The Harrod-Domar Growth Model

The Harrod-Domar models of economic growth are based on the experiences of advanced
capitalist economies to analyse the requirements of steady growth in such economy. The Harrod-Domar
economic growth model stresses the importance of savings and investment as key determinants of
growth. The model emphases on the dual character of investment:
1. It creates income which is regarded as the ‘demand effect’.
2. It augments the productive capacity of the economy by increasing its capital stock which
is regarded as the ‘supply effect’ of investment.

The main assumptions of the Harrod-Domar models are as follows:

1. A full-employment level of income already exists.
2. There is no government interference.
3. The model is based on the assumption of closed economy.
4. There are no lags in adjustment of variables.
5. The average propensity to save (APS) and marginal propensity to save (MPS) are equal to
each other. Symbollically, S/Y= ∆S/∆Y
6. Both propensity to save and “capital coefficient” (i.e., capital-output ratio) are given constant.
7. Income, investment, savings are all defined in the net sense and hence they are considered
over and above the depreciation.
8. Saving and investment are equal in ex-ante as well as in ex-post sense.

Given the above main general assumptions, we shall discuss both models separately as below.
Although Harrod and Domar models differ in some aspects, they are similar in substance as both the
models stress the essential conditions of achieving and maintaining steady growth.

The Harrod Model:

An English economist, Henry Roy Forbes Harrod (13 February 1900 – 8 March 1978) tries to
show in his model how steady growth may occur in the economy. Once the steady growth rate is
interrupted and the economy falls into disequilibrium, cumulative forces tend to perpetuate this
divergence thereby leading to either secular deflation or secular inflation.
The Harrod Model is based upon three distinct rates of growth as below:
1. The actual growth rate (G)
2. The warranted growth rate (Gw)
3. The natural growth rate (Gn)

1. The actual growth rate (G): It is defined as the ratio of change in income (∆Y) to the total
income (Y) in the given period. Mathemaically; G = ∆Y/Y
The actual growth rate (G) is determined by:
(a) Saving-Income ratio (s) known as the Average Propensity to Save which is expressed
as s =S/Y
(b) Capital- Output ratio (C) which is expressed as C=∆K/∆Y where ∆K denotes change in
Capital stock which equal investment (I)
The relationship between the actual growth rate and its determinants is expressed as: GC = s ------(1)
Now;

The above equation so derived explains that the condition for achieving the steady state growth is
that ex-post (actual, realized) savings must be equal to ex-post investment.

2. The warranted growth rate (Gw): Warranted growth Rate also known as Full-
capacity growth rate refers to that growth rate of the economy when it is working at full capacity. In other
words, Gw is interpreted as the rate of income growth required for full utilization of a growing stock of
capital.
Warranted growth rate (Gw) is determined by capital-output ratio and saving- income ratio and
their relationships is expressed as:
Gw C r = s
or Gw=s/Cr

where ;
Cr denotes the amount of capital-output ratio needed to maintain the warranted
s denotes the saving-income ratio.
The above equation reflects that if the economy is to advance at the steady rate of Gw at its full
capacity, income must grow at the rate of s/Cr per year.

3. The natural growth rate (Gn): The natural growth rate also known as the
potential or the full employment rate of growth is the rate of economic growth required to
maintain full employment. The natural growth rate regarded as ‘the welfare optimum’ by Harrod
is the maximum growth rate which an economy can achieve with its available natural resources.
The Natural growth rate is determined by natural conditions such as labor force, natural
resources, capital equipment, technical knowledge etc. The third fundamental relation in Harrod’s model
showing the determinants of natural growth rate is expressed as: G nCr = or ≠s

Condition for the Achievement of Steady Growth:

According to Harrod, the economy can achieve steady growth when there is equality between G
and Gw at the same time between C and Cr. This condition can be expressed as:
G = Gw and C = Cr
 Harrod states that a slight deviation of G from Gw will lead the economy away and further away
from the steady-state growth path. Thus, the equilibrium between G and Gw at this junction is considered
as a knife-edge equilibrium.

