The Warranted Growth Rate is a key concept within the Harrod-Domar model of economic growth. This rate represents the growth rate at which an economy must expand for the national income to be sustainable over time. Specifically, it balances the proportional relationship between saving and investment, ensuring that all savings are effectively invested in productive activities.
Historical Context
The Harrod-Domar model, developed independently by Sir Roy Harrod (1939) and Evsey Domar (1946), was one of the first formal models to describe the dynamics of economic growth. It emerged in the context of post-World War II reconstruction efforts and the need for theories that could guide economic planning and development.
Mathematical Framework
Basic Equations
-
Savings Function:
$$ S = sY $$where \( S \) is savings, \( s \) is the saving rate, and \( Y \) is the national income. -
Investment Function:
$$ I = \nu \frac{dY}{dt} $$where \( I \) is investment, \( \nu \) (nu) is the capital-output ratio, and \(\frac{dY}{dt}\) is the rate of change of income over time. -
Equilibrium Condition: For ex-ante savings and investment to be equal:
$$ sY = \nu \frac{dY}{dt} $$ -
Deriving the Warranted Growth Rate: Solving for the growth rate \( g \):
$$ g = \frac{dY/Y}{dt} = \frac{s}{\nu} $$where \( g \) is the warranted growth rate.
Importance and Applicability
The warranted growth rate is critical for:
- Economic Planning: Helps governments and planners understand the required savings and investment levels for sustainable growth.
- Development Economics: Offers insights into the growth trajectories of developing economies.
- Policy Formulation: Informs fiscal and monetary policies aimed at stabilizing and accelerating economic growth.
Diagrams
graph TD
A[National Income (Y)] -->|Savings sY| B[Savings (S)]
A -->|Change in Income dY/dt| C[Investment (I)]
B --> D{Warranted Growth Rate}
C --> D
D -->|Sustainable Growth Rate| E[Economic Stability]
Key Events and Evolution
- 1939: Sir Roy Harrod introduces the model focusing on the instability of growth.
- 1946: Evsey Domar extends the model to include aspects of productive capacity and output growth.
- Post-War Applications: Used extensively in reconstruction and development strategies, particularly in war-torn and developing economies.
Considerations
- Fixed Proportional Relationships: The model assumes constant saving rates and capital-output ratios, which may not hold in dynamic real-world economies.
- Investment Induced by Growth: Investment is driven by changes in income, not just by independent investor expectations or technological innovations.
Related Terms
- Actual Growth Rate: The rate at which the economy actually grows, which may differ from the warranted growth rate.
- Natural Growth Rate: The growth rate consistent with full employment and utilization of resources.
Comparisons
- Harrod-Domar vs. Solow Model: Unlike the Harrod-Domar model, the Solow growth model incorporates technological progress and diminishing returns to capital, making it more flexible for long-term growth analysis.
Interesting Facts
- Foundation for Modern Growth Theory: Despite its limitations, the Harrod-Domar model paved the way for subsequent growth theories, including the Solow-Swan model and endogenous growth theories.
Inspirational Stories
Countries like Japan and South Korea, post-WWII, demonstrated the practical application of growth theories similar to the Harrod-Domar model, focusing on high savings rates and effective investments to achieve rapid economic growth.
Famous Quotes
- Roy Harrod: “The problem of steady economic growth is one of the most urgent questions in economics.”
- Evsey Domar: “Growth is not only the surest, but also the cheapest way to escape inflation.”
Proverbs and Clichés
- “You cannot control the winds, but you can adjust your sails.” - Reflects the balance needed between savings and investment for sustainable growth.
Expressions
- Sustainable Growth: Growth that can be maintained without creating significant economic or environmental problems.
- Economic Equilibrium: The point at which supply and demand balance each other, applicable here as the balance between savings and investment.
Jargon and Slang
- Growth Accounting: Methodology to determine the contribution of different factors such as capital, labor, and technology to economic growth.
FAQs
What is the warranted growth rate in the Harrod-Domar model?
Why is the warranted growth rate significant?
References
- Harrod, R. F. (1939). “An Essay in Dynamic Theory.” The Economic Journal, 49(193), 14-33.
- Domar, E. D. (1946). “Capital Expansion, Rate of Growth, and Employment.” Econometrica, 14(2), 137-147.
- Solow, R. M. (1956). “A Contribution to the Theory of Economic Growth.” The Quarterly Journal of Economics, 70(1), 65-94.
Summary
The Warranted Growth Rate in the Harrod-Domar model signifies the precise rate at which an economy must grow for its national income to remain balanced between savings and investment. Its fundamental equation, \( g = \frac{s}{\nu} \), underlines the importance of savings rates and capital-output ratios in sustaining growth. Despite its limitations, the model remains a cornerstone in economic theory, offering valuable insights for developing economies and informing various economic policies.
