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Tariffs, capital accumulation and immiserizing growth
Journal of International
Economics 1 (1971) 453-460.0
North-Holland Publishing Company
TARIFFS, CAPITAL ACCUMULATION IMMISERIZING GROWTH T.J. BERTRAND
and F. FLATTERS
AND
*
Johns Hopkins University
Harry G. Johnson (1967) has demonstrated that in the framework of a two commodity, two factor model a country facing fixed terms of trade and imposing a tariff on the capital intensive commodity may fail to increase real income with capital accumulation. ’ Since many less developed countries have instituted tariff structures designed to accelerate capital accumulation, it is of some importance to study the conditions under which Johnsonian immiserization may arise. In this note we show that the Johnson result depends on both the degree of factor substitutability and.the extent of the difference in factor intensities in the two sectors of the economy. The economy, with production possibility curve TT' and international price line II, is represented in fig. 1. With free trade, production takes place at P” and consumption takes place at some point on II. If capital accumulation were to occur under free trade, production would take place along the Rybczynski line RP" and, at constant free trade prices, the consumption possibilities open to the economy would necessarily expand as the RP" line is of greater slope in absolute value * The authors are Assistant Professor and Ph.D. candidate respectively at The Johns Hopkins University. They are grateful to Bela Balassa, Jagdish Bhagwati, Harry Johnson, Jim Melyin and Jaroslav Vanek for helpful comments on a previous draft. Johnson also considered the possibility of immiserization occurring with technical progress. We restrict our analysis to the case of capital accumulation because the results for technical progress are not amenable to the same straightforward interpretation. Our results could also be applied to the case of growth of the labor supply. However, whereas with growth due to capital accumulation, changes in aggregate real income are identical (except for a scale factor) to changes in per capita real income, this is not true for growth due to labor increase. It should also be noted here that in a recent paper A.H. Tan (1968) has confirmed Johnson’s finding, that for immiserization to occur under capital accumulation the protected industry must be capital intensive.
454
T.J.Bertrand,
F. Flatters, Tariffs, capital accumulation and immiserizing growth
Fig. 1
than the price line II. With a tariff imposed on the Y industry (the capital intensive industry), the production point is at P where the distorted domestic price ratio is tangent to T’T. If capital accumulation then takes place, the production point shifts to the northeast along the negatively sloped Rybczynski line, R’P (to say P’). ’ Capital accumulation under a tariff will be immiserizing if and only if the slope of the Rybczynski line is less (in absolute terms) than the slope of the international price line since consumption possibilities will then be less than in a pre-growth situation. 3 (In the case shown the new production point P’ is below 1’1’ and hence consumption possibilities have fallen from 1’1’to I”,“.)
’ The Rybczynski line is defined as the output expansion (contraction) locus as the endowment of one factor is changed (the other remaining fixed) with constant prices. As Rybczynski (1955) showed, its slope is negative; linearity follows from the assumption of linear homogeneous production functions in both sectors. 3 It should be noted that if one of the commodities is an inferior good for the country in question, there is the possibility of multiple consumption equilibria under a tariff. Then, even if our necessary and sufficient condition is satisfied, there might exist a post-growth equilibrium consumption point that will be superior (i.e. lie on a higher social indifference curve) to one of the pre-growth consumption points that might have been chosen. Thus, if inferiority in consumption is not ruled out, immiserization must be interpreted in terms of potential welfare for it will always be true that if our condition is satisfied, any post-growth consumption point will be inferior to at least one pre-growth consumption point. For more detailed discussion of the complications produced by inferiority in consumption see Bertrand (1969), Bhagwati (1968a), Kemp (1968) and Vanek (1965).
