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Tariff protection and taxation of foreign capital: The welfare implications for a small country
Journal of International Economics 19 (1985) 181-188.North-Holland
T A R I F F P R O T E C T I O N AND T A X A T I O N O F F O R E I G N CAPITAL: THE WELFARE IMPLICATIONS FOR A SMALL COUNTRY F.R. CASAS* University of Toronto, Toronto, Ontario MSS 1A1, Canada.
Received May 1984,revisedversion receivedDecember 1984 This paper extends recent studies by deriving sufficient conditions for tadff-immi,~erizationin a small country in the presence of internationally mobile sector-speeificcapital, the returns of which are taxed or subsidized. Necessary conditions for a welfare-augmenting tariff are also discussed, and the analysis is extended to the welfare implications of changes in the tax or subsidy rate on the earnings of migrating capital.
1. Introduction The welfare implications of tariff protection when capital is internationally mobile have attracted substantial attention over the last decade. I Bhagwati (1973) first hypothesized that the conventional result whereby the imposition of a tariff or an increase in the tariff rate would reduce .a small country's real income might carry over to the case where, in addition to the usual consumption and production effects, the increased rate of protection would attract foreign capital by raising the domestic return under the assumption that the import-competing sector is relatively capital intensive. Hamada (1974) and Brecher and Alejandro (1977) subsequently demonstrated that such immiserization would necessarily obtain in this case provided the tariffimposing nation did not levy a tax on the returns of foreign capital and remained incompletely specialized in production. 2 Pursuing this line of analysis Yabuuchi (1982) confirmed the Hamada and Brecher-Alejandro result and extended it by deriving a sufficient condition for tariff immiserization in the presence of a tax on the earnings of imported capital, as well as a necessary condition for a tariff to be welfare*The author wishes to acknowledge the useful comments and advice he received from R.A. Brecher and two referees. IA closelyrelated topic of discussion has been the effectof exogenouscapital accumulation in the presenceof tariffs. See, for example, Johnson (1967). 2See also Uzawa (1969). 0022-1996/85/$3.30 © 1985)ElsevierSciencePublishers B.V. (North-Holland)
182
F.R. Casas, Tariff protection
augmenting. 3 The latter possibility might be regarded as a more paradoxical result than Bhagwati's. Both conditions derived by Yabuuchi involve the size of the tax on foreign capital, with a relatively small tax conducive to immiserization - - the H a m a d a and Brecher-Alejandro case representing the limiting situation - - while a relatively large tax is required for an increase in protection to be welfare-augmenting. However, while these results are of considerable interest, they are limited by the restrictive assumptions on which they are based, particularly that the import-competing sector is relatively capital-intensive. These results are also inconsistent with the assumption that the tariff-imposing country is a pricetaker in all world markets if international mobility of capital is unrestricted. This may be understood by noting that an increase in the tariff imposed by a country which is small in world commodity markets will raise the domestic rate of return to capital in relative and in real terms given the assumed factor intensity ranking of traded goods. This will induce an inflow of foreign capital, but since the addition of this capital to the domestic stock will not lower its rate of return as long as incomplete specialization obtains, no equilibrium can be restored in which the domestic net return to foreignowned capital is brought into equality with the world rate which remains constant if the home country is small in the world capital market. Thus, if the home country is not completely specialized in production initially, an increase in the tariff must precipitate such as state. 4 As recently pointed out by Brecher and Findlay (1983) an equilibrium with incomplete specialization is feasible - - and the H a m a d a et al. results are qualitatively valid - - if it is assumed that the home country while small in world commodity markets faces an upward-sloping supply curve for foreign capital, s However, Brecher and Findlay also develop a more fruitful approach by using a model in which capital is assumed to be sector-specific. They establish that if the internationally mobile capital is specific to the importcompeting sector - - and is therefore attracted by a t a r i f f - the imposition of a tariff by a small country must reduce its aggregate welfare. More recently, Jones (1984) has provided an even more powerful result, namely that tariff immiserization must obtain regardless of the sector in which the internation3Yabuuchi's results reveal that the sufficient condition for immiserization is also necessary if the tariff rate is initially zero, and that a small tariff would necessarily raise welfare if no foreign capital is initially employed domestically. '*It may also be noted that for a country that is small in world commodity and capital markets and which initially imposes a nonzero tariff, incomplete specialization is possible with the given tariff only if technologies are internationally different. However, with the tariff increasing the domestic relative price of the importable just enough to bring the domestic rate of return to capital into equality with the world rate, it must also be assumed that no foreign capital is initially employed domestically. 5If world commodity prices do not change, this may be possible if, for example, the foreign country has more factors than goods. Alternatively the domestic country may resort to a quota on foreign investment. I am indebted to a referee for bringing this point to my attention.
