North–South Investment Flows and Optimal Environmental Policies

Journal of Environmental Economics and Management 40, 275–296 (2000) doi:10.1006/jeem.2000.1123, available online at http://www.idealibrary.com on

North–South Investment Flows and Optimal Environmental Policies1 Hamid Beladi Department of Economics, University of Dayton, 300 College Park, Dayton, Ohio 45469

Nancy H. Chau Department of Agricultural, Resource and Managerial Economics, Cornell University, Ithaca, New York

and M. Ali Khan Department of Economics, The Johns Hopkins University, Baltimore, Maryland 21218 Received July 8, 1997; revised August 25, 1998; published online August 10, 2000

In the context of a simple North–South model that focuses on the international movement of capital, we show how neglect of pollution-generating effects of foreign investment may lead to distorted and misleading policy recommendations. Such a neglect has recently received emphasis in the empirical literature on East Asian economies, as in Bello and Rosenfeld (1990, “Dragons in Distress: Asia’s Miracle Economics in Crisis,” Food First, San Francisco), and was shown to overlook resulting tendencies in these economies toward specialization, away from agriculture and toward manufacturing. Our simple model formalizes this observation and allows us to show that even for an unspecialized capital-poor, resource-rich South, such pollution-generating effects provide incentives for the North to encourage, rather than to discourage, foreign investment abroad and strengthen Southern incentives to restrict foreign investment more sharply than is conventionally assumed. In a nutshell, it brings out the implications of Northern capital “creating its own demand” as a consequence of its adverse impact on the Southern resource base. Despite its simplicity, the model thus sheds light on three interrelated aspects of international trading relations: production asymmetry, incomplete markets, and monopolistic advantage. © 2000 Academic Press

1. INTRODUCTION It is part of conventional wisdom going back at least to Pigou’s 1912 Economics of Welfare [32] that monopolistic or monopsonistic advantages are exploited by 1 This is an extensively revised version of Working Paper No. 18, Southern Illinois University at Carbondale. The authors are grateful to Ron Jones for several illuminating conversations and to an associate editor and two anonymous referees of this journal for their reading and suggestions. This revision was undertaken while the third author was a Visiting Fellow at the Australian National University and he acknowledges with pleasure the hospitality and excellent facilities extended to him at the Research School of Social Sciences; he also thanks Max Corden for stimulating his interest in this topic.

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respectively restricting supply and demand, and external economies and diseconomies are successfully internalized by the imposition of suitable subsidies and taxes. In the context of international capital movements, these principles have been translated into the Kemp–MacDougall–Jones recommendation that a country pursuing its national advantage restrict the inflow of foreign capital by an optimum tax. Indeed, the general principles have become a staple of received international trade theory, as for example, in the work of Meade, and have been synthesized to yield the generalized theory of distortions, as in [6, 18]. However, the successful application of this work to policy issues hinges on the particular way the context is formalized and the precise model that is being investigated. In this paper, we argue that previous work on international capital movements suffers by its neglect of the pollution-generating effects of foreign capital and that conventional wisdom on policy prescriptions needs substantial modification even when these polluting effects are formalized in the simplest possible setting. There is by now considerable grass-root level concern regarding the potentially adverse environmental impact of foreign investment in developing nations (LDCs) and the associated development bias against the traditional sector. Conceptually, the argument revolves around the basic intuition that a foreign firm has no stake either in the environment or in the long-term health of workers in the host country, and these missing markets, and the consequent lack of incentives, translate into skewed development that is inimicable to the interests of the host country. Such a concern is backed by an extensive and growing empirical documentation. Bello and Rosenfeld [5], for instance, summarize a substantial literature on the resourcedepleting consequences of industrial emissions in the form of air and water pollution in the fast-growing economies of East Asia as they continue on their process of industrialization. Edoho [16] presents evidence regarding the adverse consequences of technology transfer on the resource base of the developing nations in Africa. In terms of a broader geographical perspective, Pearson and Pryor [31] lay the ground work for charting different kinds of transnational environmental abuse due to foreign investment. Despite all this attention, we still do not have a simple canonical model, rooted in previous work, that can be used to answer two of the basic questions in the field: from the point of view of national advantage, should foreign capital be taxed? And should investment abroad be curbed? More broadly, surprisingly little work has been done to illustrate either (i) the consequences of unrestricted international capital flows on the environment or (ii) the potential policy linkages between capitalexporting and capital-recipient countries.2 To date, Copeland and Taylor [11] seem to be the only exception in the former regard—they lay out the possible causes of an increase in world pollution as dirty industries relocate from rich to poor countries in response to international differences in environmental regulations. However, their primary emphasis is on world, rather than national, welfare and on implications of 2 Of course, there is an extensive literature under the general heading of “trade and the environment.” For example, there are studies which explore (i) the effect of trade and environmental policy reforms on transboundary and/or domestic environmental degradation [3, 7, 28, 30], (ii) the implications of North– South trade in the presence of common property resources [8–10], (iii) the relationship between growth and environmental controls to cope with pollution disutilities [26, 33] (iv) the relationship between income distribution and pollution control [34–36], and (v) international environmental policy games [4, 24, 29].

