Harrod-Domar model
Encyclopedia
The Harrod–Domar model is used in development economics
to explain an economy's growth rate in terms of the level of saving and productivity of capital
. It suggests that there is no natural reason for an economy to have balanced growth. The model was developed independently by Sir Roy F. Harrod in 1939 and Evsey Domar
in 1946. The Harrod–Domar model was the precursor to the exogenous growth model
.
Derivation of output growth rate:
An alternative (and, perhaps, simpler) derivation is as follows, with dots (for example,
) denoting percentage growth rates.
First, assumptions (1)–(3) imply that output and capital are linearly related (for readers with an economics background, this proportionality implies a capital-elasticity of output
equal to unity). These assumptions thus generate equal growth rates between the two variables. That is,
Since the marginal product of capital, c, is a constant, we have
Next, with assumptions (4) and (5), we can find capital's growth rate as,
In summation, the savings rate times the marginal product of capital minus the depreciation rate equals the output growth rate. Increasing the savings rate, increasing the marginal product of capital, or decreasing the depreciation rate will increase the growth rate of output; these are the means to achieve growth in the Harrod–Domar model.
Although the Harrod–Domar model was initially created to help analyse the business cycle
, it was later adapted to explain economic growth. Its implications were that growth depends on the quantity of labour and capital; more investment leads to capital accumulation, which generates economic growth. The model also had implications for less economically developed countries
; labour is in plentiful supply in these countries but physical capital is not, slowing economic progress. LEDCs do not have sufficient average incomes to enable high rates of saving, and therefore accumulation of the capital stock through investment is low.
The model implies that economic growth depends on policies to increase investment, by increasing saving, and using that investment more efficiently through technological advances.
The model concludes that an economy does not find full employment and stable growth rates naturally, similar to the Keynesian beliefs.
of labour and capital is fixed, and that they are used in equal proportions. The model explains economic boom and bust
by the assumption that investor
s are only influenced by output (known as the accelerator principle); this is now widely believed to be false.
In terms of development, critics claim that the model sees economic growth and development
as the same; in reality, economic growth is only a subset of development. Another criticism is that the model implies poor countries should borrow to finance investment in capital to trigger economic growth; however, history has shown that this often causes repayment problems later.
The endogenity of savings:
Perhaps the most important parameter in the Harrod–Domar model is the rate of savings. Can it be treated as a parameter that can be manipulated easily by policy? That depends on how much control the policy maker has over the economy. In fact, there are several reasons to believe that the rate of savings may itself be influenced by the overall level of per capita income in the society , not to mention the distribution of that income among the population.
Development economics
Development Economics is a branch of economics which deals with economic aspects of the development process in low-income countries. Its focus is not only on methods of promoting economic growth and structural change but also on improving the potential for the mass of the population, for example,...
to explain an economy's growth rate in terms of the level of saving and productivity of capital
Capital (economics)
In economics, capital, capital goods, or real capital refers to already-produced durable goods used in production of goods or services. The capital goods are not significantly consumed, though they may depreciate in the production process...
. It suggests that there is no natural reason for an economy to have balanced growth. The model was developed independently by Sir Roy F. Harrod in 1939 and Evsey Domar
Evsey Domar
Evsey David Domar was a Russian American economist, famous as co-author of the Harrod–Domar model.- Life :Evsey Domar was born on April 16, 1914 in the Polish city of Łódź, which belonged to Russia at that time...
in 1946. The Harrod–Domar model was the precursor to the exogenous growth model
Exogenous growth model
The neoclassical growth model, also known as the Solow–Swan growth model or exogenous growth model, is a class of economic models of long-run economic growth set within the framework of neoclassical economics...
.
Mathematical formalism
Let Y represent output, which equals income, and let K equal the capital stock. S is total saving, s is the savings rate, and I is investment. δ stands for the rate of depreciation of the capital stock. The Harrod–Domar model makes the following a priori assumptions:  |
1: Output is a function of capital stock |
 |
2: The marginal product of capital is constant; the production function exhibits constant returns to scale. This implies capital's marginal and average products are equal. |
 |
3: Capital is necessary for output. |
 |
4: The product of the savings rate and output equals saving, which equals investment |
 |
5: The change in the capital stock equals investment less the depreciation of the capital stock |
Derivation of output growth rate:
An alternative (and, perhaps, simpler) derivation is as follows, with dots (for example,
) denoting percentage growth rates.First, assumptions (1)–(3) imply that output and capital are linearly related (for readers with an economics background, this proportionality implies a capital-elasticity of output
Output elasticity
In economics, output elasticity is the percentage change of output divided by the percentage change of an input. It is sometimes called partial output elasticity to clarify that it refers to the change of only one input....
