Harrod domar model

The Harrod-Domar model, a foundational concept within Development economics and Economic growth theory, posits that the rate of economic growth in a country is directly proportional to its Savings rate and inversely proportional to its Capital-output ratio. This model highlights the critical role of Capital accumulation in fostering economic expansion by explaining how investment, derived from savings, increases a nation's productive capacity.

What Is Harrod-Domar Model?

The Harrod-Domar model is an early economic framework that explains how an economy grows by focusing on the roles of savings and Investment. It suggests that these two factors are primary drivers of Economic growth. Co-created by economists Sir Roy Harrod and Evsey Domar, this model belongs to the realm of Economic growth theory, specifically within Development economics. The core idea of the Harrod-Domar model is that to achieve sustained growth, an economy must generate sufficient savings to fund the investment needed to expand its Capital stock. This theoretical construct helps to understand the dynamics of capital formation and its impact on national income, forming a basis for understanding how investment leads to increased output and employment.

History and Origin

The Harrod-Domar model was independently developed by Roy F. Harrod in 1939 and Evsey Domar in 1946.⁷⁵, ⁷⁶, ⁷⁷ Their contributions emerged in the aftermath of the Great Depression and World War II, a period when economists were intensely focused on understanding the mechanisms of economic growth and how to avoid stagnation.⁷³, ⁷⁴ Harrod's initial work, "An Essay in Dynamic Theory" (1939), aimed to integrate the Keynesian economics concept of the multiplier with the investment accelerator, seeking to understand the conditions for stable economic expansion.⁷² Domar's "Capital Expansion, Growth and Employment" (1946) similarly explored how investment not only generates income (through the multiplier effect) but also increases productive capacity (through the capacity effect).⁷⁰, ⁷¹ While their approaches differed, they arrived at a similar conclusion: a constant rate of Investment is necessary to sustain a constant rate of Economic growth. The model became a significant precursor to subsequent Exogenous growth model theories.

Key Takeaways

• The Harrod-Domar model asserts that Economic growth is primarily driven by the Savings rate and the Capital-output ratio.⁶⁸, ⁶⁹
• Higher savings lead to greater Investment, which in turn increases the Capital stock and productive capacity.⁶⁶, ⁶⁷
• The model implies that for sustained growth, the actual rate of growth, the warranted growth rate (the rate at which all savings are absorbed into investment), and the natural growth rate (required to maintain Full employment) should ideally be equal.
• It highlights the potential for economic instability if these growth rates are not balanced, often referred to as "Harrod's knife-edge."⁶⁴, ⁶⁵
• The model assumes a fixed Capital-output ratio and Full employment of labor, simplifying the complex dynamics of a real economy.⁶², ⁶³

Formula and Calculation

The Harrod-Domar model's core equation relates the rate of Economic growth to the Savings rate and the Capital-output ratio. The formula is typically expressed as:⁶⁰, ⁶¹

Where:

• (g) = Rate of Economic growth (change in Gross Domestic Product divided by GDP).⁵⁹
• (s) = Savings rate (the proportion of national income that is saved, or Marginal propensity to save).⁵⁷, ⁵⁸
• (v) = Capital-output ratio (also denoted as (k) or (\sigma)), which measures the amount of Capital stock required to produce one unit of output.⁵⁴, ⁵⁵, ⁵⁶ A lower capital-output ratio indicates greater efficiency of capital.⁵³

This equation implies that a higher Savings rate or a lower (more efficient) Capital-output ratio will lead to a higher rate of Economic growth.

Interpreting the Harrod-Domar Model

Interpreting the Harrod-Domar model involves understanding that it outlines the necessary conditions for an economy to maintain a steady growth path. The model suggests that for economic growth to occur and be sustained, there must be a balance between the supply of savings and the demand for increasing the Capital stock.⁵² A high Savings rate indicates that an economy has substantial funds available for Investment, which can increase its productive capacity.⁵¹ Conversely, the Capital-output ratio reflects the efficiency with which capital is utilized; a higher ratio implies that more capital is needed to generate a given amount of output, suggesting less efficient investment.⁴⁹, ⁵⁰

The model emphasizes that if the actual rate of growth deviates from the warranted rate of growth (the rate at which all savings are invested), the economy can experience either inflationary pressures or recessionary conditions.⁴⁷, ⁴⁸ This sensitivity underscores the model's "knife-edge" characteristic, implying that achieving and maintaining a stable Economic growth path requires precise policy interventions to align savings and investment.⁴⁶

Hypothetical Example

Consider a developing nation, Country Alpha, that aims to achieve a certain Economic growth rate. Country Alpha currently has a national Savings rate of 15% (s = 0.15) and a Capital-output ratio of 3 (v = 3), meaning it takes 3 units of capital to produce 1 unit of output.

Using the Harrod-Domar formula:

According to the model, Country Alpha's economy is expected to grow at a rate of 5% per year. This growth is directly attributable to its savings being channeled into Investment to expand its Capital stock. If Country Alpha wants to increase its growth rate to, say, 7.5%, it would either need to increase its Savings rate to 22.5% (assuming the capital-output ratio remains 3) or improve its capital efficiency to reduce the Capital-output ratio to 2 (assuming the savings rate remains 15%). This example illustrates how the Harrod-Domar model provides a simplified, yet insightful, framework for setting growth targets and understanding the roles of savings and capital efficiency.

