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Optimal policy to achieve debt repayment by the LDCs
Journal of Development Economics 18 (1985) 479-483. North-Holland
OPTIMAL POLICY TO ACHIEVE DEBT REPAYMENT BY THE LDCs Amar K. PARAI* Case Western Reserve Universzty, Cleveland, OH 44196, USA
Bidhu B. MOHANTY Cleveland State University, Cleveland, OH 44115, USA Received November 1983, final version received February 1984 In this paper we examine the need for optimal intervention by an LDC to generate export surplus for repayment of its foreign debt A two-country, two-commodity model of barter trade is used to demonstrate the superiority of an income tax to a tariff or a consumption tax on exportables.
1. Introduction
This paper addresses an important current issue - - optimal policy for repayment of international debt by the LDCs. The practical significance of the problem can hardly be overemphasized. Recently, there has been a growing concern among the DCs about the LDCs' difficulties with regard to repayment of debt. For the LDCs, however, foreign loans are considered essential for development purposes. Hence, prompt repayment of their past loans is equally important for their uninterrupted flow in future) In this paper we focus on the need for optimal intervention by an LDC to achieve its non-economic objective of raising export surplus for repayment of the debt. This objective provides another example of Bhagwati's 'Distortion 4: Non-operation on the efficient production possibility curve' [-Bhagwati (1981, p. 174)]. From the point of view of its cause, it is an 'instrumental, policy-imposed distortion'. Therefore, full optimality is unattainable, although ranking of alternative policy instruments is possible. Specifically, it is shown that for debt repayment a general income tax policy is optimal and superior to a tariff or to a consumption tax on exportables. *We are deeply indebted to an anonymous referee of this journal for many valuable comments. Xpaul Streeten (1977, p. 78) has commented that '.. wnting off the past debts on the pfinctple that we roll let bygones be bygones may reduce the flow of capital in the future because we may expect the same thing to happen again' 0304-3878/85/$3.30 © 1985, Elsevier Science Pubhshers B.V. (North-Holland)
A.K. Parai and B.B. Mohanty, Debt repayment by LDCs
480
The plan of the paper is as follows. The model is specified in section 2. In section 3 we examine the policy implications using the standard tradegeometric techniques. Finally, the conclusions are given in section 4. 2. The model
It is assumed that there are two countries - - a lender or the foreign country representing the DCs and a borrower or the home country representing an LDC. Two commodities - - commodity 1, the exportables of the home country and commodity 2, its importables - - are produced and consumed under incomplete specialization. Their outputs, X1 and X2, respectively are produced by two factors - - capital (K) and labor (L) which are inelastically supplied and fully employed. The home country is small, so it faces constant international prices. The consumers in the home country have a homothetic preference. It is further assumed that the home country uses the foreign loan exelusively for the purpose of investment in productive sectors. The productive use of loan indicates either a factor endowment increase or a technological improvement. It may be considered, following Harrod's terminology, as '... the introduction of additional capital disposal and other highly qualitied factors ... regarded as fertilizing the productivity of common labor' [Harrod (1963, p. 117)]. We assume that the sum borrowed can buy B amount of additional physical capital for the home country. Let A2 denote the amount of annual repayment in terms of importables. The product of sum borrowed and capital recovery factor gives the annual repayment and thus, A2 is obtained by dividing this amount by unit price of importables. Finally, we also assume that there exists an upper limit to the supply of foreign loans. Now we can specify the following equations for the home country: U = U(Dt, D2), X,=F,(K,,L~),
(1) i=1,2,
(2)
L 1 + L 2 = L,
(3)
K , + K 2 = R + B,
(4)
B<=B,
(5)
DI=Ft(Kx,L1)-Et,
(6)
D 2 -- F2(K2,L2) + E2,
(7)
A 2 = PE1 - E2.
(8)
A.K. Parai and B.B. Mohanty, Debt repayment by LDCs
481
U denotes the social utility function with aggregate consumption of each good, Di as arguments; Fi, a conventional neoclassical production function with Ki, L, as the employment of capital and labor respectively in sector i, i= 1, 2; g and L , the given domestic supply of capital and labor respectively; B, the upper limit to the availability of foreign loan in terms of physical capital; E, and E z, the volumes of export of good 1 and import of good 2 respectively, while P denotes the exogenously given international relative price of good 1 in terms of good 2. Eq. (8) represents the home country's budget constraint which ensures that the export surplus is equal to the annual repayment.
