: the first moment at which growth in the modern sector raises the wage of an ordinary worker. Before it, the surplus labour in agriculture held the wage down; after it, expansion has to bid workers away from farming, and the wage rises.
Q19In the Lewis agricultural sector, why is the wage determined by the average product rather than the marginal product?
Correct.The slide says exactly this: the wage is determined by the average product, "where there is no labour market (subsistence economy)". Output is shared equally, so WA = TPA / LA.
Not quite.It is because there is no labour market — all workers share the product equally, so the wage is the average product. The marginal product is zero only in the surplus-labour region, not throughout.
Q20Which criticism of the Lewis model does the slide illustrate with the notion of "antidevelopment growth"?
Correct.The model assumes capitalists reinvest in the same technology. If instead they choose labour-saving technology, total output rises substantially while total wages and employment stay exactly where they were — all the gain goes to capital owners.
Not quite.It is the labour-saving-technology criticism. B and C are real criticisms too, but they are not the one this figure illustrates.

E · Extended answers

Write these out in full.
Q21Explain why capital accumulation cannot sustain long-run economic growth in the Solow model, and state the two weaknesses of the model that follow from this.

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.

  1. 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.
  2. 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.

Q22Barro (1991) found no sign of unconditional convergence but did find conditional convergence. Explain the difference, why the first result is not necessarily fatal to the Solow model, and name the statistical problem Barro had to deal with.

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.

Roadmap

Where the Course Goes Next

Chapters 4 onward — placeholder Extension reading Revision checklist

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.

1

Delivered So Far

138 slides across three chapters

Each 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.

2

Next Chapters

placeholders — awaiting slides

These 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.

Chapter 4

Contemporary Models of Development and Underdevelopment

The models that came after Solow: endogenous growth theory, the Romer and Lucas frameworks, coordination failures and multiple equilibria, and the new institutional economics. These are the answers to the gap the Solow model leaves — why technology and institutions differ across countries in the first place.
Awaiting slides
Chapter 5

Poverty, Inequality, and Development

Measuring inequality and poverty, the Kuznets curve, the functional distribution of income, and who the poor actually are. Where Chapter 2's absolute-poverty measure gets taken apart.
Awaiting slides
Chapter 6

Population Growth and Economic Development

The demographic transition in full, the causes and consequences of rapid population growth, and the Malthusian and household-choice framings. Chapter 2's crude-birth-rate table is the starting point.
Awaiting slides
Chapter 7

Urbanisation and Rural-Urban Migration

The Todaro migration model, the urban informal sector, and why migration continues despite high urban unemployment. This is where the Lewis model's assumption of full urban employment is relaxed properly.
Awaiting slides
3

Extension Reading

shown at the end of the Chapter 3 deck

The 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.

陈斌开、杜浩锋、江深哲、夏俊杰 ·《消费和投资良性互动与长期经济增长》
经济研究, 2026年第6期. The classical growth theories hold that expanding consumption crowds out investment and so harms long-run growth. This paper argues the classical theory understates the demand-side pull that consumption exerts on production. Its finding: industries with a higher final-consumption share have a higher share of small firms, more active firm entry, and faster TFP growth. The authors build an endogenous growth model with consumer goods, investment goods and heterogeneous firm entry, and derive an inverted-U relationship between the consumption rate and the long-run growth rate — at low consumption rates, expanding consumption draws in firms and raises growth; at high rates it crowds out investment and drags growth down. On Chinese data they conclude there is currently room to raise long-run growth potential by moderately expanding consumption.
Brandt, Kambourov & Storesletten · "Barriers to Entry and Regional Economic Growth in China"
Review of Economic Studies (2026) 93, 286–326. Labour productivity in manufacturing differs starkly across Chinese regions. The authors document that productivity, wages and start-up rates of non-state firms nonetheless experienced rapid unconditional regional convergence after 1995. They construct a Hopenhayn model with location-specific capital wedges, output wedges and entry barriers, estimate those wedges from Chinese Industry Census data, and find that entry barriers explain most of the differences in performance and growth across prefectures — and that changes in those barriers are causally related to changes in the size of the state sector, with a smaller state sector leading to lower entry barriers.
💬 Think

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.

📖 Beyond the slides

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.

4

Reading Alongside the Textbook

Todaro & Smith, 13th edition

The 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 itWhere 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)
📖 Beyond the slides

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.

⚠️ Trap

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.

5

Revision Checklist

what to be able to do, chapter by chapter

Each 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

All three are in Chapter 3, and all three are interactive on this site.
DiagramWhat 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

Each of these appears in the self-check blocks with a full worked answer.
CalculationWhere
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

The instructor's own Chinese glosses. If you can go from the Chinese to the English term and say why it matters, the concept question is answered.
Chapter 1
可行能力 (capability) · 尊严 (self-esteem / dignity) · 奴役 (servitude)
Chapter 2
附加价值 (value added) · 购买力平价 (purchasing power parity) · 粗出生率 (crude birth rate)
Chapter 3 — the theories
阶段增长模型 (linear stages) · 结构变革 (structural change) · 国际依附革命理论 (international-dependence revolution) · 新古典主义革命 (neoclassical counterrevolution) · 协调 (reconciling)
Chapter 3 — the concepts
分化 (divergence) · 趋同 (convergence) · 技术转移 (technology transfer) · 新殖民主义 (neocolonial) · 外围 (periphery) · 虚假范例模型 (false-paradigm model) · 二元发展论 (dualistic-development thesis) · 计划经济 (statist) · 自由市场分析 (free market approach) · 公共选择理论 (public choice) · 亲善市场理论 (market-friendly) · 索洛 (Solow) · 外生 (exogenous) · 内生 (endogenous)

D · Distinctions that are easy to blur

Every one of these is a trap flagged somewhere in the three chapters.
Do not confusewith
FunctioningsCapabilities — achievement versus freedom to achieve
GNIGDP — who owns it versus where it is produced
Old HDI (arithmetic)New HDI (geometric) — the formulas are not interchangeable
Growth convergenceAbsolute income convergence — relative gaps can narrow while absolute gaps widen
Unconditional convergenceConditional convergence — Barro's two figures give opposite answers
Free market approachMarket-friendly approach — the third one admits market failure
ExogenousEndogenous — Solow's single change is making capital endogenous
CRTS in K and LDRTS 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
6

Your Progress

stored in this browser only

Progress is saved under the key de-progress-v1 in this browser's local storage. Clearing site data, switching browsers, or opening the file on a different machine starts from zero. The reset button above clears everything at once; each chapter's self-check block also has its own reset.