International Environmental Policies in Interdependent Economy under Decentralized Control

INTERNATIONAL ENVIRONMENTAL POLICIES IN INTERDEPENDENT ECONOMY UNDER DECENTRALIZED CONTROL Hajime Myoken Faculty of Economics, Nagoya City University, Mizuhoku, Nagoya 467, Japan

SUMMARY: In this paper interdependent economy of a two-country model, in which environmental policies are incorporated, is formulated in a dynamic setting of optimal control problem, recognizing explicitly the aspects of decentralized decision by policy-maker of each country. Under such situation, the paper discusses the effects of environmental policies on international specialization (the theorem of comparative advantage). 1.

INTRODUCTION

iug renaY"ks and points out possible extensions.

Recently, attempts have been made to analyze the economic effects of the environment and of national environmental policies on international trade. (See [1], for instance.) Several kinds of international environmental studies might be investigated. First, we can observe some possible examples of environmental effects that spill over national boundaries [2]. The second problem is concerned with arrangements, institutions and policies such as nations might adopt to deal with environmental effects that spill over national boundaries, involving transfrontier pollution [3]. A third kind of international study would be concentrated on the effects of domestic environmental protection policies on a country's international trade and ba1ance-of-payments [4]. In this paper we treat environmental protection and international specialization (the theorem of comparative advantage) in an interdependent economy related to the third problem above. In [4] Pething showed how some positive and normative results of the neoclassical trade theory can be applied to countries with pollution generating industries, and that countries with relatively large environmental assimilative capacities should specialize in export of those commodities which are relatively pollution-intensive in their production. The present paper deals with the analysis of a dynamic setting for macroeconomic-environmental policy in an open economy. Mathematically, maximization (or minimization) of the expression mentioned is formulated in genera~_ optimal control problem, and the solution and some of the implications are presented. Section 2 describes the basic model of the open economy in which environmental aspects are incorporated. Section 3 constructs the state-space representation of the model and provides the solution to the optimal control problem. Section 4 discusses the relation of environmental protection and international specialization. Section 5 gives some conc1ud-

2.

THE BASIC MODEL

To obtain a model capable of inspiring useful rules for macroeconomic-environmental policy in an open economy, it is necessary to adopt one of a Keynesian type introducing at least the general level of prices, the rate of interest, ba1ance-of-payments and environmental aspects. In this section we shall construct a basic model which will be made more realistic in the following section, from the viewpoint of macroeconometric model. The equations of the basic model are the following:

Definitions and Equilibrium Equations: Y = C+ I + G+ X - M (2.1) B/p x - M + K/p (2.2) (2.3)

C

I

11 + 12

(2.4)

P

p(p l ' P2)

(2.5)

Behavior Equations and Determinant Equations: T

T(Y)

(2.6)

W

W(I, e/p)

(2.7)

S

S(G, w/p, r)

(2.8) (2.9)

M M(Y) d d L = L (w/p, e/p, r) K

793

(2.10) (2.11)

K(r - rw)

r = r(Ms/p, Y)

(2.12)

w/p = w(Ld, LS)

(2.13)

Ci Ii

Ci(Y - T, Pi)

(i = 1,2)

(2.14)

Pi

Pi(Ms/p, r, w/p, Ci ) ; (i=1,2) (2.16)

Ii(w/p, e/p, r, Ci) ; (i = 1,2)(2.15)

794 where

Hajime Myoken Y C I G

X M

T W

S

B K

national income consumption investment govenment expenditures exports imports government tax receipts the environment's waste disposal demand the environment's waste disposal service balance-of-payments capital inflow

Ld = demand for labor LS = supply of labor w = the wage rate r = the rate of interest(domestic) rw = the rate of interest(world) MS = supply of money general price level p e = effluent taxes i = commodities The approach taken here is restricted to a simple two-country model in interdependent economy, but by the specification of the basic model it is assumed that the econometric model is empirically determined from given economic data. In doing so, policy-making in a dynamic macroeconometric model is analyzed as developed in the following section. It should be noted that equations (2.3), (2.4), (2.5), (2.14), (2.15) and (2.16) are added to other equations in order to examine the effects of environmental policy on international specialization. The basic model calls for some comments. Equation (2.1) is the equilibrium condition for the market for national commodities. Equation (2.2) expresses the country balanceof-payments constraints in terms of domestic currency. Tax receipts, in equation (2.6), are assumed to depend only on the level of national income. Equation (2.7) expresses the environment's waste disposal demand as being assumed to depend on the investment and effluent taxes. The environment's waste disposal service as a function of government expenditures, the real wage rate and the rate of interest is represented by equation (2.8). Equation (2.9) presents import function in terms of national income. Demand for labor, in equation (2.10) is assumed to de-pend on the real wage rate, effluent taxes and the rate of interest. The level of capital flow, in equation (2.11), regards it as a function only of the interest rate differentials between countries, following the traditional assumption of capital flows. It should be observed that equation (2.12), the rate of interest, depends on supply of money and national income. The real wage rate, in equation (2.13), is assumed to depend demand for labor and supply of labor which is exogenously given. Equation (2.14) presents the consumption function in terms of disposable income and the general price level. The level of investment is expressed as a function of the real wage rate, effluent taxes, interest rate and the level of consumption.

