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Macroeconomic Policy
Class Notes
Long run growth 2: The Solow model
Revised: October 10, 2011
Latest version available at
www.fperri.net/teaching/macropolicyf11.htm
Why do we see such large diﬀerences in level of income across countries and in their
growth rate performance? To answer this question we introduce one of the leading
models in economics, introduced by Robert Solow (economist at MIT, winner of the
Nobel prize in economics in 1987) in the 50s. This is a pretty simple theory but quite
powerful in the sense that it can be used to analyze a whole variety of issues. The key
point of the theory is that sustained growth and high levels of income per capita in a
country can be achieved through saving and capital accumulation. Limits to capital
accumulation are posed by the fact that returns to capital are decreasing. Decreasing
returns simply means that the beneﬁt of any additional unit of capital are declining
with the stock of capital per worker. Suppose I am a weaver and I weave by hands.
My output will be quite low. If I purchase a loom I will increase my output a lot. If
I buy a second loom I will increase my output but not as much as the ﬁrst increase
because now I have to divide my time between the two looms. If I have 10 looms and
I add an 11th loom my output will not really increase by much because I don’t have
really the time to operate it.
The basic model
For now we will consider the total number of worker in a country constant and equal
to
L
. We will also assume that everybody in this economy work so GDP per capita
is also equal to GDP per worker (
L
is also equal to population).
The theory is built around two simple equations. The ﬁrst equation is the aggregate
production function of a country that is assumed to be of a particular form called
CobbDouglas
Y
=
AF
(
K,L
) =
AK
α
L
1

α
Y
here represents output produced,
K
is the capital stock in place,
L
is the amount
of labor employed and
A
is a parameter that determines the eﬃciency of the factors
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View Full DocumentThe Solow Model
2
of production.
A
sometimes is also called “Total Factor Productivity”. Note the the
particular functional form display “Constant Return To Scale” that is a doubling of
both inputs of production (labor and capital) lead to a doubling of output. The second
equation follows from the fact that national income is split it between consumption
C
and investment
I
Y
=
C
+
I
For now we are assuming that the economy is closed (no link with the rest of the
world) and we do not model the government separately from the private sector. Also
for now let’s assume that consumers consume a ﬁxed fraction of their income and
let’s call this fraction (1

s
) so
C
= (1

s
)
Y.
Using this assumption and the division
of national income we obtain
Y
=
C
+
I
= (1

s
)
Y
+
I
I
=
sY
this implies that investment is a ﬁxed fraction of income. Dividing everything by
the total number of workers
L
and denoting with lower case letters the perworker
variables we get
i
=
sy
where
i
=
I
L
y
=
Y
L
dividing by
L
both sides of the production function we also get
y
=
AK
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 Spring '11
 Michaelshaw

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