Under the theories of economic growth, economists have explained economic factors and their impact on economic growth.

The evolution of economic growth theories can be drawn back from Adam Smith’s book, Wealth of Nation. In his book, he emphasized a view that the growth of an economy depends on division of labor.

“The most necessary condition for the growth of an economy is that the demand created due to newly generated income should be sufficient enough, so that the output produced by the new investment (increase in capital) should be fully absorbed”-Harrod-Domar theory.

After that, the view presented by Smith was further succeeded by classical economists, such as Ricardo, Malthus, and Mill. The theory developed by these economists is known as classical theory of economic growth.

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Further, in late 19^{th} and 20^{th} centuries, Karl Marx presented a theory called theory of historical growth and Schumpeter developed a growth theory of technological innovations. Finally, in late 1930s, R. F. Harrod and E. Domar presented more relevant theory of economic growth popularly known as Harrod-Domar theory. Later, neo-classical theory of economic growth was also introduced. Harrod-Domar theory and neo-classical theory explain modern growth behavior more clearly by analyzing different economic aspects.

**Harrod-Domar Theory****: **

Harrod-Domar theory is considered as the extension of Keynes’ short-term analysis of full employment and income theory. The Harrod-Domar growth model provides a long-term theory of output. The economists started paying their attention toward economic stability after the Great Depression of 1930s and economic ruin caused by World War II. Harrod and Domar have provided a model that focuses on the requirements necessary for steady economic growth. According to them, capital accumulation constitutes a major factor for the growth of an economy.

They also emphasized that capital accumulation not only generates income, but also increases the production capacity of the economy. For instance, if a construction plant is established, it would generate income for suppliers of different materials, such as cement, bricks, steel, and machinery with simultaneous increase in capital and production capacity of the economy.

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The newly generated income from capital accumulation produces demand for goods and services. According to Harrod-Domar theory, the most necessary condition for the growth of an economy is that the demand created due to newly generated income should be sufficient enough, so that the output produced by the new investment (increase in capital) should be fully absorbed.

If the output is not fully absorbed, there would be excess or idle production capacity. This condition should be satisfied consecutively to maintain full employment level and achieve steady economic growth in the long term.

**Following are the main assumptions of Harrod-Domar model: **

**(a) Constant Capital-Output Ratio: **

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Assumes that the relationship between capital and output always remains the same.

**According to this assumption, the national output (which is equal to national income) is directly proportional to capital stock, which is expressed as follows: **

Y = Kk, (k>0)

Where, Y = national output

K = total capital stock

k= output/capital ratio (constant)

As Harrod-Domar model has assumed that the output/capital ratio is constant, therefore, any type of increase in the national output would result in the k time increase in capital stock, which is as follows:

∆Y = k ∆ K

Therefore the increase in the growth of national output per unit time is equal to the increase in the growth of capital stock per unit time. In case the economy is in equilibrium and the capital stock is utilized completely, then the capital/output ratio (k) can be easily determined. After that, the extra capital required to produce the extra output can also be obtained. The capital stock and net investment (I) are equal to each other.

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**Therefore, the change in national output can be represented as follows: **

∆Y = kI

**(b) Constant Saving-Income Ratio: **

Assumes that society saves a constant proportion of national income.

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**Therefore, saving is a function of income, and saving function can be written as follows: **

S = sY, (s > 0)

Where, S = saving per unit time

s = constant propensity to save

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Y = national income

**At equilibrium, savings get equal to investment, which is as follows: **

S = I = sY

**On the basis of these assumptions, Harrod-Domar has determined the growth rate, which is as follows: **

∆Y_{t} = kl_{t}

**In such case, ∆Y _{t} can be calculated with the help of following formula: **

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∆Y_{t} = Y_{t} – Y_{t-1}

Or

Y_{t} – Y_{t-1} = kI_{t}

Where, Y_{t} = income in time period t

Y_{t-1} = income in lime period t -1

According to the assumption of Harrod-Domar model, at equilibrium in time period t:

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I_{t} = S_{t} = sY_{t}

**As I _{t} = sY_{t}, therefore, we can substitute sY_{t} in place of I_{t} while calculating the income in time period t, which is represented as follows: **

Y_{t} – Y_{t-1} = k*sY_{t}

**The warranted growth rate can be calculated as follows: **

Gw = Y_{t} – Y_{t-1}/Y_{t} = k. s

Or

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Gw = ∆Y/Y_{t} = k. s

As the preceding equation of warranted growth rate shows that the growth rate is equivalent to the output/capital ratio (k) times the constant propensity to save. The growth rate, ∆Y/Y, is related to the equilibrium condition where I = S; therefore, the growth rate in such condition can also be regarded as equilibrium growth rate.

The equilibrium growth rate shows the capacity of utilizing capital stock. Warranted growth rate refers to the growth rate at which the amount of production is accurate neither too much nor too less.

One more growth rate given by Harrod-Domar model was target growth rate, which takes place due to increase in marginal propensity to save and investment or output/capital ratio. The increase in marginal propensity to save would result in the increase of saving, which further leads to an increase in investment.

Consequently, the income and production capacity of a nation also increase, which further increases the output of the nation. The increase in the production capacity in a particular period increases the income for coming years.

The increase in income leads to increase in saving and investment, and higher incomes in succeeding years. According to the principle of acceleration, the investment increases at a faster rate.

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In aforementioned discussion, we have explained the Harrod-Domar model of economic growth with respect to capital accumulation. However, another important aspect that has been discussed in the model is the employment of labor.

**The assumptions of the employment of labor aspect as per the Harrod-Domar model are as follows: **

a. Considers that labor and capital are complementary to each other not substitutes

b. Regards capital/output ratio as constant

According to such assumptions, along with the capital/output ratio, the economic growth would occur when the potential labor force IS not completely utilized. This denotes that the potential labor supply restricts economic growth at full employment condition.

