optimum population

Classification of Economies (Syllabus 11.4)

Economists group economies according to their stage of development. The Cambridge A‑Level syllabus recognises three main categories:

• Low‑income (developing) economies
• Middle‑income (emerging) economies
• High‑income (developed) economies

Key Development Indicators

Indicator	Low‑income	Middle‑income	High‑income
GDP per capita (US$, World Bank 2023)	< 1,085	1,085 – 12,695	> 12,695
Human Development Index (UNDP 2022)	< 0.550 (low)	0.550 – 0.699 (medium) / 0.700 – 0.799 (high‑middle)	≥ 0.800 (very high)
Literacy rate (age 15+)	50 % – 70 %	70 % – 90 %	90 % – 99 %
Life expectancy at birth	55 – 65 years	65 – 75 years	75 – 85 years
Urbanisation (% of population)	20 % – 40 %	40 % – 70 %	70 % – 90 %
Share of services in GDP	10 % – 30 %	30 % – 60 %	70 % – 90 %

Typical Economic Characteristics

1. Low‑income economies
   • Predominantly agricultural; low labour productivity.
   • High unemployment/under‑employment; large informal sector.
   • Limited access to capital, technology and skilled labour.
   • Export structure centred on primary commodities (e.g., raw minerals, agricultural products).
2. Middle‑income economies
   • Rapid industrialisation; shift from primary to secondary production.
   • Growing foreign direct investment and export of manufactured goods.
   • Improving infrastructure, education and health services.
   • Transition toward a knowledge‑based economy.
3. High‑income economies
   • Service‑dominant (finance, ICT, professional services).
   • High R&D intensity and innovation capacity.
   • Well‑developed financial markets and strong institutional framework.
   • Export mix: high‑value manufactured goods and services.

Population – Growth, Structure and Measurement (Syllabus 11.4.1)

Key Demographic Variables

Variable	Definition	Typical Formula
Crude Birth Rate (CBR)	Live births per 1,000 population in a year	CBR = (Births ÷ Total population) × 1,000
Total Fertility Rate (TFR)	Average number of children a woman would have if she experienced current age‑specific fertility rates throughout her reproductive life	TFR = Σ (age‑specific birth rates × 5)
Crude Death Rate (CDR)	Deaths per 1,000 population in a year	CDR = (Deaths ÷ Total population) × 1,000
Infant Mortality Rate (IMR)	Deaths of infants under one year per 1,000 live births	IMR = (Infant deaths ÷ Live births) × 1,000
Net Migration Rate (NMR)	Immigrants minus emigrants per 1,000 population	NMR = (Immigrants – Emigrants) ÷ Total population × 1,000
Population Growth Rate (PGR)	Annual percentage change in population size	PGR (%) = [(CBR – CDR) + NMR] ÷ 10

Causal Factors Behind Changes in the Variables

• Birth‑rate / TFR
  • Access to family‑planning services, contraception, and reproductive‑health education.
  • Female education and labour‑force participation.
  • Economic incentives (e.g., child‑bearing subsidies) or disincentives (e.g., tax penalties).
  • Cultural, religious and social norms.
  • Government policies: pronatalist or antinatalist programmes, cash‑transfer schemes, legal age of marriage.
• Death‑rate
  • Quality and coverage of healthcare, vaccination programmes, nutrition.
  • Living standards, sanitation and clean‑water supply.
  • Prevalence of communicable and non‑communicable diseases.
  • Public‑health policies (e.g., anti‑smoking legislation, epidemic response).
• Infant mortality
  • Maternal health, prenatal care, skilled birth attendance.
  • Post‑natal care, immunisation, and access to clean water.
• Net migration
  • Economic opportunities, wage differentials, political stability.
  • Immigration policies, visa regimes, refugee‑status legislation.
  • Push factors such as conflict, environmental degradation or natural disasters.

Dependency Ratios

Two ratios are routinely examined in the syllabus:

• Young‑age dependency ratio = (Population aged 0‑14 ÷ Population aged 15‑64) × 100
• Old‑age dependency ratio = (Population aged 65+ ÷ Population aged 15‑64) × 100

High dependency ratios increase pressure on education, health and pension systems and can lower per‑capita income if the working‑age population is not productively employed.