3. Policy analysis The home country would maximiTe the utility function (1) subject to the constraints (3) through (8). In this section we examine the policy implications of this maximization process diagrammatically. In fig. 1, the concave transformation curve (which is not drawn for the sake of simplidty) is assumed to be tangential to the given price ratio MM' at Po. The initial free trade equilibrium is characterized by the production and consumption points Po and Co respectively. National income is given by OM in terms of good 2 and initial wel|are is given by the social indifference curve U o. Now consider the impact of repayable foreign loan. Due to the Good 1 (Exportables)
N'
R'
P'
\ U3
c
S
M
H
R
Good 2 (Importables)
F*g. 1. Repayment through income tax or consumption tax
JDE
K
N
482
A,K. Parai and B.B. Mohanty, Debt repayment by LDCs
productive use of the loan the transformation curve shifts to the right and national income rises by MN in terms of good 2. The new production and consumption points are at P', and C1 respectively. The point C1 lies on the ray OCo because of the assumption of homothetic preference. The exact position of point P', of course, depends on relative factor intensities. But for our purpose all we need is to ensure that P' is located to the left of Ct so as not to reverse the trade pattern. U3 represents the full optimum. But U3 is unattainable because the trade triangle formed by points P' and Ct denotes balanced trade yielding no surplus for debt repayment. If the annual repayment in terms of good 2 were RN (i.e., Az=RN), then the home country has to raise an export surplus equal to RN (or R'N' in terms of good 1). Hence some kind of policy intervention is called for. Several alternative policies are available to the home country in this regard. We consider three of these. First, it can impose an income tax at the rate of NR/ON. This tax does not change the price ratio faced by producers and consumers. The production point remains at P' even after the tax is imposed. But due to the cut in disposable income caused by the tax, the consumption point moves to C2, thus generating an export surplus equal to C2V(=RN). The welfare level is given by U2. Secondly, a consumption tax on exportables at a rate of, say, RN/HR also can achieve the same goal. This policy does not change the price ratio for the producers. So the production point remains at P'. It, however, distorts the price ratio faced by the consumers resulting in a shift in the consumption point from Ct to C3. The welfare level Ut is achieved with an export surplus equal to RN. Finally, a suitable tariff imposed by the home country also will generate the necessary export surplus. In fig. 2, the required tariff rate is given by C4D/EC4 to raise an export surplus of C4D(=RN) in terms of good 2. The tariff distorts the relative price for both producers and consumers. The production and consumption points move to P" and C4 respectively with a welfare level of UI. From fig. 1 it is clear that Ut represents a lower level of welfare relative to U2. Similarly, in fig. 2, the indifference curve U1 represents a lower level of welfare than one with an income tax that would be tangential to RR' at a point on the ray OCt. So, given the export surplus to be raised for debt repayment, the welfare level achieved with an income tax policy is the highest. The economic explanation for the superiority of income tax is simple. A general income tax does not distort the relative price, while a specific tax introduces price distortions leading to misallocation of resources and hence loss of welfare. 4. Conclusions
In this paper we have considered different policies associated with the repayment of foreign loans by an LDC. General income tax policy is shown
483
A.K. Parai and B.B. Mohanty, Debt repayment by LDCs
Good 1 (Exportables)
N t
Tt p! R'
H v
Po Uo
T
H
R
N
Good 2 ( I ~ o r t a b l e s ) Fig. 2. Repayment through tariff. to be the o p t i m a l . By d e m o n s t r a t i n g the s u p e r i o r i t y of i n c o m e t a x to a tariff o r a c o n s u m p t i o n t a x we h a v e r e l a t e d the r e p a y m e n t s of i n t e r n a t i o n a l b o r r o w i n g to the p u b l i c finance l i t e r a t u r e o n b o r r o w i n g a n d policy. References Bhagwati, Jagdish, 1981, The generalised theory of distortions and welfare, in: Jagdish Bhagwati, ed., International trade: Selected readings (MIT Press, Cambridge, MA) 171-189. Harrod, Roy, 1963, Desirable international movements of capital in relation to growth of borrowers and lenders and growth of markets, in: Roy Harrod and Douglas Hague, eds., Internatmnal trade theory in a developing world: Proceedings of a conference held by the International Economic Association (St. Martin's, New York) 113-141. Streeten, Paul, 1977, Comment on debt relief as development assistance by Peter Kenen, in: Jagdish Bhagwati, ed., The new international econon~c order (MIT Press, Cambridge, MA) 78-80.
