Introduction
Economic growth models help us understand the drivers of long-term increases in national output and living standards. Traditional neoclassical models, like the Solow model, predict diminishing returns to capital, meaning that each additional unit of capital contributes less to output. However, new growth theories—particularly endogenous growth models—challenge this idea. Two such models are the AK model and the Lucas model. This answer explains why the AK model does not exhibit diminishing returns to capital and analyzes the Lucas model’s emphasis on human capital and its role in driving endogenous growth.
The AK Growth Model
Basic Structure
The AK model is a simple form of endogenous growth theory where output depends linearly on capital. Its production function is:
Y = AK
Where:
- Y = output
- A = productivity parameter (technology)
- K = capital stock (can include physical and human capital)
Absence of Diminishing Returns
In the AK model, the marginal product of capital is constant, because:
MPK = dY/dK = A
This implies that capital does not suffer from diminishing returns. As capital increases, output increases proportionally, enabling constant growth rates.
Assumptions Behind Constant Returns
- Capital broadly includes physical and human capital, knowledge, and infrastructure.
- No congestion effects—adding more capital does not reduce productivity.
- Technological progress is embedded in capital accumulation.
Implications
- The economy can grow indefinitely without relying on exogenous technological change.
- Policy interventions (e.g., savings incentives, investment in capital) can permanently raise growth rates.
- Poor countries can grow rapidly if they can accumulate capital efficiently.
Criticism of the AK Model
- Too simplistic—it ignores labor, institutions, and diminishing effects from overaccumulation.
- Fails to explain cross-country differences in growth rates.
- Overstates the role of capital without addressing complementary inputs.
The Lucas Model of Endogenous Growth
Overview
Proposed by Robert Lucas (1988), this model focuses on the role of human capital in driving long-term growth. The model argues that investment in human capital—through education, learning, and skill development—leads to sustained increases in productivity and economic output.
Production Function
The production function typically includes human capital (H):
Y = AK^α H^(1-α)
Or, in some variants:
Y = A (uH)^α K^(1−α)
Where:
- H = human capital (knowledge, skills, education)
- u = time devoted to working (1 − u is time spent learning)
Human Capital Accumulation
Human capital evolves according to:
Ḣ = δ(1 − u)H
Where δ is the effectiveness of education or learning. This captures the idea that time spent learning increases future productivity.
Key Features
- Endogenous Learning: Growth is driven by the internal decision of individuals to accumulate skills and knowledge.
- Externalities: Knowledge spillovers lead to increasing returns at the social level, even if private returns are constant.
- No Convergence: Poor countries may not necessarily catch up with rich countries unless they invest in human capital.
Role of Human Capital
Human capital enhances labor productivity, fosters innovation, and facilitates the adoption of new technologies. Unlike physical capital, it is non-rivalrous and can generate externalities, making it crucial for sustainable growth.
Comparison: AK vs Lucas
| Aspect | AK Model | Lucas Model |
|---|---|---|
| Main Driver of Growth | Capital accumulation | Human capital accumulation |
| Returns to Capital | Constant | Diminishing (private), but increasing (social) due to externalities |
| Role of Education | Implicit in capital | Explicit driver of productivity |
| Policy Implications | Encourage saving and investment | Invest in education, training, and R&D |
Conclusion
The AK model demonstrates that with constant returns to capital, growth can be sustained without diminishing returns. It simplifies growth dynamics by emphasizing capital accumulation. On the other hand, the Lucas model provides a richer and more realistic framework by highlighting the importance of human capital, learning, and externalities. It shows that the development of skills and knowledge is fundamental to long-run growth. For developing countries, policies that enhance human capital—such as improving education systems—are key to sustaining growth in line with the Lucas model’s insights.