F.R. Casas, Tariff protection
183
ally mobile capital is used and, hence, regardless of whether the tariff would induce a capital inflow or outflow. The purpose of this paper is to further extend the Brecher-Findlay and Jones line of analysis by investigating the welfare implications of tariff protection when the tariff-imposing country also levies a tax or provides a subsidy on the returns of internationally mobile capital. The main result which emerges is that a higher rate of protection must be immiserizing if no tax or subsidy is applied to migrating capital - - the Jones result - - or if the internationally mobile capital is taxed or subsidized at a second-best optimal rate. This enables us to derive a necessary condition for a welfareaugmenting tariff. We also show that symmetric results apply to the welfare implications of changes in the rate of taxation or subsidization of the earnings of internationally mobile capital.
2. Changes in tariffs and real income Let U = U ( C M , Cr.) denote the home country's aggregate utility level in terms of the domestic consumption of the importable and exportable commodities. Using the latter good as the numeraire, changes in domestic real income may be expressed as dy = d U / U e = p d C M + dCn,
(1)
where P=PM/Pe is the domestic relative price of the importable. With p* denoting the world commodity price ratio and K~ the net capital inflow of sector-i-specific capital (K~ < 0 if the home country is a net lender), balance of payments equilibrium requires that p*(C M - XM) + (C~, - XE) + r * K i = O,
(2)
where XM and XE are the domestic output levels and r* is the world rate of return to capital. Totally differentiating (2) and using the resulting expression in (1) yields the familiar equation: 6 dy = - M dp* - Ki dr* + (p - p*) dM + (r e - r*) dKi, where re is the domestic rental rate and M = C M - X M. For a small country unable to influence world prices or rates of return to capital, the above 6It is assumed for the sake of simplicity that the internationally mobile capital is specific to one sector, but the analysis is readily extended to the case where two types of capital are mobile whether they flow in the same or in opposite directions. See footnote 8 for a discussion of the case where capital is not sector-specific.
F.R. Casas, Tariff protection
184
expression reduces to (3)
d y = ( p - p * ) dM +(r t - r * ) dKt. Since
M = Cu(p, y)-XM(p, Ki), eq. (3) may also be written as mt ~ , aM 1--~-~)dy=(p--p )--ff-fpd p - [ ( p - p * > ~ -(rt-r*)]dKt,
(4)
where m=p(OCM/Oy) is the home country's marginal propensity to import and OM/ap is the negative own-substitution effect of a rise in the relative price of the importable. 7 Eq. (4) may be further simplified by noting that p=p*(l+t), where t is the domestic tariff on imports, so that dp=p*dt. Furthermore, aXM/OK~=OrJOpfrom Samuelson's (1953) reciprocity theorem. Finally, if the home country is a net importer of sector-i-specific capital and taxes the returns to foreign capital at a rate st(s~<0 if foreign capital is subsidized), then rt(1-st) =r* in equilibrium and since rt= rt(p,Kt) it follows that dK,
rt
(1-si)(arJdKt)
, ar.~ap dsi-p ari/aKtdt.
(5)
With p* set equal to one through an appropriate choice of units, we may now rewrite (4) as ( 1 - l ~ t ) d y = ~tFa_M_Mq_(art/ap) - - , - - s i r 2] ( L op c~rJSKtJ
rt - (1-st)(art/aKt)
t
arJap). (It OrJcgKt~
i< art ) ~t~p -slri dst.