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efficiency in the entire international economy. In this paper, we take an individual country perspective and illustrate the possible sources of conflict inherent in North– South environmental relations in the presence of international capital mobility. We begin with a two-country model in which capital investment flows form the primary economic linkage between the two countries. There is no international mobility of labor, and both countries are small in international commodity markets. These assumptions are in concert with Batra and Ramachandran [1], along with Viner’s model of custom union, which focuses on the issue of multilateral investment flows among members of the union, at given commodity prices that are determined in the rest of the world. We assume an asymmetric production structure as our point of departure, whereby one of the countries is specialized in the production of manufactures, while the other is incompletely specialized in agriculture and manufactures. We follow the literature in calling this a North–South model,3 but an alternative conception is to think of a metropolitan resource-poor economy trading with a capital-dependent, resource-rich colony.4 Where we depart from the literature is in the assumption of labor productivity in agriculture being susceptible to resource depletion arising out of the (intensive) use of capital in the production of manufactures. What is remarkable to us is that this simple additional consideration is enough to show that the traditional dose of a Pigouvian tax on foreign capital no longer suffices for the South and the monopolistic provider of investment capital finds it optimal to subsidize capital exports from the North. As is well known, the (classical) Kemp–MacDougall–Jones prescription based on standard monopoly– monopsony arguments suggests the opposite.5 Of course, there is considerable work on this prescription in the trade-theory literature, but this work has nothing to say about pollution, and its primary emphasis is on the elucidation of the general equilibrium and welfare implications of foreign investment taxation in economies that are open to international trade as well as to foreign investment flows.6 From a purely technical perspective, we find that the pollution-generating effects of foreign capital translate into a demand schedule for Northern capital that is upward sloping. This leads us to examine the conditions under which equilibrium international allocation of capital is dynamically stable, and thus robust to the parametric changes that we investigate. So long as stability is guaranteed, the upward sloping demand schedule for Northern capital modifies the optimal policy prescriptions for the two countries, and gives us interesting results. In the remainder of this Introduction, we list these below and provide some guiding intuition for the reader when he or she considers the algebraic argumentation. (i) We demonstrate that unrestricted international capital mobility may force the pollution recipient country to completely abandon the resource-using agricultural sector and specialize in the production of manufactures, even when natural resources have not been fully depleted. Thus, foreign investment exacerbates inter-country resource-disparities by facilitating the transfer of resource depletion from one country (the North) to another (the South). In addition, this possibility of investment-induced convergence in production structure in the North and the 3

As in [15, 17, 23]. See [13–15, 25] and the references therein. 5 See [20, 21, 27] and also the synthetical treatment in Chipman [8a]. 6 See, for example, [1, 12, 19]. 4

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South is “especially likely” when, for instance, the supply of capital from the North is sufficiently elastic, or when the South is resource and/or labor deficient. (ii) We show that North–South investment flows follow a pattern of cumulative causation, whereby a first round increase in the Southern use of Northern capital creates the demand for a second round increase. In particular, as natural resource depletion occurs alongside inflows of foreign direct investment, labor productivity in agriculture declines. The resulting exodus of labor out of agriculture raises the demand for foreign capital even further as the decline in agricultural labor productivity lowers the supply price of Southern laborers to the manufacturing sector. These results parallel the recent work of Copeland and Taylor [12], wherein the focus is on international trade in goods, rather than capital investment. In particular, Copeland and Taylor [12] show that pollution induces non-convexities in the long run production possibility frontier and implies commodity supply schedule of the dirty industry that is downward sloping. The underlying rationale is similarly one of cumulative causation, whereby expansion of the dirty industry negatively affects labor productivity in agriculture, and as such, the opportunity cost of output expansion in the dirty industry, in terms of agricultural output forgone, is strictly decreasing. Despite these similarities in the underlying cumulative causation story, Copeland and Taylor show that for a small open economy, incomplete specialization is inconsistent with dynamic stability. And perhaps more importantly, free trade implies an unambiguous welfare gain for a small open economy. As the paper unfolds, we show that the case of environmental deprivation generated via international investment yields interesting differences. We consider two possibilities. First, cumulative causation implies excess demand for foreign capital that strictly increases with capital inflow, and dynamic stability can only be achieved via complete specialization in manufactures. In this context, we identify a threshold level of Southern natural resource endowment, such that North–South investment flow implies a welfare loss whenever the South is more resource abundant relative to the critical threshold. In contrast, complete specialization in a resource deficient Southern economy may nevertheless increase gross national product, as foreign investment generates employment options for Southern workers that are no longer reliant on a small natural resource base. As a second possibility, we consider the case when the relative slopes of the demand and supply of Northern capital are such that excess demand for capital is strictly decreasing with Northern capital inflow. As such, North–South capital allocation can be consistent with both incomplete specialization and dynamic stability. In this context, the relevant policy question no longer involves just the discrete comparison in terms of whether or not foreign investment should be allowed. Rather, the question is on the fine-tuning of appropriate investment taxes and subsidies that reflect the environmental trade-offs due to foreign investment. (iii) In this regard, we show that in contrast to the Kemp–MacDougall–Jones prescription, the optimal investment policy for the pollution-disseminating North is a capital export subsidy. The intuition lies in the fact that it is in the interest of the North to achieve factoral terms-of-trade gains. In particular, since unfettered international capital flows only account for international differences in the average returns to investment, with an upward sloping demand curve for Northern capital,

