Increasing Returns and Long-Run Growth
Author(s): Paul M. Romer
Source:
The Journal of Political Economy,
Vol. 94, No. 5 (Oct., 1986), pp. 1002-1037
Published by: The University of Chicago Press
Stable URL: http://www.jstor.org/stable/1833190
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Increasing
Returns and
Long-Run Growth
Paul M.
Romer
University of
Rochester
This paper presents
a fully specified
model of long-run
growth in
which knowledge
is assumed to be
an input in production
that has
increasing
marginal productivity. It
is
essentially a competitive
equi-
librium model
with
endogenous
technological change.
In contrast
to
models based
on diminishing returns,
growth rates
can be
increasing
over
time, the
effects
of
small disturbances
can be amplified
by
the
actions
of private
agents,
and large
countries may always
grow
faster
than small countries.
Long-run
evidence is offered
in
support
of the
empirical
relevance
of these
possibilities.
I.
Introduction
Because of its
simplicity,
the aggregate
growth model
analyzed by
Ramsey
(1928),
Cass
(1965),
and Koopmans
(1965) continues
to form
the
basis
for
much of the intuition
economists
have
about
long-run
growth. The rate
of return on investment
and the rate
of growth of
per capita output
are expected
to be
decreasing
functions of the level
of the
per capita
capital stock. Over
time,
wage
rates and capital-labor
ratios
across different
countries
are expected
to converge.
Conse-
quently, initial
conditions or current
disturbances have
no long-run
effect on the
level
of output and consumption.
For
example,
an exog-
This
paper is
based
on
work from
my
dissertation
(Romer 1983).
An earlier
version
of
this
paper
circulated
under
the
title "Externalities
and Increasing
Returns
in
Dy-
namic
Competitive
Analysis.'
At
various
stages
I
have benefited
from comments
by
James
J.
Heckman,
Charles
M.
Kahn,
Robert
G.
King,
Robert
E.
Lucas,
Jr.,
Sergio
Rebelo,
Sherwin
Rosen,
Jose
A.
Scheinkman
(the
chairman
of
my thesis
committee),
and the
referees.
The
usual
disclaimer
applies.
I gratefully
acknowledge
the
support
of
NSF grant
no.
SES-8320007
during
the
completion
of this
work.
[oudsl of
Poldclal
Economy,
1986} vol.
94,
no. 5J
?
1986
by
T
he
University
of Chicago. All rights reserved.
0022-3808/86/9405-0009$01.50
1002
INCREASING RETURNS
1003
enous
reduction in the
stock of capital in a given country will
cause
prices for capital assets to
increase and will therefore induce an
offset-
ting increase in
investment. In the absence of technological
change,
per capita output should
converge to a steady-state value with no
per
capita growth. All these
presumptions follow directly from
the as-
sumption
of
diminishing
returns
to
per capita capital
in
the
produc-
tion of per capita output.
The
model proposed
here offers an alternative view of
long-run
prospects for growth. In a
fully specified competitive
equilibrium, per
capita output can grow
without
bound,
possibly at a rate that is
mono-
tonically increasing over
time. The rate of investment and the
rate of
return on capital may
increase rather than decrease with
increases
in
the capital stock. The level
of per capita output
in
different countries
need not converge; growth
may be persistently slower
in
less
devel-
oped
countries and may
even
fail
to
take place at all. These
results do
not depend on any kind of
exogenously specified technical
change or
differences
between
countries. Preferences and the
technology
are
stationary and identical.
Even the
size of the
population
can
be
held
constant. What is crucial for all
of these
results
is a departure
from
the
usual
assumption
of
diminishing
returns.
While exogenous
technological change is ruled
out,
the model
here
can
be
viewed as
an
equilibrium model of endogenous
technological
change
in
which long-run
growth
is
driven primarily by the accumula-
tion of knowledge by
forward-looking,
profit-maximizing
agents.
This focus on
knowledge
as the basic
form of
capital
suggests
natural
changes
in the
formulation
of the standard aggregate growth model.
In
contrast
to
physical
capital that
can
be
produced one
for
one
from
forgone output, new
knowledge
is
assumed to be the product
of
a
research
technology that
exhibits diminishing returns.
That
is,
given
the
stock
of
knowledge
at
a point
in
time,
doubling the inputs
into
research
will
not double the amount
of
new
knowledge produced.
In
addition,
investment in
knowledge suggests
a
natural
externality.
The
creation of
new knowledge
by
one
firm
is assumed to have
a
positive
external effect on the
production
possibilities
of other
firms
because
knowledge cannot be
perfectly patented
or
kept
secret.
Most
impor-
tant, production of
consumption goods
as a
function
of the
stock
of
knowledge and other
inputs exhibits increasing
returns;
more pre-
cisely, knowledge may
have an
increasing marginal product.
In con-
trast to models in which
capital exhibits diminishing marginal
produc-
tivity, knowledge will grow
without
bound.
Even
if
all other
inputs
are
held
constant, it
will
not be
optimal
to
stop at some steady state
where
knowledge
is
constant and
no
new
research
is undertaken.
These three
elements-externalities, increasing
returns
in
the
pro-
duction
of output, and
decreasing returns
in
the production
of
new
1004
JOURNAL
OF
POLITICAL
ECONOMY
knowledge-combine
to
produce
a well-specified
competitive
equilib-
rium
model
of growth.
Despite
the
presence
of increasing
returns,
a
competitive
equilibrium
with externalities
will exist.
