Harrod Domar Growth Model
• Eversince the end of Second World War,
interest in the problems of economic
growth has led economists to
formulate growth models of different
types.
• These models deal with and lay
emphasis onthe various aspects of
growth of the developed economies.
• They constitute in a way alternative
stylized pictures of an expanding economy.
Ø The Harrod–Domar model is a Keynesian
model of economic growth.
Ø It is used in development economics to explain
an economy's growth rate in terms of the
level of savingand of capital.
Ø It suggests that there is no natural reason for
an economy to have balanced growth.
Ø The model was developed independently by
R. F. Harrod in 1939 and Evsey Domar in
1946 although a similar model had been
proposed by Gustav Casselin 1924.
Ø The Harrod–Domar model may be regarded as
the precursor to the exogenous growth
model.
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Assumptions
(i) A full-employment level of income
already exists.
(ii) There is no government interference in
the functioning of the economy.
(iii) The modelis based on the assumption
of “closed economy.” In other words,
government restrictions on trade and the
complications caused by internationaltrade are
ruled out.
(iv) There areno lags in adjustment of
variables i.e., the economicvariables such as
savings, investment, income, expenditure adjust
themselves completely within the same periodof
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time. as functional equality between saving and
investment.
(v) The average propensity to save (APS)
and marginal propensity to save (MPS) areequal
to each other. APS= MPS or written in symbols,
S/Y= ∆S/∆Y
(vi) Both propensity to save and “capital
coefficient” (i.e., capital-output ratio) aregiven
constant.
This amounts to assuming that thelaw
of constant returns operates in theeconomy because
of fixity of thecapitaoutput ratio.
(vii) Income, investment, savings areall
defined in thenetsense, i.e., they areconsidered
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over and above thedepreciation. Thus, depreciation
rates arenot included in these variables.
(viii) Saving and investment areequal in ex-
anteas well as in ex-post sense i.e., there is
accounting as well.
Harrod’s growth model raised three issues:
(i) How can steady growth be achieved for
an economy with a fixed (capital- output
ratio) (capital-coefficient) and a fixed saving-
income ratio?
(ii) How can the steady growth rate be
maintained? Or what are the conditions for
maintaining steady uninterrupted growth?
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(iii) How do the natural factors put a ceiling
on the growth rate of the economy?
In orderto discuss theseissues, Harrod had
adopted threedifferent concepts of
growth rates:
(i) the actual growth rate, G,
(ii)the warranted growth rate,
Gw (iii) the natural growth
rate, Gn.
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• The Actual Growth Rate is thegrowth rate
determined by theactual rate of savings and
investment in thecountry. In other words, it can
be defined as theratio of change in income
(AT) to thetotal income (Y) in thegiven period.
If actual growth rate is denoted by G, then
• G= ∆Y/Y
• The actual growth rate (G) is determined by
saving-income ratio and capital- output ratio.
Both thefactorshave been taken as fixed in the
given period. The relationship between the
actual growth rate and its determinants was
expressed as:
• GC = s …(1)
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• where G is theactual rate of growth, C
represents thecapital-output ratio ∆K/∆Y and s
refers to thesavingincome ratio ∆S/∆Y. This relation
stales thesimple truism that saving and investment
(in theex- post sense) are equal in equilibrium.
• The actual growth rate (G) is determined
by saving-income ratio and capital- output
ratio,
taken as fixed in the given period.
The relationship betweenthe actual
growth rate and its determinants was
expressed as:
GC= s …(1)
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• where G is the actual rate of growth,
• Crepresents the capital-output ratio ∆K/∆Y
and
• s refersto the saving-income ratio ∆S/∆Y.
• This relation stales the simple truism that
savingand investment (in the ex-post sense)
are equal in equilibrium.
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• Thisrelation explainsthat the condition for
achieving the steady state growth is
that expost savings must be equal to ex-
post investment.
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Warranted growth
• It refersto that growth rate of the
economy when it is working at full
capacity.
• also known as Full-capacity growth rate.
denoted by Gw.
• is the rate of income growth required for
full utilisation of a growing stock of
capital, so that entrepreneurs would be
satisfied with the amount of investment
actually made.
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• Gwis determinedby capital-output ratio and
saving- income ratio.
• The relationship can be expressed as
G w Cr = s
• where Cr shows the needed C to maintain
the warranted growth rate and s is the
saving-income ratio.
• Harrod- Aneconomy can achieve steady
growth when
G = Gw and C =
Cr
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• This condition states, firstly, that actual
growth rate must be equal to the
warranted growth rate.