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average returns to investment understate the marginal benefits of a unit increase in capital investment. Thus, the North benefits from subsidizing the export of capital, just enough to account for the differential between average and marginal returns. (iv) We show that in contrast to the optimal policy prescription for the North, the magnitude of the traditional Pigouvian tax is strictly less than the Southern welfare-maximizing level of tax on capital imports. In particular, with the South serving the role of a monopsonistic buyer of capital, a tax on capital imports simultaneously serves two distinct roles: as an instrument for the polluter-pay principle, as well as one for the Kemp–MacDougall–Jones consideration. The former requires foreign investors to pay a tax that amounts to the marginal damage on environmental resources, and the latter corrects for the problem of overinvestment even in the absence of pollution externality, since the price paid to foreign investors overstates the marginal benefit of foreign investment, in the presence of a standard upward sloping supply schedule. (v) We show that the rationale underlying the use of a capital import tax and a capital export subsidy remains robust even when both the North and the South are large in output markets as well. In particular, we show that once the pollution externality through foreign investment is accounted for via an optimal tax (subsidy) on capital imports (exports), the South (North) can manipulate commodity terms of trade to its advantage by imposing a consumption tax (subsidy) on manufacturing imports (exports). From another perspective, this result is in keeping with the Bhagwati–Johnson prescription that a robust policy rule is to address the source of the distortion directly. Thus, in comparison to the recent literature on trade and the environment,7 this paper contributes to the understanding of North–South environmental linkages by bringing together three distinct strands of literature on economic policy formulation: (i) the theory of international factor flows and the attendant allocational inefficiencies of capital in the North and South due to the divergence between average and marginal returns, (ii) general equilibrium analysis of pollution externalities, and the potential overuse of environmental resources in the capital recipient nation, and (iii) North–South economic and policy linkages in the spirit of [17, 22, 23], whereby Northern incentives to manipulate factoral terms-of-trade conflict with the policy prescriptions for the South. The rest of this paper is organized as follows. In Section 2, we outline our North– South model and present the possibility of complete specialization in the South. In Section 3, we discuss the rationale for an upward sloping demand schedule for Northern capital and examine the dynamic stability of equilibrium capital allocation. The welfare consequences of foreign investment induced complete specialization in the South is examined in Section 4. The case of incomplete Southern specialization, and the corresponding stability criterion, is used to examine the environmental impact of foreign direct investment in the South in Section 5. In Section 6, we compare the optimal foreign investment policies of both the North and the South with the conventional prescriptions. Section 7 is devoted to the case of a large country, and the combinations of investment and import taxes that respectively account for the presence of pollution externality and the monopoly power of the North and the 7

See the literature summarized in Footnote 5 above.

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South in international goods market. In Section 8, we conclude with some additional remarks. 2. THE MODEL There are two economies, North (N) and South (S), both small in commodity markets, and linked through a capital market. The capital-rich North specializes in the production of a single composite commodity, termed manufactures (Xn ). The technology Fn
Kn  Ln  for manufactures in the North exhibits constant returns to scale in capital Kn and labor Ln , and exhibits diminishing marginal productivities of each factor. Given the exogenous stocks of labor
n and capital n , Northern firms operate in both output and factor markets in a perfectly competitive fashion. The technology Fs
Ks  Ls  for Southern manufactures is also well behaved in the sense that it exhibits constant returns to scale and diminishing marginal productivities of each factor. The South also produces a second composite commodity, termed agricultural output (Xa ), and it is produced solely by domestic labor La , whose productivity depends on the availability of environmental resources, R, with Xa = α
RLa , where α
· ≥ 0 is assumed to be twice differentiable, strictly increasing, and concave in R. Let
s and s respectively denote the endowment of labor and capital in the South. Since the two countries are small in international markets for the agricultural commodity and for manufactures, we are justified in denoting the price of manufactures relative to that of agricultural output by P. We also denote the competitively determined returns to capital and labor as rs , rn , and w. Intersectoral mobility of labor in the South guarantees that PFsL
Ks  Ls  = w = α
R

(1)

where FsL ≡ ∂Fs /Ls . In addition, full employment in the Southern labor market requires La + Ls =
s 

(2)

Turning now to the environmental impact of capital usage in Southern manufactures, let the stock of resources available for agricultural production be given as R = R¯ − ρKs 

ρ > 0

(3)

where R¯ denotes the natural limit of environmental resources when there is no production induced environmental stress. Since capital is assumed to be internationally mobile, the distribution of capital in the two countries is given by
1 − tn 
1 − ts rs = rn
1 − tn 
1 − ts PFsK
Ks  Ls  = PFnK
Kn 
n 

(4)

where ts and tn denote the ad valorem rates of capital import and export tax imposed by the two countries. Finally, material balance in the capital market requires that Kn + Ks = n + s 

(5)

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It is straightforward to verify through the use of Eqs. (1) to (5) that the presence of resource-depleting capital usage in manufactures leads to the possibility of complete specialization in the South. Perhaps more importantly, the asymmetric production structure between the North and the South, as described in Eqs. (1) to (5) above, may also be attributed to the environmental deprivation consequences of capital usage in manufactures, when the North is relatively capital-rich and/or resourcedeficient, and when the South is relatively labor and/or resource abundant. To see this, let K¯ be defined as follows: ¯
s  = α
R¯ − ρK ¯ PFsL
K

(6)

Thus, K¯ denotes the level of capital usage in the South that is just enough to induce all Southern labor force to exit agriculture, as agricultural labor productivity decreases with resource depletion. In particular, since the left (right) hand side of Eq. (6) above is strictly increasing (decreasing) in Ks , any further increase of Ks beyond K¯ drives a wedge between labor productivity in the two sectors, and workers unambiguously favor employment in manufactures. In turn, complete specialization ¯ in manufactures occurs whenever Ks ≥ K. In Fig. 1, the upward sloping MM schedule plots the relationship between the marginal value product of labor in manufactures and the level of capital usage in the South (left hand side of Eq. (6)), given that all Southern workers are engaged in the production of manufactures. The downward sloping AA schedule depicts the negative impact of capital imports on the productivity of Southern labor in agriculture (right hand side of Eq. (6)). Accordingly, K¯ is given by the intersection of the MM and the AA schedules. Clearly K¯ is always positive and uniquely defined for every R¯ and
s . In addition, from Eq. (6), ¯
s  + α
R d K¯ = −PFsLL
K ¯
s d
s + α d R ¯

PFsLK
K Thus, a relatively labor abundant country (which translates to a rightward shift of ¯ the MM curve), with a relatively large natural limit of environmental resource (R) (a rightward shift of AA), is accordingly less prone to complete specialization in ¯ manufactures as K¯ rises with both
s and R. Turning now to consider the investment supply determinants of complete specialization in the South, note that under complete specialization, the supply price of Northern capital is no less than the marginal value product of capital in the South

FIG. 1. The possibility of complete specialization.