The determinant of the general prices is represented by equation (2.16) which is assumed to depend on supply of money, interest rate, real wage rate, and the level of consumption. A similar set of relations (2.1)'-(2.16)' apply to the second country, which can be considered to be the rest of the world in interdependent economy [5]. For examples, identities are as follows: X

M'

M

X'

K

-K'

B

-B'

where a superscript (,) indicates that the variables refer to country IT • Quantitative policy decision analysis implemented by use of econometric model would require specify the above basic model and the probability distributions of the relevant variables. Furthermore, for example, endogenous, exogenous and lagged variables Ci-l, Ci-2, rand r-l which specify the consumption function Ci may be considered as explaining variables in addition to Y- 1 and Pi· All the variables used here are classified in the following:

Exogenous variables

~

Control variables: X

=

(G, MS, e)'

Data variables:

W=

(rw '

S

X, L

,

1)'

Endogenous variables: d Y = (Y, B, M, K, T, W, S, L , r, w, C,

Cl> C2 , I, Il> 1 2 , p, Pl> P2)' Let l X and l y denote the largest lags of control variables and endogenous variables respectively. Then the equations system of the model used here is represented by the following vector form: Y(t)

=

f(Y(t), Y(t-l), ••• , Y(t-l y ), X(t), X(t-l), .•• , X(t-Z X» + U(t)

where U(t) is a vector of serially uncorrelated random variables with zero means and the constant covariance matrix. 3.

3.1.

THE OPTIMAL CONTROL POLICY

The Stat e- Space Repr es entati on

Since the problem under consideration is approached from the viewpoint of optimal control theory, we convert the basic model to a control system format; first of all, this section constructs state space form of the linearized model. The formulation of shortterm planning and policy seems to be most promising in being amenable to a realistic

795

Policies in interdependent economy application of optimal control. The usual econometric models can be generally supposed to be non-linear. However, short-term econometric models are inherently linear or else easily linearizable in structure, ~nd in doing so this makes numerically optimal control solutions[6] • We define the policy variables so that the following variables approach as: --+

S L

~

B*

w-s

~

0

G-T

~

0

Ld B

ly

A

af

A

Y(t)-Y(t)~j~oaY(t_j)(Y(t-j)-Y(t-j»

lx af +jEoax(t_j)i(X(t-j)-X(t- j » A

+ aJtt) (W(t)-W(t»

+ U(t)

where superscript " A" indicates variables of nominal values. To simplify the above equation we define the new variables as yet)

yet)

x(t)

X(t) - X(t) A

MS

MS*

~

e

af )-I ( I - aY(t)

u(t) ]

e*

~

af I af I [aY(t-j) : 3X(t-j) : U(t)]

Then the policy variables can be written using exogenous and endogenous variables as

I

I

l = max(ly, l X+l)

yet») TT(t) = 5 [ X(t)

(3.1)

Using these notations the linearized approximation model can be represented by l l -I .L Lj (t)y(t-j) + .L Mj (t)x(t-j) +u(t) yet) J=I J=o (3.4)

