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Terms of trade and domestic distribution
R
July t981, final version received April 14182
n th: April I% issue of this Journal. It 8s tward shift in the demand curve of the North rsening of the terms of trade for the South. It s;%ible that the quaatity of exports from the: South may decline in the new equilibrium due to the income effect of the improved terms of trade.
This note commen shads that within t
In a recent issue of this Journal, Chichilnisky (1981) develops a generalilibrium macro model to explore the effects of export-led growth policies the terms of trade and the domestic income distribution of a developing region with abundant labor. However, her conclusion, that ;Ln increase iTathe exports of the South due to a Aghtward shift in the demand curve of the North for the South’s exports may bring about a sustained worsening of the South’s terms of trade, is incorrect. In the framework of her model it is true that such a rightward shaft in the demand curve may lead to a lower level of Southern exports (and thus horthern imports) in the new equilibrium, b only because the demand shift the terms of trade for the South, having a positive effect on the real come of the South. Since in the model any increase in income goes into the consumption of the South’s export commodity, this implies that, in the new equilibrium, the domestic dema for ex~~rtables may increase in th South reducing the volume of ex the North.
conditions, it is shown that an z*xogenous increase in the demand for the So.rLath’s export good must impro.ue the South’s terms of trade in the new eq\Jilibrium. Last, we look at tht. slopes of the export supply and import dernand curves for basic goods. Ait:hough the export supply curve may be, either upward or downward sloping., under the assumptions of the model the supply curve must al-ways be s&eper than the demand curve in the neighborhood of the world equilibrium. Chichilnisky’s model is characterized by two countries (the North and the South), two goods (investment/luxury and basic), and two factors of production (labor and capital). The following basic assumptions are made: (a) Both countries produce both goods according to fixed coeficients production functions, although the technical coeficients will in general be different in eaf;h region. W The South exports basic goods, the more labor-intensive commodity in both countrics. are an increasing function of factor rewards, and are (c) Factor sq~piies always fully employed. The demand for investment/lGxury goods is exogenous in both countries. Chichilnisky undertakes the analysis by examining the export supply (by the South) and import demand (~JJ the North) curves. In the model, for a given set of commoc’.ity prices we are able to calculate the wage and rate of profit in each country? This allows us to calculate factor supplies,’ which in turn enables us to determine the levels of cutput serp$ies of each commodity in each crjuntry which provide full employment.3 If we in i,rL?;tion specify an exogenous level of domestic demand for the investment/luxury goocr (the orth’s export), it is possible to calculate the level of demand for the basic good in each country by requiring that international payments balance.4 We are thus able to construct the export supply curve of the South and the import demand curve of the North as a function of relative commodity prices. Along each curve, the value of exports equals the value of imports for the country in question and all the equilibrium conditions within the country are met. However, world markets may not clear. World equilibrium is attained at the price of basic goods (using investment/luxury goods as the n erai Fe, which is done throughout the remainder of this comment) which equates export supply from one country with import demand from the other. i~~ilnisky states three propositions in her paper. 1 essentially deal with the slope of the export supply curve crowing that it could be either positive or negative. Propositio ~~a~te~ist~csof world equilibria (p. 18 1):
‘Assume that Iabour in the North is relatively price inelastic (CIsmall) and that the economy of the South has the characteristics descrrbed n Proposition 1. If a new woriti equilibrium with an increased volume of exports by the South is attained du12 to a positive :;hift in demand for oodv by the North (e.g., h&her growth rate of the North), then the terms of trade will worsen for the South and thz purchasing power of wages within the South will also decrease. This takes place within a Walrasian stable world eco~oi~~~ w-‘) it is this proposition that we examine in detail here. The first step in the analysis is to e:tamine how an exogenous increase in the North’s the demand for investment/luxury goods by the North shi import demand curve or the demand for basic oods the Nortil. Chiehiinisky (p. 1SO) states: ‘As the (exogenous) demand for investment goods (l’D)Nis increased within the North, eq. C?ia) implies a positive shift in its demand for B, Xi, at each price level.’ (Clrichilnisky’s variables used here are defined in table 1.) Eq. (21a) shows us the slope of an export supply curve, which is not particularly useful in calculating the direction the curve shifts. Instead we write out the equation for Xi and examine how it changes with an increase in (iD)”forany gicen relative price.