OPTIMAL POLICY TO ACHIEVE DEBT REPAYMENT BY THE LDCs Amar K. PARAI* Case Western Reserve Universzty, Cleveland, OH 44196, USA
Bidhu B. MOHANTY Cleveland State University, Cleveland, OH 44115, USA Received November 1983, final version received February 1984 In this paper we examine the need for optimal intervention by an LDC to generate export surplus for repayment of its foreign debt A two-country, two-commodity model of barter trade is used to demonstrate the superiority of an income tax to a tariff or a consumption tax on exportables.
1. Introduction
This paper addresses an important current issue - - optimal policy for repayment of international debt by the LDCs. The practical significance of the problem can hardly be overemphasized. Recently, there has been a growing concern among the DCs about the LDCs' difficulties with regard to repayment of debt. For the LDCs, however, foreign loans are considered essential for development purposes. Hence, prompt repayment of their past loans is equally important for their uninterrupted flow in future) In this paper we focus on the need for optimal intervention by an LDC to achieve its non-economic objective of raising export surplus for repayment of the debt. This objective provides another example of Bhagwati's 'Distortion 4: Non-operation on the efficient production possibility curve' [-Bhagwati (1981, p. 174)]. From the point of view of its cause, it is an 'instrumental, policy-imposed distortion'. Therefore, full optimality is unattainable, although ranking of alternative policy instruments is possible. Specifically, it is shown that for debt repayment a general income tax policy is optimal and superior to a tariff or to a consumption tax on exportables. *We are deeply indebted to an anonymous referee of this journal for many valuable comments. Xpaul Streeten (1977, p. 78) has commented that '.. wnting off the past debts on the pfinctple that we roll let bygones be bygones may reduce the flow of capital in the future because we may expect the same thing to happen again' 0304-3878/85/$3.30 © 1985, Elsevier Science Pubhshers B.V. (North-Holland)
A.K. Parai and B.B. Mohanty, Debt repayment by LDCs
480
The plan of the paper is as follows. The model is specified in section 2. In section 3 we examine the policy implications using the standard tradegeometric techniques. Finally, the conclusions are given in section 4. 2. The model
It is assumed that there are two countries - - a lender or the foreign country representing the DCs and a borrower or the home country representing an LDC. Two commodities - - commodity 1, the exportables of the home country and commodity 2, its importables - - are produced and consumed under incomplete specialization. Their outputs, X1 and X2, respectively are produced by two factors - - capital (K) and labor (L) which are inelastically supplied and fully employed. The home country is small, so it faces constant international prices. The consumers in the home country have a homothetic preference. It is further assumed that the home country uses the foreign loan exelusively for the purpose of investment in productive sectors. The productive use of loan indicates either a factor endowment increase or a technological improvement. It may be considered, following Harrod's terminology, as '... the introduction of additional capital disposal and other highly qualitied factors ... regarded as fertilizing the productivity of common labor' [Harrod (1963, p. 117)]. We assume that the sum borrowed can buy B amount of additional physical capital for the home country. Let A2 denote the amount of annual repayment in terms of importables. The product of sum borrowed and capital recovery factor gives the annual repayment and thus, A2 is obtained by dividing this amount by unit price of importables. Finally, we also assume that there exists an upper limit to the supply of foreign loans. Now we can specify the following equations for the home country: U = U(Dt, D2), X,=F,(K,,L~),
(1) i=1,2,
(2)
L 1 + L 2 = L,
(3)
K , + K 2 = R + B,
(4)
B<=B,
(5)
DI=Ft(Kx,L1)-Et,
(6)
D 2 -- F2(K2,L2) + E2,
(7)
A 2 = PE1 - E2.
(8)
A.K. Parai and B.B. Mohanty, Debt repayment by LDCs
481
U denotes the social utility function with aggregate consumption of each good, Di as arguments; Fi, a conventional neoclassical production function with Ki, L, as the employment of capital and labor respectively in sector i, i= 1, 2; g and L , the given domestic supply of capital and labor respectively; B, the upper limit to the availability of foreign loan in terms of physical capital; E, and E z, the volumes of export of good 1 and import of good 2 respectively, while P denotes the exogenously given international relative price of good 1 in terms of good 2. Eq. (8) represents the home country's budget constraint which ensures that the export surplus is equal to the annual repayment.