• Secondly, the capital-output ratio needed to
achieve G must be equal to the required
capitaloutput ratio in order to maintain Gw,
given the saving co-efficient (s).
• This amounts to saying that actual investment
must be equal to the expected investment at the
given saving rate.
Instability of Growth:
• As stated above that the steady-state
growth of the economy requiresan
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equality between G and Gw onthe one
hand and C and Cr onthe other.
• In a free-enterprise economy, these
equilibrium conditions would be satisfied
only rarely, if at all.
• Therefore, Harrod analysed the
situations when theseconditions are not
satisfied.
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When G is greater than Gw.
G>Gw
• Under this situation, the growth rate of
income being greater than the growth
rate of output,
• the demand foroutput (because of the
higher level of income) would exceed the
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supply of output (because of the lower
level of output) and the economy would
experience inflation.
• This can be explained in another way too
when
C < Cr
Under this situation, the actual amount of
capital falls short of the required amount
of capital.
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• Thiswould lead to deficiency of capital,
which would, in turn, adversely affect
the volume of goods to be produced.
• Fall in the level of output would result
in scarcity of goods and hence inflation.
• This, under this situation the
economy will find itself in the
quagmire of inflation.
when G is less than Gw,
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G<Gw
• the growth rate of income would be less
than the growth rate of output.
• In this situation, there would be excessive
goods forsale, but the income would
not be sufficient to purchase those goods.
• In Keynesian terminology, there would be
deficiency of demand and consequently the
economy would face the problem of
deflation.
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• This situationcan also be explained when C
is greater than Cr.
• Here the actual amount of capital would
be larger than the required amount of
capital for investment.
• The larger amount of capital available for
investment would dampenthe marginal
efficiency of capital in the long period.
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• Secular decline in the marginal
efficiency of capital would lead to
chronic depressionand unemployment.
• Thisis the state of secular stagnation.
• From the above analysis, it can be
concluded that steady growth implies a
balance between G and Gw.
• In a free-enterprise economy, it is
difficult to strike a balance between G
and Gw as the two are determined by
altogether different sets of factors.
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• Since a slightdeviation of G from Gw leads
the economy away and further away
from the steady-state growth path, it is
called ‘knifeedge’ equilibrium.
Natural growth Rate Gn
• determined by natural conditions such as labour
force, natural resources, capital equipment,
technical knowledge etc.
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• These factors place a limit beyond which
expansion of output is not feasible.
• This limit is called Full-Employment Ceiling.
• This upper limit may change as the production
factors grow, or as technological progress
takes place.
• Thus, the natural growth rate is the
maximum growth rate which an economy can
achieve with its available natural resources.
• The third fundamental relation in Harrod’s model
showing the determinants of natural growth
rate is
GnCr is either = or ≠s
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Interaction ofG,Gw and Gn:
• If G„ exceeds Gw,(G > Gw)
• Gn would also exceed
Gw for
most of thetime and
there would be a
tendency in theeconomy
for cumulative boom and
fullemployment.
• Sucha situation will
create an inflationary
trend.
• To check this trend,
savings become
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desirable because these would enabletheeconomy
to have a high level of employment without
inflationary pressures.
Interaction of
G,Gw and Gn:
• If Gw > G,
• G must be belowGn,
• for most of the time
and there wouldbe a
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tendencyfor cumulative recessionresulting in
unemployment
TheDomar Model:
• The main growth model of Domar bearsa
certain resemblance to the model of
Harrod.
• In fact, Harrod regarded Domar’s
formulation as a rediscovery of his
own version after a gap of seven years.
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1. Investmenthas twoeffects
(a) An income-generating effect and
(b) Productivity effect by creatingcapacity.
• The keynes’ Analysis which is short-run
analysis ignored the second effect.
2. Unemployment of labour generally
attracts attention and one feels
sympathy for the jobless, but
unemployment of capital attracts little
attention.
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It should be understood that
unemployment of capital inhibits
investment and hence reduces income.
Reduction of income bringsabout
deficiency in demand and hence
unemployment.
Thus the Keynesian concept of
unemployment misses the root cause of the
problem.
Domar wanted to analyse the genesis
of unemployment in a wider sense.He explained
following relations:
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1. Income is determined by investment through
multiplier. For simplicitysaving-income ratio
(s) is assumed constant.This implies that
Y(t) = I(t)/s
where Y is the output, I is the actual investment and s
is saving-income ratio(saving propensity) and (t) shows the time
period.
