The document discusses several economic growth models: 1) The Harrod-Domar model which expanded Keynesian analysis to the long-run and analyzed investment's role in creating output capacity. 2) The Roy Harrod and Evsey Domar models which also expanded Keynesian analysis and emphasized investment's dual role of generating income and increasing productive capacity. 3) The Solow growth model which views capital accumulation and labor as the drivers of economic growth assuming full employment and perfect competition. Technological progress is treated as exogenous. 4) The Meade model which incorporates natural resources and technological progress as additional factors influencing economic growth.

1. Theories of Economic
Growth
Vaibhav

2. Introduction
Ever since 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 on the various
aspects of growth of the developed economies. They constitute in a way
alternative stylized pictures of an expanding economy.
A feature common to them all is that they are based on the Keynesian saving-
investment analysis. The first and the simplest model of growth—the Harrod-
Domar Model—is the direct outcome of projection of the short-run Keynesian
analysis into the long-run.
The economic literature ever since the dawn of modern economics has been
much preoccupied with the issue of economic growth. Economic growth has
also been understood to establish the conditions for economic development. The
better-known models of economic growth such as the Lewis, Rostow, Harrod-
Domar, Solow, and Romer growth models are discussed.

3. Roy Harrod and Evsey Domar Model
Roy Harrod and Evsey Domar worked separately to develop their
highly similar models of economic growth and business cycles. The
two economists expanded the short-run Keynesian framework to analyze
the growth process in the developed economies. Both of them criticized
the basic Keynesian framework of income determination in the short
run for ignoring the role of investment to create more capacity for
the production of output. The investment in physical capital, according
to these economists, has a dual role. Dual role of investment here means
that investment spending generates income on one hand and also
increases the productive capacity of the economy on the other hand.
Increase in the income as a result of increase in investment is called the
demand side effect while the increase in the productive capacity of
economy due to investment is called the supply side effect.

4. Assumptions
• (1) There is an initial full employment equilibrium level of income.
• (2) There is the absence of government interference.
• (3) These models operate in a closed economy which has no foreign trade.
• (4) There are no lags in adjustments between investment and creation of productive capacity.
• (5) The average propensity to save is equal to the marginal propensity to save.
• (6) The marginal propensity to save remains constant.
• (7) The capital coefficient, i.e., the ratio of capital stock to income is assumed to be fixed.
• (8) There is no depreciation of capital goods which are assumed to possess infinite life.
• (9) Saving and investment relate to the income of the same year.
• (10) The general price level is constant, i.e., 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 productive process.
• (13) Fixed and circulating capital are lumped together under capital.
• (14) There is only one type of product.

5. The Domar Model
Domar builds his model around the following
question: since investment generates income on the
one hand and increases productive capacity on the
other at what rate investment should increase in
order to make the increase in income equal to the
increase in productive capacity, so that full
employment is maintained?
He answers this question by forging a link between
aggregate supply and aggregate demand through
investment.

6. Increase in Productive Capacity.
Domar explains the supply side like this. Let the annual rate of investment
be I, and the annual productive capacity per dollar of newly created
capital be equal on the average to s (which represents the ratio of
increase in real income or output to an increase in capital or the
reciprocal of the accelerator or the marginal capital-output ratio). Thus
the productive capacity of I dollar invested will be I. s dollars per year. But
some new investment will be at the expense of the old. It will, therefore,
compete with the latter for labour markets and other factors of production.
As a result, the output of old plants will be curtailed and the increase in the
annual output (productive capacity) of the economy will be somewhat less
than I.s. This can be indicated as I σ, where σ (sigma) represents the net
potential social average productivity of investment (= Δ Y/I). Accordingly Iσ
is less than I.s. Iσ is the total net potential increase in output of the
economy and is known as the sigma effect. In Domar's words, this “is the
increase in output which the economy can produce,” it is the “supply side of
our system.”