This
equilibrium
is
not Pareto
optimal,
but
it is
the outcome
of a well-behaved
positive
model
and is
capable
of
explaining
historical
growth
in the absence
of
government
intervention.
The
presence
of the externalities
is
essen-
tial
for the
existence
of
an equilibrium.
Diminishing
returns
in
the
production
of
knowledge
are required
to ensure
that
consumption
and utility
do not
grow too
fast.
But the
key feature
in the reversal
of
the
standard
results
about
growth
is
the
assumption
of
increasing
rather
than
decreasing
marginal
productivity
of
the
intangible
capital
good
knowledge.
The paper
is organized
as follows.
Section
II
traces
briefly
the
his-
tory
of
the
idea that
increasing
returns
are important
to the explana-
tion of long-run
growth
and
describes
some of the
conceptual
difficulties
that impeded
progress
toward
a formal
model that
relied
on
increasing
returns.
Section
III
presents
empirical
evidence
in sup-
port
of
the
model
proposed
here.
Section
IV
presents
a
stripped-
down,
two-period
version
of
the
model
that
illustrates
the tools that
are
used to
analyze
an equilibrium
with
externalities
and increasing
returns.
Section
V presents
the
analysis
of the
infinite-horizon,
con-
tinuous-time
version of the
model,
characterizing
the
social
optimum
and the
competitive
equilibrium,
both
with and
without
optimal
taxes.
The primary
motivation
for the
choice
of continuous
time
and the
restriction
to a single
state
variable
is the
ease
with
which qualitative
results can
be derived
using
the
geometry
of the phase
plane.
In
particular,
once
functional
forms for
production
and
preferences
have been
specified,
useful
qualitative
information
about
the dynam-
ics
of the social
optimum
or the
suboptimal
competitive
equilibrium
can be
extracted
using simple
algebra.
Section
VI
presents
several
examples
that illustrate
the extent
to which conventional presump-
tions
about growth
rates,
asset
prices,
and
cross-country
comparisons
may
be reversed
in
this
kind of economy.
II.
Historical
Origins
and Relation
to
Earlier
Work
The idea that increasing
returns
are
central
to the
explanation
of
long-run growth
is at least
as old
as
Adam Smith's
story of
the pin
factory.
With
the
introduction by
Alfred
Marshall
of the distinction
between
internal
and
external
economies,
it appeared
that this
expla-
nation
could
be
given
a consistent,
competitive
equilibrium
interpre-
tation.
The most
prominent
such
attempt
was
made by
Allyn
Young
in his
1928
presidential
address
to the
Economics
and
Statistics
sec-
tion
of
the British Association
for the
Advancement
of
Science
INCREASING RETURNS
1005
(Young 1969),
Subsequent economists
(e.g.,
Hicks 1960;
Kaldor
1981) have credited Young
with a fundamental insight about
growth,
but because of the verbal
nature of his argument and the
difficulty of
formulating explicit
dynamic
models,
no formal model
embodying
that insight was developed.
Because of the technical
difficulties presented by dynamic
models,
Marshall's concept of
increasing returns that are external to a firm but
internal to an industry
was most widely used in static models,
espe-
cially in the field of
international trade. In the 1920s the logical
consis-
tency and relevance of
these models began to be seriously
challenged,
in
particular by Frank
Knight,
who had been a student of
Young's at
Cornell.' Subsequent work
demonstrated that
it
is possible
to con-
struct
consistent,
general
equilibrium models
with
perfect
competi-
tion,
increasing
returns,
and externalities
(see, e.g.,
Chipman
1970).
Yet Knight was at least
partially correct in objecting that the
concept
of
increasing returns that
are external to the firm was
vacuous,
an
"empty economic
box"
(Knight 1925). Following
Smith,
Marshall,
and
Young, most authors
justified the existence of increasing returns
on
the basis
of increasing
specialization and the division of labor.
It is
now clear
that these
changes
in
the organization of production
cannot
be
rigorously treated as
technological externalities.
Formally,
in-
creased
specialization
opens
new
markets and introduces
new
goods.
All
producers
in
the
industry may benefit
from the introduction of
these
goods,
but
thev
are
goods,
not
technological externalities.2
Despite the objections
raised by
Knight,
static models of
increasing
returns with externalities
have been widely used
in
international
trade.
Typically,
firm
output is simply assumed to be
increasing,
or
unit
cost
decreasing,
in
aggregate industry output.
See
Helpman
(1984) for
a
recent survey.
Renewed interest
in
dynamic
models of
growth driven by
increasing
returns was
sparked
in
the
1960s follow-
ing the publication of
Arrow's (1962) paper on learning by
doing.
In
his
model, the productivity of
a
given
firm is assumed
to
be an increas-
ing function of
cumulative aggregate investment
for
the
industry.
Avoiding the
issues
of specialization
and the division of
labor,
Arrow
argued
that
increasing returns
arise
because
new
knowledge
is discov-
ered
as
investment and production take
place.
The
increasing
returns
were
external to individual firms
because
such
knowledge
became
publicly
known.
To
formalize his
model,
Arrow
had to face two
problems
that arise
l
For an
account
of
the development
of Young's
ideas
and
of
his
correspondence
with Knight.
see Blitch
(1983).
2For
a
treatment
of
increasing
returns based
on
specialization,
see Ethier
(1982).
Although
the model
there
is
essentially
static,
it
demonstrates
how specialization
can be
introduced
in
a
differentiated
products
framework
under imperfect
competition.
