Economic Growth and International Trade

Economic Growth and International Trade in Pure Theory
Author(s): Jaroslav Vanek
Reviewed work(s):
Source: The Quarterly Journal of Economics, Vol. 85, No. 3 (Aug., 1971), pp. 377-390
Published by: Oxford University Press
Stable URL: http://www.jstor.org/stable/1885928 .
Accessed: 24/12/2011 21:24
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .
http://www.jstor.org/page/info/about/policies/terms.jsp
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of
content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms
of scholarship. For more information about JSTOR, please contact [email protected].
Oxford University Press is collaborating with JSTOR to digitize, preserve and extend access to The Quarterly
Journal of Economics.
http://www.jstor.org
ECONOMIC GROWTH AND INTERNATIONAL TRADE
IN PURE THEORY *
JAROSLAV VANEK
I. Introduction, 377.-II. The rate of growth, existence, and stability of
equilibrium for a small open economy, 378.- III. The terms of trade and the
growth solution for a small open economy, 382. -IV. The rate of growth,
existence, and stability of equilibrium in a large open economy, 384.-V. The
open economy growth model and technological progress, 386. - VI. The golden
rule solutions, 390.
I. INTRODUCTION
Many of my fellow international economists may have experi-
enced the same difficulties as I have in teaching graduate courses
in our field. Considering the importance that economic science is
giving lately to the problem of economic growth, one feels that a
substantial part of the graduate offering in international trade ought
to contain a synthesis between the theory of economic growth on
the one hand and the pure theory of trade on the other. But very
often one does not get very much beyond contributions such as those
of J. Bhagwati, H. G. Johnson, or T. N. Rybczynski,l wherein ex-
ogenously given changes in factor endowments or technology are
translated into changing production possibilities and changing pat-
terns of trade.
The explanation why generally one finds it very difficult to go
beyond these writings is that the literature integrating the theory
of growth with that of international trade is quite difficult. For
example, the paper by P. K. Bardham and that of H. Oniki and
H. Uzawa (cited below) are, judging from my experience, too diffi-
cult for an average graduate student in international economics.2
I would like to submit that this difficulty is by no means a
necessary one, and the first purpose of this paper is to substantiate
*
In preparing this paper I benefited from discussions with Mr. Alan Dear-
dorif of the Cornell Department of Economics and Professor Trent Bertrand of
Johns Hopkins University.
1. Jagdish Bhagwati, "International Trade and Economic Expansion,"
American Economic Review, XLVIII, No. 4 (Dec. 1958), 941-53. Harry G.
Johnson, International Trade and Economic Growth (Cambridge: Harvard
University Press, 1958). T. N. Rybezynski, "Factor Endowment and Relative
Commodity Prices," Economica, n.s. XXII, No. 4 (Nov. 1955), 336-41.
2. P. K. Bardhan, "Equilibrium Growth in the International Economy,
this Journal, LXXIX, No. 3 (Aug. 1965), 455-64. H. Oniki and H. Uzawa,
"Patterns of Trade and Investment in a Dynamic Model of International
Trade," Review of Economic Studies, XXXII (1), No. 89 (Jan. 1965), 16-38.
378 QUARTERLY JOURNAL OF ECONOMICS
this claim by offering a considerably simpler, yet rigorous, growth
theory for an open economy. But this is not the only purpose. In
the course of presenting the simplified theory I am able either to
derive new results or to establish results previously obtained through
new methods. In the following section I derive the rate of growth
and study the existence and stability of growth equilibrium for a
small country. In Section III I derive the effects of changes in the
terms of trade on the equilibrium growth solution. In Section IV
the rate of growth, existence, and stability of equilibrium is studied
in the context of a large country facing a less than infinitely elastic
foreign offer curve. In Section V I extend the theory of growth with
technological progress to situations involving international trade,
and, finally, in Section VI I derive some conclusions regarding
golden rule solutions for an open economy.
II. THE RATE OF GROWTH, EXISTENCE, AND STABILITY OF
EQUILIBRIUM FOR A SMALL OPEN ECONOMY
The economy whose growth behavior under international trade
we want to examine is very simple. The defining characteristics that
will remain with us for all five sections of this paper are as follows.
