Understanding the Harrod-Domar Growth Model

The Harrod-Domar model is an early economic model of economic growth used in development economics to explain the growth rate in terms of the level of saving and of capital. It suggests that economic growth depends on two things: the level of saving and the capital-output ratio.

Key Concepts in Harrod-Domar Model

The model uses three specific growth rates to analyze the path of an economy:

• Actual Growth Rate (G): This is the actual rate at which the economy's income is growing. It is determined by the society's saving rate and the capital needed to produce a unit of output (the actual capital-output ratio). Mathematically, it is represented as \( G = \frac{s}{v} \), where \( s \) is the saving rate and \( v \) is the actual capital-output ratio.
• Warranted Growth Rate (Gw): This is the growth rate required to ensure that producers are satisfied with their investment decisions. It's the growth rate that maintains full capacity utilization of the existing capital stock. If the economy grows at this rate, there is just enough demand to justify the investment that has taken place. It is given by \( Gw = \frac{s}{v_r} \), where \( s \) is the saving rate and \( v_r \) is the required or desired capital-output ratio. When \( G = Gw \), the capital stock is fully utilized, preventing excess capacity or capital shortage.
• Natural Growth Rate (Gn): This is the maximum possible rate of growth allowed by the increase in the labour force and technological improvements (which increase labour productivity). It represents the rate of growth necessary to maintain full employment of the growing labour force. It is often represented as \( Gn = n + m \), where \( n \) is the rate of growth of the labour force and \( m \) is the rate of labour-augmenting technological progress.

Condition for Full Employment and Full Capacity Use

According to the Harrod-Domar growth model, for an economy to experience steady growth with continuous full employment of labour and full utilization of its capital stock (full capacity use), a specific condition must be met. This condition requires a precise balance between the actual growth rate, the warranted growth rate, and the natural growth rate.

The necessary condition for the full capacity use of capital and full employment of labour simultaneously is that:

\( G = Gw = Gn \)

Explanation of the Condition \( G = Gw = Gn \)

Let's break down why this specific condition is necessary for achieving both full capacity and full employment in the Harrod-Domar framework:

• \( G = Gw \): This part of the condition ensures that the actual growth rate matches the rate required for full capacity utilization. If \( G < Gw \), actual output grows slower than warranted, leading to a deficiency in demand relative to capacity, causing producers to cut investment and leading to excess capacity and recession. If \( G > Gw \), actual output grows faster than warranted, leading to demand exceeding current capacity, encouraging more investment, potentially leading to inflation and capital shortages. Only when \( G = Gw \) is investment just right to match desired saving at full capacity, leading to balanced growth without excess capacity or shortage relative to demand.
• \( Gw = Gn \) (or implicitly \( G = Gn \)): This part ensures that the growth rate required to maintain full capacity utilization is also the rate needed to keep the growing labour force fully employed. If \( Gw < Gn \) (and assuming \( G = Gw \)), the economy is growing slower than the rate needed to absorb the new workers entering the labour force, resulting in rising unemployment. If \( Gw > Gn \) (and assuming \( G = Gw \)), the economy is growing faster than the labour force can support at full employment, leading to labour shortages. Only when \( Gw = Gn \) does the capacity-warranted growth rate match the labour force growth rate, ensuring full employment is maintained alongside full capacity.

Therefore, for the Harrod-Domar model to exhibit steady growth with both full employment of labour and full utilization of capital, all three rates must be equal. This equilibrium is often described as a "knife-edge" because any deviation of G from Gw or Gn can lead to cumulative instability away from this desired path.

Revision Table: Harrod-Domar Model Rates

Additional Information: Harrod-Domar Model Stability

The Harrod-Domar model highlights the potential for instability in economic growth. The condition \( G = Gw = Gn \) is a very specific requirement that the economy must continuously meet. There are no automatic mechanisms within the model that pull the economy back to this equilibrium if it deviates. For example, if G starts to fall below Gw, it creates excess capacity, which discourages investment, causing G to fall even further below Gw, leading to a cumulative contraction. Similarly, deviations in relation to Gn can lead to persistent unemployment or labour shortages. This lack of a self-correcting mechanism is a key characteristic and often seen as a limitation of the Harrod-Domar model, contrasting with later growth models that include mechanisms like flexible factor proportions or technological change that can help stabilize growth.