equal to unity). These assumptions thus generate equal growth rates between the two variables. That is,
Since the marginal product of capital, c, is a constant, we have
Next, with assumptions (4) and (5), we can find capital's growth rate as,
In summation, the savings rate times the marginal product of capital minus the depreciation rate equals the output growth rate. Increasing the savings rate, increasing the marginal product of capital, or decreasing the depreciation rate will increase the growth rate of output; these are the means to achieve growth in the Harrod–Domar model.
Although the Harrod–Domar model was initially created to help analyse the business cycle
Business cycle
The term business cycle refers to economy-wide fluctuations in production or economic activity over several months or years...
, it was later adapted to explain economic growth. Its implications were that growth depends on the quantity of labour and capital; more investment leads to capital accumulation, which generates economic growth. The model also had implications for less economically developed countries
Least Developed Countries
Least developed country is the name given to a country which, according to the United Nations, exhibits the lowest indicators of socioeconomic development, with the lowest Human Development Index ratings of all countries in the world...
; labour is in plentiful supply in these countries but physical capital is not, slowing economic progress. LEDCs do not have sufficient average incomes to enable high rates of saving, and therefore accumulation of the capital stock through investment is low.
The model implies that economic growth depends on policies to increase investment, by increasing saving, and using that investment more efficiently through technological advances.
The model concludes that an economy does not find full employment and stable growth rates naturally, similar to the Keynesian beliefs.
Criticisms of the model
The main criticism of the model is the level of assumption, one being that there is no reason for growth to be sufficient to maintain full employment; this is based on the belief that the relative pricePrice
-Definition:In ordinary usage, price is the quantity of payment or compensation given by one party to another in return for goods or services.In modern economies, prices are generally expressed in units of some form of currency...
of labour and capital is fixed, and that they are used in equal proportions. The model explains economic boom and bust
Boom and bust
A credit boom-bust cycle is an episode characterized by a sustained increase in several economics indicators followed by a sharp and rapid contraction. Commonly the boom is driven by a rapid expansion of credit to the private sector accompanied with rising prices of commodities and stock market index...
by the assumption that investor
Investor
An investor is a party that makes an investment into one or more categories of assets --- equity, debt securities, real estate, currency, commodity, derivatives such as put and call options, etc...
s are only influenced by output (known as the accelerator principle); this is now widely believed to be false.
In terms of development, critics claim that the model sees economic growth and development
Economic development
Economic development generally refers to the sustained, concerted actions of policymakers and communities that promote the standard of living and economic health of a specific area...
as the same; in reality, economic growth is only a subset of development. Another criticism is that the model implies poor countries should borrow to finance investment in capital to trigger economic growth; however, history has shown that this often causes repayment problems later.
The endogenity of savings:
Perhaps the most important parameter in the Harrod–Domar model is the rate of savings. Can it be treated as a parameter that can be manipulated easily by policy? That depends on how much control the policy maker has over the economy. In fact, there are several reasons to believe that the rate of savings may itself be influenced by the overall level of per capita income in the society , not to mention the distribution of that income among the population.
See also
- Solow growth model (neo-classical growth model)Exogenous growth modelThe neoclassical growth model, also known as the Solow–Swan growth model or exogenous growth model, is a class of economic models of long-run economic growth set within the framework of neoclassical economics...
- Economic growthEconomic growthIn economics, economic growth is defined as the increasing capacity of the economy to satisfy the wants of goods and services of the members of society. Economic growth is enabled by increases in productivity, which lowers the inputs for a given amount of output. Lowered costs increase demand...
- Mahalanobis modelMahalanobis modelThe Mahalanobis model is a model of economic development, created by Indian statistician Prasanta Chandra Mahalanobis in 1953. Mahalanobis became essentially the key economist of India's Second Five Year Plan, becoming subject to much of India's most dramatic economic debates.-The...
- Endogenous growth theoryEndogenous growth theoryEndogenous growth theory holds that economic growth is primarily the result of endogenous and not external force. In Endogenous growth theory investment in human capital, innovation and knowledge are significant contributors to economic growth. The theory also focus on positive externalities and...