T.J.Bertrand,
F. Flatters, Tariffs, capital accumulation and immiserizing growth
455
First we derive an expression for the slope of the R-line. Then we establish the conditions under which the imposition of a tariff will: (a) cause the R-line to rotate in a counterclockwise direction - a necessary condition for immiserization, and (b) cause it to rotate enough that it becomes less steep than the world price line - a necessary and sufficient condition for immiserization. Assuming constant returns to scale, the production functions for Y and X may be written: Y = LyFY(Ky/Ly) X = LxFx(Kx/Lx)
(2)
where KY and L y are the capital and labor inputs used in the production of Y, Kx and Lx are the capital and labor inputs used in the production of X, and KY/L y is assumed to be greater than K,/L, at all factor price ratios. With a given domestic price ratio between X and Y, factor price ratios are uniquely determined and therefore the factor input ratios are fixed. Thus by taking the total differentials of (l).and (2) and noting that dL, = -dL, from the assumption of full employment of the constant labor force, we obtain the slope of the Rybczynski line:
_-
dY dX
F”
y/L;
FX
x/Lx
Z-C a=0
Expression (3) can be used to restate tion, that the slope of the Rybczynski world price line: my
X/L,
px < p,
(3)
the condition for immiserizaline be less than that of the
py YIL y
Or
PxX/Lx
<
l
(4)
That is, output per laborer employed, evaluated at world prices, must be greater in the labor intensive sector than in the capital intensive sector. In order that the new capital be absorbed, labor must shift into the capital intensive industry; if its output at world prices is lower there,
456
T.J.Bertrand,
F. Flatters, Tariffs, capital accumulation and immiserizing growth
income at world prices must fall. It is immediately clear that at any given set of domestic prices (since factor prices, factor intensities and therefore average products are constant) the slope of the Rybczynski line will be constant and thus, as long as Y continues to be imported, the possibilities of immiserization under any given tariff will be independent of the amount of accumulation. 4 We shall now examine the precise conditions under which immiserization will occur. The imposition of a tariff on Y, by lowering the wage-rental ratio, ’ will lead to the use of more labor intensive techniques of production in both sectors. It may be shown that the relative change in the slope of the Rybczynski line due to a change in the wagerental ratio is: 6
=G+y-@$q
w
0 ;
*
where * indicates the percentage change in a variable, 4$ and $$ the competitive shares of capital, and u‘y and ux the elasticities of tor substitution, in the Y and X industries. Since (W/T)* is negative the imposition of a tariff on Y, the Rybczynski line will become steep than under free trade if: 4y CJ => 6
1
are facfor less
(6)
ux
4 This demonstrates the inaccuracy of the following observation made by Johnson (1967): in producing the pro“If . . . there were an increase in the stock of the factor used intensively production point P’ would in this case also have to be to tected output . . . the new equilibrium the northwest of P, again entailing the possibility of loss or gain of real income, the necessity of loss if the factor increment is small enough, and the necessity of gain.if the factor increment exceeds some initial minimum quantity.” p. 153, (our emphasis). Of course it is true that after accumulation has proceeded so far that production has shifted sufficiently towards the import competing industry, the tariff will become prohibitive. Further accumulation will lead to gains from growth with autarky and eventually a reversal in the trade patterns. ’ See Stolper and Samuelson (1941). and by definition ‘7~ = (KY/LY)*/(w/r)*. We therefore 6 Note (Y/LY)* = @KY(KY/LY)* have (Y/L y)* = @J&Y (w/r)*. Using a similar relation for (X/L,)*, we obtain relation (5).
T.J.Bertrand, F.Flatters, Tariffs, capital accumulation and immiserizing growth
4.51
that is, if the elasticity of factor substitution in the capital intensive sector, weighted by its competitive share of capital, is greater than the elasticity of factor substitution in the labor intensive sector weighted by its competitive capital share. Thus (6) is a necessary condition for immiserization to occur. Clearly, if elasticities of factor substitution are the same in both sectors (as, for instance, with Cobb-Douglas pro duction functions), then by the factor intensity assumption this condition will always be fulfilled. It has been argued ’ that in less developed countries the elasticity of substitution in the capital intensive sector is typically less than in the labor intensive sector. Even if this is correct, however, the type of immiserization noted by Johnson may still occur because of differences in the factor share of capital between the two sectors. Given that condition (6) is satisfied, immiserization will not occur unless the increase in the tariff is sufficient to cause the Rybczynski line to rotate so that its percentage change from free trade be at least as great as the percentage difference between its free trade slope and that of the international price line; that is,
PX
YIL y
PY
Xl&
(
-_
l/i
YIL y
XL,
1
(7)
Then, noting that the right-hand side of (7) may be written as (4f - $$‘) 4’ (by use of the condition for equal value of marginal product in both sectors), using a well known relationship between percentage changes in relative factor prices and goods prices ’ ((W/Y)* = of the left hand side (P,/P,)*/(@$~ - 414$) w h ere the denominator is greater than zero by the factor intensity assumption), and noting that the percentage change in domestic relative goods prices, (Px /Py )*, is simply -4, the negative of the tariff rate on Y, we obtain as a necessary and sufficient condition for immiserization: 9
’ See for instance, Eckaus (1955). * See eqs. (3.2) and (4.2) on p. 560 of Jones (1965). 9 See footnote 9 on following page.