Practical Applications

The Harrod-Domar model gained significant prominence in Development economics during the post-World War II era, particularly for guiding policies in newly independent and developing countries.⁴³, ⁴⁴, ⁴⁵ Its simplicity made it an attractive tool for economic planners attempting to determine the amount of Investment required to achieve specific Economic growth targets.⁴¹, ⁴²

Policymakers used the model to:

• Estimate Investment Needs: By setting a desired growth rate, countries could estimate the necessary Investment level, often leading to calls for increased domestic Savings rate or foreign aid to bridge the "savings gap."⁴⁰
• Formulate Development Plans: The model informed strategies focused on industrialization and infrastructure development, as these areas require substantial Capital stock and can directly contribute to increasing productive capacity.³⁸, ³⁹
• Highlight Capital's Dual Role: It emphasized that Investment not only creates demand but also adds to the economy's productive capacity, a crucial insight for economies aiming to expand output.³⁶, ³⁷

The Harrod-Domar model has been applied in various contexts, from post-war reconstruction efforts to development planning in countries like the Philippines and Vietnam, where studies have examined its applicability in explaining Gross Domestic Product growth.³³, ³⁴, ³⁵ While its direct application has evolved with more complex models, its fundamental premise about savings, investment, and capital efficiency remains relevant in understanding the basic mechanics of economic expansion.

Limitations and Criticisms

While influential, the Harrod-Domar model faces several significant limitations and criticisms that limit its applicability in modern economic analysis.

• Fixed Capital-output ratio: One of the major criticisms is its assumption of a fixed Capital-output ratio.³¹, ³² In reality, this ratio can change due to Technological advancements, improvements in Productivity, or shifts in production techniques, which the model largely ignores.²⁸, ²⁹, ³⁰
• Full employment Assumption: The model often assumes the economy operates at Full employment.²⁶, ²⁷ This is unrealistic, as real-world economies frequently experience unemployment and fluctuations related to Business cycles.²⁴, ²⁵
• Oversimplification of Growth Factors: The model focuses almost exclusively on savings and capital investment as determinants of growth, largely overlooking other critical factors such as human capital development, institutional quality, government policies, and Technological advancements.²¹, ²², ²³
• Instability of Growth ("Knife-edge"): The model's "knife-edge" property suggests that stable Economic growth is highly precarious.¹⁹, ²⁰ Any deviation from the warranted growth rate can lead to cumulative instability, either through persistent excess capacity or inflationary pressure, a feature that many economists find too rigid to reflect real-world economic adjustments.¹⁸
• Constant Savings rate: It assumes a constant Marginal propensity to save, which may not hold true as income levels change or as economies develop.¹⁶, ¹⁷

These limitations led to the development of more complex models, particularly within Neoclassical economics, that attempt to address these shortcomings.

Harrod-Domar Model vs. Solow-Swan Model

The Harrod-Domar model and the Solow-Swan model represent two distinct, yet foundational, approaches in Economic growth theory. The Harrod-Domar model is a Keynesian-based framework primarily focused on how savings and investment drive short-term output and employment dynamics. It assumes a fixed Capital-output ratio and emphasizes that continuous Investment is necessary to absorb growing productive capacity and maintain Full employment. This often leads to the "knife-edge" instability, where deviations from the warranted growth rate can cause persistent recessions or booms.¹⁴, ¹⁵

In contrast, the Solow-Swan model, developed by Robert Solow and Trevor Swan in the mid-1950s, is a neoclassical model that builds upon and extends the Harrod-Domar framework by introducing the concepts of diminishing returns to capital, labor as a factor of production, and crucially, Technological advancements as an exogenous driver of long-run growth.¹², ¹³ The Solow-Swan model relaxes the assumption of a fixed capital-output ratio, allowing for substitutability between capital and labor.¹¹ It predicts that economies will converge to a steady state where capital per worker and output per worker grow at the rate of technological progress, suggesting that changes in the Savings rate have only temporary effects on the growth rate, unlike the permanent effects implied by the Harrod-Domar model.⁹, ¹⁰ While the Harrod-Domar model excels in simple short-run investment-gap analysis, the Solow-Swan model provides a more comprehensive framework for understanding long-term Economic growth and cross-country convergence.⁸

FAQs

What is the main idea behind the Harrod-Domar model?

The central idea of the Harrod-Domar model is that Economic growth depends on the level of Savings rate and the efficiency with which capital is used, represented by the Capital-output ratio. Essentially, more savings lead to more investment, which expands productive capacity and drives growth.⁶, ⁷

Why is the Harrod-Domar model important in development economics?

The Harrod-Domar model was historically significant in Development economics because it provided a clear framework for developing countries to understand the importance of Capital accumulation for growth. It helped policymakers estimate the investment needed to achieve specific growth targets and often underpinned arguments for foreign aid to supplement domestic savings.⁴, ⁵

What are the main limitations of the Harrod-Domar model?

Key limitations include its assumptions of a fixed Capital-output ratio and Full employment, which are unrealistic in dynamic economies. It also largely overlooks other crucial drivers of Economic growth, such as Technological advancements, human capital, and institutional factors.¹, ², ³