Economic growth and economic development 525

Introduction to Modern Economic Growth
It also pins down the initial level of consumption as
Ô
Ê
(11.16)
c (0) = (A )( 1)θ−1 + ρθ−1 − n k (0) .

Note also that in this simple AK model, growth is not only sustained, but it

is also endogenous in the sense of being affected by underlying parameters. For
example, consider an increase in the rate of discount, ρ. Recall that in the Ramsey
model, this only influenced the level of income per capita–it could have no effect
on the growth rate, which was determined by the exogenous labor-augmenting rate
of technological progress. Here, is straightforward to verify that an increase in the
discount rate, ρ, will reduce the growth rate, because it will make consumers less
patient and will therefore reduce the rate of capital accumulation. Since capital
accumulation is the engine of growth, the equilibrium rate of growth will decline.
Similarly, changes in A and θ affect the levels and growth rates of consumption,
capital and output.
Finally, we can calculate the saving rate in this economy. It is defined as total investment (which is equal to increase in capital plus replacement investment)
divided by output. Consequently, the saving rate is constant and given by
s =
=

K˙ (t) + δK (t)
Y (t)
k˙ (t) /k (t) + n + δ

A
A − ρ + θn + (θ − 1)δ
(11.17)

,
=
θA
where the last equality exploited the fact that k˙ (t) /k (t) = (A − δ − ρ)/θ. This
equation implies that the saving rate, which was taken as constant and exogenous

in the basic Solow model, is again constant, but is now a function of parameters,
and more specifically of exactly the same parameters that determine the equilibrium
growth rate of the economy.
Summarizing, we have:
Proposition 11.1. Consider the above-described AK economy, with a representative household with preferences given by (11.1), and the production technology
given by (11.6). Suppose that condition (11.12) holds. Then, there exists a unique
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