Instability of Growth:
As discussed above, to achieve steady growth in economy, a balance between G and G w must be
maintained otherwise the economy will be in disequilibrium. Therefore, Harrod analysed two situations
when equilibrium condition is not satisfied:

The first situation implies that if such situation occurred, the economy will find itself in the
quagmire of inflation. This is because under this situation, the growth rate of income being greater than
the growth rate of output, the demand for output would exceed the supply of output.
In contrast, the second situation implies if such situation occurred, the economy will lead to
secular stagnation because actual income grows more slowly than what is required by the productive
capacity of the economy leading to an excess of capital goods (C>Cr).

For once if steady growth equilibrium path is disturbed, it is not self-correcting. Therefore, it
follows that one of the major tasks of public policy is to bring G and Gw together in order to maintain
long-run stability. For this purpose, Harrod introduces his third concept of the natural rate of growth. The
whole argument can also be shown with the help of the following diagram:

As shown in Panel –(A) of the above figures, starting from the initial full employment level of
income Y0, the actual growth rate G follows the warranted growth path Gw up to point E through period
t2. However, from t2 onward G deviates from Gw and is higher than the latter. In subsequent periods, the
deviation between the two becomes larger and larger.
As shown in Panel–(B), from period t2 onward, G deviates from Gw where G falls below Gw and
the two continue to deviate further away in subsequent periods.

Interaction of G, Gw and Gn:

To achieve full employment equilibrium growth, the economy must satisfy the condition where
Gn=Gw = G. But this is a knife-edge balance. For once there is any divergence between natural,
warranted and actual rates of growth conditions of secular stagnation or inflation would be generated in
the economy. The same argument can be shown through the following diagram:
 As shown in Panel-(A), if Gw>Gn, secular stagnation will develop resulting in unemployment. In
such a situation, Gw is also greater than G for most of the time because the upper limit to the actual rate is
set by the natural rate.
If Gw < Gn, secular inflation will develop in the economy. In such a situation, Gw is also less
than G for most of the time as the one shown in Panel-(B) of the above diagram.
The instability in Harrod’s model is due to the rigidity of its basic assumptions such a fixed
production function, a fixed saving ratio, and a fixed growth rate of labor force. The policy implications
of the model are that saving is a virtue in any inflationary gap economy and vice in a deflationary gap
economy. Thus, in an advanced economy, s has to be moved up or down as the situation demands.

THE DOMAR MODEL (DM)

The fundamental question around which E.D. Domar builds his model can be stated As follows:
Investment leading to an increase in productive capacity and income, what should be The rate of increase
in investment which would equalise the increase in income and The increase in productive capacity, so
that full employment is maintained?
Domar answers this question by forging a link between aggregate supply and Aggregate demand through
investment.

Statement of the Model

Domar model 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.,
(Mps =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.

COMPARISON OF HARROD MODEL AND DOMAR MODEL

Similarities:
(i) The models are based on similar assumptions. It is for this reason that the names of Harrod and
Domar are clubbed in any discussion of growth models.
(ii) Both the models employ Keynesian saving-investment equality as a condition for steady growth.

(iii) (iii) Both these models stress the “Knife-edge equilibrium”.

(iv) Both the models have been built in the context of advanced economies where capital is found in
abundance.

(v) As against Keynes’ macro-static theory, Harrod and Domar hold that a dynamic approach to
growth should be introduced in the long run.

Dissimilarities:
(1) Domar assigns a key role to investment in the process of growth while Harrod regards the level of
income as the most important factor in the growth process.

(2) Domar forges a link between demand and supply of investment while Harrod equates demand and
supply of saving.

(3) The Domar model is based on one growth rate αϬ. But Harrod uses three distinct rates of growth: the
actual rate (G), the warranted rate (Gw) and the natural rate (Gn).

(4) Domar gives expression to the multiplier but Harrod uses the accelerator about which Domar appears
to say nothing.

(5) Domar’s assumption that ∆I/I = ∆Y/Y. But Harrod does not make such assumptions.