Key Takeaways
- 1% capital increase raises productivity by 0.33%.
- Labor productivity = TFP + one-third capital deepening.
- Derived from Cobb-Douglas production function formula.
- Capital deepening boosts output per labor hour.
What is One-Third Rule?
The One-Third Rule is an economic principle derived from the Cobb-Douglas production function that states a 1% increase in capital per hour of labor results in approximately a 0.33% rise in labor productivity, holding other factors constant. It quantifies how capital deepening contributes to output growth relative to labor input.
This rule helps explain the relationship between capital investment and productivity improvements within a broader macroeconomics framework.
Key Characteristics
The One-Third Rule highlights how capital and labor inputs combine to affect productivity levels. Key features include:
- Capital’s share: Roughly one-third of output growth is attributed to capital, reflected in the exponent 1/3 in the production function.
- Labor’s share: Labor accounts for about two-thirds of output, emphasizing its dominant role in production.
- Labor productivity growth: Results from both total factor productivity (TFP) advances and capital deepening.
- Application: Useful for analyzing how investments in physical capital, like machinery or technology, boost output per worker.
- Link to wages: Higher labor productivity often leads to increased take-home pay by raising output per hour worked.
How It Works
The One-Third Rule comes from the Cobb-Douglas production function, where output is a product of capital, labor, and efficiency factors. By isolating output per labor unit, the rule shows labor productivity growth equals total factor productivity growth plus one-third of capital deepening.
This means when you increase the amount of capital available per worker, such as upgrading equipment or software, labor productivity rises proportionally but at a reduced rate (about 33%). This relationship helps in growth accounting by decomposing productivity changes into capital and technology-driven components.
Examples and Use Cases
Understanding the One-Third Rule is practical across industries and economic analyses. Consider these examples:
- Airlines: Microsoft investing in advanced technology can increase capital per worker, enhancing productivity in sectors like aviation management.
- Agriculture: Historical U.S. farm mechanization exemplifies capital deepening raising labor productivity dramatically.
- Stock selection: Leveraging insights from the One-Third Rule can guide choices among best growth stocks by focusing on companies efficiently increasing capital per labor unit.
- Large-cap firms: Many large-cap stocks benefit from capital deepening, boosting their labor productivity and competitive advantage.
Important Considerations
While the One-Third Rule provides a useful average estimate, actual capital’s contribution to productivity varies by sector and country due to different market conditions and labor qualities. It assumes competitive markets and constant returns to scale, which may not hold in all contexts.
When applying this rule, factor in ongoing innovation and improvements in human capital, as total factor productivity can significantly alter growth outcomes beyond just capital deepening.
Final Words
The One-Third Rule highlights that boosting capital per worker yields a predictable gain in productivity, but innovation and skills remain crucial drivers. To leverage this, analyze how your investments in equipment or technology translate into real output improvements alongside workforce development.
Frequently Asked Questions
The One-Third Rule states that a 1% increase in capital per hour of labor leads to roughly a 0.33% increase in labor productivity, assuming other factors remain constant. It comes from the Cobb-Douglas production function used in economic growth models.
Capital deepening means more capital, like machines or software, per worker. According to the One-Third Rule, this increase boosts labor productivity by about one-third of the percentage increase in capital per worker.
The 1/3 exponent reflects empirical data showing that roughly one-third of total output is attributed to capital, such as machines and infrastructure, while the other two-thirds is attributed to labor. This division helps explain how capital deepening influences productivity.
Technological progress is captured by total factor productivity (TFP), which boosts labor productivity beyond just capital and labor inputs. The One-Third Rule specifically quantifies the capital contribution, while TFP represents gains from innovation and efficiency.
Yes, but indirectly. Improvements in education increase human capital, which is treated as higher effective labor input. The One-Third Rule focuses on capital deepening, while labor quality improvements increase productivity via the labor share in the production function.
Higher labor productivity, boosted by capital deepening as described by the One-Third Rule, tends to raise wages and reduce unit labor costs. This can lower inflationary pressures by making production more efficient.
In U.S. agriculture, increased mechanization raised capital per worker, boosting labor productivity significantly. This allowed fewer workers to produce more output, illustrating the One-Third Rule's effect of capital deepening on productivity growth.