458
T. J.Bertrand,
F.Flatters,
Tariffs, capital accumulation and immiserizing growth
(8)
Relation (8) shows that the tariff required for immiserization to result from capital accumulation is greater the larger is ux and the smaller is uy. The effect of a greater divergence in factor intensities between the two sectors is hard to evaluate from relation (8), because the rise in @Ky and c#$’ and the fall in 4% and 61 resulting from an increase in the capital-labor ratio in Y and its fall in X will increase both the numerator and denominator in (8). However, a simple graphical analysis shows that the result is unambiguous. In fig. 2, the relationships between product prices, factor prices, and average products valued at fixed world prices (all variables in log form) have been plotted. At the international price ratio a, the average product in the capital intensive Y sector (g) is greater than in the labor intensive X sector cf). But as a tariff is imposed on imports of the Y commodity, the domestic price ratio (Px /Pr >D falls leading to a fall in w/r and the adoption of more labor intensive techniques in both sectors. If the slope of function X, l/$lux, is greater than the slope of (6) satisfied) then a sufficiently high function Y, l/GyK u y, (condition non-prohibitive tariff (condition (8) satisfied) will lead to a fall in the average product valued at world prices in the Y sector below that of the X sector at a wage-rental ratio below i. Subsequent capital accumulation will not yield any increase in real income. This graphical analysis can be used to investigate the effects of variations in the differences in factor intensities between the two sectors. I0 Thus, if the capital-labor ratio is decreased in the X sector and increased in the Y sector at all factor price ratios, this means that since average productivity is an increasing monotonic function of the capital-labor ratios, the X and Y functions will uniformly shift upwards and downwards, respectively, say to X’ and Y’. Therefore, even though the slope of X’ will be steeper ’ This relationship is exact only for a Cobb-Douglas production function where both the factor shares and the elasticity of factor substitution are constant. It may be of interest to note that on the assumption of Cobb-Douglas production functions with ol= 0.6 and @J$ = 0.4, the tariff that leads to the borderline of immiserization is, from (8), equal to 33 l/3 percent. lo Greater differences in factor intensities are defined as an increase in the capital-labor ratio in the Y sector or a fall in the capital-labor ratio in the X sector or a combination of the two.
T J.Bertrand,
F. Flatters, Tariffs, capital accumulation and immiserizing growth
459
Fig. 2
than X and the slope of Y’ less than Y (i.e. the @ox - @$uX term in (8) increases), the wage-rental ratio at which immiserization occurs must fall (from i to h in fig. 2) because of the greater initial difference between the world price line and the free trade Rybczynski line as given by the increase in the (c#$ - #I)/$* term in relation (8). Even if the relationship between product price changes and factor price changes were not altered by the greater divergence in factor intensities in the two sectors, a higher tariff would be required for the immiserization result. But the greater difference in factor intensities also implies a greater percentage change in the product price ratio corresponding to a given percentage change in the factor price ratio (i.e. the slope of the z function, l/(+Ky@ET - #@Ly), in fig. 2 decreases). This means that an even greater change in relative prices (i.e. a still higher tariff) is necessary. Greater differences in factor intensity, despite relaxing the necessary condition (6), tighten the necessary and sufficient condition (8). Thus, a high elasticity of factor substitution in the labor intensive sector, a low elasticity of factor substitution in the capital intensive sector, and large differences in factor intensities between sectors all unambiguously decrease the likelihood of immiserizing growth with capital accumulation in a tariff distorted economy. Finally, it is of interest to note a fundamental difference between the type of immiserization described by Johnson and that originally discussed by Bhagwati (1958). Whereas Bhagwati analyzed the possibility
460
T.J.Bertrand,
RFlatters,
Tariffs, capital accumulation
and immiserizinggrowth
of immiserization due to terms of trade deterioration resulting from growth biased towards the export good, ” Johnson’s immiserization depends on growth biased towards the import competing sector. If we relax the assumption of fixed world prices, growth biased towards the import competing sector could lead to a terms of trade improvement and the risk of Johnsonian immiserization is correspondingly reduced.