where

Y

B

MKT

W

d

5

L

r

w

C

Cl

C2

11

I

12

P

PI

P2

s

G

M

e

__ J___ ~ __ l ___:___ L__ i ___ L~ _~ __ j ___ :___ i __ J___ L__ i ___:___ ~ __ J___ :__ J __:___ :___ _ I I I

1

1 I

_ _ .... __ -t- _ I I

I

I I I

-

I I I

_ __ 1 __ - .... -

-

-

1 I I -, -

I I

-

-

I 1 I ~ -

1 1

-

-

I .. -

1

I I

I

I I

-1

I -

-1- -

I I

I

.. -

-

I I I "f -

I

I I

-1

-

I

I

I

I I

I I

I I ... -

... -

-

I -4 -

I

I

I

I

I

I

I I

I -

I

I

-1- __ I I I

-1- __ ... _ _ ... _ _ _ 1_ _ _

I -

I I

I

-

I

-

I

_ -1- _ _ "" _ _ ... _ _ _ 1_ _ _ ... _ -

I I

t

5= - - ....I - - - It-

I ~

-1- I I

I

-

I

t-- - - ... - 1

I I

I I I

-1- 1 I

-

I

~

_ -

I

I

I

I

I I

I 1

I

I

I

..... _ __ I- _ _ .. -

+- __ ..... - __

I- _ -

+ - _

I I I

I I I

t

I I I of' -

I I

I

-

I

I I -t _ _ _ ~ _ -

I

I I I

1

I I I

I L.. -

I _

I _ ... -

_1_ 1 1

-

I I

I

I

I

I

I ~ -

I

I

I

-

... I 1

I

I

I I

I I _ _ 1_ _ _ L _

I I I

-1- _ _ L- __ .J _

I

I

I

I

I I I I I I I I I _ _ 1_ _ _ L _ _ .J _ _ _ 1_ _ _ _ _ -1 _ _ _ L

I

I

I I I -

I I ~

I

I _ _ 1 __ -

I I I

1

I I I

I I

I I I


I

I 1 I 1 I I I I _ _ I- __ ... _ _ _ 1 _ _ _ ~ __

I I I

I I I

I

I

I

-1- 1

-

I

... 1 1 t

I I

-

I I I ~ -

I

1

I

I

1 I I

I I I

__ _

_ _ _ _ _ , _ __ L __ _

I

-

__ _

I I

_ .J ___ , _ _ _ _ _ _ , ___ L

I I I I I I __ 1_ _ _ L __ ..J _ _ _ L

-

I I I

I I

I - ~ -

I

-

I 1

-

-

-1- 1

1 -

I

I I 1

L I

-

-

1

A

TT*(t)=(Ls(t), B*(t), 0, 0, MS*(t), e*(t»' Next suppose the performance criterion function is given by

Now we use the nominal path Wet) of Wet) as the forecasting value of the data variables vector at the control period. Then the following equation holds

N t~1

(TT(t)-TT*(t»'WTT(t) (TT(t)-TT*(t»

(3.2)

where WTT(t) indicates the policy-maker's desired weight for each of the policy target variables and is an nxn symmetric (usually diagonal)positive semi-definite matrix. The optimal control problem is to find a control sequence X(t) such that the performance index (3.2) is minimized subject to the dynamic constraint yet) = f(Y(t), ••• , Y(t-l y ), X(t), ••• , X(t- l x ),

Wet»~

+ U(t)

(3.3)

While the model (3.3) contains non-linearities, it is usually isolated and lends itself to linearization. Linearized approximation is implemented in the neighborhood of nominal paths. Namely

af aW(t) (W(t) -

Wet»~

0

Notice that 0

for j > ly

Mj (t) = 0

for j > lX

Lj (t) and that

The linearized model (3.4) is respecified in state space description by defining new state variables to replace those variables that appeared in the model with lags greater than one period: that is, the state equation is s(t) = A(t)s(t-l) + B(t)x(t) + S et) the output equation is

(3.5)

796

Ha jime Myoken y(t)) = Cs(t) [ x(t)

(3.6)

and the state-observation equation is s(t) = H(t)z(t)

analytical framework used here is sufficiently general one introduced by Tinbergen approach [7], allowing for the aspect of decentralized decision-making by policy-makers between two countries.

(3.7)

3.2.

where

o

0

o A(t)

The soZution to the ProbZem

The optimal control problem is that of minimizing the performance index (3.8) with respect to the control input, subject to the dynamical constraints represented by (3.5), (3.6) and (3.7). The method of dynamic programming is applied to the solution of the control problem [8]. The optimal feedback control solut i on is given

o I

o o

I

x (t) = -F(t)s(t-l) + g (t)

which s hows that the optimal policy for period t is a linear func tion of all the variables s(t-l) that will affect the output s (t) through the model, where

y (t-l)

u(t)

MO (t)

B(t)= M1(t)

; s (t)=

(3 . 9)

;z(t-l)= y( t - Z+l )

o

F(t) = (B(t) 'R(t)B(t))-lB(t) 'R(t)A(t) (3.10)

x (t-l)

g(t) = (B(t) 'R(t)B(t))-lB(t) 'r(t)

o

)c't- Z+l )