(6)
Consider the effect of a change in the tariff rate for a given tax or subsidy on the income of foreign capital (dst=(3). If the home country does not tax the latter, i.e. if st = 0, then 1--
mt ~dy 1+tJ dt
tFaM_F (a~dap)'q ^ ~,== o L- p
-ar,/aK, -./
(7)
since ardOKt
F.R. Casas, Tariffprotection
185
ally mobile capital is used, and whether the rise in the tariff rate expands or reduces the net indebtedness position of the home country, s However, this result should more generally be viewed as establishing that a zero tax on the earnings of imported capital is a sufficient condition for an increase in the domestic rate of protection to be immiserizing. It is possible to derive another such condition for the case where the tax in nonzero. In particular, if for any given tariff rate the home country sets the value of s~ at the level which maximizes domestic real income, eq. (6) then reveals that the second-best rate of taxation of the earnings of foreign capital is
+++=
t Or~ ri 0p
.
(8)
This will be positive if the internationally mobile capital is specific to the import competing sector, and vice versa. Substituting for s,. from (8) into (6), we now obtain: I
mt ~ dy
-TTT)
OM
<°
(9)
As in the case of a zero tax on foreign capital earnings, an increase in the tariff rate will necessarily be immiserizing if the home country consistently adopts the second-best tax or subsidy policy. If follows from these results that a necessary condition for an increase in the
rate of protection to be welfare-augmenting in a small country is that foreign capital be taxed or subsidized at a nonoptimal rate, Examination of eq. (6) reveals that it will also be necessary that ar+/ap>O, i.e. that the internationally mobile capital be specific to the import-competing sector if foreign capital is taxed and vice versa? It should be noted that these results remain valid if the home country is a net capital exporter. In this case, the equilibrium condition in the domestic capital market becomes r+=r*(1-s'~), where s'~ is the tax on the earnings of domestic capital invested abroad. It is readily shown that a rise in the tariff rate would unambiguously reduce domestic real income if s'~=O or if s~ is chosen in such a way as to maximize domestic income for any given tariff rate. x° If s~ in nonoptimal, a necessary condition for an increase in the rate of sJones also extends the analysis to the case where capital is intersectorally mobile. In this instance, if the home country is initially incompletely specialized - - which rules out internationally identical technologies - - a rise in the tariff rate would wipe out imports through the induced capital inflow or outflow. 9For example, if t=O and sl~0 initially, dy/dt <>0 if and only if st(OrJOp)~0. t°The optimum value of the tax is given by ~-= -(t/r~)(OrJOp)in this case.
186
F.R. Casas, Tariff protection
protection to be welfare-augmenting is that the internationally mobile capital be specific to the export sector if s't > 0 and vice versa. Fig. 1 illustrates the results derived in this section. The curve labelled (st = 0) shows the change in the home country's real income level if the earnings of imported foreign capital (or those of exported domestic capital) are not taxed or subsidized. On the other hand, the curve labelled (st =~t) shows the change in real income if the tax or subsidy on imported or exported capital is adjusted to the second-best level for each tariff rate. In both cases, a higher tariff or subsidy will lead to immiserization. The third curve labelled s t > 0 shows the effect of changes in the role of protection for the case where the internationally mobile capital is specific to the import-competing sector and where the (positive) tax rate on the earnings of foreign capital is given. Increasing the tariff from, say, tA to tB would raise real income in such a case. REAL INCOME
/ (si = o ) ( s i > o )
0 tA
B
(si= ~i)
TARI FF RATE
Fig. 1
3. Changes in capital taxation and real income The results of the preceding section can readily be applied to an analysis of the welfare impact of a change in the tax or subsidy rate on the earnings
F.R. Casas,Tariffprotection
187
of the internationally mobile capital. Thus, for example, in the case of a capital-importing country which pursues a free-trade policy, eq. (6) reveals that
I - 1 +t,lds, ],=o =(1-s,)(0r,/0K,) ~0, ifs,,~0,
(10)
that is, an increase in the tax or subsidy rate will necessarily be immiserizing. On the other hand, for any given tax rate the welfare-maximizing tariff rate is given by
Op)lkOK,)
r=s,,,FoM+lor
s,r~ ,=,=(1-s,)(OreOK,) I-iM
><0, if s;~0.