l1 Bhagwati (1968b) has discussed other differences between these phenomena. Bhagwati-style immiserization can occur with neutral growth, but the phenomenon likely to occur when growth is strongly biased towards the export good.
Actually, is most
References Bertrand, T.J., 1969, Trade and welfare with multi-person communities, Canadian Journal of Economics, 2, 3,427-434. Bhagwati, J.N., 1958, Immiserizing growth: A geometrical note, Review of Economic Studies, 25, 3, 201-205. Bhagwati, J.N., 1968a, The gains from trade once again, Oxford Economic Papers, 20, 2,137148. Bhagwati, J.N., 1968b, Distortions and immiserizing growth: A generalization, Review of Economic Studies, 35,4,481-485. Eckaus, R., 1955, The factor proportions problem in underdeveloped areas, American Economic Review, 45,539-565. Johnson, Harry G., 1967, The possibility of income losses from increased efficiency or factor accumulation in the presence of tariffs, Economic Journal, 77, 151-154. Kemp, Murray C., 1968, Some issues in the analysis of trade gains, Oxford Economic Papers, 20, 2,149-161. Jones, R.W., 1965, The structure of simple general equilibrium models, Journal of Political Economy, 73,557-572. Rybczynski, T.M., 1955, Factor endowments and relative commodity prices, Economica, 22, 3366341. Stolper, W.F. and P.A. Samuelson, 1941, Protection and real wages, Review of Economic Studies, 9,58-73. Tan, A.H., 1968, Immiserizing tariff-induced capital accumulation and technical change, Malayan Economic Review, 13, 2, l-7. Vanek, J., 1965, General Equilibrium of International Discrimination (Harvard University Press).
Economics 1 (1971) 453-460.0
North-Holland Publishing Company
TARIFFS, CAPITAL ACCUMULATION IMMISERIZING GROWTH T.J. BERTRAND
and F. FLATTERS
AND
*
Johns Hopkins University
Harry G. Johnson (1967) has demonstrated that in the framework of a two commodity, two factor model a country facing fixed terms of trade and imposing a tariff on the capital intensive commodity may fail to increase real income with capital accumulation. ’ Since many less developed countries have instituted tariff structures designed to accelerate capital accumulation, it is of some importance to study the conditions under which Johnsonian immiserization may arise. In this note we show that the Johnson result depends on both the degree of factor substitutability and.the extent of the difference in factor intensities in the two sectors of the economy. The economy, with production possibility curve TT' and international price line II, is represented in fig. 1. With free trade, production takes place at P” and consumption takes place at some point on II. If capital accumulation were to occur under free trade, production would take place along the Rybczynski line RP" and, at constant free trade prices, the consumption possibilities open to the economy would necessarily expand as the RP" line is of greater slope in absolute value * The authors are Assistant Professor and Ph.D. candidate respectively at The Johns Hopkins University. They are grateful to Bela Balassa, Jagdish Bhagwati, Harry Johnson, Jim Melyin and Jaroslav Vanek for helpful comments on a previous draft. Johnson also considered the possibility of immiserization occurring with technical progress. We restrict our analysis to the case of capital accumulation because the results for technical progress are not amenable to the same straightforward interpretation. Our results could also be applied to the case of growth of the labor supply. However, whereas with growth due to capital accumulation, changes in aggregate real income are identical (except for a scale factor) to changes in per capita real income, this is not true for growth due to labor increase. It should also be noted here that in a recent paper A.H. Tan (1968) has confirmed Johnson’s finding, that for immiserization to occur under capital accumulation the protected industry must be capital intensive.
