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Harrod-Domar Growth Model
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JOIN KHALID AZIZ
ECONOMICS OF ICMAP, ICAP, MA-ECONOMICS, B.COM.
FINANCIAL ACCOUNTING OF ICMAP STAGE 1,3,4 ICAP MODULE B, B.COM, BBA, MBA & PIPFA.
COST ACCOUNTING OF ICMAP STAGE 2,3 ICAP MODULE D, BBA, MBA & PIPFA.
CONTACT: 0322-3385752 0312-2302870 R-1173,ALNOOR SOCIETY, BLOCK
19,F.B.AREA, KARACHI, PAKISTAN.
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Topics for today
Lord Harrod and Mr. Domar Keynesian based models Saving rates Capital/Output ratio or
Capital Productivity Capital stock GDP
Personal Consumption Gross Savings Gross Investment Net Investment, or Capital
Accumulation Depreciation Dynamic models
In growth models, we will encounter the following terms:
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What is a Keynesian Growth Model?Keynes’ model and Keynesian models were
developed to explains business cycles• A short run phenomena
As such they attribute a major role to aggregate expenditures (demand side)
Regarding the supply side, they assume that there is unemployment: production responds fast to increases in aggregate demand because capital and labor is unemployed.
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Aggregate Demand, AD– AD = C + I + G + X-M– C, Consumption expenditures– I, Investment expenditures– G, Government expenditures– X-M, Foreigners’ Expenditures
Aggregate Supply– AS < ASfe – Aggregate Supply, at full employment
Macroeconomic Equilibrium– AS = AD– Or – S = I
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A Keynesian Model
A Keynesian growth model takes a long run perspective.– Aggregate demand (or savings=investment)
still is important, but– It also includes the aggregate supply
• Investment has two impacts:– On expenditures (in the short run)– On capital stock (in the long run)
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Trends and business cyclesR
eal G
DP
Years
One business cycle
Trend
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Main Propositions
Economic growth can be accelerated by – changing the saving rate – improving technology.
Saving rates and technology can be changed – government interventions without consideration
to prices
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v= K/Y ora=Y/K
Capital
Capital/Output Ratio or Productivity
GDP
s
Saving Rate
C
Sd
Depreciation Rate
D
In
Ig
Production function
Harrod-Domar Growth Model A Flow chart model
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Factors Explaining the growth rateAccording to Harrod-Domar model
g
s
a
d
Saving rate
Capital productivity
Capital depreciation
Rate ofEconomicGrowth
Explained variable Explanatory Variables
+
+
_
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Arithmetic specificationWithout Depreciation
a=dY/dK
Y=K.a
S=Y.s s=dS/dY
I
K
dK
If we know the initial capital stock K; and we
know a, (how much output increases when
capital increases 1 unit) then we know what will
total output Y be.
If we know output Y, and we know s, which is the saving rate, then we know total savings S.
If we know total savings S, we know how much we can invest (I) in new
capital (dK)
If we know dK and a, we know growth
of output dY
dY
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Numerical specificationWithout Depreciation
a=.20
Y=1
S=.10 s=.10
.10
K=5dK=.10
If we know the initial capital stock K=5; and
we know its productivity a=.20 then we know
total output Y=1
If we know output Y=1 and we know the saving rate s=.10, then we know
total savings S=.10
If we know total savings S=.10 we know that we can
invest I=.10 in new capital (dK=.10)
If we know dK=.10 and a=.20, we know
growth of output dY=0.02=2%
dY=.02=2%
Or …dY = s.a
By approximation: dY/Y=s.a/Y
g=s.aSince Y=1
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Economic growth formulaAccording to Harrod-Domar the rate of economic growthis defined by the formula:
g = s.a – d
that is, if s=10% and a=0.20 and d =1%, then
g=0.10*0.20 - 0.01 = 0.02 -0.01 = 0.01 = 1%
What happens if the rate of saving (s) increases to 20% ?What happens if the productivity of capital (a) increases to 0.40?What happens if the depreciation (d) rate is 2% ?
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.Conventional Keynes’ Model
Specification
Saving function (demand side) S = s.Y where s is the average propensity to save or average saving rate.
In the conventional short run Keynesian model investment (I) is given. I = Ia
In equilibriumS = I
Solving the models.Y = Ia
Y = 1/s.Ia = m.Ia where m is the investment multiplier
Mathematical derivation of Harrod-Domar model
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In this model national GDP increases because the autonomous demand (I) increases. It is assumed that aggregate supply responds as to producewhat is demanded. But, what will happen if the economy was at full employment? The only way for production to increase will be an increasein the capital stock. With more capital (and labor) the economy will produce more GDP.
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Mathematical derivation of Harrod-Domar model (2)
Keynes’ Model Expanded to Consider Growth
Harrod and Domar explained how the aggregate supply expands. For them, investment has two effects, one on the aggregate demand side (businesses expend more) and another in the aggregate supply side (more investment increases capital stock and thereby businesses produce more the next period).
We, therefore, need to add a production function:
Y = a.K production function
Where a is the productivity of capital: Y/ K, which is constant
Now we can determine how a change in capital changes income.
Y = a.K
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Mathematical derivation of Harrod-Domar model (3)
What we need to know is how capital changes. It changes by businesses, and government investment:
K = Ia
We are assuming that capital doesn’t ware out, i.e. there is not depreciation.
Returning to the equilibrium condition (S=I) we solve the model again for the long run case
s.Y = Ia = K, but we know that K = Y/a, then
s.Y = Y/a
s.a = Y/Y
Calling Y/Y = g : rate of GNP growth
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Mathematical derivation of Harrod-Domar model IV
g = s.a
If we recognize that capital depreciates:
g = s.a – d
Where d is the depreciation rate per year.
Notice that in this model the rate of growth (g) is constant. Why?
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Harrod’s way:
K = v.Y where v = 1/a
g = s/v
And with depreciation
g = s/v - d
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Production function
K
NGDP1
GDP2> GDP1
Production function
GDP
K
GDP
Productivity rate
To growth model
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Assumptions– Labor/capital proportions are fixed
– Saving rate is given
K
NGDP1
GDP2> GDP1
S
S
Income = GDP
Production function
Saving function
GDP
K
GDP
Saving rate
Productivity rate
To growth model
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Non-existence of equilibrium
K
Y,S,D,I Y
S
DIn
C
D
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Review
Technology or capital/output ratio
Saving rate
Depreciation rate Capital accumulation Growth rate
You should now be familiar with the following terms:
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JOIN KHALID AZIZ
ECONOMICS OF ICMAP, ICAP, MA-ECONOMICS, B.COM.
FINANCIAL ACCOUNTING OF ICMAP STAGE 1,3,4 ICAP MODULE B, B.COM, BBA, MBA & PIPFA.
COST ACCOUNTING OF ICMAP STAGE 2,3 ICAP MODULE D, BBA, MBA & PIPFA.
CONTACT: 0322-3385752 0312-2302870 R-1173,ALNOOR SOCIETY, BLOCK
19,F.B.AREA, KARACHI, PAKISTAN.