The North’s balance-of-payments constraint prices are equal to international prices)5
states that (when domestic
92
S.1.
Ranney,
Terms
cf trade
and
domestic
distribution
Substituting into (1) we get
x; == [(lqN -(TD)Nyp&
( “11 .’
Recall that once the relative price (pB) is specified, corrlmodity supplies are detenninexi. Thus, holding pB fixed, we r=~ determine the horizontal shift in the demand curve as aX,Nla(iD)Nlp,=
-
(4)
l/~&I.
An exogenous increase in the dt;;mand for investment/luxury goods by the North implies a lt$ward shift in its demand curve for imports of basic goods. The remainder of the analysis is straightforward. World equilibrium requires that exports of the South equA imports of the North, or equivalently [referring to eq, (@)I, tha!. the world market for investment/h~xury goods clears. Thus the wor’ld equilibrium value of pB can be calculated by the following:
Totally differentiating, we can calculate how ps will change in response to an exogenous change in the demand for investment/luxury goods in the new ~rlh equilibrium,
[t?(lS)N/dp, + iVs/t3pa]dp, = d(rD)N+ dFD.
(6)
In each country an increase in pB would increase real wages and decrease the rate ~rf profits (as in the Stolper-Samuelson theorem). This increases the supply of labor and decreases the supply of capital. Full employment of factors requires a shift ti,way from the production of capital-intensive luxury/investment good!; towards the production of labor-intensive basic goods (as in the Rybcz,/aski theorem). Thus an increase in pB results in a eiine in the producticbn of I goods in both countrissY6 and the model is aLsian stable. . (6) tells us that an exogenous increase in the demand for 1~~1~~~~~ goods by either country results in 8 decrease in pB. That i8iy’r~~i~~~ out the elipession for the output of investment/luxury goods in the Socth nction Jf pa by substituting eqs. (3), (4), (7), and (8) into (12) (from Chiohilnisky’s article), P- lm,[R 4”/?(a, -P,a,)lD]:n-c,[%fsc(c~,-c,/p,)/D]/D,
so that
22s a
93 is, u g0si~it.x
must uwit
shift in the demand for i~~ports by the North (a decrease in (TD)” in an improvement in the tems of trade for .
Proposition 3 cannot be correct. The result here is also inconsistent with fig. 2b in Chichiinisky’s paper.’ In the figure, as she explains on p. 180, Xi crosses Xt (I assume it should be X”,) from above. This is in fact inconsistent with the assumptions of her model. To w this, we first examine the slopes of the import demand and y Curves. Differentiating eq. (3) with respect to g,., pe-[(rS!N-(lf~)N]jp~
(7)
We have seen the supply of investment/luxury goods declines in both countries as ps rises. By assumption the North is an exporter of investment~luxury goods, so Is)N-(r’)N is greater than zero. Thus the import demand curve for the orth is al*.qays downward-sloping. Using the balance-of-payments constr4nt for the South, we can derive a similar expression for the export supply of basic goods. x$=BS-BD=(iD-IQ/p,.
Differentiating with respect to
(8) pe,
-(2Pfap,)/p, -(iD-
;‘pB= L.___~_J
L_.,,
P)JP; -1 6 0.
(9)
+
As Chich4nisky points out in Proposition,, 1 and 2, the export supply curve may be upward or downward-sloping.* It should also be noted that the export suppfy curve is unambiguously downward-sloping if the labor ejupply in the South IS abundant but factor supplies are totally unresponsive to changes in their returns. If factor supplies are fixed, full employment requires that the supply of investment/luxury goods remain unchan ed for any change in ps. Thus, the first term in eq. (9) becomes zero, and the slope of the ex c rt supply curve is negative with the magnitude depending on the initial c vel of trade? if we iwease, hvAlthough the h~ri~~~~~~iaxis is labelled ‘quan~~t); of expwtable
in fig. 2b, the ncte hrlou
rt
as an L elsewhere in the text) and an export in the text).