454
T.J.Bertrand,
F. Flatters, Tariffs, capital accumulation and immiserizing growth
Fig. 1
than the price line II. With a tariff imposed on the Y industry (the capital intensive industry), the production point is at P where the distorted domestic price ratio is tangent to T’T. If capital accumulation then takes place, the production point shifts to the northeast along the negatively sloped Rybczynski line, R’P (to say P’). ’ Capital accumulation under a tariff will be immiserizing if and only if the slope of the Rybczynski line is less (in absolute terms) than the slope of the international price line since consumption possibilities will then be less than in a pre-growth situation. 3 (In the case shown the new production point P’ is below 1’1’ and hence consumption possibilities have fallen from 1’1’to I”,“.)
’ The Rybczynski line is defined as the output expansion (contraction) locus as the endowment of one factor is changed (the other remaining fixed) with constant prices. As Rybczynski (1955) showed, its slope is negative; linearity follows from the assumption of linear homogeneous production functions in both sectors. 3 It should be noted that if one of the commodities is an inferior good for the country in question, there is the possibility of multiple consumption equilibria under a tariff. Then, even if our necessary and sufficient condition is satisfied, there might exist a post-growth equilibrium consumption point that will be superior (i.e. lie on a higher social indifference curve) to one of the pre-growth consumption points that might have been chosen. Thus, if inferiority in consumption is not ruled out, immiserization must be interpreted in terms of potential welfare for it will always be true that if our condition is satisfied, any post-growth consumption point will be inferior to at least one pre-growth consumption point. For more detailed discussion of the complications produced by inferiority in consumption see Bertrand (1969), Bhagwati (1968a), Kemp (1968) and Vanek (1965).
T.J.Bertrand,
F. Flatters, Tariffs, capital accumulation and immiserizing growth
455
First we derive an expression for the slope of the R-line. Then we establish the conditions under which the imposition of a tariff will: (a) cause the R-line to rotate in a counterclockwise direction - a necessary condition for immiserization, and (b) cause it to rotate enough that it becomes less steep than the world price line - a necessary and sufficient condition for immiserization. Assuming constant returns to scale, the production functions for Y and X may be written: Y = LyFY(Ky/Ly) X = LxFx(Kx/Lx)
(2)
where KY and L y are the capital and labor inputs used in the production of Y, Kx and Lx are the capital and labor inputs used in the production of X, and KY/L y is assumed to be greater than K,/L, at all factor price ratios. With a given domestic price ratio between X and Y, factor price ratios are uniquely determined and therefore the factor input ratios are fixed. Thus by taking the total differentials of (l).and (2) and noting that dL, = -dL, from the assumption of full employment of the constant labor force, we obtain the slope of the Rybczynski line:
_-
dY dX
F”
y/L;
FX
x/Lx
Z-C a=0
Expression (3) can be used to restate tion, that the slope of the Rybczynski world price line: my
X/L,
px < p,
(3)
the condition for immiserizaline be less than that of the
py YIL y
Or
PxX/Lx
<
l
(4)
That is, output per laborer employed, evaluated at world prices, must be greater in the labor intensive sector than in the capital intensive sector. In order that the new capital be absorbed, labor must shift into the capital intensive industry; if its output at world prices is lower there,
456
T.J.Bertrand,
F. Flatters, Tariffs, capital accumulation and immiserizing growth
income at world prices must fall. It is immediately clear that at any given set of domestic prices (since factor prices, factor intensities and therefore average products are constant) the slope of the Rybczynski line will be constant and thus, as long as Y continues to be imported, the possibilities of immiserization under any given tariff will be independent of the amount of accumulation. 4 We shall now examine the precise conditions under which immiserization will occur. The imposition of a tariff on Y, by lowering the wage-rental ratio, ’ will lead to the use of more labor intensive techniques of production in both sectors. It may be shown that the relative change in the slope of the Rybczynski line due to a change in the wagerental ratio is: 6
=G+y-@$q
w
0 ;
*
where * indicates the percentage change in a variable, 4$ and $$ the competitive shares of capital, and u‘y and ux the elasticities of tor substitution, in the Y and X industries. Since (W/T)* is negative the imposition of a tariff on Y, the Rybczynski line will become steep than under free trade if: 4y CJ => 6
1
are facfor less
(6)
ux
4 This demonstrates the inaccuracy of the following observation made by Johnson (1967): in producing the pro“If . . . there were an increase in the stock of the factor used intensively production point P’ would in this case also have to be to tected output . . . the new equilibrium the northwest of P, again entailing the possibility of loss or gain of real income, the necessity of loss if the factor increment is small enough, and the necessity of gain.if the factor increment exceeds some initial minimum quantity.” p. 153, (our emphasis). Of course it is true that after accumulation has proceeded so far that production has shifted sufficiently towards the import competing industry, the tariff will become prohibitive. Further accumulation will lead to gains from growth with autarky and eventually a reversal in the trade patterns. ’ See Stolper and Samuelson (1941). and by definition ‘7~ = (KY/LY)*/(w/r)*. We therefore 6 Note (Y/LY)* = @KY(KY/LY)* have (Y/L y)* = @J&Y (w/r)*. Using a similar relation for (X/L,)*, we obtain relation (5).
