# Harrod- Domar model

Another model which is in line with the Neo Classical theories of development is the Harrod Domar model. In this section we will learn about these models and their limitations from the standpoint of less developed economies.

The Harrod and Domar models are the result of their interest in working out the rate of income growth which would be necessary for a smooth and uninterrupted working of the economy. Both the models emphasize on the dual characteristics of investment. Firstly it creates income (demand effect of investment) and secondly it increases the capital stock (supply effect of investment), thereby increasing the productive capacity of the economy. At full employment equilibrium, the real income in an economy expands at the same rate as the productive capacity of the capital stock. Any divergence leads to excess or idle capacity, forcing entrepreneurs to curtail their investment expenditure.

This further leads to lowering of income and employment and moving the economy off the equilibrium path of steady growth. Hence to maintain full employment, net investment should expand continuously. This further requires growth in real income at a rate sufficient enough to ensure full capacity use of growing stock of capital.
This required rate of income growth is called ‘the full capacity growth rate’ or the warranted rate of growth.

### Assumptions of Harrod Domar models

The Harrod and Domar models are based on the following assumptions:

1. Initial full employment equilibrium level of income
2. Absence of government interference
3. Closed economy and absence of foreign trade
4. No lags in adjustments between investment and creation of productive capacity
5. The average propensity to save is equal to marginal propensity to save
6. Marginal propensity to save remains constant
7. The capital coefficient or the ratio of capital stock to income is assumed to be fixed.
8. Capital goods are assumed to possess infinite life and there is absence of depreciation of the same
9. Savings and investment relate to income of the same year.
10. General price level is constant ie. The money income and real income are the same.
11. There are no changes in interest rates
12. There is a fixed proportion of capital and labour in the production process
13. Fixed and circulating capital both together constitute the capital
14. There is only one type of product

### The Domar Model

Domar’s model is a result of his probe into the question that … At what rate investment should increase so as to make increase in income equal to increase in productive capacity, so that full employment is achieved.

Let I = annual rate of investment

s = productive capacity per dollar of newly created capital

Therefore, productive capacity of I dollar invested = I.s
It is also true that the new investment would be at the expense of old. The new investment will compete with the old for labour and other factors of production. Hence the output of old plants will be curtailed and the increase in productive capacity or annual output of the economy will be less than I.s.

Let the net potential increase in output of the economy be

$I\sigma$

Where

$\sigma =∆Y/I$

……………… (1)
(ratio of annual increase in income to annual rate of investment)

According to Domar this is the increase in output which the economy can produce and it is the supply side of our system. Domar’s explanation of the demand side Domar explains the demand side by the  eynesian multiplier.
Let the annual increase in income be =

$∆Y$

Annual increase in investment =

$∆I$

Propensity to save (

$\alpha$

) =

$∆S/∆I$

According to Keynes, increase in income will be multiplier times increase in investment.

$∆Y=∆I\left(1/\alpha \right)$

…………………………. (2)

Equilibrium: To maintain full employment level of income, aggregate demand should be equal to aggregate supply.

From Equations (1) and (2) undefined

Solving the equation,

$\alpha I\alpha =∆I$$∆I/I=\alpha \sigma$

The above equation shows that to maintain full employment, the growth rate of investment should be equal to the Marginal Propensity to Save times productivity of capital. If investment grows at this rate then there would be a steady growth of the economy at full employment.

### The Harrod Model

The Harrod Model is based on three distinct rates of growth: the actual growth rate, the warranted growth rate and the natural growth rate. Let us see each one of these in detail.
I) The Actual Growth Rate: Basic equation of Harrod model is GC = s ………… (1)

Where G = rate of growth of output in a given period of time (

$∆Y/Y$

)
C = net addition to capital or the ratio of investment to increase in income (

$I/∆Y$

)
s = average propensity to save (S/Y)
Substituting these equations in (1),

or

or

I = S

This restates that ex-post savings equals ex-post investment.

#### II) The Warranted Rate of Growth:

This growth rate is related to behavior of businessmen. At this rate of growth, the demand is high enough for businessmen to sell what they have produced and continue to produce at the same rate of growth. Given the propensity to save, this is the path on which the supply and demand for goods and services will remain in equilibrium.