Population Structure and Development Stage

Development level	Typical age‑structure	Implications for the economy
Low‑income	Broad base; large proportion of children (0‑14 %)	High young‑age dependency; pressure on education and health; limited labour‑force growth.
Middle‑income	Base narrows, working‑age cohort (15‑64 %) expands	Potential “demographic dividend” if jobs are created; lower young‑age dependency.
High‑income	More rectangular; larger share of elderly (65 + %)	High old‑age dependency; greater demand for pensions and health care; slower labour‑force growth.

Real‑World Illustrations

• India – Later stage of the Demographic Transition; TFR fell from 5.9 (1990) to 2.0 (2022), creating a large working‑age cohort that fuels growth.
• Japan – High‑income, ageing society; >28 % of the population is 65+, creating a high old‑age dependency ratio.
• China (1979‑2015) – One‑child policy aimed at moving the population toward a perceived optimum; CBR fell from 17.9 to 12.1.
• Ethiopia – Low‑income country with a very broad base; young‑age dependency ratio ≈ 95 % (2023), constraining per‑capita income gains.
• Norway – High‑income, relatively balanced structure; old‑age dependency ≈ 35 % but mitigated by high productivity and generous welfare provisions.

Income Distribution (Syllabus 11.4.2)

Measuring Inequality

• Lorenz curve – Plots the cumulative share of total income earned against the cumulative share of the population (from poorest to richest). The 45° line represents perfect equality.
• Gini coefficient – Quantifies the area between the Lorenz curve and the line of equality.
  When data are grouped, the Gini can be calculated as:
  G = 1 – Σ (S_i + S_i‑1) · (P_i – P_i‑1)
  where S_i is the cumulative share of income up to group i and P_i is the cumulative share of population.

Limitations of the Gini Coefficient

• Insensitive to where in the distribution changes occur (e.g., a transfer from the richest to the middle does not affect the Gini as much as a transfer from the poorest to the middle).
• Does not reflect absolute levels of poverty or wealth.
• Requires reliable income data; informal economies can distort the measure.

Typical Patterns by Development Level

Development level	Typical Gini coefficient	Key features of the Lorenz curve
Low‑income	0.30 – 0.45 (moderate)	Curve relatively close to the line of equality; income concentrated in primary‑sector employment.
Middle‑income	0.40 – 0.55 (higher)	Curve bows outward as a growing middle class co‑exists with a wealthy elite.
High‑income	0.30 – 0.45 (often lower, but can exceed 0.45 in some advanced economies)	Curve may return nearer to equality, though financialisation can push it outward again.

Policy Tools to Influence Distribution

• Progressive taxation and targeted social transfers.
• Minimum‑wage legislation.
• Public provision of education and health (human‑capital investment).
• Labour‑market institutions (trade unions, collective bargaining).
• Policies that promote inclusive growth (e.g., support for SMEs, rural development programmes).

Economic Structure – Employment and Trade (Syllabus 11.4.3)

Definitions of Economic Sectors

• Primary sector – Extraction and production of natural resources (agriculture, mining, fishing, forestry).
• Secondary sector – Transformation of raw materials into manufactured goods and construction.
• Tertiary sector – Provision of services (finance, education, health, tourism, information‑technology, etc.).

Structural Transformation

As economies develop they typically move labour from the primary to the secondary and finally to the tertiary sector. This shift is accompanied by rising productivity, higher wages and a change in the composition of exports.

Employment by Economic Sector

Sector	Low‑income economies	Middle‑income economies	High‑income economies
Primary (agriculture, mining, fishing)	≈ 60 % of employment	≈ 30 % of employment	≤ 5 % of employment
Secondary (manufacturing, construction)	≈ 20 % of employment	≈ 40 % of employment	≈ 20 % of employment
Tertiary (services)	≈ 20 % of employment	≈ 30 % of employment	≥ 75 % of employment

Typical Trade Patterns

• Low‑income – Export of primary commodities (e.g., coffee, oil, minerals); import of capital goods and processed foods.
• Middle‑income – Export of manufactured goods (textiles, electronics); import of advanced machinery and high‑tech equipment.
• High‑income – Export of high‑value services (finance, software, education) and sophisticated manufactures (aerospace, pharmaceuticals); import of a wide range of consumer goods.

Illustrative Examples

Brazil (middle‑income) – Exports soybeans, iron ore and aircraft; imports high‑tech machinery and consumer electronics.