“ln this extreme case a world equilib:wm probably doesn’t exist, sin= neither the suppij’ df nor the demand br investment,luxury goods responds to price changes. JDE
D
example, the labor supp&*response to the real wage holding the initial iabor supply fixed (and thus ,the initial 1eveIsof product&on ~nndexports) the slope of the export supply curve becomes mol*e positive. An increase in pB now decreases the production of investment~~uxury goods, which increases impor* demand (equal to. the valurt:of export suppiy).”* Returning to- bg. 2b,, can. Xg ever cross xi from above? That is, as the price of basic goods rises above its world equilibrit:m level, could it ever result in an excess &MM for ‘basic goods exports as indicated in fig* 2b’b Algebraicall!r,’ we ask if 8(X”,-X#?JI, can ever be riegative when evaluated at a world equilibrium?
At a world equilibrium, world markets must clear, so that the last term L ahap cmss X~jbm belowin the context of beC3mes ZWO. Thus, x! REW’ this model. This can be more easily understood by considering the two components of (10) separately: the effect of the price change on factor supplies and : income effect of the change in the terms of trade. As discussed eartier, and increase in pe within each country results in an increase in the supply of labor and a decrease in the supply of capital, and thus a shift in production from luxury/investment goods towards basic goods in both countries. The demand for basic goods is determined by the balance of payments condition. For each country,
Since the income elasticity of demand for I goods is zero, examination of (11)
shows that any tendency towards an increase in BS (due to an increase in the labor supply) is ex14ctlymet by an increase in BD. A decrease in Is, however, will result in an excess supply of B goods (holding the terms of trade fixed for the moment). Thus the ‘factor supply” effect [the first term In eq. (IO)] is that an incret,se in pR results in an excess apply of B goods in each countr e seconldl term in eq. (10) shows the direct incame erects of nn increase ate that cliflerentiating t 11=slope of the export supply curve with re$ t to 31takes into ~~~~~~t changes; in both the r :spcllnsivencss of labor zlnd the ~~~~ndanc~ of MXM im the initial ~~~~~j~r~~rn(at the initial wag@. Thus, a higher a implies a larger ~n~r~~ in t es fdP/i& larger), but &a a larger initial level af imps 6) above, impii63 that
it
in pB. With the demrrrld for t oods fixed, a change in real incump due to 3. change in the terms of trade is completely absorbed by the demand for 3 ain as incaicat d in eq. (1 I). Beginning at world equ;Iibriurin, a the terms of trade (now holding factor supplies fixed) wdistrabut:: income from onz Country t another (and between wc)rkers and capitalists). se the demand for B goods in the An onward pres~re on pa South, but desteases the de ods in the North by exactly the same amount since trade is initially balanced. The net impact of the direcr ‘terms of trad:’ efiect on the world market is zero, as indicated by the second terms in eq. ( 0). Thus on the world leveI, only the factor sl;pply effects art: relevant in thz neighbourho~d of world equilibrium, and any small increase an excess supply of B goods. in pB must result What then is t appropria1.e diagram arld explanation to accompany the simulation reported in the appendix ? The comparative static results are (p. 18’7):‘the parameter of investment demand is increased in the North from 1.~ to 2. Equilibrium value of exports of basic goods by the Swth increases and their prim piJ decreases”. Fig. 1 provide; the explanatlozt The export supply cw be may be downward-sloping!n the experiment, but we know it must be sf :cwr that1 the import demand. curve. We also know that an exogenous in&ease in investment demand-' Jay !he hforth is equivalent to a leftward shift m the import demand curve. As in any simple Walrasian system, an exogenouq decrease in demand res llts in a fall in the price of that commodity. The new equilibrium quantity, i&wever, may either rise or fall. In this case it rim in the new equilibrium, even though the trsogenous shaft wus to the kfi. The simulation ctxperiment is consistent with the fact that, under the
assumptions of the model, an exogenous incregise in the demand for basic goods by the North will never result in a worsering of the terms of trade for the South or a decrease in the purchasingpower $)fwages within the South.