OM/Op I'Or,~2/l" Or, '~-]
(12)
Thus, there exists a perfect parallel between the effects of changes in the rate of taxation/subsidization of the earnings of internationally mobile capital and those of changes in the rate of tariff protection. For a small country with a nonoptimal tariff on imports, eq. (6) reveals that the imposition of small tax would increase real income if the internationally mobile capital is specific to the import competing sector, whereas a small subsidy would~ have the same effect in the opposite case. More generally, an increase in the rate of taxation on imported or exported capital would be welfare-augmenting only if that capital is used in the importcompeting sector and vice versa. These results are of particular interest and relevance where changes in tariff rates are subject to external constraints such as a country's commitments under international trade agreements.
4. Concluding remarks Although the results derived here represent a Significant extension and generalization of earlier studies, it is important to note that the model with
188
F.R. Casas, Tariff protection
two t r a d e d g o o d s a n d one t r a d e d factor - - sector specific c a p i t a l - - s h o u l d be c o n s i d e r e d a special case of the m o r e general m o d e l with m a n y t r a d e d c o m m o d i t i e s i n c l u d i n g t r a d e d factor services. W i t h this m a n y - c o m m o d i t y a n o l o g y , it b e c o m e s clear that a similarity exists between the effects of tariff changes with a c o n s t a n t tax on c a p i t a l earnings a n d those of tax changes with a c o n s t a n t tariff. T h e d u a l i t y a p p r o a c h to t r a d e t h e o r y which has received increasing a t t e n t i o n in recent years m a k e s the s y m m e t r y in these results easier to see. 11 ~lSee, for example, Dixit and Norman (1980) and Woodland (1982).
References Bhagwati, J.N., 1973, The theory of immiserizing growth: Further applications, in: M.B. Connolly and A.K. Swoboda, eds., International trade and money (University of Toronto Press, Toronto) 45-54. Brecher, R.A. and C. Diaz-Alejandro, 1977, Tariffs, foreign capital and immiserizing growth, Journal of International Economics 7, 317-322. Brecber, R.A. and R. Findlay, 1983, Tariffs foreign capital and national advantage with sectorspecific factors, Journal of International Economics 14, 277-288. Dixit, A.K. and V. Norman, 1980, Theory of international trade (Nisbet and Cambridge University Press, Cambridge). Hamada, K., 1974, An economic analysis of the duty-free zone, Journal of International Economics 4, 225-241. Johnson, H.G., 1967, The possibility of income losses from increased efficiency or factor accumulation in the presence of tariffs, Economic Journal 77, 151-154. Jones, R.W., 1984, Protection and the harmful effects of endogenous capital flows, Mimeo. Samuelson, P.A., 1953, Prices of factors and goods in general equilibrium, Review of Economic Studies, 1-20. Uzawa, H., 1969, Liberalization of foreign investments and the national economy, Ekonomisuto 23, 106-122. Woodland, A.D., 1982, International trade and resource allocation (North-Holland, Amsterdam). Yabuuchi, S., 1982, A note on tariff-induced capital inflow and immiserization in the presence of taxation of foreign profits, Journal of International Economics 12, 183-189.
T A R I F F P R O T E C T I O N AND T A X A T I O N O F F O R E I G N CAPITAL: THE WELFARE IMPLICATIONS FOR A SMALL COUNTRY F.R. CASAS* University of Toronto, Toronto, Ontario MSS 1A1, Canada.
Received May 1984,revisedversion receivedDecember 1984 This paper extends recent studies by deriving sufficient conditions for tadff-immi,~erizationin a small country in the presence of internationally mobile sector-speeificcapital, the returns of which are taxed or subsidized. Necessary conditions for a welfare-augmenting tariff are also discussed, and the analysis is extended to the welfare implications of changes in the tax or subsidy rate on the earnings of migrating capital.