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if and only if ¯
n  ≤ PFsK
K ¯
s  ≡ r¯s  r¯n ≡ PFnK
n − K Since the left hand side of the above equation is strictly decreasing in n , complete specialization in the South is possible whenever the North is sufficiently capital abundant. In the context of pollution induced by international capital mobility, two observations seem to stand out on examining Fig. 1 and Eqs. (4) and (6). First, resource depletion in the capital-abundant and/or resource-deficient North, along with the attendant possibility of complete specialization in the allocation of resources, can be transmitted, through international capital flows, to the labor- and/or resourceabundant South, precisely when Ks , as determined by Eq. (4) above, is greater than ¯ Second, if both the North and the South are completely specialized in the proK. duction of manufactures, the marginal environmental damage of an increase in capital import/export, as measured by the output loss due to resource depletion, is essentially nil. Thus, Eqs. (2) to (4) reduce to the standard MacDougall–Kemp setup.8 In addition, the solution to the decision problem facing policymakers collapses to the standard monopsonistic (monopolistic) argument of a capital importer (exporter). What remains to be determined, however, is whether complete specialization constitutes the only possible equilibrium configuration in our two country setup. We turn to this in the next section and examine the scope of policy intervention depending on the degree of specialization in the South. 3. DEMAND AND SUPPLY OF CAPITAL We begin our analysis by demonstrating that the asymmetric production structure and the environmental consequences of international capital flows emphasized by our model render the demand side of the international capital market to operate in a way that is contrary to standard intuition. Toward this end, Eq. (1), the material balance equation (2), and the definition of R in Eq. (3) can be combined to yield9 ∂Ls α
Rρ F LK =− − sLL > 0 (7) LL ∂Ks
1 + τPFs Fs Thus, the demand price for Northern capital, rs , can be obtained via Eqs. (4), (5), and (7) above, with 
∂L ∂rs = P FsKK + FsKL s ∂Ks ∂Ks    α
Rρ FsLK KK KL =
1 + τP Fs − Fs − LL
1 + τPFsLL Fs =−

α ρFsLK > 0 FsLL

(8)

Hence, the demand schedule for capital is upward sloping.10 8 ¯ the equality sign in Eq. (1) should be replaced by a With complete specialization, so that Ks > K, strict inequality. 9 To economize on notation, we suppress the arguments of the production functions for Xn and Xs and denote Fi
Ki  Li  as Fi  i = n s, whenever there is no risk of confusion. 10 In arriving at the last equation, we have used the following property of constant returns to scale production functions: FsKL FsLK − FsKK FsLL = 0.

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The intuition here, while straightforward, deserves particular attention. Note that as capital inflow to the South reduces the stock of resources, the productivity of, and hence the competitive returns to, labor in agriculture falls (Eq. (1)). In turn, the resulting reallocation of labor leads to an increase in Southern employment in manufactures. At constant international prices and given the increase in labor use in manufacturing, returns to capital in the South rise. In other words, the adverse environmental impact of capital inflows, by distorting Southern input allocation in favor of the production of manufactures, has the effect of creating an even larger demand for Northern capital, and hence the upward sloping capital demand schedule. In contrast, the supply price of capital from the North is given by the left hand side of Eq. (4), with ∂rs = −PFsKK
Kn 
n  > 0 ∂Ks While both the demand and the supply schedules for capital are upward sloping, it can be readily confirmed, using Eqs. (4) and (5) above, that the supply schedule has a slope that is greater than the demand schedule if and only if ∂rn ∂r −
1 − tn 
1 − ts  s > 0 ∂Ks ∂Ks

⇔

ηn − ηs > 0

(9)

where ηi  i = n s, denotes the elasticity of ri with respect to Ks , i = n s. The inequality displayed in Eq. (9) above plays an important role in the analysis that follows. We illustrate this in Fig. 2, which depicts the case where the inequality in Eq. (9) above is violated. The SS and NN schedules respectively depict the capital demand and supply schedules in Eqs. (7) and (8), with the demand schedule strictly steeper than the supply schedule. Thus, if foreign investment is feasible starting from Ks = s , with rs0 = rs Ks =s > rn Kn =n = rn0 , then opening up the South to foreign capital inflow always leads to complete specialization, and the only stable equilibrium involves the South completely specializing in the production of manufactures. From Eq. (8), opening up the South to foreign investment further raises the demand price of capital in the South, from rs0 to rs1 , as labor productivity in agriculture declines. The result, therefore, is a second round increase in the supply of capital from the North, from Ks1 to Ks2 , and Southern resources deplete even further. The cumulative causation of environmental stress results in a continuous outflow of labor from the Southern agricultural sector to the manufacturing sector, ¯ as international capital allocation moves closer to Ks = K. ¯ Note that once foreign capital inflow moves beyond K, the South is completely specialized in manufacturing and as such, Southern demand for capital is given by rs = PFsK
Ks 
s . Thus, in Fig. 2, the kink at the Ks = K¯ curve reflects the onset of complete specialization, and equilibrium capital allocation occurs at Ks = Ksc , where Ksc is given by the equalization of the rewards to capital in both the North and the South, PFsK
Ksc 
s  = PFnK
Knc 
n  We can formalize this discussion by considering the following Marshallian adjustment process: ˙ s = ψ
ws − wa  = ψ

1 + τPFsL − α
R¯ − ρKs  L

ψ > 0

(10)

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FIG. 2. Complete specialization and dynamic instability.