Chichilnisky, Gracielu, 1981, Terms of trade and domestic distribution: Expcwt4 abundant labour, Journal of Dwelopment Economics 8, no. 2, l@--192.
owth with
July t981, final version received April 14182
n th: April I% issue of this Journal. It 8s tward shift in the demand curve of the North rsening of the terms of trade for the South. It s;%ible that the quaatity of exports from the: South may decline in the new equilibrium due to the income effect of the improved terms of trade.
This note commen shads that within t
In a recent issue of this Journal, Chichilnisky (1981) develops a generalilibrium macro model to explore the effects of export-led growth policies the terms of trade and the domestic income distribution of a developing region with abundant labor. However, her conclusion, that ;Ln increase iTathe exports of the South due to a Aghtward shift in the demand curve of the North for the South’s exports may bring about a sustained worsening of the South’s terms of trade, is incorrect. In the framework of her model it is true that such a rightward shaft in the demand curve may lead to a lower level of Southern exports (and thus horthern imports) in the new equilibrium, b only because the demand shift the terms of trade for the South, having a positive effect on the real come of the South. Since in the model any increase in income goes into the consumption of the South’s export commodity, this implies that, in the new equilibrium, the domestic dema for ex~~rtables may increase in th South reducing the volume of ex the North.
conditions, it is shown that an z*xogenous increase in the demand for the So.rLath’s export good must impro.ue the South’s terms of trade in the new eq\Jilibrium. Last, we look at tht. slopes of the export supply and import dernand curves for basic goods. Ait:hough the export supply curve may be, either upward or downward sloping., under the assumptions of the model the supply curve must al-ways be s&eper than the demand curve in the neighborhood of the world equilibrium. Chichilnisky’s model is characterized by two countries (the North and the South), two goods (investment/luxury and basic), and two factors of production (labor and capital). The following basic assumptions are made: (a) Both countries produce both goods according to fixed coeficients production functions, although the technical coeficients will in general be different in eaf;h region. W The South exports basic goods, the more labor-intensive commodity in both countrics. are an increasing function of factor rewards, and are (c) Factor sq~piies always fully employed. The demand for investment/lGxury goods is exogenous in both countries. Chichilnisky undertakes the analysis by examining the export supply (by the South) and import demand (~JJ the North) curves. In the model, for a given set of commoc’.ity prices we are able to calculate the wage and rate of profit in each country? This allows us to calculate factor supplies,’ which in turn enables us to determine the levels of cutput serp$ies of each commodity in each crjuntry which provide full employment.3 If we in i,rL?;tion specify an exogenous level of domestic demand for the investment/luxury goocr (the orth’s export), it is possible to calculate the level of demand for the basic good in each country by requiring that international payments balance.4 We are thus able to construct the export supply curve of the South and the import demand curve of the North as a function of relative commodity prices. Along each curve, the value of exports equals the value of imports for the country in question and all the equilibrium conditions within the country are met. However, world markets may not clear. World equilibrium is attained at the price of basic goods (using investment/luxury goods as the n erai Fe, which is done throughout the remainder of this comment) which equates export supply from one country with import demand from the other. i~~ilnisky states three propositions in her paper. 1 essentially deal with the slope of the export supply curve crowing that it could be either positive or negative. Propositio ~~a~te~ist~csof world equilibria (p. 18 1):
‘Assume that Iabour in the North is relatively price inelastic (CIsmall) and that the economy of the South has the characteristics descrrbed n Proposition 1. If a new woriti equilibrium with an increased volume of exports by the South is attained du12 to a positive :;hift in demand for oodv by the North (e.g., h&her growth rate of the North), then the terms of trade will worsen for the South and thz purchasing power of wages within the South will also decrease. This takes place within a Walrasian stable world eco~oi~~~ w-‘) it is this proposition that we examine in detail here. The first step in the analysis is to e:tamine how an exogenous increase in the North’s the demand for investment/luxury goods by the North shi import demand curve or the demand for basic oods the Nortil. Chiehiinisky (p. 1SO) states: ‘As the (exogenous) demand for investment goods (l’D)Nis increased within the North, eq. C?ia) implies a positive shift in its demand for B, Xi, at each price level.’ (Clrichilnisky’s variables used here are defined in table 1.) Eq. (21a) shows us the slope of an export supply curve, which is not particularly useful in calculating the direction the curve shifts. Instead we write out the equation for Xi and examine how it changes with an increase in (iD)”forany gicen relative price.
