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Harrod Domar model, assumptions of Harrod Domar model, it's working and limitations of Harrod Domar model

Harrod domar model is an economic growth model, the model suggest that economic growth rates depend upon two things savings and capital output ratio. Higher savings enables higher investment thus higher growth rate , while lower-output ratio means Investment is more efficient thus the growth rate will be higher.
growth rate (g) α level of savings 
growth rate (g) α 1/capital output ratio(k)

Assumtions of the Harrod Model- 

1. Savings leads to investment S= I
2. Investment leads to change in capital stocks I= ΔK
3. Constant capital output ratio (r) = K/Y.
4. There is no government intervention it the functioning of the economy.
5. A full- employment level of income already exist.
6. There are no lags in adjustment of variables.
7. Average propensity to save (aps) equals to marginal propensity      to save (mps) that means absolute change equals to relative change.

Harrod model is depends upon three growth rates 

a) Actual growth rates (G).
b) Wwarranted growth rates (Gw).
c) Natural growth rates(Gn).

a) Actual growth rates (G). 

It is determined by actual rate of savings and investment in the country ,in other words it can be defined as the ratio of change in income to the change in total income. denoted by G = ΔY/Y.
Relationship between the actual growth rate and and it's determinants is given by 
GC = s ..........(1)
C represents the capital-output ratio(K/Y)= ΔK/ΔY= I/ΔY
and s = S/Y
substituting these values in eq.(1)
ΔY/Y * I/ΔY = S/Y
I/Y = S/Y
I = S 

this relation explains that the condition for achieving the steady state growth.

                             b) Warranted growth 

It is the full capacity growth rate of income in an economy. It is also known as 'full employment growth rate' or 'potential growth rate'The equation for warranted growth can be stated as follows:
                    Gw Cr = s..................(2)
Cr is the minimum C to maintain Warranted growth rate and s is saving income ratio.

Equilibrium or steady state in warranted growth rate 

Eq.(2) states that if the economy is to advance at the steady rate of Gw that will fully utilize its capacity, income must grow at the rate of s/Cr per year, i.e., Gw = s/Cr. If income grows at the warranted rate, the capital stock of the economy will be fully utilized, the entrepreneurs will be willing to continue to invest the amount of saving generated at full potential income.

In brief, the warranted growth rate equation in the model implies that actual investment (ex-post investment) must be equal to expected investment (ex-ante investment), if an economy is to achieve stable growth. In such a situation, the following equalities will obtain: 
 G = Gw, and C = Cr
The economy would be in equilibrium. 

If these equalities do not obtain, the economy will be pushed into a state of disequilibrium if either of the following situations obtain. ) a) G > Gw or C < Cr 
b) G < Gw or C > Cr

a) State if disequilibrium when G > Gw

Under this situation, growth rate of income is higher than the growth rate of output. It means that the demand for output(because of higher lever of income) would exceed the supply of output (because of lower level of output). The economy would experience inflation.
Stated another way, if C<Cr, the actual amount of capital falls short of the requiredamount of capital. This will lead to the deficiency of capital. This, in turn, would adversely affect the goods to be produced. Fall in output would affect the goods to be produced. Fall in output would affect the goods to be produced. Fall in output
would result in scarcity of goods, and hence inflation.
Either of the two ways lead to inflation. And growth under inflationary situation is not stable.

b) State of disequilibrium when G < Gw

In this situation, the growth rate of income is less than the growth rate of output. There would be more goods for sale but the income would be insufficient to purchase these goods. There would be deficiency of demand and the economy would face the problem of over production. Similarly, when C>Cr, actual amount of capital would be larger than the required amount of capital for investment. The larger amount of capital available for investment. The larger amount of capital available for investment would lower the marginal efficiency of capital in the long-period. Secular decline in the marginal efficiency of capital would lead to depression and unemployment. Economic growth under the situation of depression cannot be stable. Harrod stated that once g departs from Gw, it will further depart away from equilibrium. He writed: “Around that line of advance which it adhered to would alone give satisfaction, centrifugal forced are at work, causing the system to depart further and further form the required line of advance.” Thus, equilibrium between G and Gw is a knife-edge equilibrium. It follows that one of the major tasks of public policy is to bring G and Gw together in order to mainatain long-run stability. 
For this purpose, Harrod introduces his third concept of natural rate of growth. 

3) Natural Growth-rate (Gn):
 It is the maximum growth rate that an economy can achieve with its available natural resources. The equation for the natural growth rate can be state as follows: Gn Cr = or ≠ s ................(3) It stated that the natural growth rate is determined by macro variables like population, technology, natural resources and capital equipment. These factors, place a ceiling beyond which expansion of output is not possible. 