K˙ s = φ

1 − tn 
1 − ts rs − rn = φ

1 − tn 
1 − ts PFsK − PFnK 

φ > 0

(11)

Equation (10) requires that Southern labor flows into the production of manufactures, whenever there exists a wage advantage to do so. In addition, in Eq. (11), foreign direct investment is assumed to respond to any differences in international rates of returns to capital, with K˙ s > 0 if and only if
1 − tn 
1 − −ts rs > rn . On linearizing Eqs. (10) and (11) around an equilibrium point (L∗s  Ks∗ ), and by making use of Eqs. (1) to (5), we obtain


 ≡

˙s L K˙ s



 =

Ls − L∗s Ks − Ks∗

 


1 − tn 
1 − ts PFsLL


1 − tn 
1 − ts PFsLK + α ρ


1 − tn 
1 − ts PFsKL


1 − tn 
1 − ts PFsKK + PFnKK

 

It can now be easily checked that the trace of  is strictly negative, and the determinant of  is positive if and only if Eq. (9) is satisfied. Thus, equilibrium capital allocation between the North and the South is dynamically stable if and only if the schedule of Southern demand for capital imports is flatter than that of Northern capital export supply. In what follows, we focus on two categories of equilibrium configurations,11 depending respectively on whether the stability criterion in Eq. (9) is satisfied. 11 There are, of course, other possible equilibrium configurations whenever both the demand and supply prices of Ks are upward sloping. In particular, there may be a continuum of equilibrium points when the SS and NN schedules coincide. Alternatively, there may be multiple but a finite number of equilibrium points, when the two curves intersect more than once. The existence of equilibrium may also be an issue, for instance, when NN always lies above SS.

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4. DYNAMIC INSTABILITY AND RESOURCE DEPRIVATION Consider, therefore, the case where investment-induced resource depletion occurs so fast, or when Northern supply of capital is sufficiently elastic, so that the stability ¯ The welfare consequences of such condition in Eq. (9) is violated for all Ks ≤ K. an equilibrium outcome with complete specialization can be readily ascertained. In particular, the gross national product of the South in the absence (presence) of capital inflow is given by Ys0 = α
R¯ − ρs L0a + PFs
s  L0s , where the allocation of Southern laborers between agriculture and manufacturing is determined by the equalization of rewards to labor in the two sectors (w0 ), PFsL
s 
s − L0a  = α
R¯ − ρs  ≡ w0 

(12)

Meanwhile, complete specialization implies that Southern gross national product is given by Ys∗ = PFs
Ks∗ 
s  − rn∗
Ks∗ − s , where rn∗ = PFsK
Ks∗ 
s 

(13)

and the associated reward to labor inputs in the South is given by w∗ ≡ PFLs
Ks∗ 
s . Thus, Ys0 − Ys∗ = α
R¯ − ρs L0a + PFs
s 
s − L0a  −α
R¯ − ρs L∗a + PFs
Ks∗  L∗s  − rn∗
Ks∗ − s  =
w0 − w∗ 
s + rs0 − rn∗ s 

(14)

where the second equality follows from the linear homogeneity of the production function. Equation (14) summarizes the income distribution consequences of capital inflows. In particular, since w0
w∗  is strictly increasing in (independent of) R¯ from Eq. (12), Southern laborers are strictly better off in the absence of foreign capital inflow if the South is sufficiently resource abundant. Likewise, competitive rewards to capital in the absence of capital inflow is strictly increasing in R¯ as well (Eq. (13)). In view of these observations, let R∗ be a critical threshold level of Southern resource endowment R∗ , such that R∗ = R¯  Ys0 − Ys∗ = 0 As such, if the South is resource abundant relative to the critical threshold, with R¯ > R∗ , complete specialization in the presence of foreign investment is necessarily welfare worsening. Summarizing these arguments, we have the following result: Proposition 1. If foreign investment is feasible, with rs0 > rn , and Eq. (9) is vio¯ free inflow of foreign capital is harmful (confers benefits) to the lated for all Ks ≤ K, South if and only if R¯ ≥
<R∗ . 5. DYNAMIC STABILITY AND INCOMPLETE SPECIALIZATION If the stability criterion in Eq. (9) is satisfied, and incomplete specialization is consistent with dynamic stability, a relevant question that confronts the two countries has to do with whether policy interventions in the form of taxes or subsidies

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should be in place in order to account for the pollution externality of foreign investment. With this in mind, we make use of Eqs. (1)–(8) to ascertain the equilibrium response of international capital flows with respect to tn and ts :     0 dLs =   δ dKs δ ≡
1 − ts PFsK dtn +
1 − tn PFsK dts  On taking the restrictions imposed by the stability criterion of the Marshallian adjustment process (10), (11) into account, we have, therefore, arrived at the following substantive result: Proposition 2. (1) Barriers to international capital flows either through increases in capital taxation in the North or the South (tn or ts ) lead to a reduction in factor employment in the South as given by Ks and Ls . (2) Returns to capital in the North and the South decrease with restrictions on capital flows originating from either countries. In Fig. 3, the SS and NN schedules are such that the stability condition in Eq. (9) is satisfied. Clearly, in order that a positive capital import/export tax drives a wedge between rs and rn , with rs > rn , the resulting capital inflow from the North to the South must be less than that under perfect capital mobility. In addition, the associated returns to capital in the South and in the North, as given by point A and B in the diagram, must be lower. Barriers to international capital movements, therefore, have a tendency to favor the South, both in terms of the degree of environmental deprivation induced by international capital mobility, as well as the reduction in payments to Northern capital. However, the same argument does not apply to the monopolistic supplier of capital, since the North now faces an upward sloping demand schedule for Ks . In particular, the North can benefit from an increase in rs through payments to its capital exports by encouraging the outflow of capital.

FIG. 3.