The North’s balance-of-payments constraint prices are equal to international prices)5
states that (when domestic
92
S.1.
Ranney,
Terms
cf trade
and
domestic
distribution
Substituting into (1) we get
x; == [(lqN -(TD)Nyp&
( “11 .’
Recall that once the relative price (pB) is specified, corrlmodity supplies are detenninexi. Thus, holding pB fixed, we r=~ determine the horizontal shift in the demand curve as aX,Nla(iD)Nlp,=
-
(4)
l/~&I.
An exogenous increase in the dt;;mand for investment/luxury goods by the North implies a lt$ward shift in its demand curve for imports of basic goods. The remainder of the analysis is straightforward. World equilibrium requires that exports of the South equA imports of the North, or equivalently [referring to eq, (@)I, tha!. the world market for investment/h~xury goods clears. Thus the wor’ld equilibrium value of pB can be calculated by the following:
Totally differentiating, we can calculate how ps will change in response to an exogenous change in the demand for investment/luxury goods in the new ~rlh equilibrium,
[t?(lS)N/dp, + iVs/t3pa]dp, = d(rD)N+ dFD.
(6)
In each country an increase in pB would increase real wages and decrease the rate ~rf profits (as in the Stolper-Samuelson theorem). This increases the supply of labor and decreases the supply of capital. Full employment of factors requires a shift ti,way from the production of capital-intensive luxury/investment good!; towards the production of labor-intensive basic goods (as in the Rybcz,/aski theorem). Thus an increase in pB results in a eiine in the producticbn of I goods in both countrissY6 and the model is aLsian stable. . (6) tells us that an exogenous increase in the demand for 1~~1~~~~~ goods by either country results in 8 decrease in pB. That i8iy’r~~i~~~ out the elipession for the output of investment/luxury goods in the Socth nction Jf pa by substituting eqs. (3), (4), (7), and (8) into (12) (from Chiohilnisky’s article), P- lm,[R 4”/?(a, -P,a,)lD]:n-c,[%fsc(c~,-c,/p,)/D]/D,
so that
22s a
93 is, u g0si~it.x
must uwit
shift in the demand for i~~ports by the North (a decrease in (TD)” in an improvement in the tems of trade for .
Proposition 3 cannot be correct. The result here is also inconsistent with fig. 2b in Chichiinisky’s paper.’ In the figure, as she explains on p. 180, Xi crosses Xt (I assume it should be X”,) from above. This is in fact inconsistent with the assumptions of her model. To w this, we first examine the slopes of the import demand and y Curves. Differentiating eq. (3) with respect to g,., pe-[(rS!N-(lf~)N]jp~
(7)
We have seen the supply of investment/luxury goods declines in both countries as ps rises. By assumption the North is an exporter of investment~luxury goods, so Is)N-(r’)N is greater than zero. Thus the import demand curve for the orth is al*.qays downward-sloping. Using the balance-of-payments constr4nt for the South, we can derive a similar expression for the export supply of basic goods. x$=BS-BD=(iD-IQ/p,.
Differentiating with respect to
(8) pe,
-(2Pfap,)/p, -(iD-
;‘pB= L.___~_J
L_.,,
P)JP; -1 6 0.
(9)
+
As Chich4nisky points out in Proposition,, 1 and 2, the export supply curve may be upward or downward-sloping.* It should also be noted that the export suppfy curve is unambiguously downward-sloping if the labor ejupply in the South IS abundant but factor supplies are totally unresponsive to changes in their returns. If factor supplies are fixed, full employment requires that the supply of investment/luxury goods remain unchan ed for any change in ps. Thus, the first term in eq. (9) becomes zero, and the slope of the ex c rt supply curve is negative with the magnitude depending on the initial c vel of trade? if we iwease, hvAlthough the h~ri~~~~~~iaxis is labelled ‘quan~~t); of expwtable
in fig. 2b, the ncte hrlou
rt
as an L elsewhere in the text) and an export in the text).
