Economic growth and economic development 533

Introduction to Modern Economic Growth
instantaneous return of rI (t). In addition, the individual will get back the one unit
of capital, which has now experienced a change in its price of p˙I (t) /pI (t), and finally, he will have to buy consumption goods, whose prices changed by p˙C (t) /pC (t).
Therefore, the general formula of the rate of return denominated in consumption
goods in terms of the rate of return denominated in investment goods is
rI (t) p˙I (t) p˙C (t)
+
−
.
rC (t) =
pI (t) pI (t) pC (t)
In our setting, given our choice of numeraire, we have p˙C (t) /pC (t) = 0. Moreover,
p˙I (t) /pI (t) is given by (11.30). Finally,
rI (t)
=A−δ
pI (t)
given the linear technology in (11.28). Therefore, we have
rC (t) = A − δ +

p˙I (t)
.
pI (t)

and in steady state, from (11.30), the steady-state consumption-denominated rate
of return is:
rC = A − δ − (1 − α) gK .
From (11.4), this implies a consumption growth rate of
C˙ (t)
1
(11.31)
gC ≡

= (A − δ − (1 − α) gK − ρ) .
C (t)
θ
Finally, differentiate (11.27) and use the fact that labor is always constant to
obtain

K˙ C (t)
C˙ (t)
=α
,
C (t)
KC (t)
which, from the constancy of κ(t) in steady state, implies the following steady-state
relationship:
gC = αgK .
Substituting this into (11.31), we have
(11.32)
and
(11.33)

∗
gK
=

A−δ−ρ
1 − α (1 − θ)

gC∗ = α

A−δ−ρ

.
1 − α (1 − θ)
519