1. Introduction The welfare implications of tariff protection when capital is internationally mobile have attracted substantial attention over the last decade. I Bhagwati (1973) first hypothesized that the conventional result whereby the imposition of a tariff or an increase in the tariff rate would reduce .a small country's real income might carry over to the case where, in addition to the usual consumption and production effects, the increased rate of protection would attract foreign capital by raising the domestic return under the assumption that the import-competing sector is relatively capital intensive. Hamada (1974) and Brecher and Alejandro (1977) subsequently demonstrated that such immiserization would necessarily obtain in this case provided the tariffimposing nation did not levy a tax on the returns of foreign capital and remained incompletely specialized in production. 2 Pursuing this line of analysis Yabuuchi (1982) confirmed the Hamada and Brecher-Alejandro result and extended it by deriving a sufficient condition for tariff immiserization in the presence of a tax on the earnings of imported capital, as well as a necessary condition for a tariff to be welfare*The author wishes to acknowledge the useful comments and advice he received from R.A. Brecher and two referees. IA closelyrelated topic of discussion has been the effectof exogenouscapital accumulation in the presenceof tariffs. See, for example, Johnson (1967). 2See also Uzawa (1969). 0022-1996/85/$3.30 © 1985)ElsevierSciencePublishers B.V. (North-Holland)
182
F.R. Casas, Tariff protection
augmenting. 3 The latter possibility might be regarded as a more paradoxical result than Bhagwati's. Both conditions derived by Yabuuchi involve the size of the tax on foreign capital, with a relatively small tax conducive to immiserization - - the H a m a d a and Brecher-Alejandro case representing the limiting situation - - while a relatively large tax is required for an increase in protection to be welfare-augmenting. However, while these results are of considerable interest, they are limited by the restrictive assumptions on which they are based, particularly that the import-competing sector is relatively capital-intensive. These results are also inconsistent with the assumption that the tariff-imposing country is a pricetaker in all world markets if international mobility of capital is unrestricted. This may be understood by noting that an increase in the tariff imposed by a country which is small in world commodity markets will raise the domestic rate of return to capital in relative and in real terms given the assumed factor intensity ranking of traded goods. This will induce an inflow of foreign capital, but since the addition of this capital to the domestic stock will not lower its rate of return as long as incomplete specialization obtains, no equilibrium can be restored in which the domestic net return to foreignowned capital is brought into equality with the world rate which remains constant if the home country is small in the world capital market. Thus, if the home country is not completely specialized in production initially, an increase in the tariff must precipitate such as state. 4 As recently pointed out by Brecher and Findlay (1983) an equilibrium with incomplete specialization is feasible - - and the H a m a d a et al. results are qualitatively valid - - if it is assumed that the home country while small in world commodity markets faces an upward-sloping supply curve for foreign capital, s However, Brecher and Findlay also develop a more fruitful approach by using a model in which capital is assumed to be sector-specific. They establish that if the internationally mobile capital is specific to the importcompeting sector - - and is therefore attracted by a t a r i f f - the imposition of a tariff by a small country must reduce its aggregate welfare. More recently, Jones (1984) has provided an even more powerful result, namely that tariff immiserization must obtain regardless of the sector in which the internation3Yabuuchi's results reveal that the sufficient condition for immiserization is also necessary if the tariff rate is initially zero, and that a small tariff would necessarily raise welfare if no foreign capital is initially employed domestically. '*It may also be noted that for a country that is small in world commodity and capital markets and which initially imposes a nonzero tariff, incomplete specialization is possible with the given tariff only if technologies are internationally different. However, with the tariff increasing the domestic relative price of the importable just enough to bring the domestic rate of return to capital into equality with the world rate, it must also be assumed that no foreign capital is initially employed domestically. 5If world commodity prices do not change, this may be possible if, for example, the foreign country has more factors than goods. Alternatively the domestic country may resort to a quota on foreign investment. I am indebted to a referee for bringing this point to my attention.
F.R. Casas, Tariff protection
183
ally mobile capital is used and, hence, regardless of whether the tariff would induce a capital inflow or outflow. The purpose of this paper is to further extend the Brecher-Findlay and Jones line of analysis by investigating the welfare implications of tariff protection when the tariff-imposing country also levies a tax or provides a subsidy on the returns of internationally mobile capital. The main result which emerges is that a higher rate of protection must be immiserizing if no tax or subsidy is applied to migrating capital - - the Jones result - - or if the internationally mobile capital is taxed or subsidized at a second-best optimal rate. This enables us to derive a necessary condition for a welfareaugmenting tariff. We also show that symmetric results apply to the welfare implications of changes in the rate of taxation or subsidization of the earnings of internationally mobile capital.
