Model Answer
0 min readIntroduction
The Harrod-Domar model, a cornerstone of post-Keynesian growth theory developed in the 1940s, attempts to explain the determinants of long-run economic growth. Central to this model is the concept of the ‘warranted rate of growth’ – the rate of growth that allows the economy to maintain full employment and price stability. However, the model also highlights a significant problem: ‘knife-edge instability’. This implies that achieving and sustaining a stable growth path is exceptionally difficult, as the actual rate of growth needs to precisely match the warranted rate. This answer will delve into the meaning of the warranted rate of growth and comprehensively explain the knife-edge instability problem inherent in Harrod’s growth model.
The Warranted Rate of Growth
The warranted rate of growth (gw) is the rate of growth of capital stock that is consistent with maintaining full employment and stable prices. It is determined by the savings ratio (s) and the capital-output ratio (v). Mathematically, it is represented as: gw = s/v. Here, 's' represents the proportion of income saved and invested, and 'v' represents the amount of capital required to produce one unit of output. Therefore, a higher savings ratio or a lower capital-output ratio will lead to a higher warranted rate of growth.
Several factors influence the warranted rate of growth:
- Savings Rate (s): A higher propensity to save leads to more investment and a higher warranted rate.
- Capital-Output Ratio (v): Technological advancements that reduce the capital needed for each unit of output (lower v) increase the warranted rate.
- Demographic Changes: Changes in the size and age structure of the population can affect savings and investment patterns.
The Knife-Edge Instability Problem
The knife-edge problem arises from the model’s assumption that the actual rate of growth (ga) must equal the warranted rate of growth (gw) to maintain full employment. If ga deviates from gw, the economy faces either unemployment or inflation.
Let's consider two scenarios:
- Actual Growth Exceeds Warranted Growth (ga > gw): If the actual rate of growth is higher than the warranted rate, investment demand will exceed the supply of savings. This leads to rising prices (inflation) as firms bid up the cost of capital. The increased prices reduce the real value of capital, increasing the capital-output ratio (v). This, in turn, lowers the warranted rate of growth, eventually bringing it down to meet the actual rate, but only after a period of inflation.
- Actual Growth Falls Short of Warranted Growth (ga < gw): Conversely, if the actual rate of growth is lower than the warranted rate, savings will exceed investment demand. This leads to a fall in prices (deflation) and unused capacity. The decreased prices reduce the profitability of investment, increasing the capital-output ratio (v). This raises the warranted rate of growth, eventually bringing it up to meet the actual rate, but only after a period of unemployment.
The ‘knife-edge’ refers to the precarious balance required. The economy is constantly teetering on the edge of either inflation or deflation, with even small deviations from the warranted rate triggering significant adjustments. The model suggests that maintaining a stable growth path is extremely difficult, requiring precise coordination between savings and investment.
Assumptions and Limitations
The Harrod-Domar model relies on several simplifying assumptions:
- Fixed Capital-Output Ratio (v): The model assumes a constant capital-output ratio, which is unrealistic in the long run due to technological progress.
- Constant Savings Rate (s): The savings rate is assumed to be fixed, ignoring the influence of income distribution and other factors.
- No Technological Progress: The model doesn’t explicitly account for technological advancements, which can significantly alter the growth process.
- Closed Economy: The model assumes a closed economy, neglecting the impact of international trade and capital flows.
These limitations mean that the knife-edge instability is likely overstated in reality. Modern growth models, such as the Solow-Swan model, incorporate technological progress and other factors to provide a more nuanced and stable view of long-run growth.
Conclusion
In conclusion, the warranted rate of growth is a crucial concept in Harrod-Domar’s growth model, representing the growth rate consistent with full employment. However, the model’s inherent knife-edge instability highlights the difficulty of achieving and maintaining a stable growth path due to the sensitive relationship between actual and warranted growth rates. While the model’s assumptions are restrictive and its predictions somewhat pessimistic, it remains a valuable contribution to growth theory, emphasizing the importance of savings, investment, and capital efficiency in driving long-run economic development. Modern growth models have built upon this foundation, addressing some of its limitations to provide a more comprehensive understanding of economic growth.
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.