“ln this extreme case a world equilib:wm probably doesn’t exist, sin= neither the suppij’ df nor the demand br investment,luxury goods responds to price changes. JDE
D
example, the labor supp&*response to the real wage holding the initial iabor supply fixed (and thus ,the initial 1eveIsof product&on ~nndexports) the slope of the export supply curve becomes mol*e positive. An increase in pB now decreases the production of investment~~uxury goods, which increases impor* demand (equal to. the valurt:of export suppiy).”* Returning to- bg. 2b,, can. Xg ever cross xi from above? That is, as the price of basic goods rises above its world equilibrit:m level, could it ever result in an excess &MM for ‘basic goods exports as indicated in fig* 2b’b Algebraicall!r,’ we ask if 8(X”,-X#?JI, can ever be riegative when evaluated at a world equilibrium?
At a world equilibrium, world markets must clear, so that the last term L ahap cmss X~jbm belowin the context of beC3mes ZWO. Thus, x! REW’ this model. This can be more easily understood by considering the two components of (10) separately: the effect of the price change on factor supplies and : income effect of the change in the terms of trade. As discussed eartier, and increase in pe within each country results in an increase in the supply of labor and a decrease in the supply of capital, and thus a shift in production from luxury/investment goods towards basic goods in both countries. The demand for basic goods is determined by the balance of payments condition. For each country,
Since the income elasticity of demand for I goods is zero, examination of (11)
shows that any tendency towards an increase in BS (due to an increase in the labor supply) is ex14ctlymet by an increase in BD. A decrease in Is, however, will result in an excess supply of B goods (holding the terms of trade fixed for the moment). Thus the ‘factor supply” effect [the first term In eq. (IO)] is that an incret,se in pR results in an excess apply of B goods in each countr e seconldl term in eq. (10) shows the direct incame erects of nn increase ate that cliflerentiating t 11=slope of the export supply curve with re$ t to 31takes into ~~~~~~t changes; in both the r :spcllnsivencss of labor zlnd the ~~~~ndanc~ of MXM im the initial ~~~~~j~r~~rn(at the initial wag@. Thus, a higher a implies a larger ~n~r~~ in t es fdP/i& larger), but &a a larger initial level af imps 6) above, impii63 that
it
in pB. With the demrrrld for t oods fixed, a change in real incump due to 3. change in the terms of trade is completely absorbed by the demand for 3 ain as incaicat d in eq. (1 I). Beginning at world equ;Iibriurin, a the terms of trade (now holding factor supplies fixed) wdistrabut:: income from onz Country t another (and between wc)rkers and capitalists). se the demand for B goods in the An onward pres~re on pa South, but desteases the de ods in the North by exactly the same amount since trade is initially balanced. The net impact of the direcr ‘terms of trad:’ efiect on the world market is zero, as indicated by the second terms in eq. ( 0). Thus on the world leveI, only the factor sl;pply effects art: relevant in thz neighbourho~d of world equilibrium, and any small increase an excess supply of B goods. in pB must result What then is t appropria1.e diagram arld explanation to accompany the simulation reported in the appendix ? The comparative static results are (p. 18’7):‘the parameter of investment demand is increased in the North from 1.~ to 2. Equilibrium value of exports of basic goods by the Swth increases and their prim piJ decreases”. Fig. 1 provide; the explanatlozt The export supply cw be may be downward-sloping!n the experiment, but we know it must be sf :cwr that1 the import demand. curve. We also know that an exogenous in&ease in investment demand-' Jay !he hforth is equivalent to a leftward shift m the import demand curve. As in any simple Walrasian system, an exogenouq decrease in demand res llts in a fall in the price of that commodity. The new equilibrium quantity, i&wever, may either rise or fall. In this case it rim in the new equilibrium, even though the trsogenous shaft wus to the kfi. The simulation ctxperiment is consistent with the fact that, under the
assumptions of the model, an exogenous incregise in the demand for basic goods by the North will never result in a worsering of the terms of trade for the South or a decrease in the purchasingpower $)fwages within the South.
Chichilnisky, Gracielu, 1981, Terms of trade and domestic distribution: Expcwt4 abundant labour, Journal of Dwelopment Economics 8, no. 2, l@--192.
owth with