The economy produces in each period from capital and labor two
products, a consumer good x and a capital good y. The production
functions are neoclassical, subject to constant returns to scale and
diminishing returns to a single factor everywhere, and do not in-
volve any interindustry flows. A constant share of national product
so is saved every year and invested in capital goods that can be
either procured domestically or imported in exchange for the other
nationally produced commodity. The rate of growth of the labor
force is exogenously given; call it n. In addition to those assump-
tions, which will remain with us throughout this paper, we assume
for the purposes of the present section an infinitely elastic foreign
offer curve. In other words, the international and internal prices
are perfectly invariant in the course of the process of growth.
Consider now Figure Ia, defined by two coordinate axes re-
flecting labor supply L and the capital availability K of the -economy.
More specifically, consider the factor endowments given by points
Lo
and
K2. Corresponding
to these
endowments,
to the fixed inter-
national terms of trade, and to the given production functions, the
efficient allocation of resources is to be found at point a on the con-
tract curve in the box diagram.
On observing that the marginal rates of substitution at a, -indi-
ECONOMIC GROWTH AND INTERNATIONAL TRADE 379
L
Lo
ox
K, Z, IK2 K3 Z2 Z3 K(
FIGURE, Ia
cated by the common tangency passing through a, are equal to the
slope of the line
Z20,2,
it is immediately apparent that the segment
OIZ2
measures national product in terms of capital wage units. The
ratio of that segment to the segment OK2 thus measures, except for
a constant factor of proportionality, the output-capital ratio Z/K.
Of course, the factor of proportionality must be there to convert the
nondimensional ratio of the two segments to the output-capital ratio
expressed in terms of income at world market prices per physical
unit of capital.
We now observe that, if the capital endowment of the economy
changes with that of labor remaining invariant, the dimensions of
the box will change. However, the significant price ratios within
a certain range will not change. As we know from the proof of the
factor price equalization theorem, as long as international prices
remain the same and as long as the economy does not specialize,
changes in factor endowments in the economy will not affect factor
prices. And consequently we can now expand the capital availa-
bility from K2 to K3, leaving labor supply unchanged at
Lo,
and
this will make the national income increase to OZ3- It is immedi-
ately apparent from the construction that the output-capital ratio
Z/K must have declined, as the result of an expansion in supply
of capital. Similarly, a contraction of the stock of capital to K1
would increase the Z/K ratio.
Thus, at least for the range of no specialization corresponding
to levels of capital supply K1 through K3, we have established that
380 QUARTERLY JOURNAL OF ECONOMICS
the output-capital ratio will be
declining. This is shown in
Figure
lb. When we expand the supply of capital beyond K3, or contract
ZA/
so Z/K-k (dK/dt4/K
n
K
n2~~~~~~~~6
n3
0
(K/L)i
(K/L)2 (K/L)3
FIGURE lb
it below K1, the relationship between the capital endowment and
the output-capital ratio still will be of the same declining nature.
However, the rate of decline will be somewhat more pronounced
because of the effect of changing relative factor prices and diminish-
ing returns that must occur once the economy specializes in one or
the other of the two goods produced.
If we now multiply the ratio Z/K by the constant average pro-
pensity to save
soy
we obtain investment per unit of capital, which
is nothing else but the rate of growth of capital, k
=
(dK/dt) 1K.
Corresponding to alternative levels of the capital-labor ratio, this
rate of growth is shown in Figure lb. Of course we have shown all
this thus far only for a given labor endowment
Lo.
As is well known,
because of the constancy of international product prices, and the
linear homogeneity of the production functions, the absolute scale
of the construction is immaterial, and only the factor proportions
and output to factor proportions are significant. Consequently, Fig-
ure lb has a general validity whatever the absolute levels of factor
endowments.
For a prescribed rate of growth of the labor force n the equi-
librium capital-labor ratio, that is, the capital-labor ratio belonging
to the corresponding steady state, will now be found at the inter-
section of the contour k with a horizontal line drawn at the level n.
ECONOMIC GROWTH AND INTERNATIONAL TRADE 381
For example, for a prescribed rate of growth of population n2 we
find the equilibrium e2 in Figure lb. It is apparent that for the
rate of growth n2 the economy will indefinitely keep producing
both products x and y in the proportions indicated in Figure Ia by
the resource allocation at point a. Of course it is not important
that the output levels of product y, that is, of the capital good,
exactly match the capital requirements of the economy. Whatever
the net excess or deficit of capital goods, the economy can barter
it in the world markets at the prescribed market prices.
