Harrod-Domar Equation Calculator
This calculator determines the economic growth rate (g) based on the Harrod-Domar model. This simple model highlights the relationship between savings, investment efficiency, and economic growth.
Enter the national Savings Rate (s) and the Capital-Output Ratio (k). Ensure you use consistent assumptions for your inputs.
Enter Economic Variables
Understanding the Harrod-Domar Model & Formula
What is the Harrod-Domar Model?
The Harrod-Domar model is one of the earliest post-Keynesian models of economic growth. It suggests that an economy's rate of growth depends directly on the level of national saving (s) and inversely on the productivity of capital, known as the capital-output ratio (k). It's a foundational concept in development economics.
The Harrod-Domar Growth Formula
The core formula is elegantly simple:
g = s / k
Where:
- g = Economic Growth Rate: The percentage increase in Gross Domestic Product (GDP).
- s = Savings Rate: The proportion of national income that is saved rather than consumed. It's assumed that all savings are invested.
- k = Capital-Output Ratio: The amount of capital required to produce one unit of output. A lower 'k' means capital is more productive.
Key Assumptions and Limitations
The model's simplicity comes from its strong assumptions, which are also its main limitations in the real world:
- It assumes the savings rate and capital-output ratio are fixed and constant.
- There is no allowance for technological progress, which is a major driver of modern growth.
- It assumes a surplus of labor, so growth is never constrained by labor shortages.
- It implies that growth is the only goal, ignoring factors like income distribution or environmental impact.
Despite these limitations, it is a powerful educational tool for understanding the mechanics of capital accumulation.
10 Examples of the Harrod-Domar Model in Action
Click on an example to see how different scenarios affect the growth rate.
Example 1: Classic Developing Nation
Scenario: A developing country with a moderate savings rate and standard capital efficiency.
1. Known Values: Savings Rate (s) = 15%, Capital-Output Ratio (k) = 3.
2. Formula: g = s / k
3. Calculation: g = 15 / 3 = 5
4. Result: The predicted economic growth rate is 5%. This is a common baseline example.
Example 2: High-Saving "Asian Tiger" Economy
Scenario: An economy known for its extremely high national savings, fueling rapid industrialization.
1. Known Values: Savings Rate (s) = 40%, Capital-Output Ratio (k) = 4.
2. Formula: g = s / k
3. Calculation: g = 40 / 4 = 10
4. Result: The predicted growth rate is a very high 10%, showing how a high savings rate can drive massive growth.
Example 3: Inefficient Investment
Scenario: A country saves a decent amount, but its investments are inefficient (e.g., due to corruption or poor infrastructure).
1. Known Values: Savings Rate (s) = 20%, Capital-Output Ratio (k) = 5.
2. Formula: g = s / k
3. Calculation: g = 20 / 5 = 4
4. Result: The growth rate is only 4%. This shows that simply saving is not enough; capital must also be used productively.
Example 4: Highly Efficient Technology Sector
Scenario: An advanced economy where technology makes capital extremely productive.
1. Known Values: Savings Rate (s) = 18%, Capital-Output Ratio (k) = 2.5.
2. Formula: g = s / k
3. Calculation: g = 18 / 2.5 = 7.2
4. Result: A growth rate of 7.2%. A low 'k' can turn a modest savings rate into very strong growth.
Example 5: Economy in Recession (Dissaving)
Scenario: A country is consuming more than its national income, possibly by taking on foreign debt or selling assets.
1. Known Values: Savings Rate (s) = -5%, Capital-Output Ratio (k) = 4.
2. Formula: g = s / k
3. Calculation: g = -5 / 4 = -1.25
4. Result: The economy is predicted to shrink by -1.25%.
Example 6: Stagnant, Low-Trust Economy
Scenario: An economy where people do not save much and capital is used very inefficiently.
1. Known Values: Savings Rate (s) = 6%, Capital-Output Ratio (k) = 6.
2. Formula: g = s / k
3. Calculation: g = 6 / 6 = 1
4. Result: The growth rate is a minimal 1%, barely keeping up with population growth in many cases.
Example 7: Zero Savings (Subsistence Economy)
Scenario: A very poor economy where all income is consumed just to survive, leaving no room for savings.