7. Required Increase in Aggregate Demand.
The demand side is explained by the Keynesian
multiplier. Let the annual increase in income be
denoted by ΔY and the increase in investment
by ΔI and the propensity to save by α(alpha)
(=ΔS/ΔY). Then the increase in income will be
equal to the multiplier (1/ α) times the increase
in investment:

9. • The line S(Y) indicates the level of saving
corresponding to different levels of income. I0I0,
I1I1 and I2I2 are the various levels of investment.
Y0P0 and Y1P1 measure the productivity of capital
corresponding to different levels of investment.
• The lines Y0P0 and Y1P1 are drawn parallel so as to
show that productivity of capital remains
unchanged. At the level of income Y0, the saving is
Y0S0. When the saving Y0S0 is invested, it will
increase the income level from OY0 to OY1.
• Higher is the level of income higher the
productive capacity. Similarly, when the level of
income is OY1 the level of saving is S1Y1. With
investment of S1Y1 income will further rise to the
level Y2. This increase in income means
expansion of purchasing power of the economy.
But the coefficient of capital productivity would
remain constant, this being an important
assumption of Domar’s model.

10. The Harrod Model
R.F. Harrod tries to show in his model how steady (i.e., equilibrium) 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. First, there
is the actual growth rate represented by G which is determined by the
saving ratio and the capital-output ratio. It shows short-run cyclical
variations in the rate of growth. Second, there is the warranted growth rate
represented by Gw which is the full capacity growth rate of income of an
economy. Third, there is the natural growth rate represented by Gn which is
regarded as ‘the welfare optimum’ by Harrod. It may also be called the
potential or the full employment rate of growth.

12. Growth Process
• The line S(Y) drawn through the origin shows the
levels of saving corresponding to different levels of
income. The slope of this line (tangent α) measures
the average and marginal propensity to save. The
slopes of lines Y0I0, Y1I1, Y2I2 measure the
acceleration co-efficient v which remains constant
at each income level of Y0, Y1, and Y2.
• At the initial income level of Y0, the saving is S0Y0.
When this saving is invested, income rises from
Y0 to Y1. This higher level of income increases
saving to S1Y1. When this amount of saving is
reinvested, it will further raise the level of income
to Y2. The higher level of income will again raise
saving to S2Y2. This process of rise in income,
saving and investment shows the acceleration effect
on the growth of output.

13. • Given the capital-output ratio, as long as the average propensity to save is equal
to the marginal propensity to save, the equality of saving and investment fulfils
the conditions of equilibrium rate of growth.
• Looked at from another angle, the two models are similar. Harrod’s s is Domar ’s
α. Harrod’s warranted rate of growth ( Gw) is Domar ’s full employment rate of
growth (ασ). Harrod’s Gw = s/Cr ≡Domar ’s ασ.

14. The Solow Growth Model
Assumptions
Neo-Classical Theory of growth has been Propounded by
modern economist like Solow, Meade, Swan etc. It based
on following assumptions:-
•Capital and labour are the two factors of production.
•Substitution of Capital for labour is possible.
•There is a full employment in the economy.
•There prevails perfect competition in the economy.
•Prices are flexible.

15. Meaning and Determinants of Economic Growth
•Economic growth means Increase in production. Economic
growth has following characteristics:-
•Gradual
•Continuous
•Harmonious
•Cumulative
According to neo-classical Economist capital can be
substituted for labour thus accumulation of capital is possible
even without making any increase in labour power which
Results into increase in National Income and Per Capita
Income.

16. Capital
Accumulation
Rate of
Saving
Level of
Income
&
Rate of
Interest
Investment
Economic
Growth
Neoclassical Economic
Growth

17. Solow’s Equation
• According to Solow, net investment refers to the rate of increase in the capital stock and
denoted by K’
• The proportion of the function of real income saved is denoted by ‘S’ and regarded as
constant.
• The rate of saving , therefore, would be sY. The basic saving an investment can be expressed
as
K’=sY .......................(1)
• Production is the function of two factors i.e. capital (K) and Labour (L) or
Y=F(K,L) ........................(2)
• Solow assumes that composite product with multiple use is produced in the economy. A part
of it is saved and invested. Substituting the value of Y in (1) it becomes
K’=sF(K,L) .......................(3)
• Eq.(3) represent the supply side of the system. Solow’s demand side is represented by
.......................(4)
L(t)=Loeth

18. • Here L(t) represents the number of workers employed in ‘t’ period of
time.
• Lo implies the level of employment or number of workers employed in
initial period of time.
• n represent the growth of labour at a constant
• exogenous rate.
• The right hand side of equation (4)implies that labour force expands
at exponential
• Rate n from the initial period to the ‘t’ period of time. By substituting
the value of L(t)in eq.(3) it can be expressed as
K’=sF(K,Loent) ………..(5)
Solow regards eq. (5)as the basic eq. As it helps in determining the
volume of capital stock needed to provide employment to available
labour.

