Model Answer
0 min readIntroduction
Domar's growth model, developed by Evsey Domar in 1946, is a Keynesian economic model that explains economic growth through the interaction of savings and investment. It posits that the level of investment is the primary determinant of economic growth, and this investment is driven by the savings rate and the capital-output ratio. The model simplifies the complexities of economic growth by focusing on aggregate variables and assumes a fixed capital-output ratio. Understanding the equilibrium path of investment within this framework is key to comprehending the model’s implications for long-run economic expansion.
Domar's Growth Model: Core Assumptions and Equations
The Domar model rests on several key assumptions:
- Fixed Capital-Output Ratio (v): This implies that a constant amount of capital is required to produce one unit of output.
- Constant Savings Rate (s): A fixed proportion of income is saved.
- Full Employment: The model assumes the economy operates at or near full employment.
- No Government Intervention: The model initially excludes government spending and taxation.
The core equation of the model is:
ΔY = sY / v
Where:
- ΔY = Change in Income (Growth of Output)
- s = Savings Rate
- Y = National Income
- v = Capital-Output Ratio
Derivation of the Exponential Investment Path
To demonstrate the exponential nature of the investment path, we need to analyze how investment changes over time. Investment (I) is equal to savings (S), and savings is a fraction (s) of income (Y).
I = S = sY
Since v = K/Y (where K is capital stock), then Y = K/v. Substituting this into the investment equation:
I = s(K/v)
The change in capital stock (ΔK) is equal to investment (I):
ΔK = I = sK/v
This equation shows that the change in capital stock is proportional to the existing capital stock. This is the defining characteristic of exponential growth.
Mathematical Representation of Exponential Growth
We can express the growth of capital stock over time as follows:
Kt+1 = Kt + ΔK = Kt + (sKt/v) = Kt(1 + s/v)
Where:
- Kt+1 = Capital stock at time t+1
- Kt = Capital stock at time t
Repeatedly applying this equation, we get:
Kt = K0(1 + s/v)t
Where K0 is the initial capital stock.
This equation clearly demonstrates that the capital stock grows exponentially over time, with the growth rate being (s/v). Since investment is directly linked to the capital stock (I = sY = s(K/v)), the investment path also follows an exponential trajectory.
Implications and Limitations
The exponential growth path of investment implies that even small changes in the savings rate or capital-output ratio can have significant long-run effects on economic growth. However, the model is a simplification and has limitations. The assumption of a fixed capital-output ratio is often unrealistic, as technological progress and changes in production techniques can alter this ratio over time. Furthermore, the model doesn't account for population growth, technological advancements, or other factors that influence economic growth.
Conclusion
In conclusion, Domar’s growth model demonstrates that, under its core assumptions, the equilibrium path of investment is indeed exponential. This is a direct consequence of the proportional relationship between the change in capital stock and the existing capital stock, driven by the savings rate and capital-output ratio. While a simplified representation of reality, the model provides valuable insights into the dynamics of economic growth and the importance of savings and investment. However, its limitations necessitate considering more complex models that incorporate factors like technological progress and population growth for a more nuanced understanding of economic development.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.