(3.11)

where R( t-l)

W(t-l) + A(t)'R(t)[A(t)-B(t)F(t)] (3.12)

I

o

o

I

o

I I - -1'- - - - - - - - - - - - - - - - - - - - - - - - - - -,- - - - - - - - - - - - - - - - - - - - - - - - - - - - -

0 I'

0

I

I

0

- -.., - - - - - - - - - - - - - - - - - - - - - - - - - - - -r - - - - - - - - - - - - - - - - - - - - - - - - - - - --

: Ml (t) I

H(t)

: M2 (t) I

o L

Z(t-l)

Z- 1 (t-l)

M

o

where z(t-l) stands for the predetermined variables vector appearing in the econometric model in the reduced form at the period t. It follows from (3.1) and (3.6) that the performance index (3.2) becomes

r(t-l) = a (t-l) + A(t)'[r(t)-R(t)B(t)F(t)] (t=1,2, •.• ,N)

L {s(t)'W(t)s(t) - 2a (t)'s(t)

t=l

(3.8)

where

In this paper we start ed with a model of interdependent economy under decentralized control process and arrived at the mathematical formulation of the optimal control for a linear econometric model represented in state space form with quadratic welfare loss. The

R(N)

W(N)

(3.14)

r(N)

a (N)

(3.15)

It follows from (3 . 9) and (3.7) that the optimal control policy is given

W(t)

a (t)

(3.13)

where

N

+ constant term}

o

x (t) = -F(x)H(t-l) z (t-l) + g(t)

(3.16)

which contains the fe edback term of the predetermined variables. (3.16) can be also written as X ( t)

X(t) + G(t)[ z (t-l)-z(t-l)] (3.17)

X(t)

" X(t) + g (t)

(3.18)

G( t)

F(t)H(t-l)

(3.19)

where

Policies in interdependent economy where z(t-l) stands for the vector of the nominal values of the predetermined variables at period t excluding X(t). It is assumed that the model used here is linear and that the performance index is quadratic, so that the principle of multiperiod certainty equivalence [9] applies to the first part of the solution. Short term properties of the time paths generated by the optimal control approach is analysed. The dynamic procedure adopted, in which the concept of feedback control is used, is to derive quantitative properties rather than qualitative ones of the system. Hence it should be pointed out that the types of dynamic decision rules implied by this procedure are different from decision rules provided by Theil's method [9]. For further discussion of the optimal control solution and some emirical evidence of economic applications the reader may refere to Myoken [10] and Myoken and Uchida [11]. 4.

INTERNATIONAL SPECIALIZATION AND ENVIRONMENTAL POLICIES

Since the last half of 1960's, a great deal of attention has been paid to the public concern over environmental quality and environmental policies. Most recently, international environmental problems have attracted much att:ntion from politicians, economists, and eng1neers. The present paper is concerned with the effects of domestic environmental protection controls on a country 's terms of trade, balance-of-payments, national income, and other macroeconomic variables [12][13]. In particular, an attempt is made to analyze some economic effects of the environment and of national environmental policies in the most used Heckscher-Ohlin model for international trade [4] [14] [15]. Environmental protection controls tend to make domestic goods expensive relative to foreign goods. The problems considered here are related to the theorem of comparative advantage: Does the mere existence of environmental policy distorts comparative advantage?: To what extent does environmental policy alter the basis for comparative price advantages between countries? In this paper we consider these problems in view of both static and dynamic approaches.

4.1

A Stat ic Analysi s

A diagramatically static anal ysis is firstly developed. We consider a large country 's production possibility frontier which has been derived from the construction of the Heckscher-Ohlin model and examine likely terms of trade effects of environmental protection controls on the output of one good initiated first by country I alone and then by both countries. It is assumed that pollutions are generated only in connection with production, and that for simplicy the environmental quality of country I is independent of the production level of country IT • Let the good X indicate country I's import and country IT's export good respectively, and let the good Y be true for the opposite. The two offer curves for countries I and IT

797

are described in Fig.l. The Terms of Trade Effects of Environmental Protection Control

Fig.l.

T

,..

