Economics 202A
Lecture Outline #5 (version 1.3)
Maurice Obstfeld
Endogenous Growth
We have already seen one crude endogenous growth model, the socalled
°AK±model. It is crude because it does not give a realistic account of the
channels through which productivity grows over time ²namely, innovation
and the creation of new knowledge.
We now turn to a class of models that indeed endogenize the innovative
process. The challenge in thinking about these problems is that the creation
of knowledge, which has a publicgood aspect, is di/erent from the production
of other economic goods.
The endogenous growth literature began with contributions of Robert
Lucas and especially Paul Romer in the 1980s and 1990s, although the ideas
certainly had important precursors in the growth literature of the 1960s.
A Model of Endogenous Growth: The Basic Idea
The model builds on some of the ideas about di/erentiated products that
also underlie the °new trade theory±developed by Paul Krugman and others
in the late 1970s and early 1980s.
In the model, additional °varieties± of
di/erentiated capital goods will boost productivity, and the process through
which new capital goods are invented is endogenized.
In this economy, production of a
°nal
consumption good is given by
Y
t
=
F
(
K
1
;t
; :::; K
A
t
;t
; L
Y;t
) =
A
t
X
j
=1
K
°
j;t
!
L
1
°
°
Y;t
=
A
t
X
j
=1
K
°
j;t
L
1
°
°
Y;t
;
where
L
Y;t
is the amount of labor employed in the ³nal goods sector at
t
and
j
2 f
1
;
2
; :::; A
t
g
indexes the di/erent types of capital that can be used in
production as of
t
. Labor not devoted to ³nalgoods production will, as we
shall see, be devoted to research and development into new capital goods.
We assume that the capital depreciation rate is
°
= 1
;
so that the price
of a machine is its rental rate.
Note some interesting features of this production setup
:
At any point in
time, there are constant returns to scale with respect to the existing factors of
1
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production, no matter how many there are. But while the marginal product
of an existing capital good is ³nite, the marginal product of a
new
capital
good is in³nite.
A di/erent thought experiment gives a good illustration of why the pre
ceding production function can generate endogenous growth. Imagine com
bining 1 unit each of
N
capital goods with 1 unit of Labor; we get
Y
=
N
.
Instead, imagine we combine
N=
(
N
+ 1)
units each of
N
+ 1
capital goods
with 1 unit of labor. We get
Y
=
N
+1
X
j
=1
°
N
N
+ 1
±
°
= (
N
+ 1)
°
N
N
+ 1
±
°
=
N
a
(
N
+ 1)
1
°
°
> N:
So with more capital goods, the output/labor ratio rises holding constant the
amount
of capital input (measured in terms of consumption goods). Thus,
the creation of new capital goods has the potential to raise productivity and
perworker output over time.
Notice, ³nally, that if
K
j;t
=
~
K
t
for all varieties
j
(as is the case in
equilibrium when all goods are symmetric), then
Y
t
=
A
t
X
j
=1
~
K
°
t
L
1
°
°
Y;t
=
A
t
~
K
°
t
L
1
°
°
Y;t
=
~
K
°
t
°
A
1
1
°
°
t
L
Y;t
±
1
°
°
;
so the production side looks equivalent to what we assumed for the Solow
model.
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 Fall '07
 AKERLOF
 Economics, Endogenous growth theory, Exogenous growth model, capital goods

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