On the other hand, if the labor force experiences a considerably
higher rate of growth, such as the one indicated by
n,
in Figure Ib,
the steady state of the economy will be found at equilibrium point
el
corresponding to a full specialization by the economy in the con-
sumer good. The economy must now acquire all of its capital goods
year after year from the world market by bartering them for ex-
ports of consumer goods. On the other side of the spectrum, for a
very low rate of growth of the labor force, such as n3 or lower, the
economy indefinitely specializes in the production of the investment
good. It is also apparent that, with rates of growth of population
falling short of
n3,
wages and the relative income share of labor
must be higher than that found at points e3 or e2. Of course, the
results regarding specialization depend critically on the relative
factor intensities and would be reversed if x were capital-intensive
and y labor-intensive.
Because the locus k is single-valued with respect to the vertical
axis in Figure Ib, there can be only one equilibrium steady state for
each prescribed level of rate of growth of the labor force. Moreover,
the negative slope of the locus guarantees stability of all the equi-
libria, such as
el,
e2, or e3. As is indicated by the arrows in the vicin-
ity of these equilibrium points, if the economy is temporarily away
from equilibrium (for a prescribed rate of growth of the labor
force), it will gradually return to equilibrium. This becomes imme-
diately apparent if we realize that, for example, for points to the left
of e2, the rate of growth of capital exceeds the rate of growth of
labor. Under such conditions, of course, the capital-labor ratio
must be increasing, that is, the point must be moving along the k
contour in the direction of e2. And the process will not be arrested
until e2 is reached.
Noting, moreover, that everywhere, even for extremely high
levels or extremely low levels of the capital-labor ratio, the contour
k in Figure lb must be negatively sloped, we also establish the global
stability and uniqueness of the equilibrium point.
382 QUARTERLY JOURNAL OF ECONOMICS
We have thus come to what we have set out to do in this section
We have found for a small open economy its steady state growth
solution and established the uniqueness and local as well as global
stability of such an equilibrium state. Obviously the comparative
simplicity of the solution of this two-sector growth model resides
in the fact that the economy need not supply all of its capital goods.
The Uzawa closed-economy model, although it also contains only
two sectors, is a good deal more complicated, because the economy
has another constraint to operate under, namely, to secure exactly
the amount of capital goods it needs for all investments.
III. THE TERMS OF TRADE AND THE GROWTH SOLUTION
FOR A SMALL OPEN ECONOMY
The effects of a change in the terms of trade on the growth
equilibrium of a small economy need not detain us very long. Given
what we have done already, the answers can be obtained very easily.
In Figure II we show an instantaneous production possibility locus
y
TT
0
X
FIGURE II
of our small economy as of a given period. Suppose that the economy
is in a steady state at
PO
facing international terms of trade given
by the slope
PO.
Without loss of generality we have drawn our dia-
ECONOMIC GROWTH AND INTERNATIONAL TRADE 383
gram in such a way as to make the economy exactly self-sufficient.3
The 'equilibrium corresponding to
Po, analogous to Figure Ib, is
found in Figure III at eo,
for the exogenously prescribed rate of
growth of the labor force no.
~~~~~~~~0~ ~
\ X e ,~~~~~e
nobl
eo
k,
OdK/dt/K),
ko= (dK/dt/K)o
0 K/L
FIGURE III
Suppose now that the terms of trade line becomes steeper and
assumes the position C1P1. In other words, the consumer good has
now become more expensive in international markets. As is indi-
cated in Figure II, more of x and less of y will now be produced,
and at the new terms of trade there will be a need to trade from
P1 to C1. The point C1 is characterized by the fact that the same
proportion of national product as at
PO
is allocated to the consumer
good; the savings propensity sO
is some 40 or 45 percent.
Now what does this'instantaneous change in the terms of trade
do to the rate of growth of capital? It must be obvious that over
short periods of time, with capital stock remaining by and large
unchanged, the increase in demand for capital goods and investment
from that indicated by
PO
to that indicated by C1'must have raised
instantaneously the rate of growth of capital. Such an increase is
shown in Figure III from
eo
to e'.: But, as we have noted in the
preceding section, the k line drawn against the capital-labor ratio
3. Of course, any other position involving exports or imports of the con-
sumer good x in the (initial) steady state would be conceivable.