Y

Exporting Country I's and Importing Country IT's Good

.T

o

--- - .---- -> X

lreporting Country I's and Exporting Country IT's Good

First, consider that environmental protection control is imposed on the production of country IT's export good X. The offer curve changes to 0 Y1 1 1 , so that the pollution control leads to an improvement of country I's terms of trade. When the production of good Y causes pollutant, but when the production of good X does not, the offer curve changes to B Y2 O. Country IT can expect the possibility of an improvement in the terms of trade. Now we turn to the case in which both countries I and IT introduce the environmental protection policies on the production of good X, while good Y is free from pollution. Country IT's offer curve is given by S1 Y10. On the other hand, country I's offer curve is a Y3 0, and the terms of tra de is favorable to country I whose export good is associated with production pollution. The results obtained above is developed on the assumption that the production has no spill over effects of externalities. Grubel [14] showed that, when considering spillover of externalities, an efficient solution requires expenditures on environmental policies in every country up to the point where the marginal outflow yields equal returns in terms of reduced global pollution. The above findings are basically incompatible with the results obtained from different versions and interpretations of the theorem of comparative advantage with respect to environmental scarcity (or aboundanc e)[14][15].

4. 2 The Leontie f Par adox and Environmental Protect i on In the two-country case, the superscript"#" the optimal control policy of the model in which the environmental policy is in corporated, and the notation without additional superscript referes to the optimal control policy in case that the environmental policy is not ~posed. For the ith good, we denote Pi and pi. Now assume that domestic price ratio between two countries before imposing

798

Hajime Myoken

the environmental protection control is (4.1)

In such a case, the theorem of comparative advantage implies an increase in the welfare between both countries: country I imports the ith good for country Il, and country Il exports the j th good for country 1. However, assume that country I imposes a pollution control program due to the environmental scarcity. Country I of industrialized and growing economy should specialize in the ith capitalintensive good rather than the jth laborintensive good. Now assume that the effluent change in imposed on the production of pollutants. As a result, let the following equation be satisfied. (4.2)

Then country I, with environmental policy, exports the jth good based on its specialization on labor-intensive, rather than capital-intensive, lines of production. Inversel~ country 11 of less industrialized and developing economy moves in favor of exporting the ith capital-intensive good. This observation is consistent with a highly controversial result investigated by Leontief [16]: The United States was expected to export those commodities in whos e production is relatively abundant factor, capital, was important, and then to import those which are relatively labor-intensive. However, thls paradox is not true straightforwardly for the optimal control problem under consideration. The neoclassical trade model developed above is of a static nature and is not beyond the scope of comparative static. Leontief model, in which the environmental protection is not incorporated, is also static and therfore logically incompatible \vith dynamic international trade to the extent that an industry may respond to external stimuli by acquiring and disposing of fixed equipment and readjusting the scale of its operations [17]. The dynamic model constructed in section 2 is of macroeconomic-environmental policy under decentralization control of policy-making, showing how the gains derived from cordination of economic-environmental policies vary according to the degree of economic interdependence. Our model under consideration is similar to that of Cooper [5] into which environmental protection is introduced: The model is also made to deal with the analysis of the growing economic interdependence among the industrialized countries, especially in exploring how well national policy-maker, acting independently, can be expected to perform according to the increasing degree of mutual interdependence. How the environmental policies followed by industrialized and less industrialized countries should substantially affect the pattern of international trade depends upon empiri-

cal evidence of the dynamic model considered in the paper. However, when the policy-maker for each country takes into account the independence of the economic system and internal coordination between policy targets and instrument, the environmental protection policies between industrialized countries do not seem to have seriously affected international trade patterns rather than expected. Instead, it should be noted that less industrialized and developing countries are increasing tendency to specialize in the import of the commodities which are relatively pollution-intensive in their production. As a result, they play a role to provide the so-called pollution havens.

5.

REMARKS AND POSSIBLE EXTENSIONS

There has been a great deal of controversial issue about the possibility that the environmental protection controls can reverse patterns of comparative advantage for international trade. Various exercises in pure theoretic approaches always have considerable elegance, and their theoretical limitations of the models, which are of a static and qualitative, often have the results incompatibled with empirical evidence derived from the realistic situations. A lot more empirical work is needed in this area to test a more general theoretical analysis. In this paper one possible approach, which is possible to estimate quantitatively the short-run impacts of environmental pollution controls on particularly a country's terms of trade,. have been presented in the context ofdynam~c macroeconomic-environmental policy model, focusing on the interdependence of the system and the decentralization and coordination for each country. Then the optimal control problem of the model has been investigated, which is different from linear decision rules provide by Tinbergen-Theil approach [9]. The model and the solution algorithms presented here can be also applied to other linear or linearized large-scale econometric models. There have recently various applications of optimal control theory to national policy and planning using econometric models on the assumption that there a single controller and implementing policy on a single of objectives. On the other hand, the macroeconomic policy of typical international trade model is the product of a decentralized control process in which different agencies for each country control different sets of policy instruments for each country. The analytical framework presented here c an be extended to deal with the more general problem of decentralized stabilization policies in the international economy. The two-country model of linear time-invariant econometric systems is described in state space form as x(t+l) C·x(t) ~

