Immiserizing Growth: A Geometrical Note
Author(s): Jagdish Bhagwati
Source: The Review of Economic Studies, Vol. 25, No. 3 (Jun., 1958), pp. 201-205
Published by: Oxford University Press
Stable URL: http://www.jstor.org/stable/2295990
Accessed: 28-06-2017 12:44 UTC
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 support@jstor.org.
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at
http://about.jstor.org/terms
Oxford University Press is collaborating with JSTOR to digitize, preserve and extend access to The
Review of Economic Studies
This content downloaded from 147.251.185.127 on Wed, 28 Jun 2017 12:44:53 UTC
All use subject to http://about.jstor.org/terms
Immiserizing Growth:
A Geometrical Note
The effect of economic expansion on international trade has been receiving increasing
attention from economic theorists since the publication of Professor Hicks' stimulating
analysis of the " dollar problem ".- It has, however, been insufficiently realised that,
under certain circumstances, economic expansion may harm the growing country itself.2
Economic expansion increases outpvt which, however, might lead to a sufficient deterioration
in the terms of trade to offset the beneficial effect of expansion and reduce the real
income of the growing country. It is the purpose of this note to formulate the conditions
Y | F~~~~~~~~~~~~~g. (1)
-4~~ \s
T
0 X
EXPORTABLES
FIGURE 1
1 J. R. Hicks, " An Inaugural Lecture," Oxford Economic Papers, N.S. Vol. 5, No. 2 (June, 1953).
The following are of interest: H. G. Johnson, " Economic Expansion and International Trade," The
Manchester School of Economic and Social Studies, May, 1955 ; E. J. Mishan, " The Long-Run Dollar
Problem: A Comment," Oxford Economic Papers, N.S. Vol. 7, No. 2 (June, 1955) ; and W. M. Corden,
" Economic Expansion and International Trade : A Geometric Approach," Oxford Economic Papers,
N.S. Vol. 8, No. 2 (June, 1956).
2 Exception must be made, however, in the case of Professor Johnson, " Equilibrium Growth in A
Expanding Economy," The Canadian Journal of Economics and Political Science, Vol. XIX, No. 4, (Nov.,
1953), p. 495 ; and also his Manchester Schtool, May 1955, article. It should also be mentioned that
Prof. Johnson has independently worked out mathematically, in an unpublished note, a criterion for
immiserizing growth which confirms the results derived geometrically in this note.
201
This content downloaded from 147.251.185.127 on Wed, 28 Jun 2017 12:44:53 UTC
All use subject to http://about.jstor.org/terms
REVIEW OF ECONOMIC STUDIES
under which immiserizing growth will occur. Section I sets out the analysis
and arrives at the criterion for immiserizing growth. Section II discu
implications of this criterion.
In the ensuing analysis we assume the traditional two-country, two com
model where full-employment always obtains. We also assume, to simpl
that growth is confined to a single country so that the other country (i.e.,
world) is not experiencing any growth in output; this assumption enab
the offer curve of the rest-of-the-world as "given " during the course
Finally, we simplify the problem by beginning with an investigation of th
which growth would leave the country just as well off as before, and then de
the equilibrium actually realised would involve still less favourable term
approach has the convenience of avoiding the need for an explicit analy
effect of growth.
Consider now Fig. (1) which represents the growing economy. Co is t
consumption point, Po the pre-expansion production point, PoCo the pr
of trade or price-line, CoRo the imports of Y into the country and RoPo th
from the country. The production-possibility curve tangential to P0Co has
in to avoid cluttering up the diagram; the indifference curve through C
PoCo at Co and has been drawn partially. Consider now growth which p
tion-possibility curve outwards and which, at constant terms of trade, wou
tion from Po to P;. Now assume that the terms of trade are changed just en
indifference and the new production-possibility curve. We later assume
infinitesimal changes, that C1 P1 coincides with C0 P;.
The combined effect of the expansion and the compensating adjustment
of trade is to reduce the demand for imports from CoRo to CiR'. This
analysed into the sum of three effects:
(1) The increase in production of importables due to the economic expansion:
This increase (RoR1 in the diagram) may be analysed as follows. L
the original and the zero-gain prices respectively, measured as the nu
exportables required to buy a unit of importables. Then the change i
valued at initial prices, is:
PoT + TQ = PoQ = SP'
And SP' - PR1--R1S CoR, = (P-po). CoR1CoR1
The change in the production of importables is:
RoR=- PT=-K T PQ - where
K is defined to be the country's productive capacity which
fully employed and is measured by the value in terms of exportab
202
This content downloaded from 147.251.185.127 on Wed, 28 Jun 2017 12:44:53 UTC
All use subject to http://about.jstor.org/terms
ERRATA
In " Immiserizing Growth: A Geometrical Note ", by J. Bhagwati, this Review, June 1958
(i) Read " the gain from growth; the relevent price-line being C1F1 which is
tangential to the old" after line 8, second paragraph, Section 1, p. 202.
This content downloaded from 147.251.185.127 on Wed, 28 Jun 2017 12:44:53 UTC
All use subject to http://about.jstor.org/terms
IMMISERIZING GROWTH: A GEOMETRICAL NOTE 203
country would produce at the initial terms, of trade and Y is the domestic output of importables.
Then,
ROR, CORI. K (P1 Po)
Since we have assumed the changes to be infinitesimal, it follows that we can assume
CoR, = CORO, the initial volume of imports, so that
aiy
ROR1= M. K. dp (Sm M) (1)
where M is the quantity of imports.