384 QUARTERLY JOURNAL OF ECONOMICS
must always be downward sloping. Consequently the improvement
in the price of x, that is, the improvement in the terms of trade of
our small country, must eventually lead to a new equilibrium point
for the prescribed rate of growth of population
no,
found at point
e1. Unambiguously at that point the equilibrium capital-labor ratio
is higher than the initial ratio corresponding to
eo.
Now, observing
that the price consumption line in Figure II must always show an
increase in demand for capital if the price of capital goods declines
in international markets, we find that the result that we have
just
obtained for points
PO
and P1 becomes perfectly general. Specifi-
cally, an increase in the price of the consumer good in international
markets must always lead to an increase in the equilibrium capital-
labor ratio of the small trading economy. It follows from the nature
of the proof that the result does not depend on relative factor in-
tensities.
The increase in the equilibrium capital-labor ratio may, but
need not, increase the equilibrium consumption per capita. This
follows from the offsetting effects of a higher price of the consump-
tion good on the one hand and of a higher capital-labor ratio on
the other. It also follows that an improvement in terms of trade, or
introduction of trade starting from autarky, need not imply an
improved living standard for a country in the long run. In fact, it
is now possible to show without difficulty that steady state con-
sumption per head will be maximized for extreme (zero and infi-
nite) values of the terms of trade, and a minimum consumption per
head will correspond to some intermediate terms of trade
ratio,
generally different from the autarky ratio.
IV. THE RATE OF GROWTH, EXISTENCE AND STABILITY OF
EQUILIBRIUM IN A LARGE OPEN ECONOMY
Once the assumption of an infinitely elastic foreign offer is
abandoned, matters become more complicated because of the in-
creased technical difficulty not only of analysis, but also of concep-
tion. What do we mean by a less than infinitely elastic foreign offer
curve in the case of an economy that is indefinitely growing? Obvi-
ously, if we assume a foreign offer curve of finite elasticity, which
is fixed and does not expand with time, we have only to wait until
our economy grows large enough and becomes entirely dependent
on its own resources, and cannot trade any significant amounts with
the rest of the world. In that case we are back in the traditional
Uzawa closed-economy model, and except for the transitional period
ECONOMIC GROWTH AND INTERNATIONAL TRADE 385
during which the economy is expanding to assume its large size,
Uzawa's results and conclusions obtain. On the other hand, if we
postulate that the foreign offer curve expands over time at a rate
exceeding the rate of growth of the labor force in the economy con-
sidered, then again it is only a matter of time for the foreign offer
curve to become, from the point of view of the growing country,
infinitely elastic; and in that case we are back in what we have
done in Section II.
Thus we have two extreme solutions characteristic of two more
general situations. One involves a rate of expansion of the foreign
offer curve falling short of the rate of growth of population and
labor force in the country considered, and the other, a rate of ex-
pansion of the foreign curve that is higher. In the very long run
we do not have to worry about either of the two because they will
eventually degenerate into cases known to us already. The first
will turn into the Uzawa closed model, while the second will become
the case of a small country studied in the previous sections of this
paper.
Thus the only remaining case that we must be concerned with is
the one where the rate of expansion of the foreign offer curve that
is less than infinitely elastic equals the rate of growth of the labor
force in the country considered.
Recall from the small country case studied in Section II that
in a steady state where the economy expands at the rate n, vectors
such as
P1Cj
in Figure II must expand also at the rate n per annum.
If it so happened in our discussion of Section II that the expanding
trade vector was exactly matched by an expanding foreign offer
curve of finite elasticity, which for the prescribed terms of trade
corresponds to the required volume of exports and imports, then the
steady state solution of Section II would in effect have become a
steady state solution of a large country facing a less than infinitely
elastic foreign offer curve, expanding at the rate n.
And thus we can conclude that a steady state solution exists
for the -large country case provided that the rate of expansion n
is also the rate of expansion of the foreign offer curve.
A question that remains to be answered is whether such an
equilibrium is stable, or under what conditions it will be stable. Be-
cause the likelihood that the foreign offer curve would expand at
the rate n is one out of infinity, we will not devote much space to
the question. However, the reader will find it easy to verify, using
the analytical apparatus of this paper, that, as in the Uzawa closed-
economy model, the sufficient condition of stability now is the rela-
386 QUARTERLY JOURNAL OF ECONOMICS
tive capital intensity of the consumption good, and the necessary
(but not sufficient) condition of instability is the relative labor in-
tensity of the consumption good.