19. Y
yF(r,1)
nr
sF(r,1)
1)
E
O
r’’
Capital Labour Ratio (r)
X
Output
per
head
(Y)
Saving
per
head
sF(r,1)

20. Meade’s Equation
• Meade is of the view that production does not depend on labour and Capital
alone.
• Beside, labour and capital it depends on natural resources (N) and Technical
Progress (T)
Hence Y=F(K,L,N,T) ...................(1)
• If natural resources (N) remain constant then increase in (Y),depends upon the
increases in the remaining three factors i.e K,L,T.
• Suppose the increase in the stock of capital is represented by K and if V is
marginal productivity of capital then increase in the net national income due
to capital stock would be VK.
• Similarly, increase in labour force  L multiplies by its marginal net productivity
would raise the level of net national income by WL. Y’ is used to represent
the increase in the net national product due to technical progress. The
increase in net annual output in one year would be the sum of contribution of
three factors.
Hence Y=VK+WL+Y’ ...................(2)

21. • To find out the growth rate of net national income in terms of growth rate of capital, labour and technology the
eq. Will be;
Y= VK. K + WL. L+ Y’ ...................(3)
Y Y K Y L Y
• Where Y is the proportionate growth rate of output
Y
• K is the is the proportionate growth rate of capital
K
• L is the is the proportionate growth rate of labour force
L
• Y’ is the is the proportionate growth rate of technical progress during a year
Y
• VK/Y and WL/Y represent the proportionate marginal product of capital and labour respectively.
• VK/Y represent the proportion of the net national income being paid as profit.
• WL/Y is proportion of income going to the labour force as wages if proportionate growth rates of income ,
capital , labour , and technical progress are represented as y=Y/Y’, k=K/K,I=L/L,r=Y’/Y and marginal
productivity of capital as U and marginal productivity of labour as Q then eq. (3) can be rewritten as
• y=Uk+QI+r ...................(4)

22. •The true index of economic growth of an economy is the
growth rate of real income rather than growth rate of income
(y).
•In order to find out the growth rate of real income, the growth
rate of labour (I) is to be subtracted from the growth rate of
income (y).
•The growth rate of real per capita income is considered the
true indicator of growth of any economy. Subtracting the
growth of the labour force(I)
from both side of eq. (4) we get modified eq. as:
y-I = Uk+QI-I+r
= Uk-(Q-I)+r ………….(5)

23. Y
Total
Annual
Output
B
D
A
C
K K1
X
Total Stock of Machinery

24. Y
K
y
H
B
C
D
G
U
X
E F
Growth rate of capital stock
Growth
Rate
of
National
Income

25. Optimism Concerning Development
• Optimistic approach of the theory is evident from the following
Facts:
• It is not always necessary that growth of population may always take place
according to Malthusian Theory.
• Due to technical progress , production can be had in accordance with the
law of decreasing returns can be postponed.
• Wages rate of the labourer and rate of profit both can increase
simultaneously. In order to increase the wage-rate , it is not necessary to
lower the rate of profit, or to increase the rate of Profit, it is not necessary
to lower the wage rate.
• Whereas growth rate of population can be controlled by the spread of
knowledge , the wage rate can be increased by more capital accumulation.
• Class struggle is not necessary.

26. Technical Progress
It had been assumed that growth manifested itself
in the factor growth. Several empirical studies,
however, have led to the conclusion that
contribution of technical progress in an increase in
national income or product is much more
significant than that of growth of labour supply or
capital accumulation. The effect of technical
progress on growth process and trade is much
more complex than that of factor growth.

27. • J.R. Hicks has classified the technical progress into neutral, labour-saving
and capital-saving.
• Whatever is the nature of the technical innovations, they cause a shift of
the isoquant towards the origin, the level of output remaining the same.
It means the technical progress enables a firm to produce the same
quantity of a commodity by employing lesser quantities of the factor
inputs.
• The technical progress is neutral, when it raises the marginal productivity
of capital and labour in the same proportion at the given capital-labour
ratio or alternatively, it leaves the capital-labour ratio unchanged.
• The technical progress is said to be labour- saving, when it raises the
marginal productivity of capital relative to that of labour at constant ratio
of capital to labour. In other words, in case of labour- saving or capital-
using technical progress, the capital- labour ratio marks an increase.