T.J.Bertrand, F.Flatters, Tariffs, capital accumulation and immiserizing growth
4.51
that is, if the elasticity of factor substitution in the capital intensive sector, weighted by its competitive share of capital, is greater than the elasticity of factor substitution in the labor intensive sector weighted by its competitive capital share. Thus (6) is a necessary condition for immiserization to occur. Clearly, if elasticities of factor substitution are the same in both sectors (as, for instance, with Cobb-Douglas pro duction functions), then by the factor intensity assumption this condition will always be fulfilled. It has been argued ’ that in less developed countries the elasticity of substitution in the capital intensive sector is typically less than in the labor intensive sector. Even if this is correct, however, the type of immiserization noted by Johnson may still occur because of differences in the factor share of capital between the two sectors. Given that condition (6) is satisfied, immiserization will not occur unless the increase in the tariff is sufficient to cause the Rybczynski line to rotate so that its percentage change from free trade be at least as great as the percentage difference between its free trade slope and that of the international price line; that is,
PX
YIL y
PY
Xl&
(
-_
l/i
YIL y
XL,
1
(7)
Then, noting that the right-hand side of (7) may be written as (4f - $$‘) 4’ (by use of the condition for equal value of marginal product in both sectors), using a well known relationship between percentage changes in relative factor prices and goods prices ’ ((W/Y)* = of the left hand side (P,/P,)*/(@$~ - 414$) w h ere the denominator is greater than zero by the factor intensity assumption), and noting that the percentage change in domestic relative goods prices, (Px /Py )*, is simply -4, the negative of the tariff rate on Y, we obtain as a necessary and sufficient condition for immiserization: 9
’ See for instance, Eckaus (1955). * See eqs. (3.2) and (4.2) on p. 560 of Jones (1965). 9 See footnote 9 on following page.
458
T. J.Bertrand,
F.Flatters,
Tariffs, capital accumulation and immiserizing growth
(8)
Relation (8) shows that the tariff required for immiserization to result from capital accumulation is greater the larger is ux and the smaller is uy. The effect of a greater divergence in factor intensities between the two sectors is hard to evaluate from relation (8), because the rise in @Ky and c#$’ and the fall in 4% and 61 resulting from an increase in the capital-labor ratio in Y and its fall in X will increase both the numerator and denominator in (8). However, a simple graphical analysis shows that the result is unambiguous. In fig. 2, the relationships between product prices, factor prices, and average products valued at fixed world prices (all variables in log form) have been plotted. At the international price ratio a, the average product in the capital intensive Y sector (g) is greater than in the labor intensive X sector cf). But as a tariff is imposed on imports of the Y commodity, the domestic price ratio (Px /Pr >D falls leading to a fall in w/r and the adoption of more labor intensive techniques in both sectors. If the slope of function X, l/$lux, is greater than the slope of (6) satisfied) then a sufficiently high function Y, l/GyK u y, (condition non-prohibitive tariff (condition (8) satisfied) will lead to a fall in the average product valued at world prices in the Y sector below that of the X sector at a wage-rental ratio below i. Subsequent capital accumulation will not yield any increase in real income. This graphical analysis can be used to investigate the effects of variations in the differences in factor intensities between the two sectors. I0 Thus, if the capital-labor ratio is decreased in the X sector and increased in the Y sector at all factor price ratios, this means that since average productivity is an increasing monotonic function of the capital-labor ratios, the X and Y functions will uniformly shift upwards and downwards, respectively, say to X’ and Y’. Therefore, even though the slope of X’ will be steeper ’ This relationship is exact only for a Cobb-Douglas production function where both the factor shares and the elasticity of factor substitution are constant. It may be of interest to note that on the assumption of Cobb-Douglas production functions with ol= 0.6 and @J$ = 0.4, the tariff that leads to the borderline of immiserization is, from (8), equal to 33 l/3 percent. lo Greater differences in factor intensities are defined as an increase in the capital-labor ratio in the Y sector or a fall in the capital-labor ratio in the X sector or a combination of the two.