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287

6. OPTIMAL FOREIGN INVESTMENT POLICIES We begin by first examining the optimal tax on capital flows t e which jointly maximizes the welfare of the North and the South. Let Yn
t e  and Ys
t e  denote the associated national incomes evaluated at international prices of the two countries. Maximum welfare is now given by the problem max Yn
t + Ys
t = max P
Fn
Kn 
n  + Fs
Ks  Ls  + α
RLa t

t

subject to Eqs. (1) through (5). It can be readily confirmed that the necessary condition is given by P
FsK
Ks  Ls  − FnK
Kn 
n  = rs − rn = rs − rs
1 − t e  = rs t e = α ρLa  Accordingly, rs t e amounts to precisely the magnitude of the Pigouvian tax, which penalizes Northern capital importers for the marginal damage of capital inflow on the agricultural production in the South. Let tn∗ be the optimal tax on capital exports which maximizes Northern national income Yn
tn∗  tn  evaluated at international prices. Given ts , Yn
tn  ts  is equal to the sum of the value of total Northern output, and the payments from capital exports. The maximum of Northern welfare is now given by the problem max Yn
tn  ts  = max PFn
Kn 
n  + rs
1 − ts Ks  tn

tn

subject to Eqs. (1) through (6). We obtain the necessary condition rs
1 − ts  − rn = rs tn∗ = −Ks
1 − ts 

∂rs  ∂Ks

Thus, whether the optimal capital export policy of the North is a tax or a subsidy depends only on the slope of the Southern capital demand schedule. In particular, from our discussion in Section 4, the demand schedule for capital is upward sloping. Thus, the right hand side of the above equation is strictly negative and we have Proposition 3. If the stability condition in Eq. (9) is satisfied, and the South is incompletely specialized in the production of goods m and a, tn∗ is a subsidy on capital exports with tn∗ = −ηs
1 − ts  < 0 Recall that the North performs the role of a monopolistic supplier of capital. Hence, as in [21, 27], the appropriate investment policy is determined by the elasticity of capital import demand of the South. Since the demand schedule for capital is upward sloping (ηs > 0), the average return of capital exports, rs
1 − ts , understates the marginal benefits of foreign investment rs
1 − ts  + Ks
1 − ts 
∂rs /∂Ks  > rs
1 − ts . The appropriate policy thus calls for a capital export subsidy with tn∗ < 0. The optimal tax on Southern capital imports, ts∗ , given any particular Northern tax tn , can be similarly ascertained. Let Ys
tn  ts∗  denote the value of Southern national output net of the payment for Northern capital imports. The maximization problem of the South is given by max Ys
t = max PFs
Ks  Ls  + α
RLa − ts

ts

r n Ks  1 − tn

(15)

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beladi, chau, and khan

subject to Eqs. (1) through (6). Recall that rn is the supply price of capital and rn Ks /
1 − tn  = rs Ks
1 − ts  represents Southern payment for capital imports. The first order condition is given by rs −

rn Ks ∂rn

= α ρLa + 1 − tn 1 − tn ∂Ks

⇔

ts∗ =

α ρLa +
1 − ts∗ ηn  rs

Southern optimal capital import tax thus consists of two parts, where α ρLa /rs accounts for the pollution externality of foreign investment, and
1 − ts∗ ηn captures the factoral terms of trade impact of capital inflows. Since ηn > 0 as a result of the argumentation furnished in Section 4, we have thus obtained Proposition 4. If the stability criterion in Eq. (9) is satisfied, and free mobility of capital implies that the South is incompletely specialized in the production of goods m and a, ts∗ is a tax on capital imports with ts∗ =

α ρLa /rs  + ηn
1 − ts∗  > 0 7. OPTIMAL COMMERCIAL POLICIES AND THE LARGE COUNTRY CASE In this section, we turn to a discussion of the robustness of the foregoing results to the case where both countries are large in the traditional sense that the world price of manufactures is determined by demand and supply factors. In terms of comparative statics analysis, we show that commodity terms of trade vary in a predictable fashion with foreign investment taxes or subsides. In terms of welfare of the two countries, we explore the possibility that a foreign investment tax ts (foreign investment subsidy tn ) along with a tax on consumption on importables τs (consumption subsidy on exportables τn ) can be employed to enable the South (North) to simultaneously exploit potential gains in factoral and commodity terms of trade. Accordingly, let consumer preferences in the South be represented by a community utility function u
C m  C a , where C m and C a respectively denote consumption of manufactures and agricultural output. In addition, let e
Pi  u, i = n s denote the expenditure function where Ps = P
1 + τs  and Pn = P
1 + τn  denotes the possibly distorted prices of manufactures that consumers face in the South and the North, respectively. By Shephard’s lemma, ∂e
Ps  us /∂Ps ≡ ePs = cm
Ps  us  and ePn
Pn  un  = Cm
Pn  us , where cm
· and Cm
· respectively denote the Hicksian demand functions of manufactures in the two countries. We also follow Copeland and Taylor [12] in assuming that consumer preferences are of the Mill–Graham variety, where β denotes the share of income spent on the agricultural output. Equilibrium in goods market thus requires12 1−β P

1 + τs cm +
1 + τn Cm  = β ca + C a ⇔

P=

β c a + Ca  1 − β
1 + τs cm +
1 + τn Cm

(16)

12 To see this, market clearance for the manufacturing and agricultural outputs respectively requires
1 − β
Ys + Yn  = P
1 + tn Cm + P
1 + ts cm , and likewise, β
Ys + Yn  = Ca + ca .

north–south investment flows

289

In addition, since commodity market clearance requires ca + Ca = α
R¯ − ρKs La cm + Cm = Fn
Kn 
n  + Fs
Ks  Ls  it follows that international relative price of manufactures is given by13 P=

α
R¯ − ρKs  β 1 − β
1 + τs cm +
1 + τn Cm

=

α
R¯ − ρKs  β 1 − β
1 + τs Fs +
1 + τn Fn +
1 + ts 
cm − Fs  −
1 + tn 
Fn − Cm 

=

β α
R¯ − ρKs   1 − β
1 + τs Fs +
1 + τn Fn +
ts − tn 
mm 

(17)

where mm = cm − Fs
= Fn − Cm  is the quantity of manufacturing imports of the South (exports of the North). Equation (17), together with Eqs. (1)–(6), thus furnishes a two-country setup wherein international capital allocation as determined via Eq. (4), along with the Southern labor market equilibrium condition in Eq. (1), can be used to solve for the world price of manufactures. As should be expected, the presence of terms of trade effects in international goods market implies that the both the Southern demand for capital schedule, rs = PFsK
Ks  Ls , in general equilibrium, along with the Northern supply of capital schedule, rn = PFnK
Kn 
n , should appropriately account for any changes in world prices subsequent to international capital flows. In particular, Proposition 5.