3. Policy analysis The home country would maximiTe the utility function (1) subject to the constraints (3) through (8). In this section we examine the policy implications of this maximization process diagrammatically. In fig. 1, the concave transformation curve (which is not drawn for the sake of simplidty) is assumed to be tangential to the given price ratio MM' at Po. The initial free trade equilibrium is characterized by the production and consumption points Po and Co respectively. National income is given by OM in terms of good 2 and initial wel|are is given by the social indifference curve U o. Now consider the impact of repayable foreign loan. Due to the Good 1 (Exportables)
N'
R'
P'
\ U3
c
S
M
H
R
Good 2 (Importables)
F*g. 1. Repayment through income tax or consumption tax
JDE
K
N
482
A,K. Parai and B.B. Mohanty, Debt repayment by LDCs
productive use of the loan the transformation curve shifts to the right and national income rises by MN in terms of good 2. The new production and consumption points are at P', and C1 respectively. The point C1 lies on the ray OCo because of the assumption of homothetic preference. The exact position of point P', of course, depends on relative factor intensities. But for our purpose all we need is to ensure that P' is located to the left of Ct so as not to reverse the trade pattern. U3 represents the full optimum. But U3 is unattainable because the trade triangle formed by points P' and Ct denotes balanced trade yielding no surplus for debt repayment. If the annual repayment in terms of good 2 were RN (i.e., Az=RN), then the home country has to raise an export surplus equal to RN (or R'N' in terms of good 1). Hence some kind of policy intervention is called for. Several alternative policies are available to the home country in this regard. We consider three of these. First, it can impose an income tax at the rate of NR/ON. This tax does not change the price ratio faced by producers and consumers. The production point remains at P' even after the tax is imposed. But due to the cut in disposable income caused by the tax, the consumption point moves to C2, thus generating an export surplus equal to C2V(=RN). The welfare level is given by U2. Secondly, a consumption tax on exportables at a rate of, say, RN/HR also can achieve the same goal. This policy does not change the price ratio for the producers. So the production point remains at P'. It, however, distorts the price ratio faced by the consumers resulting in a shift in the consumption point from Ct to C3. The welfare level Ut is achieved with an export surplus equal to RN. Finally, a suitable tariff imposed by the home country also will generate the necessary export surplus. In fig. 2, the required tariff rate is given by C4D/EC4 to raise an export surplus of C4D(=RN) in terms of good 2. The tariff distorts the relative price for both producers and consumers. The production and consumption points move to P" and C4 respectively with a welfare level of UI. From fig. 1 it is clear that Ut represents a lower level of welfare relative to U2. Similarly, in fig. 2, the indifference curve U1 represents a lower level of welfare than one with an income tax that would be tangential to RR' at a point on the ray OCt. So, given the export surplus to be raised for debt repayment, the welfare level achieved with an income tax policy is the highest. The economic explanation for the superiority of income tax is simple. A general income tax does not distort the relative price, while a specific tax introduces price distortions leading to misallocation of resources and hence loss of welfare. 4. Conclusions
In this paper we have considered different policies associated with the repayment of foreign loans by an LDC. General income tax policy is shown
483
A.K. Parai and B.B. Mohanty, Debt repayment by LDCs
Good 1 (Exportables)
N t
Tt p! R'
H v
Po Uo
T
H
R
N
Good 2 ( I ~ o r t a b l e s ) Fig. 2. Repayment through tariff. to be the o p t i m a l . By d e m o n s t r a t i n g the s u p e r i o r i t y of i n c o m e t a x to a tariff o r a c o n s u m p t i o n t a x we h a v e r e l a t e d the r e p a y m e n t s of i n t e r n a t i o n a l b o r r o w i n g to the p u b l i c finance l i t e r a t u r e o n b o r r o w i n g a n d policy. References Bhagwati, Jagdish, 1981, The generalised theory of distortions and welfare, in: Jagdish Bhagwati, ed., International trade: Selected readings (MIT Press, Cambridge, MA) 171-189. Harrod, Roy, 1963, Desirable international movements of capital in relation to growth of borrowers and lenders and growth of markets, in: Roy Harrod and Douglas Hague, eds., Internatmnal trade theory in a developing world: Proceedings of a conference held by the International Economic Association (St. Martin's, New York) 113-141. Streeten, Paul, 1977, Comment on debt relief as development assistance by Peter Kenen, in: Jagdish Bhagwati, ed., The new international econon~c order (MIT Press, Cambridge, MA) 78-80.