V. THE OPEN ECONOMY GROWTH MODEL AND
TECHNOLOGICAL PROGRESS
Obviously, all the models that we have discussed up to this
point are highly unrealistic in the sense that in a steady state the
income per man remains unchanged. In fact all such models could
just as well be called theories of secular stagnation, rather than
theories of economic growth. To obtain actual growth we must
bring into the picture technological progress, and that is the pur-
pose of this section. Of course matters can become quite compli-
cated, and consequently we will have to restrict ourselves to some
simple assumptions. I will discuss rigorously only the case where
Hicks-neutral technological progress takes place, and proceeds at
the same rate A in both industries. Afterwards I will make some
general and less rigorous remarks about other more general situa-
tions. I will proceed fairly rapidly, relying on a previous article
of mine dealing with technological progress in a closed economy.4
Throughout I will be dealing with the case of a small country facing
fixed international prices.
Let us place ourselves in the initial period, and postulate that
the world market prices are fixed at
p,
and
d,,-
respectively. We
want to construct for the base period a relation between the value
of national product per unit of labor on the one hand and the
capital-labor ratio on the other. Let us call the function relating
the former to the latter variable f. The task is a comparatively
simple one if we turn to Figure Ia. Let us make the additional as-
sumption that
LO
as it appears in that diagram is exactly equal -to 1.
We know already that if the capital endowment of the country falls
short of K1 in Figure Ia, then only the consumer good can be pro-
duced. For such values of capital stock the function f, the value
of the national product per laborer, can be obtained by multiplying
the fixed price p$ by the amounts of output read from the isoquants
of the production function of x in Figure Ia. This portion of the
function f is plotted for the range of capital-labor ratios between
o and (K/L)1 in Figure IV as the broken contour stretching from
the origin 0 to b.
4. Jaroslav Vanek, "A Theory of Growth With Technological Change,"*
American Economic Review, LVII, No. 1 (March 1967), 73-89.
ECONOMIC GROWTH AND INTERNATIONAL TRADE 387
On the other hand, if in Figure Ia the capital endowment of
the country exceeds the level K3, the country will specialize in the
capital good y; and thus the value of national product per laborer
can now be easily constructed by multiplying by the fixed price
p,
the amounts of physical output x read from Figure Ia for points
to the right of 0 3.
Finally, for the stretch of relative capital endowments between
K1 and K3 the value of gross national product per laborer can be
obtained from the conventional box diagram by reading the levels
of output at such points as a in Figure Ia, and multiplying these
outputs by the corresponding fixed market prices. The reader will
easily verify that this stretch of the function f in Figure IV must
f
(KI/L ):
Pyy(K/L)/L
C
x
(K/L)/L
I I
a 0 (K/L)1
(K/L)2 K/L
FIGURE IV
be a straight line. An intuitive proof can be obtained if we realize
that for movements of the capital endowment to the right of K1
in Figure Ia the point, such as Z1, moves to the right at the same
rate as does K1. More specifically, for every inch of movement of
K1, Z1 also moves by one inch; of course this holds only up to the
point K3, beyond which the relationship becomes nonlinear.
Thus we have obtained for the base period the entire function
f for the whole range of capital-labor ratios between 0 and infinity.
Except that it is expressed in terms of value at constant world
market prices, it is the same as the all-important function f encoun-
tered in the analysis of growth with technological change for a
388 QUARTERLY JOURNAL OF ECONOMICS
closed one-sector economy. It is the function f appearing in relation
(2) of my paper dealing with growth under Hicks-neutral techno-
logical- change.5 In fact, from here on, once relation f is obtained,
the analysis of my earlier paper and that which concerns us here
become perfectly identical. Consequently I can make only a few
comments and use some relevant relations from the earlier paper
to make the results more accessible to the reader and more closely
related to the situation of the open economy with two sectors.
First, it must be realized that, with technological progress at
the rate A identical in both industries, the function expressing in-
come per capita following period 0 will be the function
f
constructed
in Figure IV, but drifting in the upward direction at the relative
rate A per annum at all its points. Obviously the critical points
of full specialization b' and c' in Figure IV will remain invariant
with respect to time. As is well known (e.g., see H. Uzawa) 6 and as
the reader may verify for himself by a simple calculation, the all-
important competitive income share of capital p, depending on K/L
only, can now be'obtained for any point of f by a simple construc-
tion. For example, at
b,
4 is equal to the ratio Ob' divided by ab'.