Mathematically,
GwCr = s ………… (2)

Gw = warranted rate of growth or full capacity rate of growth of income which will fully utilize the growing stock of capital (

$∆$

Y/Y)

Cr = Amount of capital needed to maintain the warranted rate of growth or the required capital output ratio (I/

$∆$

Y)
s = average propensity to save (S/Y)
From Eq. (2),
Gw = s/Cr
This equation therefore states that if the economy has to grow at a steady rate of growth that will fully utilize its capacity, income must grow at the rate of s/Cr per year.

#### III) Long run disequilibrium:

For full employment, the actual rate of growth must be equal to the warranted rate of growth (G=Gw) and the actual capital goods (C) must be equal to the required capital goods for steady growth (Cr). If G and Gw are not equal then there would be a disequilibrium in the economy. If G exceeds Gw, then C will be less than Cr.

In such circumstances there would be insufficiency of goods and equipments leading to secular inflation as the actual income grows at a faster rate than that allowed by productive capacity of the economy. There would be further deficiency of capital goods and the aggregate production would fall short of aggregate demand leading to chronic inflation.
On the other hand if G is less than Gw, then C is greater than Cr.
Such situation leads to secular depression because, actual income grows more slowly than required by the productive capacity of the economy leading to excess of capital goods and the aggregate demand falls short of aggregate supply. This results in fall in output, employment and income and there would be chronic depression.

#### IV) The Natural Rate of Growth:

The natural rate of growth is one that the population and technological improvements allow. It is the rate of increase in output at full employment as determined by a growing
population and the rate of technological progress.
GnCr = s

#### V) Divergence of G, Gw and Gn:

For full employment Gn=Gw=G.
However if there are divergences from this state then secular inflation or secular stagnation may occur. If G>Gw, investment increases faster than savings and income rises faster than Gw. On the other hand if  G<Gw, saving increases faster than investment and rise of income is less than Gw. If Gw>Gn, secular stagnation will develop.

In such situation Gw is also greater than G. When Gw exceeds Gn, C>Cr and there is excess of capital goods due to shortage of labour. The shortage of labour keeps the rate of increase in output to a level less than Gw. There is excess capacity and this dampens investment, output, employment and income. The economy will be gripped by chronic
depression and in such situations, saving is a vice.

In another situation where Gw<Gn, Gw is also less than G and there is a tendency to develop secular inflation in the economy. When Gw<Gn, C<Cr. There is a shortage of capital goods and labour is in abundance. Profits are high and businessmen have a tendency to increase their capital stock. This will lead to secular inflation and in such a situation, saving is a virtue as it allows Gw to increase.

### Limitations of Harrod and Domar Models

from the Standpoint of Less Developed Countries

The Harrod Domar models are more relevant to capitalist economies and cannot be applied in less developed countries due to the following reasons:

1. Different Conditions: Harrod Domar models evolved with the intention to prevent advanced economies from the possible effects of secular stagnation and hence cannot be used to guide industrialization programmes in less developed countries.
2. Saving Ratio: Harrod and Domar growth models are characterized by high saving ratio and high capital output ratio whereas people in less developed countries lead a subsistence life and not many are in a position to save.
3. Capital-output ratio: According to Hrischman, the predictive and operational value of models based on propensity to save and capital output ratio is low and hence would be far less useful in underdeveloped economies.
4. Structural Unemployment: When the population grows faster than accumulation of capital as is the case in less developed countries, structural unemployment arises due to lack of capital equipments.
Harrod Domar model is more suited to solve the problem of Keynesian unemployment arising out of deficiency of effective demand than that of structural unemployment which is more likely to be the case of less developed countries
5. Disguised Unemployment: These models start with a full employment level of income which is nonexistent in underdeveloped countries. These countries are marred by the problem of disguised unemployment, the solution to which cannot be found using Harrod Domar models.
6. Government Intervention: Harrod Domar models assume the absence of government intervention which is not the case in less developed countries. In such countries the state plays an important role in starting large industries and in regulating and directing the private enterprise.
7. Foreign Aid and Trade: Harrod Domar model assumes a closed economy whereas less developed countries are rather open economies where foreign trade plays an important role in economic development.
8. Price Changes: These models assume constant prices whereas in less developed countries, price change is inevitable with development.
9. Institutional Changes: Institutional factors are assumed to be given in these models whereas as far as less developed countries are concerned, economic development is not possible without institutional changes. Due to the above mentioned reasons, Harrod Domar models have lesser suitability to developing and less developed countries. As an alternative explanation for these countries, Solow model was developed.