29. Technological Change
• The manufacturing sector offers special opportunities for both
embodied and disembodied technological progress.
• Rapid capital accumulation is associated with embodied technological
progress, as new generations of capital goods embody the latest state
of the art of technology.
• Disembodied technological progress refers to changes in the
knowledge of product and process technologies in firms and in the
economy as a whole.
• Since, the industrial revolution, technological advance has been
concentrated in the manufacturing sector and diffuses from there to
other economic sectors such as the service sector. Cornwall (1977) in
particular has argued that manufacturing is the locus of technological
progress

31. Embodied Technological change:
• Embodied Technological change: the shift over time from technologically less
sophisticated to technologically more advanced capital goods
• In the course of economic development, output per unit of input (total factor
productivity) can increase due to various factors, among which shifts from one
economic sector to another, economies of scale and more efficient allocation of
resources within sectors. One of the most important factors, which can cause
increases in output per unit of input, is so-called disembodied technological change
• Disembodied technological change refers to general advances in science, technology
and the state of knowledge, changes in the stocks of knowledge available to firms,
sectors or countries; improvements in the level of knowledge absorbed by
employees and managers in educational institutions and on the job (Maddison,
1987, p. 662), learning by doing by workers and managers on the job, improvements
in the collective technological capabilities of firms or the social capabilities of
countries and finally positive external effects of investment in knowledge and new
technologies, through spill-overs from firm to firm or from country to country.

32. JOAN ROBINSON’S GROWTH MODEL
• Joan Robinson, a student of J. M. Keynes, rejected Neo classical models
and assumptions. She made an immense contribution to the Theory of
Capital and its valuation.
• She eschewed the concepts of:
– Malleable and homogeneous capital as depicted in Neo Classical production functions.
– She argued that Physical Capital is specific in form and function (durable and
heterogeneous), and takes time to be produced.
– Capital-Labour ratios are constant for a given technique, at a given time; capital and
labour are not substitutes, but complementary inputs in production.
– Production takes place in Historical time, not logical time.
– Hence it is not possible to move up and down the production function, as argued by
Neo Classical Theory.

33. Model
• She extended Harrod’s and Domar’s models of growth.
• She took the following aspects into account:
•− Investment leads to Savings,
–Role of heterogeneous, durable capital, and problems
of valuing capital,
–Importance of capital accumulation and its impact on the
economy.
–Technical progress and its impacts.

34. Objective of JR’s Model
• What are the conditions that lead to full capacity, full
employment, steady growth in a capitalist system?
– Economic conditions differ across countries.
– So it is not possible to apply the same growth model to all
countries or at all times,
– Different economic situations require different types of models.
– She therefore built several models of growth for different
economies depending on their economic conditions .

35. Golden and Platinum Ages
• Free Enterprise, free market economy,
• Driving force behind growth is entrepreneurs’ urge to invest, determined by
expectations of profit on Investment.
• The different Golden and Platinum Ages are different growth paths that apply to
different economies with different characteristics.
– In a closed economy, the concepts of Golden age and Platinum age are to be
discussed. In simple words, Golden age is a situation of smooth steady growth
with full employment arising out of the equality of the ‘Desired’ and ‘Possible’
rates of accumulation and has been designated by Mrs. Joan Robinson as the
Golden age equilibrium.
– In the platinum age, the growth rate of output and employment are given from
outside and technical advance is zero. Thus, in platinum age, the development
parameters are considered to be rigid. The steady growth cannot occur in initial
stages due to rigidity of development parameters.

36. Assumptions:
1. Free enterprise economy, no government interference.
2. Closed economy,
3. Three classes – entrepreneurs, workers, rentiers.
4. Capital is fixed, durable and heterogeneous, no substitution between K and L.
5. Neutral technical progress,
6. Tranquility conditions: entrepreneurs assume that present conditions will
continue in future
7. Worker save nothing

37. The Determinants of Equilibrium
• According to JR, seven conditions, all independent, are required
• to determine the equilibrium level of output:
1. Technical conditions: a) Number and quality of labour force and its
growth rate. b) Technical knowledge and technical progress. c)
Supply of natural resources. This gives the natural rate of growth
= GN = GL + GT.
2. Thriftiness conditions: s = S/Y, determined by distribution.
Entrepreneurs and rentiers save, mps= se. Labour, whose w =
subsistence, does not save.
3. Market: Need not be PC. Monopoly makes Pr/Y
• independent, raises “animal spirits” (urge to Invest).

