2. It also satisfies ‘Inada conditions’
(a)
lim
0
'( )
k
f
k
which means that when capital stock is too small the MPK is very large.
(b)
lim
'( )
k
f
k
0 which means that MPK is very small when capital stock is too large.
Demand for Goods:
In a solow model, it is assumed that goods are demanded for consumption and investment
purposes.
Therefore,
Y
= C + I
...(v)
On dividing eqn.
(vi)
by AL, we get
Y
AL
C
I
AL
Al
y
c
i
...(vi)
For simplification, we have assumed the economy to be a two-sector economy.
Each year people save some proportion of their income (1 –
b
), then, (1 –
b
) is the saving rate and it lies between
0 and 1.
Saving per effective labour = (1 –
b
)
y
\ C
= (
b
)
y
y
= by + i
...(vii)
y – by
= i
(1 –
b
)
y
= i
...(viii)
The relationship between output and saving is shown with the help of following diagram:

THE GOLDEN RULE
In this section, we shall consider the effect of change in saving rate on steady state. Let us assume that saving
rate increases while the
n
,
g
and d remain to be same. As we know that
i
=
sf
(
k
), there will be higher investment
which will lead to capital accumulation and output growth and the economy will finally reach to a new steady state
with higher capital and output. When rate of savings increase from
s
1
to
s
2
then the investment curve also increases
from
s
1
f
(
k
) to
s
2
f
(
k
). Therefore the economy reaches at new steady state
k
*2 through the process of capital accumulation
and output growth.
From the above explanation, one may jump to a hurried conclusion that a higher saving is always desirable as
higher savings will lead to higher capital accumulation and thereby increased output in the economy. You may also
misinterpret that the 100% saving rate will lead to highest possible capital accumulation and output in the economy,
but it is not true. At different levels of
s
, there are different levels of capital accumulation but there is one optimum
level of capital accumulation which is called golden rule level of capital.
At the golden rule level of capital the level of saving is such that consumption per effective labour is maximum
at the steady state. The reason is that individuals are concerned with the amount of output they consume. T = for
them capital stock or total output of the economy is not of much significance. Therefore, that level of saving rate
which maximizes the consumption per effective labour is the most desirable and the optimum. It is known as Golden
rule level of saving rate. we can say that in a two sector economy national income is the sum total of consumption
and investment assuming that saving and investment are equal to each other. Therefore, steady state consumption
can be found by deducting investment from income.
c
* =
y
* –
i
*
and we know
y
is a function of capital and
i
is a function of
n
,
g
and d, therefore we can rewrite above equation as:
c
* =
f
(
k
*) – (
n
+ g + d)
k
*
...(xiv)
It is interesting to see that this increase in steady state capital has a contrasting effect on steady state consumption.

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- Winter '17
- Economics