T J.Bertrand,
F. Flatters, Tariffs, capital accumulation and immiserizing growth
459
Fig. 2
than X and the slope of Y’ less than Y (i.e. the @ox - @$uX term in (8) increases), the wage-rental ratio at which immiserization occurs must fall (from i to h in fig. 2) because of the greater initial difference between the world price line and the free trade Rybczynski line as given by the increase in the (c#$ - #I)/$* term in relation (8). Even if the relationship between product price changes and factor price changes were not altered by the greater divergence in factor intensities in the two sectors, a higher tariff would be required for the immiserization result. But the greater difference in factor intensities also implies a greater percentage change in the product price ratio corresponding to a given percentage change in the factor price ratio (i.e. the slope of the z function, l/(+Ky@ET - #@Ly), in fig. 2 decreases). This means that an even greater change in relative prices (i.e. a still higher tariff) is necessary. Greater differences in factor intensity, despite relaxing the necessary condition (6), tighten the necessary and sufficient condition (8). Thus, a high elasticity of factor substitution in the labor intensive sector, a low elasticity of factor substitution in the capital intensive sector, and large differences in factor intensities between sectors all unambiguously decrease the likelihood of immiserizing growth with capital accumulation in a tariff distorted economy. Finally, it is of interest to note a fundamental difference between the type of immiserization described by Johnson and that originally discussed by Bhagwati (1958). Whereas Bhagwati analyzed the possibility
460
T.J.Bertrand,
RFlatters,
Tariffs, capital accumulation
and immiserizinggrowth
of immiserization due to terms of trade deterioration resulting from growth biased towards the export good, ” Johnson’s immiserization depends on growth biased towards the import competing sector. If we relax the assumption of fixed world prices, growth biased towards the import competing sector could lead to a terms of trade improvement and the risk of Johnsonian immiserization is correspondingly reduced.
l1 Bhagwati (1968b) has discussed other differences between these phenomena. Bhagwati-style immiserization can occur with neutral growth, but the phenomenon likely to occur when growth is strongly biased towards the export good.
Actually, is most
References Bertrand, T.J., 1969, Trade and welfare with multi-person communities, Canadian Journal of Economics, 2, 3,427-434. Bhagwati, J.N., 1958, Immiserizing growth: A geometrical note, Review of Economic Studies, 25, 3, 201-205. Bhagwati, J.N., 1968a, The gains from trade once again, Oxford Economic Papers, 20, 2,137148. Bhagwati, J.N., 1968b, Distortions and immiserizing growth: A generalization, Review of Economic Studies, 35,4,481-485. Eckaus, R., 1955, The factor proportions problem in underdeveloped areas, American Economic Review, 45,539-565. Johnson, Harry G., 1967, The possibility of income losses from increased efficiency or factor accumulation in the presence of tariffs, Economic Journal, 77, 151-154. Kemp, Murray C., 1968, Some issues in the analysis of trade gains, Oxford Economic Papers, 20, 2,149-161. Jones, R.W., 1965, The structure of simple general equilibrium models, Journal of Political Economy, 73,557-572. Rybczynski, T.M., 1955, Factor endowments and relative commodity prices, Economica, 22, 3366341. Stolper, W.F. and P.A. Samuelson, 1941, Protection and real wages, Review of Economic Studies, 9,58-73. Tan, A.H., 1968, Immiserizing tariff-induced capital accumulation and technical change, Malayan Economic Review, 13, 2, l-7. Vanek, J., 1965, General Equilibrium of International Discrimination (Harvard University Press).