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XET 504
LONG-RUN ECONOMIC GROWTH
HARROD – DOMAR MODEL
Japheth
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Awiti, Ph
...
February 27, 2020
Japheth
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Awiti, Ph
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XET 504
February 27, 2020
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Outlne
1
2
3
4
5
Introduction
Assumptions
The Model
Applications
Limitations
Japheth
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Awiti, Ph
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XET 504
February 27, 2020
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Introduction
The model was independently developed by Roy
Harrod (Harrod 1939, 1948) and Evsey Domar
(Domar 1946, 1947)
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Japheth
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Awiti, Ph
...
XET 504
February 27, 2020
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Assumptions
The assumptions underlying the model include
the following:
a
...
b
...
That is,
K
the capital–labour ratio, , is constant
...
O
...
D
...
)
c
...
e
...
Y
Total new investment spending is
determined by total savings
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Japheth
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Awiti, Ph
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XET 504
February 27, 2020
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The Model
If we assume that the economy consists of only
two sectors, households and firms, we can
express the national income equation as
Yt = Ct + St
(1)
where Yt = GDP, Ct = consumption, and St =
saving
...
O
...
D
...
)
For the economy to be in equilibrium, investment
spending must equal savings
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Japheth
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Awiti, Ph
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XET 504
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February 27, 2020
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Model (Contd
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(3)
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Model (Contd
...
If we assume capital depreciates
over time at the rate δ, we can express the
evolution of the capital stock over time as
follows:
Japheth
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Awiti, Ph
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February 27, 2020
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Model (Contd
...
(4)
= (1 − δ) Kt + It
Japheth
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Model (Contd
...
O
...
D
...
)
then it follows that
K = vY
and
∆K
=v
∆Y
∆K
where
is the incremental capital–output
∆Y
ratio (ICOR)
...
O
...
D
...
)
Since total saving is some proportion of output,
the savings function can be written as
St = sYt
(5)
where s is the savings rate (also referred to as
the savings ratio)
...
O
...
D
...
)
Using the results that Kt = vYt and
It = St = sYt (since total new investment is
determined by total savings), we can rewrite
Equation (4) as
vYt+1 = (1 − δ) vYt + sYt
...
O
...
D
...
)
If we divide through by v , simplify, and then
subtract Yt from both sides of Equation (6), we
get Equation (7):
i
hs
− δ Yt
...
O
...
D
...
)
If we divide Equation (7) through by Yt , we
obtain Equation (8):
s
Yt+1 − Yt
= −δ
Yt
v
where
(8)
Yt+1 − Yt
is the growth rate of GDP
...
O
...
D
...
)
Yt+1 − Yt
, then the
Yt
Harrod–Domar growth equation can be written
as
s
g = − δ
...
O
...
D
...
)
According to this equation, the growth rate of
GDP is jointly determined by the savings rate, s,
the capital–output ratio, v , and the rate of
depreciation, δ
...
O
...
D
...
)
The higher the savings rate and the lower the
capital–