Handout for
Kremer (1993)
by Hakan Yilmazkuday
1
POPULATION GROWTH AND TECHNOLOGICAL CHANGE:
ONE MILLION B.C. TO 1990
MICHAEL KREMER
This paper combines the following two findings in the literature:
1.
The
size of
population is proportional to the
growth rate of
technology. This is
claimed by
o
Kuznets (1960) and Simon (1977,1981) –
A higher population means more
potential inventors
.
o
Endogenous growth literature – Aghion and Howitt (1992), Gorssman
and Helpman (1991) –
The size of
population spurs technological change.
2.
Population is limited by the available technology, so that
growth rate of
population
is proportional to the
growth rate of
technology. This is assumed by
o
Malthus (1978) – In the original paper, Malthus (1798) mentions about
the state of food production (as technology)
In sum, this paper claims:
And by using this, the paper states that the size of population is proportional to the
growth of population:
Size of
Population
↔
Growth of
Technology
↔
Growth of
Population
Size of
Population
↔
Growth of
Population
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2
A
SIMPLE
MODEL
Assume that the output is given by
Y
Ap T
α
α
−
=
1
(1)
where
A
is the level of technology,
p
is the population and
T
is the land.
After normalizing the land to one
1
, at the steadystate, we have
/(
)
y
p
A
α
−
⎛
⎞
⎜
⎟
⎜
⎟
⎝
⎠
=
1 1
(2)
where
p
is the steady state level of population and
y
is the steady state level of per
capita income.
The growth rate of technology is given by
A
pg
A
=
±
(3)
where
g
is the research productivity. Thus, growth rate of technology is
proportional to the level of population. Here, we have the assumption that the
research productivity is independent of the population size. By taking the logarithm
of equation (2), and differentiate with respect to time, we obtain
p
A
p
A
α
=
−
1
1
±
±
(4)
Therefore, the growth rate of population is proportional to the growth rate of
technology. By substituting (3) into (4), we get
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 Fall '11
 HAKANYILMAZKUDAY
 Population Ecology, An Essay on the Principle of Population, Per capita income

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