If the stability condition in Eq. (9) is satisfied, then

1. A move away from free capital mobility either through increases in capital taxation in the North or the South (tn or ts ) leads to a reduction in factor employment in the South as given by Ks and Ls . 2. The relative price of manufactures rises with restrictions on capital flows originating from either country. 3. A move away from free trade through increases in consumption tax either in the North or the South (τn or τs ) leads to a reduction in factor employment in the South as given by Ks and Ls . 4. The relative price of manufactures falls with restrictions on consumption originating from either countries. Proof.

See Appendix A.

To begin with, Proposition 5 shows that with endogenous world price, barriers to international capital movements have the additional impact of turning terms of trade in favor of the North. Specifically, by restricting the import of capital, the resulting improvement in agricultural productivity, along with the increase in labor employment in agriculture, implies that aggregate supply of agricultural output 13 It may be of interest to point out here that the issue of complete specialization does not arise in this two-country setup, wherein strictly positive amounts of good m and a must be produced to meet demand.

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beladi, chau, and khan

rises. From Eq. (16), it follows that excess supply of agricultural output calls for an increase in the world price of Northern manufacturing exports. Meanwhile, barriers to international goods trade via a tax on the consumption of manufactures originating from either the North of the South have the effect of turning terms of trade against the North. In turn, such adverse revenue impact of a tax on consumption also leads to a reduction in the aggregate output and, thus, factor employment in manufacturing. The result is accordingly an increase in environmental resources and an increase in the output in the agricultural sector. These observation suggest that with endogenous world prices, the design of optimal foreign investment may be complicated by the welfare consequences of terms of trade changes. Meanwhile, the choice of consumption taxes may also need to account for its impact on North–South capital allocation, as the resulting reduction in the price of P steers Southern labor input away from Southern manufactures. To this end, we have the following result: Proposition 6. With endogenous world prices, and if Eq. (9) is satisfied, 1. Southern welfare maximization involves the use of a tax on foreign capital inflow, with ts∗ =

α ρLa /rs  + ηn
1 − ts∗  along with a consumption tax as given by 1 τs∗ = ∗ ∗ 1 + τs ηm where η∗m denotes the elasticity of Northern import demand for good m. 2. The North optimally chooses capital export subsidy, tn∗ , with tn∗ = −ηs
1 − ts  < 0 and a consumption subsidy on manufactures, τ∗ , with 1 τn∗ = ∗ < 0 1 + τn∗ (a where (∗a < 0 denotes the elasticity of Southern export supply of good a with respect to P. Proof.

See Appendix B.

In the presence of monopoly–monopsony power in output markets, Proposition 6 shows that the orthodox optimal tariff rule applies, so that the size of the optimal import consumption tax of the South is inversely related to the Northern import demand elasticity. By Lerner’s symmetry, the North can similarly exploit terms of trade changes by appropriately restricting exports, and in our case, the optimal policy of the North involves the use of a subsidy on the consumption of its exportables. Thus, Proposition 6 can be viewed as a reiteration of Tinbergen’s insistence on the equality of objectives and instruments and the Bhagwati–Johnson general theory of distortions which prescribes that remedial policies should be directed to the source of the problems. In the context of foreign investment induced pollution externality in which relative world price is endogenously determined, there are two

north–south investment flows

291

distortions—the divergence between social and average returns to foreign investment, and the monopoly power of the two countries in output markets. Accordingly, once commodity terms of trade gains are appropriately accounted for by choice of consumption taxes or subsidies, the South can be made better off by limiting capital inflows by imposing a tax on capital imports. Meanwhile, the North continues to prefer a subsidy on capital exports, which exploits the positive relationship between the competitively determined rewards to foreign investment and the volume of capital inflow. 8. CONCLUDING REMARKS In this paper, we investigate the optimality of investment policies in an asymmetric two-country framework when international capital flows facilitate pollution in the South. We find particularly interesting the tendency for foreign investment to “create its own demand” once the possibility of resource-depleting foreign capital investment is accounted for, as in Section 4 above. Thus, contrary to standard intuition, factoral terms of trade shift in favor of the supplier of capital whenever the volume of foreign investment rises, as in Proposition 1 above. In addition, optimal capital investment policies of the North and the South deviate from the Pigouvian tax in opposite directions, favoring respectively a subsidy and a tax on North–South capital flows, as in Proposition 2 and 3 above. Finally, we show that optimal commercial policy of the South remains that of free trade, even though it is to its advantage to pursue restrictionist capital import policies; under the asymmetrical production structure between the North and the South, an import tariff only succeeds in encouraging the inflow of foreign capital, as in Proposition 4 above. The next step, it seems to us, is to delve more deeply into the formalization of conflicting North–South interest and the resulting game-theoretic aspects of policy competition. One can focus on the Nash competition outcome, or alternatively on the Stackelberg leader–follower relationship between the North and the South, and ask whether the tendency for the North to exploit the South through the use of capital export subsidy remains, when manufacturing is “pollution intensive.”14 APPENDIX A Totally differentiating Eqs. (1), (4), and (16), making use of the definition of the slope of the capital import demand in general equilibrium (Eq. (8)), we obtain     dLs 0 ˜  dKs  =  δt    (18) dP δτ where



 PFsLL PFsLK + α ρ FsL KK KK KL 0  ˜ ≡   Fs 

Fs + Fn FsL αρ 1 − α − L + c +C − P1 a

14

m

m

Preliminary results on this question are established in [4] and are available on request.