Of course a point such as a always must be the foot of a tangency
to the broken line f. The generalized asymptotic rate of growth
of capital k*, given in relation (10) of my earlier paper, is now
illustrated by the solid line marked k* in Figure V. The formula
defining k*, also shown in the diagram, is
k*: A(K/L) B+n)
ko
_
k
* A/(1^0)+n
.'~~-k
(K/L)| (K/L)3 K/L
FIGURE
V
5. Op. cit.
6. Uzawa, "On a Two-Sector Model of Economic Growth," Review of
Economic Studies, XXIX (1), No. 78 (Oct. 1961), 4047.
ECONOMIC GROWTH AND INTERNATIONAL TRADE 389
(1) k* =
n+Al(l
The actual rate of growth of capital k, on the other hand, can be
derived from the divergence of the actual rate from the asymptotic
rate and from initial conditions. The key formula here is relation
(15) of my earlier paper, given below in relation (2), where
(dk/dt)7k is the rate of acceleration of capital:
(2) (dk/dt)//k = A
k
*
k
A typical path of the actual rate of growth of capital is shown
by the curved broken line in Figure V, corresponding to the initial
condition
ko.
As is required by relation (2), k passes through an
extreme level (maximum or minimum) when it crosses the asymptote
k*. Also, it will be noted that whenever k is above k* it must be
declining, and whenever it is below it must be increasing. It is
that property that I have in my earlier paper referred to as asymp-
totic. The reader will also find it easy to verify that for the stretch
of incomplete specialization, that is between endowments (K/L)1
and (K/L)3, the generalized asymptote must be linear. This is also
indicated in Figure V.
Because k* can never fall short of n, and given the nature of
convergence of k to k*, shown in relation (2), it is obvious that k
can never remain indefinitely at or below n. Consequently, the
capital-labor ratio with positive technological progress (that is,
A > 0) must always be increasing in the long run. But this indi-
cates that on the assumptions made it is only a matter of time for the
economy to reach a state of complete specialization in the capital-
intensive product, that is, in the case actually envisaged in Figure
Ia and throughout most of this paper, in the capital good y. To
remain in the nonspecialization range, it would be necessary either
for the terms of trade to keep gradually changing in favor of the
labor-intensive product or for the technological progress to be biased
in favor of the labor-intensive good.
The latter alternative would, as can easily be verified by con-
sidering Figure IV, make the contour marked
p,,x(K/L)/L
drift
upwards at a faster rate than the rate corresponding to the move-
ment of the contour marked p-y(K/L)/L. This, loosely speaking,
would keep shifting the linear stretch, such as be, to the right and
upwards together with the increasing capital-labor ratio. It is also
apparent from Figure V that if the actual rate of growth of capital
remains in the vicinity of the asymptotic rate without specialization
for a substantial period of time, then it must be accelerating.
390 QUARTERLY JOURNAL OF ECONOMICS
VI. THE GOLDEN RULE SOLUTIONS
The function f (K/L) of the preceding section (as derived in
Figure IV) makes it possible to study the golden rule for a growing
small open economy.7 Its slope, f'(K/L), is the marginal produc-
tivity of capital, measured at world market prices, p0, and pa,. As
is well known, for a golden rule solution -that is, a steady state in
which consumption per capita is maximum
-
so must be so selected
astomake f(K/N)
= n(= k).
But it is immediately apparent from the linearity of f within
the nonspecialization range that f must be a constant for that range,
call it to'. And thus, the small economy's golden rule never will
necessitate production of both goods, x and y. Exceptionally, with
n =
to'
the
economy may produce
both
goods,
but it
might just
as
well have specialized then in either product without loss in per capita
consumption.
It may also be interesting to note the effects of changes in
product prices on the golden rule. For example, an increase in p$
in Figure IV will shift the linear nonspecialization range of f to
the right and lower to'. If initially the country followed- the golden
rule and specialized in the (capital-intensive) product y, the in-
crease in the other good's price may now call for a switch in speciali-
zation and a considerable change in the saving rate if the golden
rule is to be retained.
CORNELL UNIVERSITY
7. Of course, we now abandon the assumption of technological progress.