Economic Principles Ch22. Economic Growth Theory: Solow Model

Chapter 22. Economic Growth Theory: The Solow Model

Why are some countries rich while others are poor? Addressing economics’ grandest question, Robert Solow provided the answers of capital productivity and technological progress. We analyze the drivers of growth that determine long-term living standards.

1. Foundations of the Solow Growth Model

(1) Production Function and Output per Worker

Assuming constant returns to scale (CRS), we substitute variables in per capita terms.

(2) Fundamental Equation

The capital stock of an economy increases through saving ( $s$ ) and decreases due to population growth ( $n$ ) and depreciation ( $\delta$ ).

2. Steady State

This refers to an equilibrium state where the capital stock per worker ( $k$ ) no longer changes.

Condition: $sy = (n + \delta)k$
Implications:
- The higher the saving rate ( $s$ ), the higher the income level per worker ( $y^*$ ), but the growth rate ultimately converges to the population growth rate plus the rate of technological progress.
- It demonstrates that simple capital accumulation alone cannot explain sustained growth.

3. Golden Rule of Capital Accumulation

If consumption, rather than growth itself, is the objective, there exists a capital level ( $k_G$ ) that maximizes consumption per worker ( $c$ ).

Condition: Marginal Product of Capital ( $MPK$ ) = $n + \delta$
if $MPK > n + \delta$ : State of capital scarcity $\rightarrow$ saving must be increased.
if $MPK < n + \delta$ : State of excess capital (dynamic inefficiency) $\rightarrow$ consumption must be increased.

4. Growth Accounting

Economic growth is analyzed by breaking it down into the contributions of labor, capital, and Total Factor Productivity (TFP).

Solow Residual: The remaining growth unexplained by labor and capital is defined as technological progress ( $\Delta A/A$ ), which is the true key to long-term growth.

5. Conclusion: Technological Progress is the Future of Growth

The Solow Model mathematically proved that savings and investment alone eventually hit growth limits. Subsequent research, Endogenous Growth Theory, emphasizes that this ‘technological progress’ is not given exogenously, but can be generated by nations themselves through education and R&D investment.

📖 References

[Macroeconomics] - Byung-ryul Jung: Analytical review of the Solow model and the Golden Rule.
[A Contribution to the Theory of Economic Growth] - Robert Solow: The starting point of modern growth theory.

Great work. In the next session, we will study Endogenous Growth Theory, which moves beyond the limitations of the Solow model to emphasize human capital and innovation.