2. Changes in tariffs and real income Let U = U ( C M , Cr.) denote the home country's aggregate utility level in terms of the domestic consumption of the importable and exportable commodities. Using the latter good as the numeraire, changes in domestic real income may be expressed as dy = d U / U e = p d C M + dCn,
(1)
where P=PM/Pe is the domestic relative price of the importable. With p* denoting the world commodity price ratio and K~ the net capital inflow of sector-i-specific capital (K~ < 0 if the home country is a net lender), balance of payments equilibrium requires that p*(C M - XM) + (C~, - XE) + r * K i = O,
(2)
where XM and XE are the domestic output levels and r* is the world rate of return to capital. Totally differentiating (2) and using the resulting expression in (1) yields the familiar equation: 6 dy = - M dp* - Ki dr* + (p - p*) dM + (r e - r*) dKi, where re is the domestic rental rate and M = C M - X M. For a small country unable to influence world prices or rates of return to capital, the above 6It is assumed for the sake of simplicity that the internationally mobile capital is specific to one sector, but the analysis is readily extended to the case where two types of capital are mobile whether they flow in the same or in opposite directions. See footnote 8 for a discussion of the case where capital is not sector-specific.
F.R. Casas, Tariff protection
184
expression reduces to (3)
d y = ( p - p * ) dM +(r t - r * ) dKt. Since
M = Cu(p, y)-XM(p, Ki), eq. (3) may also be written as mt ~ , aM 1--~-~)dy=(p--p )--ff-fpd p - [ ( p - p * > ~ -(rt-r*)]dKt,
(4)
where m=p(OCM/Oy) is the home country's marginal propensity to import and OM/ap is the negative own-substitution effect of a rise in the relative price of the importable. 7 Eq. (4) may be further simplified by noting that p=p*(l+t), where t is the domestic tariff on imports, so that dp=p*dt. Furthermore, aXM/OK~=OrJOpfrom Samuelson's (1953) reciprocity theorem. Finally, if the home country is a net importer of sector-i-specific capital and taxes the returns to foreign capital at a rate st(s~<0 if foreign capital is subsidized), then rt(1-st) =r* in equilibrium and since rt= rt(p,Kt) it follows that dK,
rt
(1-si)(arJdKt)
, ar.~ap dsi-p ari/aKtdt.
(5)
With p* set equal to one through an appropriate choice of units, we may now rewrite (4) as ( 1 - l ~ t ) d y = ~tFa_M_Mq_(art/ap) - - , - - s i r 2] ( L op c~rJSKtJ
rt - (1-st)(art/aKt)
t
arJap). (It OrJcgKt~
i< art ) ~t~p -slri dst.
(6)
Consider the effect of a change in the tariff rate for a given tax or subsidy on the income of foreign capital (dst=(3). If the home country does not tax the latter, i.e. if st = 0, then 1--
mt ~dy 1+tJ dt
tFaM_F (a~dap)'q ^ ~,== o L- p
-ar,/aK, -./
(7)
since ardOKt
F.R. Casas, Tariffprotection
185
ally mobile capital is used, and whether the rise in the tariff rate expands or reduces the net indebtedness position of the home country, s However, this result should more generally be viewed as establishing that a zero tax on the earnings of imported capital is a sufficient condition for an increase in the domestic rate of protection to be immiserizing. It is possible to derive another such condition for the case where the tax in nonzero. In particular, if for any given tariff rate the home country sets the value of s~ at the level which maximizes domestic real income, eq. (6) then reveals that the second-best rate of taxation of the earnings of foreign capital is
+++=
t Or~ ri 0p
.