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beladi, chau, and khan

and δt = FsK
1 − ts dtn +
1 − tn dts δτ =

cm Cm dτs + dτ cm + C m cm + C m n

˜ is strictly negative if Eq. (9) is It can be readily verified that the determinant of  LL KK KL  satisfied
Fs Fn − Fs α ρ > 0. Routine manipulation using Eq. (18) yields



1 dLs = δt FsKL + δτ FsKK + F  KKn FsL ˜       L 1 1 F s dKs = + δτ FsKL FsL δt −FsLL + FsL + ˜ La cm + C m        L 1 α ρ 1 F s dP = δt −PFsLL + + PFsKL + α ρ ˜ α La cm + C m    + δτ FsLL FnKK − FsKL α ρ



Thus, policy restrictions on either trade in goods of capital decrease both Ls and Ks . Meanwhile, Northern terms of trade deteriorate with a consumption tax originating from either country but improve with a tax on capital investments. APPENDIX B Balance of trade in the South requires that consumer expenditure equals gross domestic product along with any tariff revenue, e
Ps  us  = Ys ≡ PFs
Ks  Ls  + α
RLa −

r n Ks + τs PePs
Ps  us  1 − tn

(19)

where the term τs PePs
Ps  us  denotes consumption tax revenue. On totally differentiating the balance of the trade equation, we obtain    
1 − βτs FnK Ks ∂c eu
Ps  us  1 − dus = Fs − cm − dP + τs P m dPs 1 + τs 1 − tn ∂Ps   rn Ks ∂rn  dKs  (20) + rs − − α ρLa − 1 − tn 1 − tn ∂Ks     ∂Ma FnK Ks =
1 + τs  Fs − cm − + τs dP 1 − tn ∂P   Ks ∂rn + rs ts − α ρLa − dKs  (21) 1 − tn ∂Ks To recall,
1 − β =
∂
1 + τs Pcm /∂Ys  denotes the marginal propensity to consume manufactures. If τs is less than one, the distortion multiplier
1 −

1 −

north–south investment flows

293

βτs /
1 + τs  is strictly positive. In addition, Eq. (21) follows from the balance of trade relationship15 P
cm − Fs  +

rn Ks = Ma  1 − tn

where Ma denotes the quantity of agricultural imports of the North. It follows, therefore, that Southern welfare can be maximized by setting     FnK Ks ∗ ∗ ∂Ma
1 + τs  Fs − cm − + τs =0 1 − tn ∂P and rs ts∗ − α ρLa −

Ks ∂rn = 0 1 − tn ∂Ks

Or equivalently, τs∗ is given by   − Fs − cm − FnK Ks /
1 − tn  Pτs∗ = ∂Ma /∂P 1 + τs∗ τs∗ 1 Ma = = > 0 ∗ P ∂Ma /∂P ηa 1 + τs where ηa denotes the elasticity of Northern import demand with respect to P. In addition, the optimal tax on foreign investment
ts∗  is given by ts∗ = ηn
1 − ts  +

α ρ  rs

Turning now to the maximization problem of the North, note that balance of trade in the North requires that e
Pn  un  = Yn ≡ PFn
Kn 
n  + rs Ks
1 − ts  + τn PePn
Pn  un  15

To see this, note that Eq. (19) above can be rewritten as r n Ks + τs PePs
Ps  u 1 − tn r Pcm + ca = PFs
Ks  Ls  + α
RLa − Ks n 1 − tn e
Ps  us  = PFs + αLa −

⇔ ⇔

P
cm − Fs  +

rn K s = αLa − ca 1 − tn = Ca = M a 

Thus,

 cm − Fs +

and Eq. (20) follows.

 FnK Ks ∂Ma ∂c dP + m dPs = dP 1 − tn ∂Ps ∂P

(22)

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beladi, chau, and khan

On totally differentiating Eq. (22), we have16 P
Fn − Cm  +

rn Ks = αLa − ca  1 − tn

where αLa − ca is just the quantity of agricultural exports of the South,  
1 − βτn ∂C eu
Pn  un  1 − du =
Fn − Cm  − FsK Ks
1 − ts dP + τn P m dPn 1 + τn ∂Pn   ∂rs dKs  + −rn + rs
1 − ts  + Ks
1 − ts  ∂Ks  =
1 + τn 
Fn − Cm  + FsK Ks
1 − ts   ∂
αLa − ca  + τn dP ∂P   ∂r + rn tn + Ks
1 − ts  s dKs  ∂Ks

(23)

It follows, therefore, that Southern welfare can be maximized by setting   FnK Ks

∗ ∗ ∂
αLa − ca 
1 + τn  Fs − cm − − τs =0 1 − tn ∂P and rn tn∗ + Ks
1 − ts 

∂rs = 0 ∂Ks

Or, equivalently, τn∗ is given by τn∗ 1
αLa − ca  = = < 0 1 + τn∗ P ∂
αLa − ca /∂P (a where (a denotes the elasticity of Southern export supply with respect to P. In addition, the optimal tax on foreign investment
ts∗  is given by tn∗ = −ηs
1 − ts  < 0 16

As before, Eq. (23) follows from the balance of trade relation: e
Pn  un  = PFn − rs Ks
1 − ts  + τn PePn
Pn  un  ⇔ ⇔

PCm + Ca = PFn
Kn 
n  + rs Ks
1 − ts 

P
Fn − Cm  + rs Ks
1 − ts  = Ma = αLa − ca 

Thus,

 Fn − Cm +

 ∂C FnK Ks ∂
αLa − ca  dP + P m dPn = dP 1 − tn ∂Pn ∂P

north–south investment flows

295

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