2. Productive capacity is created by investment
to the extent of the potential (social)
average productivity of investment denoted by
σ.
For simplicity, this is also assumed to be
constant.In notation form the relation can be
written as
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Y(t) – Y(t-1)= I(t)/α
Where Y(t) – Y(t-1) refers to change in Productive Capacity
in t period of time.
• α is the marginal capital-output ratio
which is the reciprocal of “potential
social average investment productivity”
(α= 1/σ).
• Therefore, Equation (2)can also be
expressed as ∆Yt = σIt
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• This equation shows that the change in
productive capacityis the product of
capital productivity (σ) and
investment.
• Hence, it reveals the productivity effect.
3) Investment is induced by output growth together with
entrepreneur confidence.
4) Employment depends upon the 'utilization ratio'
expressed as the ratio between actual output and
productive capacity.
5) Past and present investment can greater productive
capacityat a given ratio.
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Statement of the Model
• investment increases productive capacityDomar model is based
on the dualcharacter of investment: , and two,
investment generates one, income.
• following symbols are used in DM.The two sides of
investment provide solution for steady growth. The
• Yd= Level of employment (demand side) national income
or level of effectivedemand at full
• Ys= Level of (supply side) productive capacity or
supply at full employment level
• K= real capital
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• I= net investment, which implies change in stock of real
capital, i.e. ∆K
• ( mps ç = marginalpropensity to save, which is the
reciprocal of multiplier i.e., =1/multiplier) • σ=
productivity of capital
help formulate the DM.We can make use of these notations
to frame a set of equations that
The demand side of investment canbe represented
by an equation as follows:
Y = I/
d α
…........................(1)
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This equation explains two things as follows:
i) to the level of investment(I)The level of
effective demand (Y. An increase in d) is
directly related
investment willresult in an increase in effective
demand, and vice versa.
ii) The effective demand is inversely relatedto
the marginal propensity to save (α). An
increase in marginal propensity to save will
decrease the level of effective demand and
vice-versa.
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The supply side of investment canbe represented
by an equation as follows:
Ys = σ k
.................................................(2)
Eq.(2) explainsthat supply of output at full employment (Ys
)depends upon twofactors, ie.., productive capacityof capital(σ
) and the s amount of real capital(K).
Any change in any of these factors 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.
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Equilibrium:
In equilibrium, the demand and supply should balance.
Therefore,
Y =
d
Y
s…..........................................(3)
/
or I α=σ K
By cross multiplication,
I=α σK
Thisis the condition for steady growth.Steady growth is
possiblewhen: Investment equals the product of saving-income
ratio, capital productivity and capital stock.
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For this we have to giveincrement to the demand and supply
conditions presented above.
The demand equation in its incremental form can be stated
as follows:
∆Yd = ∆I/α ........................,....................( 4)
Incrementshave been shownin the level of
effective demand and investment because they
arevariables,
but increment has not been shownin α
because it is constant in terms of the
assumptions employed.
The supplyequation it its incremental form can be
stated as follows:
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∆Ys = σ ∆K ........................(5)
• Eq.(5)explains that change in thesupply of output
(∆Ys) would be equal to theproduct of change
in real capital (∆K), and theproductivity of
capital (σ ).
• The change in real capital is expressed as net
investment.
Therefore, ∆K represented investment (I).
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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 thecondition for maintaining the
steady growth. In equilibrium
∆Yd = ∆Ys
or ∆I/α = σ I
cross-multiplying , we get,
∆I/I = σ α ......................................(7)
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Eq.(7) explainsthat the growth-rate of net investment ∆I/I
should be equal to the product if marginal propensity
to save (α) and productivity of capital (σ ).
This equalitymust be maintained to ensure stable and
steady growth.
Path of Disequilibrium
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Under the first situation,long-term inflation
wouldappear in the economy because the
higher growth rate of income will provide
greater purchasing power to the people and
the productive capacity (σα) wouldnot be able
to cope with the increased level of income.
The first situation of disequilibrium will,
therefore, create inflation in the economy.
The second situation, under which growth
rate of income or investment is lagging
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behind the productive capacity, will result
in over production.
The reducedgrowth rate of income will put
a constraint onthe purchasingpower of the
people, thereby reducing the level of
demandand resulting in over-production.
This is the situation in which there
would be secular stagnation.
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References:
1 Harrod, Roy F. (1939). "An Essay in DynamicTheory". The
Economic Journal.
2 Domar, Evsey (1946). "Capital Expansion, Rate of Growth,
and Employment". Econometrica.
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Thank You
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