Interaction between G, Gw and Gn 
Comparing Gw and Gn, it may be concluded that Gn may or may not be equal to Gw. In case Gn happen to be equal to Gw, the condition of steady growth would prevail. But such a possibility is remote one because a variety of factors (influencing Gn and Gw) come into play and make balance between these two growth-rated difficult. There exists a greater probability of inequality between Gn and Gw. It may take two terms: 

a) Gw>Gn 
b) Gn>Gw 
a) Gw>Gn: It Gw exceeds Gn, G would lie below Gn for most of the time. In this situation, there would be a tendency for cumulative recession. A downward trend would set in, resulting in unemployment and depression. However, downward trend cannot continue indefinitely. The reason is that lower limit to depression is set by the minimum consumption level. The consumption cannot fall below a minimum level. The minimum consumption requirements can be made possible by reducing the working capital. The entrepreneurs may not reduce fixed capital in the hope that future might entail bright prospects for investment. These two factors would gradually set the wheels of recovery in motion. The economy would experience upward trend. 
In this situation, G would also exceed Gw for most of the time, There would be a tendency for cumulative boom and full employment. Such a situation will create inflationary trend. To check this trend, savings should be encouraged, as these would ensure a high level of employment without inflationary pressures. 

Domar Model
               Assumptions of the Model 
The Domar model is based on the following assumption. 
1) Income is determined by investment through multiplier. For the sake of simplicity, saving-income ratio is assumed constant. 
2) Productive capacity is created by investment according to the potential social average investment productivity. For the sake of simplicity this is also assumed to be constant. 
3) Investment is induced by output growth together with entrepreneur confidence. 
4) Employment depends upon the 'utilisation ratio' expressed as the ratio between actual output and productive capacity. 
5) Past and present investment can greater productive capacity at a given ratio.
Statement of the Domar model 
it is based on the dual character of investment: one, investment increases productive capacity, and two, investment generated income. The two sides of investment provide solution for steady growth. The following symbols are used in DM. 
Yd = Level of national income or level of effective demand at full employment (demand side) 
Ys = Level of productive capacity or supply at full employment level (supply side) 
K = real capital 
I = net investment, which implies change in stock of real capital, i.e. ∆K d = marginal propensity to save, which is the reciprocal of multiplier i.e., (mpλ =1/multiplier) σ = productivity of capital We can make use of these notations to frame a set of equations that help formulate the DM. The demand side of investment can be represented by an equation as follows: Yd = I/d 
This equation explains two things as follows: 
i) The level of effective demand (Yd) is directly related to the level of investment(I). An increase in investment will result in an increase in effective demand, and vice versa. 
ii) The effective demand is inversely related to the marginal propensity to save (d). An increase in marginal propensity to save will decrease the level of effective demand and vice-versa. 
 Eq.(1) represents the demand side of investment. 
 The supply side of investment can be represented by an equation as follows: 
Y = σ k ....................(2) 
Eq.(2) explains that supply of output(Ys) at full employment depends upon two factors, ie.., productive capacity of capital(σ ) and the amount of real capital(K). A change in the supply of any of these will result in a corresponding change in the supply of output. For example, an increase in the productivity of capital will result in an increase in output, and vice-versa. 
Likewise, an increase in the amount of real capital will lead to an increase in output, and vice-versa. Equilibrium: 
In equilibrium, the demand and supply should balance. Therefore,
 Yd = Ys or I/d = σ K 
By cross multiplication,
 I = dσ K ..........................(3) 
 Eq.(3) explains the condition for steady growth. Steady growth is possible when: Investment equals the product of saving-income ratio, capital productivity and capital stock. From this the condition for maintaining the steady growth can be explained. For this we have to give increment to the demand and supply conditions presented above. The demand equation in its incremental form can be stated as follows: 
∆Yd = ∆I/d ........................(4) 
Increments have been shown in the level of effective demand and investment because they are variables, but increment has not been shown in d because it is constant in terms of the assumptions employed. The supply equation it its incremental form can be stated as follows: 
∆Ys = σ ∆K ........................(5)
 Eq.(5) explains that change in the supply of output (∆Ys) would be equal to the product of change in real capital (∆K), and the productivity of capital (σ ). The change in real capital is expressed as net investment. Therefore, ∆K represented investment(I). Substituting I in place of ∆K in eq.(5), we get. ∆Ys = σ I ........................(6) 
The equilibrium between eq.(4) and eq.(6) provides us the condition for maintaining the steady growth. In equilibrium 
∆Yd = ∆Ys or ∆I/d = σ I cross-multiplying , 
we get, ∆I/I = σ d .......................(7) 
Eq.(7) explains that the growth-rate of net investment ∆I/I should be equal to the product if marginal propensity to save (d) and productivity of capital (σ ). This equality must be maintained to ensure stable and steady growth.

                           Thanks for reading if any problem related to this article feel free to comment.


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