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Chapter # 7
Long Run Growth Models
Introduction
• J.M Keynes presented theory of NI
determination, but his theory of income and
employment is concerned with short run.
• Keynes in his analysis, assumed that
amount of capital, technology, natural
resources, tastes of people and population
remains the same. But such assumptions can
be justified in short run, but in long run it is
not possible.
Steady Growth
• Both Harrod and Domar (the two
Economist) were interested in discovering
the rate of income growth necessary for a
smooth and uninterrupted working of the
economy.
• As per them, investment has a key role in
the process of economic growth. They
established a dual role of investment.
Dual Character of Investment
1 Investment creates income,
2 It increases the productive capacity of the
economy by increasing its capital stock.
The former may be regarded as demand effect
and the latter the supply effect of investment.
Hence so long as net investment taking place,
real income and output will continue to expand.
Assumptions of Domar Model
1 There is full employment equilibrium level of
income
2 No government intervention
3 APS = MPS
4 The value of MPS (α) remains the same
5 The capital coefficient (COR = σ) is constant.
Domar model….
• Domar tried to find the rate of change in
Investment (∆I) while the rate of change in
NI could become equal to the rate of
increase in productive capacity.
• In other words, if a country wishes to
maintain their growth rate, it will have to
make the capital more productive and will
have to increase the proportion of saving.
Domar model….
• More saving means more investment, and it
will lead to increase capital, and more
productive capacity, hence increase in output.
Therefore more should be the expenditure to
purchase such increased goods and services.
• Saving→ increasing stock of capital →
growth of output
Mathematical explanation
• Mathematically it is explained as….
• ∆Y = 1 (∆I) ..…(1) (Multiplier effect)
α
• As Yf is to be maintained, NI & productive
capacity must grow at the same rate
• It is as 1 (∆I) = Iσ ……(2)
α
• Where Iσ= productive capacity.
Numerical example
• Now by dividing eq 2 by “I” and
multiplying it by α
(α ) 1 (∆I)
α)
Iσ
(
α
_____________
=
or (∆I) = α.σ
I
I
Now if σ is 25%, α is 12% then
(∆I) = 25% x 12% = 3%
I
I
Numerical example……
• This shows if Yf is to be maintained then
investment or NI must rise by 3%. If at the level of
Yf , Y= 150 bn then to maintain Yf, investment
must increase by 18 bn as
150 x 12/100 = 18
• When investment increases by 18bn, it will lead to
increase the productive capacity which is the
product of investment and COR, it is as
Numerical example……
• 18 x 25/100 = 4.5 bn
• All this shows if resources are to be saved
from being unemployed then NI will have
to increase by 4.5 bn
Conclusion
1 If α (MPS) is more, more investment will
have to be made so that Yf could be
maintained
2 If COR(σ) is more, more will be the
increase in productive capacity
Harrod Model
• Harrod Model is based on three distinct rates
of growth.
1 Firstly there is Actual Growth Rate
represented by G, which is determined by
saving ratio & Capital Output Ratio (COR).
2 Secondly there is Warranted Growth Rate
represented by Gw, which is the full capacity
of growth rate of income of an economy.
Harrod Model…
3 And lastly there is the Natural Growth
Rate represented by Gn which is regarded
as “welfare optimum” by Harrod.
It may be called the potential or the full
employment rate of growth.
1
Actual Growth rate
• In Harrodian model first fundamental equation is
GC = s
– Where G is the rate of the growth of output, which
can be expressed as ∆Y/Y
– C is the net addition to capital and is defined as I/∆Y
– And “s” is the APS i.e S/Y
• Now substituting these ratios in the above
equation we get
Cont`d…
• GC = s
• Putting the ratios in equation we get
• ∆ Y x I = S or I = S or I=S
Y ∆Y Y
Y
Y
whereas S depends upon Y, and I depends
upon change in income, and rest is just an
acceleration principle.
2
Warranted Growth
• The equation for the warranted growth rate is
GwCr = s
 Where Gw is warranted Growth rate,
it is the value of ∆Y/Y ,
 Cr is the capital requirements, denoting the amount
of capital needed to maintain the warranted growth
i.e. required capital output ratio… I/∆Y
 And s is the same as in first eq i.e. S/Y
explanation
• The equation therefore states that if the
economy is to advance at 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
Cont`d
If income grow at warranted growth rate,
the capital stock of the economy will be
fully utilized and entrepreneur will be
willing to continue to invest the amount of
saving generated at full potential income.
Gw is therefore, a self-sustaining rate of
growth and if the economy continues to
grow at this rate it will follow the
equilibrium path
3
The Natural Rate of Growth
• This is the growth rate which is permitted
by the resources of the country. Thus it is
the growth rate which is possible in the
presence of natural resources, technology,
amount of capital and labor.
• Thus it is the highest growth rate.
Cont`d
• The rate of population growth and the rate
of technological progress are the two most
important factors that determine the Natural
Growth rate.
• It is assumed that there is no unemployed
labor that can be used and there is no further
scope of technological improvement.
Mathematical expression
• So if “p” represent the population growth
rate and “t” technological progress, then
Natural Growth rate Gn will be shown by
the following equation
Gn = p + t
• Here Gn is the natural growth rate
• thanx