This shows the change in the production of importables due to the economic expansion
itself. The expression is normally positive, indicating that the output of importables
increases, consequent on economic expansion, at constant terms of trade. It should be
noted here, however, that, as argued in Section II, the output of importables may actually
contract due to the expansion.
(2) The decrease in consumption of importables due to the price-change:
The price-change (from po to Pl) shifts consumption along the indifference curve to
C1. The consumption of importables is then reduced by:
COC - - . dp (2)
where C is the total deman
(3) The increase in production of importables due to the price-change:
The price-change shifts production along the production-possibility curve to P1.
The production of importables is then increased by:
R1R' = 8 . dp (3)
The total decrease in the do
(1), (2) and (3):
a~ y a y ac
(M YK + A Y ap dp 4)
This expression measures the decrease in deman
on real income is exactly offset by an adverse m
normal case where output of importablesfalls as a result of growth, the expression may be
negative, indicating an increase in the demand for imports.
Whether the country will actually be made worse off or not depends on what would
happen to the quantity of imports supplied if the terms of trade were adjusted as assumed.
The change in imports supplied as a result of such a price change is
aSm
ap . dp (5)
As distinguished from im
This content downloaded from 147.251.185.127 on Wed, 28 Jun 2017 12:44:53 UTC
All use subject to http://about.jstor.org/terms
REVIEW OF ECONOMIC STUDIES
The sum of (4) and (5) constitutes the excess supply of imports at the zero
of trade : if it is positive, the terms of trade will not move against the grow
enough to deprive it of all gain from growth ; but if it is negative, the p
will have to rise still further to preserve equilibrium, and the growing count
be made worse off by growth.
The economic meaning of this criterion for immiserizing growth will be
the next section ; for this purpose a neater formulation of the criterion
this can be derived by subjecting it to some algebraic manipulation.
Multiplying (4) and (5) by 4dp d we get our criterion for immiserizin
({. -+ M.C +Y + rm) <0 (6)
which may be written as:
- + g ±Y ) <-rm (7)
where
p sC p asm
C. = aC . , rm ~-M * p (S - M)
p aY sy
= - . y - and y=P -K
This criterion is also expressible in the alternative equivalent form:
( 'S M .a +y) < I -rx (8)
where ix = X-. 8p and X° is the quantity of e
that rix and rm are the total elasticities of the rest-of
elasticity of the rest-of-the-world's demand for i
response to an infinitesimal change in the terms of t
rest-of-the-world's supply of (its) exports (to the
finitesimal shift in the terms of trade. It is a we
international trade that T x- rm = 1; hence, 1 - rl -- -rm.
II
What are the implications of the criterion that we have derived in Section I ? It
p aY p 8C
will be remember
which again, being t
204
This content downloaded from 147.251.185.127 on Wed, 28 Jun 2017 12:44:53 UTC
All use subject to http://about.jstor.org/terms
IMMISERIZING GROWTH: A GEOMETRICAL NOTE 205
with respect to a change in the price of importables, is necessarily positive.' We can see
from (6), (7) or (8) that the possibility of imniiserizing growth is increased if:
(i) M , the ratio of domestic production to import of importables is small. Since
C Y C y.
M = I + (ii)
r, the constant-utility demand-elasticity for importables with respect to a
change in the price of importables, is small; this would depend on the
substitution effect against importables being negligible when the price of
importables rises ; and
(iii) G, the elasticity in supply of importables when production shifts along the
production-possibilitycurveinresponseto a change in the price of importables,
is small.
These are, neither singly nor in combination, sufficient conditions for immiserizing
growth. In fact, the possibility of immiserizing growth arises only when, with these conditions
favourably fulfilled, either or both of the following crucial conditions are fulfilled:
(a) the offer of the rest-of-the-world is inelastic, (i.e., r,n is negative, which may be
for the extreme, and by no means necessary, reason that the growing country's exports
are Giffen goods abroad) ; and
(b) growth actually reduces the domestic production of importables at constant
relative commodity prices (i.e., y is negative).
Stringent as the latter condition may appear at first sight, recent analyses have shown
that it is feasible under relatively simple assumptions. Thus the Rybczynski proposition
states that under a two-commodity, two-factor model where, say, labour and land being
the factors, one good is labour-intensive and the other land-intensive, if labour (land)
increases in supply, then the output of the land-intensive (labour-intensive) industry must
actually contract if the relative commodity prices are maintained constant.2 Professor
Johnson has recently advanced the proposition thta uinder neutral technical progress in
one industry, the technology of the other and the total factor endowment remaining
unchanged, the output of the other industry must actually fall under constant relative
commodity prices.3 It may be of interest to note that under biased progress as well it is
possible to establish conditions under which the output of the non-innovating industry
will contract.4
Oxford. JAGDISH BHAGWATI.*
1 This argument obviously rests on th
and (concave) transformation curves, co
strict mathematical sense.
2 Rybczynski, " Factor Endowments and Relative Commodity Prices," Economica, Nov., 1955.
Linear homogeneity of the production functions and diminishing returns are sufficient conditions for the
proposition to hold. The strong Samuelson notion of factor-intensity is not necessary.
3 Johnson, Manchester School, op. cit. Diminishing returns are sufficient for this proposition to hold.
The proposition can be readily extended to more than two goods and factors.
4The conditions under which this result will obtain can be established for specified production
functions.
*1 wish to thank Professor Harry Johnson for his generous assistance and encouragement in the writing
of this paper. My thanks are also due to Sir Donald MacDougall and J. Black for helpful comments. The
responsibility for any errors that remain is entirely mine.
This content downloaded from 147.251.185.127 on Wed, 28 Jun 2017 12:44:53 UTC
All use subject to http://about.jstor.org/terms