38. • 4. Wage bargain: Money wages constant, except when:
–(a) capital or plants are available for Investment, but labour
is not,
–(b) The rate of Investment calls for a lower real wage, not
acceptable to labour, (Inflation barrier wage). Rate of
Accumulation , wage rate
• 5. Finance: Financial institutions developed to offer
finance for investment. But rate of interest and
Monetary Policy play only a small role in price stability.

39. 6. Investment Policy: firms alone make Investment
decisions, based on “animal spirits” i.e. urge to grow in
managerial economies.
• 7. Stock of Capital: If entrepreneurs are satisfied, then
capital stock composition will not change. Employment
remains constant. Expectations are fulfilled and
entrepreneurs do not revise their investment.
• – JR states that to be in steady growth, the economy should have a
history of steady growth. Not possible for an economy to shift from unsteady
to steady growth!

45. Kaldor model of distribution
The Kaldor model is an attempt to make
the saving-income ratio a variable in the
growth process. It is based on the
‘classical saving function’ which implies
that saving equals the ratio of profits to
national income, i.e., S = P/Y.

46. Assumptions.
• (1) There is a state of full employment so that total output or income ( Y)
is given.
• (2) National income or output consists of wages (W) and profits (P) only.
W comprises both manual labour and salaries, while P includes the
income of property owners and of entrepreneurs.
• (3) The marginal propensity to consume of workers is greater than that of
capitalists whereby the marginal propensity to save of the workers, sw, is
small in relation to those of capitalists sp, i.e., sp>sw.
• (4) The inyestment-output ratio ( I/Y) is an independent variable.
• (5) Elements of imperfect competition or monopoly power exist.

47. THE MODEL
Y = W + P
I = S
S = Sw + Sp

48. • this model operates when the two
savings propensities differ, sp ≠ sw.
sp>sw is the stability condition. If sp
is less than sw, a fall in prices
• would cause a fall in demand and to
a cumulative fall in prices. Similarly,
a rise in prices would be
cumulative.

49. The Endogenous Growth Models:
•1. Arrow’s Learning by Doing and Other Models
•The Levhari-Sheshinski Model
•The Levhari-Sheshinski Model
•The Romer Model
•2. The Lucas Model:
•3. Romer’s Model of Technological Change

50. The Romer Model:
• Romer in his first paper on endogenous growth in 1986 presented a variant
on Arrow’s model which is known as learning by investment. He assumes
creation of knowledge as a side product of investment. He takes knowledge
as an input in the production function of the following form
Y = A(R) F (Ri,Ki,Li)
• Where Y is aggregate output; A is the public stock of knowledge from
research and development R; Ri is the stock of results from expenditure on
research and development by firm i; and Ki and Li are capital stock and labour
stock of firm i respectively. He assumes the function F homogeneous of
degree one in all its inputs Ri, Ki, and Li, and treats Ri as a rival good.

51. •Romer took three key elements in his model, namely
externalities, increasing returns in the production of output
and diminishing returns in the production of new knowledge.
According to Romer, it is spillovers from research efforts by a
firm that leads to the creation of new knowledge by other
firms. In other words, new research technology by a firm
spills-over instantly across the entire economy.
•In his model, new knowledge is the ultimate determinant of
long-run growth which is determined by investment in
research technology. Research technology exhibits
diminishing returns which means that investments in research
technology will not double knowledge.

52. •Moreover, the firm investing in research technology will
not be the exclusive beneficiary of the increase in
knowledge. The other firms also make use of the new
knowledge due to the inadequacy of patent protection and
increase their production.
•Thus the production of goods from increased knowledge
displays increasing returns and competitive equilibrium is
consistent with increasing aggregate returns owing to
externalities. Thus Romer takes investment in research
technology as endogenous factor in terms of the
acquisition of new knowledge by rational profit
maximisation firms.

53. In the Romer model, new knowledge enters into the
production process in three ways.
•First, a new design is used in the intermediate goods
sector for the production of a new intermediate input.
•Second, in the final sector, labour, human capital and
available producer durables produce the final product.
•Third, and a new design increases the total stock of
knowledge which increases the productivity of human
capital employed in the research sector