United Kingdom (high‑income) – Runs a trade surplus in services (financial services, education) while importing most manufactured goods.

Optimum Population – Economic Perspective (Syllabus 11.4)

What Is “Optimum Population”?

Optimum population is the size of a country’s population that maximises average welfare – measured by per‑capita income, health, education and overall living standards – given the existing resources, technology and institutional framework. The optimum is dynamic; it shifts when productivity, capital stock, environmental limits or policy settings change.

Theoretical Foundations

1. Malthusian Theory – When population grows faster than the food (or broader resource) supply, a “Malthusian trap” forces mortality up or fertility down until the population matches the carrying capacity.
2. Demographic Transition Model (DTM) – Economic development first reduces mortality, then fertility, moving an economy from high‑growth to low‑growth population regimes. The expanding working‑age cohort can generate a “demographic dividend” if productive employment is available.
3. Scarcity and Choice – Resources (land, water, energy) are limited; a larger population intensifies competition for these inputs, potentially lowering per‑capita welfare unless productivity rises.

Diagrammatic Representation (revision tip)

Draw a graph with Population size (P) on the x‑axis and Per‑capita welfare (W) on the y‑axis. The curve is upward‑sloping at low levels of P (economies of scale) and then bends downwards as congestion, resource depletion and diminishing returns set in. The peak of the curve marks the optimum population (P* ). Arrow annotations can show how:

• Technological progress shifts the curve upward, moving the optimum rightward.
• Environmental degradation shifts the curve downward, moving the optimum leftward.
• Policy measures (e.g., education, family‑planning) can move the economy along the curve toward P*.

Factors Influencing the Optimum Population

1. Resource endowment – Quantity/quality of arable land, water, energy sources and raw materials.
2. Technology level – Increases labour and capital productivity, effectively expanding the carrying capacity.
3. Human capital – Healthier, better‑educated workers produce more output per head.
4. Institutional quality – Secure property rights, efficient markets and good governance enable optimal resource use.
5. Environmental constraints – Pollution, climate change and biodiversity loss can reduce the effective resource base.

Why the Optimum Is Not a Fixed Number

• Technological advances (e.g., Green Revolution, digitalisation) raise output per unit of resource.
• Improvements in health and education increase the effective labour supply.
• Policy changes (family‑planning programmes, immigration rules) can accelerate or decelerate population growth.
• External shocks (climate events, pandemics) may temporarily lower the optimum.

Policy Levers that Can Move the Optimum

• Investment in technology and infrastructure – Enhances productivity, shifting the optimum rightward.
• Human‑capital development – Education and health programmes increase the effective labour force.
• Environmental management – Sustainable resource use and renewable‑energy adoption expand the resource base.
• Family‑planning and reproductive‑health policies – Influence the speed at which the population approaches the optimum.
• Immigration policy – Can be used to fill skill gaps or adjust demographic structure.

Real‑World Policy Examples

• China’s one‑child policy (1979‑2015) – Intended to bring the population closer to the perceived optimum; later relaxed as the population aged and the optimum shifted.
• Bangladesh family‑planning programme – Reduced the CBR from 6.3 (1975) to 2.1 (2020), contributing to rapid poverty reduction and a move toward a more optimal population size.
• Renewable‑energy investments (e.g., Germany’s Energiewende) – Expand the effective energy resource base, allowing a larger population to be supported sustainably.
• Ethiopia’s agricultural extension and irrigation projects – Aim to raise the resource‑carrying capacity, moving the optimum upward.
• Norway’s emphasis on high‑skill immigration – Supplements the domestic labour force, helping the economy stay near its optimum despite a low natural population growth rate.

Key Take‑aways for Exam Revision

1. Understand the distinction between CBR (per 1 000) and TFR (average children per woman) and be able to convert the former into a percentage growth rate.
2. Be able to draw and label the Lorenz curve, calculate the Gini (including the grouped‑data formula), and discuss its limitations.
3. Know the three‑sector definitions, the typical employment shares, and how structural transformation alters both employment and trade patterns.
4. Memorise the shape of the “optimum‑population” diagram and the factors that shift it left or right.
5. Use a balanced set of country examples (low‑income, middle‑income, high‑income) to illustrate each sub‑topic.