Economic growth and economic development 64
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Introduction to Modern Economic Growth
comparisons based on the Solow model have to be taken with a grain of salt, since
we do not know what the preferences of the individuals are.
Since the economy is closed (and there is no government spending), aggregate
investment is equal to savings,
S (t) = I (t) = Y (t) − C (t) .
Individuals are assumed to save a constant fraction s of their income,
(2.9)
S (t) = sY (t) ,
while they consume the remaining 1 − s fraction of their income:
C (t) = (1 − s) Y (t)
(2.10)
In terms of capital market clearing, this implies that the supply of capital resulting
from households’ behavior can be expressed as K s (t) = (1 − δ)K (t) + S (t) =
(1 − δ)K (t) + sY (t). Setting supply and demand equal to each other, this implies
¯ (t). Combining these
K (t) = K s (t). Moreover, from (2.3), we have L (t) = L
market clearing conditions with (2.1) and (2.7), we obtain the fundamental law of
motion the Solow growth model:
(2.11)
K (t + 1) = sF [K (t) , L (t) , A (t)] + (1 − δ) K (t) .
This is a nonlinear difference equation. The equilibrium of the Solow growth model
¯ (t)) and
is described by this equation together with laws of motion for L (t) (or L
A (t).
2.2.2. Definition of Equilibrium. The Solow model is a mixture of an oldstyle Keynesian model and a modern dynamic macroeconomic model. Households
do not optimize when it comes to their savings/consumption decisions. Instead,
their behavior is captured by a behavioral rule. Nevertheless, firms still maximize
and factor markets clear. Thus it is useful to start defining equilibria in the way
¯ (t) from (2.3),
that is customary in modern dynamic macro models. Since L (t) = L
throughout we write the exogenous evolution of labor endowments in terms of L (t)
to simplify notation.
Definition 2.2. In the basic Solow model for a given sequence of {L (t) , A (t)}∞
t=0
and an initial capital stock K (0), an equilibrium path is a sequence of capital stocks,
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