Therefore, economic growth would occur when the increase in labor exceeds the full employment condition. In addition, the actual growth rate becomes equal to warranted growth rate only when the warranted growth rate becomes equal to growth rate of labor force. In case the increase in the growth rate of labor is slow, then the growth can only be normalized with the help of labor-saving technology.

In such a condition, the growth in the long term is dependent on the growth rate of labor force (∆L/L) and labor-saving technology. Therefore, maximum growth rate in the long run would be equal to ∆L/L plus m, which is the rate of substitution of capital in place of labor.

**This growth rate is termed as the natural growth rate (G _{n}) that can be calculated with the help of the following formula: **

G_{n} = ∆L/L + m

The Harrod-Domar model provides more relevant theory of economic growth.

**However, the model is not free from limitations. Some of the shortcomings of the model are as follows: **

**(c) Impractical Assumptions: **

Refer to one of the major shortcomings of the model. The Harrod-Domar model involves assumptions that cannot be applied in practical situations. According to the Harrod-Domar Model, savings becomes equal to investment when warranted and actual growth rate are equal to each other.

**This can be possible only under certain conditions, which are as follows: **

i. Keeping marginal propensity to consume at constant

ii. Assuming output/capital ratio at constant

iii. Assuming that the technology for production is given

iv. Keeping economy at equilibrium initially

v. Considering government expenditure and foreign trade negligible

vi. Assuming that there are no adjustment gaps between demand and supply as well as investment and saving

However, these conditions cannot always be fulfilled; therefore, the warranted growth may not be equal to actual growth rate always. This makes the model unrealistic.

**(d) Razor-Edge Model: **

Refers to another name of the Harrod-Domar model. The economic factors that are used in the Harrod-Domar model are capital/output ratio, marginal propensity to consume, growth rate of labor force, and improvement in labor-saving technology.

These factors are derived independently from the model. Therefore, the equilibrium growth rate concept according to this model cannot be confirmed in long-run. Any deviation in these parameters can affect the equilibrium condition of an economy. Therefore, the model is sometimes referred as the razor-edge model.

**Neo-Classical Theory****: **

The collective work of economists Tobin, Swan, Solow, Meade, Phelps and Johnson is termed as neo-classical theory of economic growth. The assumptions adopted by these theorists in the neo-classical theory are based on the views and norms given by neo- classical economists, such as Alfred Marshall, Wicksell, and Pigou.

**Following are some of the assumptions of the neo-classical theory: **

a. Assuming perfect competition in commodity as well as factor markets

b. Making factor payments equal to the marginal revenue productivity

c. Maintaining a variable ratio between capital and output

d. Assuming full employment condition

**The assumptions of the neo-classical theory would be clearer by comparing them with the assumptions of the Harrod-Domar model, which is shown in Table-1: **

According to the neo-classical theory, the economic growth is determined with the help of certain factors, such as stock of capital, supply of labor, and technological development over time.

**The production function for the neo-classical theory can be expressed as follows: **

Y = F (K, L, T)

Where, Y = National output

K = Capital stock

L = Labor supply

T = Scale of technological development

According to the assumption of constant return to scale, increase in national output (∆Y) would be equal to the marginal productivity (MP) times AK and ∆L. Therefore,

∆Y = ∆K. MP_{k} + ∆L. MP_{l}

Where, MP_{k} = marginal physical product of capital

MP_{l} = marginal physical product of capital

**When the equation of increase in national output is divided by Y, then we get the following equation: **

∆Y/Y = ∆K (MP_{k}/Y) + ∆L (MP_{l}/Y)

**The first term in the R.H.S is multiplied by K/K and second term by L/L; the resultant equation would be as follows: **

∆Y/Y = ∆K/Y (K. MP_{k}/Y) + ∆L/Y (L.MP_{l}/Y)

The K. MP_{k} and L. MP represent the total stake of capital and labor in the national output, whereas K/Y* MP_{k} and L/Y* MP_{l} represent the relative stake of capital and labor in the national output. Therefore,

(K.MPk/Y) + (L.MP_{l}/Y) = 1

Let us assume that (K.MP_{k}/Y) = b, then

(L.MP_{l}/Y) = 1-b

**Putting the value of (K.MP _{k}/Y) and (L.MP_{l}/Y) in the following equation, we get: **

∆Y/Y = ∆K/Y (K.MP_{k}/Y) + ∆L/Y (L.MP_{l}/Y)

∆Y/Y = b ∆K/K + (1 – b) ∆T/T

In the preceding equation, the values of b and 1- b represents the elasticity of output with reference to the capital and labor respectively.

**Therefore, according to the neo-classical theory, the economic growth rate is represented as follows: **

Economic growth (at a given level of technology) = Elasticity of output with reference to the increase in capital stock + Elasticity of output with reference to the increase in labor

**However, in case of technological change, the change in national output can be represented as follows: **

∆Y/Y = b ∆K/K + (1 – b) ∆T/T

**Therefore, in case of technological development, the economic growth rate can be represented as follows: **

Economic growth (at a given level of technology) = Elasticity of output with reference to the increase in capital stock + Elasticity of output with reference to the increase in technological progress.

**Some of the limitations of the neo-classical theory are as follows: **

a. Regards technology as a constant factor, which is not true. This is due to the fact that a technology keeps advancing with time

b. Considers factor prices as the major factor for determining economic growth. However, the adjustments of factor prices can be interrupted with a change in liquidity.

c. Does not include the investment functions; therefore, the neo-classical theory has failed to describe the expectations of entrepreneurs and capital accumulation by them.

d. Considers capital assets as homogeneous, which is not real.