Long-Run Economic Growth and Productivity

For example, if a farmer has a small plot of land and buys one tractor, their output will jump significantly. However, if they already own 100 tractors, buying a 101st tractor will add very little to their total production.

Exam Tip: Note that while capital and labor typically face diminishing returns, economists do not necessarily assume the same for knowledge, human capital, or technology. These can drive growth indefinitely.

Productivity: The Key to Living Standards

While total GDP measures the size of an economy, productivity—defined as output per worker ($\frac{Y}{L}$) —is the primary determinant of a nation's living standards. A nation can only enjoy a high standard of living if it can produce a large quantity of goods and services per person.

Productivity increases when workers have greater access to:

1. Physical capital per worker ($\frac{K}{L}$)
2. Human capital per worker ($\frac{H}{L}$)
3. Natural resources per worker ($\frac{N}{L}$)
4. Knowledge and technology

The Productivity Paradox and AI

In our modern era, we see a "productivity paradox": despite spectacular digital innovations like Artificial Intelligence (AI), measured productivity growth has sometimes been disappointing. This may be because new technologies are slow to diffuse through the economy, or because firms require significant time to reorganize their entire production processes to fully reap the benefits of the new tech.

Growth Accounting and Capital Accumulation

To understand what drives a country's growth, economists use growth accounting to decompose the GDP growth rate into its constituent parts:

$\begin{aligned} \dot{v} &= \alpha \dot{k} + (1 - \alpha) \dot{l} + \dot{z} \end{aligned}$

Where:

• $\dot{v}$ is the GDP growth rate.
• $\alpha$ is the capital share (the portion of income going to capital).
• $\dot{k}$ is the capital stock growth rate.
• $(1 - \alpha)$ is the labor share (the portion of income going to wages).
• $\dot{l}$ is the labor hours growth rate.
• $\dot{z}$ is the technology (or Total Factor Productivity) growth rate.

Managing the Capital Stock

The capital stock does not grow automatically. It changes based on the relationship between investment and depreciation (the rate at which capital wears out):

$\text{Change in Capital Stock} = \text{Investment} - \text{Depreciation}$

Investment comes from national savings (private savings plus government surplus) and borrowing from abroad.

Convergence and Divergence

A major question in economics is whether poor countries will "catch up" to rich ones, a process called convergence.

• Convergence: Occurs when a poorer country grows faster than a richer one. This is possible because the marginal product of capital is higher when the capital stock is low; essentially, an extra dollar of investment goes much further in a country with very few machines than in one that is already highly mechanized.
• Divergence: Occurs when the gap between rich and poor countries widens. This often happens due to differences in social infrastructure (like corruption or lack of property rights) or lower levels of human capital and technology.

Summary Table: Why GDP Varies

Global Mobility and Competitiveness

In a globalized world, inputs like capital and labor move toward where they can earn the highest returns.

Labor Mobility: Workers tend to migrate toward higher wages. However, significant barriers—such as legal restrictions (visas), cultural differences, and language—prevent labor from equalizing wages perfectly across the globe.

Capital Mobility: It is generally easier to move capital than labor. Owners of capital look for the highest marginal product of capital. While we might expect capital to flow from rich to poor countries, it often flows to rich countries because poor countries may lack the human capital (skilled workers) or social infrastructure (legal stability) necessary to make that capital productive.

Ultimately, a nation's competitiveness—its ability to attract these vital inputs—depends on its ability to invest in education, research and development (R&D), and a stable, corruption-free business environment.