(8)
This will be positive if the internationally mobile capital is specific to the import competing sector, and vice versa. Substituting for s,. from (8) into (6), we now obtain: I
mt ~ dy
-TTT)
OM
<°
(9)
As in the case of a zero tax on foreign capital earnings, an increase in the tariff rate will necessarily be immiserizing if the home country consistently adopts the second-best tax or subsidy policy. If follows from these results that a necessary condition for an increase in the
rate of protection to be welfare-augmenting in a small country is that foreign capital be taxed or subsidized at a nonoptimal rate, Examination of eq. (6) reveals that it will also be necessary that ar+/ap>O, i.e. that the internationally mobile capital be specific to the import-competing sector if foreign capital is taxed and vice versa? It should be noted that these results remain valid if the home country is a net capital exporter. In this case, the equilibrium condition in the domestic capital market becomes r+=r*(1-s'~), where s'~ is the tax on the earnings of domestic capital invested abroad. It is readily shown that a rise in the tariff rate would unambiguously reduce domestic real income if s'~=O or if s~ is chosen in such a way as to maximize domestic income for any given tariff rate. x° If s~ in nonoptimal, a necessary condition for an increase in the rate of sJones also extends the analysis to the case where capital is intersectorally mobile. In this instance, if the home country is initially incompletely specialized - - which rules out internationally identical technologies - - a rise in the tariff rate would wipe out imports through the induced capital inflow or outflow. 9For example, if t=O and sl~0 initially, dy/dt <>0 if and only if st(OrJOp)~0. t°The optimum value of the tax is given by ~-= -(t/r~)(OrJOp)in this case.
186
F.R. Casas, Tariff protection
protection to be welfare-augmenting is that the internationally mobile capital be specific to the export sector if s't > 0 and vice versa. Fig. 1 illustrates the results derived in this section. The curve labelled (st = 0) shows the change in the home country's real income level if the earnings of imported foreign capital (or those of exported domestic capital) are not taxed or subsidized. On the other hand, the curve labelled (st =~t) shows the change in real income if the tax or subsidy on imported or exported capital is adjusted to the second-best level for each tariff rate. In both cases, a higher tariff or subsidy will lead to immiserization. The third curve labelled s t > 0 shows the effect of changes in the role of protection for the case where the internationally mobile capital is specific to the import-competing sector and where the (positive) tax rate on the earnings of foreign capital is given. Increasing the tariff from, say, tA to tB would raise real income in such a case. REAL INCOME
/ (si = o ) ( s i > o )
0 tA
B
(si= ~i)
TARI FF RATE
Fig. 1
3. Changes in capital taxation and real income The results of the preceding section can readily be applied to an analysis of the welfare impact of a change in the tax or subsidy rate on the earnings
F.R. Casas,Tariffprotection
187
of the internationally mobile capital. Thus, for example, in the case of a capital-importing country which pursues a free-trade policy, eq. (6) reveals that
I - 1 +t,lds, ],=o =(1-s,)(0r,/0K,) ~0, ifs,,~0,
(10)
that is, an increase in the tax or subsidy rate will necessarily be immiserizing. On the other hand, for any given tax rate the welfare-maximizing tariff rate is given by
Op)lkOK,)
r=s,,,FoM+lor
s,r~ ,=,=(1-s,)(OreOK,) I-iM
><0, if s;~0.
OM/Op I'Or,~2/l" Or, '~-]
(12)
Thus, there exists a perfect parallel between the effects of changes in the rate of taxation/subsidization of the earnings of internationally mobile capital and those of changes in the rate of tariff protection. For a small country with a nonoptimal tariff on imports, eq. (6) reveals that the imposition of small tax would increase real income if the internationally mobile capital is specific to the import competing sector, whereas a small subsidy would~ have the same effect in the opposite case. More generally, an increase in the rate of taxation on imported or exported capital would be welfare-augmenting only if that capital is used in the importcompeting sector and vice versa. These results are of particular interest and relevance where changes in tariff rates are subject to external constraints such as a country's commitments under international trade agreements.
4. Concluding remarks Although the results derived here represent a Significant extension and generalization of earlier studies, it is important to note that the model with
188
F.R. Casas, Tariff protection
two t r a d e d g o o d s a n d one t r a d e d factor - - sector specific c a p i t a l - - s h o u l d be c o n s i d e r e d a special case of the m o r e general m o d e l with m a n y t r a d e d c o m m o d i t i e s i n c l u d i n g t r a d e d factor services. W i t h this m a n y - c o m m o d i t y a n o l o g y , it b e c o m e s clear that a similarity exists between the effects of tariff changes with a c o n s t a n t tax on c a p i t a l earnings a n d those of tax changes with a c o n s t a n t tariff. T h e d u a l i t y a p p r o a c h to t r a d e t h e o r y which has received increasing a t t e n t i o n in recent years m a k e s the s y m m e t r y in these results easier to see. 11 ~lSee, for example, Dixit and Norman (1980) and Woodland (1982).
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