1. Known Values: Savings Rate (s) = 0%, Capital-Output Ratio (k) = 3.
2. Formula: g = s / k
3. Calculation: g = 0 / 3 = 0
4. Result: The growth rate is 0%. Without savings and investment, the economy cannot grow.
Example 8: Policy Goal: Target Growth Rate
Scenario: A government wants to achieve a 7% growth rate. They know their capital-output ratio is 4. What savings rate do they need to encourage?
1. Known Values: Target Growth (g) = 7%, Capital-Output Ratio (k) = 4.
2. Formula (rearranged): s = g * k
3. Calculation: s = 7 * 4 = 28
4. Result: The country would need to achieve a national savings rate of 28%.
Example 9: Post-War Reconstruction
Scenario: A country after a conflict receives foreign aid, boosting its savings/investment rate. Capital is very productive as it rebuilds basic, essential infrastructure.
1. Known Values: Savings Rate (s) = 25% (includes aid), Capital-Output Ratio (k) = 2.
2. Formula: g = s / k
3. Calculation: g = 25 / 2 = 12.5
4. Result: A massive growth rate of 12.5% is predicted, typical of post-war recovery periods.
Example 10: Mature, Developed Economy
Scenario: A stable, wealthy country with a moderate savings rate and a high capital base, meaning new investments are less impactful.
1. Known Values: Savings Rate (s) = 18%, Capital-Output Ratio (k) = 6.
2. Formula: g = s / k
3. Calculation: g = 18 / 6 = 3
4. Result: A modest but stable growth rate of 3%.
Frequently Asked Questions (FAQs)
1. What is the core idea of the Harrod-Domar model?
The core idea is that economic growth is determined by two key factors: how much a nation saves (the savings rate 's') and how efficiently that saving is converted into output (the capital-output ratio 'k'). More savings and more efficient investment lead to higher growth.
2. Why is the Savings Rate (s) important?
In this model, savings are assumed to equal investment. Therefore, the savings rate directly determines the amount of new capital (machinery, infrastructure, etc.) being added to the economy each year.
3. What does a high or low Capital-Output Ratio (k) mean?
A low 'k' is good; it means capital is highly productive (e.g., k=2 means $2 of capital generates $1 of output per year). A high 'k' is bad; it means capital is inefficient and a lot of investment is needed for a small return (e.g., k=6 means $6 of capital is needed for $1 of output).
4. Is the Harrod-Domar model accurate for real-world predictions?
No, it is not considered accurate for modern forecasting. Its assumptions are too rigid. It famously ignores technological progress, which is a primary driver of long-term growth. It is best used as a simplified educational tool to understand the basic mechanics of capital accumulation.
5. What is the "knife-edge" problem associated with this model?
The "knife-edge" problem refers to the model's instability. It implies that if the actual growth rate differs even slightly from the "warranted growth rate" (the rate that keeps capital fully utilized), the economy will spiral into ever-increasing unemployment or inflation, which is not observed in reality.
6. Can I enter a negative savings rate?
Yes. A negative savings rate ('dissaving') means a country is consuming more than it produces, often by taking on debt. The calculator will correctly show a negative growth rate (economic decline) in this scenario.
7. Why can't the Capital-Output Ratio be zero or negative?
A 'k' of zero would imply you can generate output with no capital, which is impossible. A negative 'k' is economically meaningless. Therefore, the calculator requires a positive number for 'k'.
8. How can a country improve its growth rate according to this model?
According to the model, there are two ways: 1) Increase the national savings rate (e.g., through tax incentives for saving). 2) Decrease the capital-output ratio (e.g., by improving technology, reducing corruption, and investing in more productive sectors).
9. Does this model consider population growth?
Not directly. The calculated growth rate 'g' is for total GDP. To find the growth in GDP per capita (a better measure of living standards), you would need to subtract the population growth rate from 'g'. For example, if g=5% and population grows at 2%, GDP per capita grows at approximately 3%.
10. What replaced the Harrod-Domar model?
The Solow-Swan model became the dominant neoclassical growth model. It improved upon Harrod-Domar by incorporating technological progress, diminishing returns to capital, and allowing for substitution between capital and labor, making it more stable and realistic.
