The concept of an optimum population

Economic Development – Population

Objective

To understand the concept of an optimum population and its relevance to economic development.

1. What is Optimum Population?

The optimum population is the size of a country’s population at which the maximum possible standard of living can be achieved, given the available resources, technology and institutions. It is the point where the marginal benefit of an additional person equals the marginal cost.

Mathematically, it can be expressed as:

\$\text{Marginal Benefit (MB)} = \text{Marginal Cost (MC)}\$

When MB > MC, the population is below the optimum and can grow without reducing per‑capita welfare. When MB < MC, the population is above the optimum and welfare falls.

2. Factors Determining the Optimum Population

• Resource endowment – land, minerals, water, energy.
• Technology level – productivity of labour and capital.
• Institutional quality – governance, health, education systems.
• Human capital – skills, health, education of the workforce.
• External trade – access to imports of food, raw materials and export markets.

3. Why an Optimum Population Matters for Development

At the optimum population:

1. Per‑capita income is maximised.
2. Unemployment is low and labour markets are efficient.
3. Pressure on the environment is sustainable.
4. Public services (health, education) can be provided at an adequate level.

4. Consequences of Being Below the Optimum

If the population is below the optimum:

• Under‑utilisation of resources – idle land, labour and capital.
• Higher per‑capita income potential, but not realised.
• Possible labour shortages, especially in skilled sectors.

5. Consequences of Being Above the Optimum

If the population exceeds the optimum:

• Unemployment or under‑employment rises.
• Per‑capita income falls.
• Increased pressure on housing, health, education and the environment.
• Higher incidence of poverty and inequality.

6. Illustrative Diagram

7. Example Calculation (Simplified)

Assume a country’s total output (GDP) is given by the production function:

\$Y = A \cdot K^{\alpha} \cdot L^{\beta}\$

where:

• \$Y\$ = total output
• \$A\$ = technology factor
• \$K\$ = capital stock
• \$L\$ = labour force (population)
• \$\alpha\$ and \$\beta\$ are output elasticities (with \$\alpha + \beta = 1\$ for constant returns to scale).

Per‑capita output is \$y = Y/L\$. Differentiating \$y\$ with respect to \$L\$ and setting the derivative to zero gives the optimum \$L\$ (population) that maximises \$y\$.

\$\frac{dy}{dL}=0 \;\Rightarrow\; \frac{d}{dL}\left(\frac{A K^{\alpha} L^{\beta}}{L}\right)=0\$

Solving yields the optimum labour force:

\$L^{*}= \frac{\beta}{1-\beta}\; \frac{K}{A^{1/\beta}}\$

In practice, policymakers use such relationships to assess whether current population trends are moving towards or away from \$L^{*}\$.

8. Summary Table

9. Policy Implications

Governments aiming to approach the optimum population may consider:

• Investing in education and health to raise human capital.
• Promoting family planning and reproductive health services.
• Encouraging migration policies that balance labour market needs.
• Improving technology and productivity to shift the optimum upward.
• Ensuring sustainable resource management and environmental protection.

10. Key Take‑aways

1. The optimum population is the size that maximises per‑capita welfare.
2. It depends on resources, technology, institutions and human capital.
3. Both under‑population and over‑population have distinct economic and social costs.
4. Policy measures can move a country towards its optimum population.