+ n.(t) ~

(i=1,2)

The quadratic performance measure may be

Policies in interdependent specified by N

J = E{ E [x(t)-x*(t)]'W(t)[x(t)x*(t)]} t=l

Before implementing the optimal stabilization policy, we need an exact description of how and why the policy-maker for each country will arrive at policies different from those that would result in the informationally centralized case [18]. In simple case, for example, we could consider: The policymaker for each country arrives at its policy using the same econometric models but has a different set of objectives. In such a case, the model can be view as nonzero-sum differential game of a two-country faced by the indepedence of the fortunes [19] [20]. In addition, conflicting objectives as seen in such systems may be naturally considered as multi-criterion optimal control problem.

REFERENCES [1] 1. Walter(ed.): Studips in International Environmental Economics, John Wiley & Sons, New York, 1975. [2] OECD: Problems of Environmental Economics, 1972. [3] R. C. d'Arge: On the Economics of Transnational Environmental Externalities, in ed. by E. S. Mills; Economic Analysis of Environmental Problems, Columbia University Press, 1975. [4] R. Pething: Pollution, Welfare, and Environmental Policy in the Theory of Comparative Advantage, J. Environmental Economics and Management, 2(1976), 160-169. [5] R. N. Cooper: Macroeconomic Policy Adjustment in Interdependent Economies, Q. J. Economics, 83(1969), 1-24. [6] A. R. Bergstrom: Nonrecursive Models as Discrete Approximations to Systems of Stochastic Differential Equations, Econometrica, 34(1966), 173-82. [7] J. Tinbergen: Economic Policy: Principles and Design, North-Holland Pub. Co., Amsterdam, 1956. [8] R. Bellman: Dynamic Programming, Princeton Univeristy Press, Princeton, 1957. [9] H. Theil: Optimal Decision Rules for Government and Industry, North-Holland Pub. Co., Amsterdam, 1964. [10] H. Myoken: Optimal Control Problem of Decentralized Dynamic Economic Systems, Proceedings of the 8th International Congress on Cybernetics (to appear), Namur, Belgium, 1976.

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799

[11] H. Myoken and Y. Uchida: The Use of State Space Representations for Econometric Models and the Optimal Control Policy, Working paper No. 7506, Research Program on Decision and Control of Socio-economic Systems, Nagoya City University, 1975. [12] R. C. d'Arge and A. V. Kneese: Environmental Quality and International Trade; reprinted in D. A. Kay and E. B. Skolnikoff, World Economic Crisis: International Organization in Response, University of Wisconsin Press, 1972 . [13] S. P. Magee and W. F. Ford: Environmental Pollution, the Terms of Trade and Balance of Payments of the United States, ~,25(1972), 101-118. [14] H. G. Grubel: Some Effects of Environmental Controls on International Trade: The Heckscher-Ohlin Model: in ed. by I. WaIter: in Studies in International Environmental Economics, John Wiley & Sons, New York, 1976. [15] H. Siebert: Environmental Protection and International Specialization, Weltwirtschaftliches Archiv, 110(1974), 494-508. [16] W. Leontief: Factor Proportions and the Structure of American Trade: Further Theoretical and Empirical Analysis, ~ Econ. and Stat. , 38(1956), 386-407. [17] D. F. Wahl: Capital and Labour Requirements for Canada's Foreign Trade, Canadian J. of Economics and Political Science, 27(1961), 349-358. [18] R. S. Pindyck: Optimal Stabilization Policies Under Decentralized Control and Conflicting Objectives, presented at the 3rd. World Congress of Econometric Society, Toronto, 1975. [19] W. C. Ho and K. C. Chu: Team Decision Theory and Information Structures in Optimal Control Problems - Part I, IEEE Trans. on Aut. Control. AC-17(1972), 15-22. [20] H. Myoken: Non-zero-sum Differential Games for the Balance-of-Payments Adjustment in an Open Economy, I. J. of Systems Science, 6(1976), 501-511.