A CONGESTIBLE PUBLIC INPUT AS A DETERMIN ANT OF TRADE. SAJID ANWAR* Northern Territory University and University of British Columbia 1.

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1 INTERN ATIONAL ECONOMIC JOURN AL 75 Volume 8, Number 4, Winter 1994 A CONGESTIBLE PUBLIC INPUT AS A DETERMIN ANT OF TRADE SAJID ANWAR* Northern Territory University and University of British Columbia This paper examines the re l ationship between the supply of a conge s t i ble publ i c input and the pattern of international trade in the context of an extended Heckscher- Ohlin model. It is shown that differences in the supply of a public input alone can determine the pattern of trade even if (i) both industries derive equal benefits from the p u blic input and (ii) the public and the private sectors are equally capital intensive. C o n gestion within an industry and congestion across industries are considere d separately. [F11, H41] 1. INTRODUCTION One of the main objectives of international trade theory is to explain the pattern of international trade. Explanations based on differences in production technologies led to the Ricardian Th e o rem, wh e reas ex p l a n ations based on diffe rences in fa c t o r e n d owments resulted in the Heck s ch e r-ohlin Th e o rem. More recent ex p l a n at i o n s consider the role of increasing re t u rns and imperfect competition in the wo rl d e c o n o my. The role of gove rnment spending on industries in determining tra d e patterns however has not received much attention. Most open economy studies wh i ch ex p l i c i t ly include gove rnment spending on industries are mainly concerned with the shape of the production possibility curve. 1 In the context of a one-factor and two-good model, Manning and McMillan (1979) have s h own that the comparat ive adva n t age of an economy depends on the level of gove rnment spending on a pure input. Abe (1990) has incorp o rated gove rn m e n t spending on a pure public input into a two-country general equilibrium model. Each country produces two final goods by means of capital, labour and a pure public input. The pure public input, wh i ch is supplied free of ch a rge by the gove rnment, is p roduced by means of capital and lab o u r. Abe has shown that when two countri e s *I am grateful to B. Copeland, D. Donaldson, Y. C. Ko t wal and the re fe rees for helpful comments and suggestions. An earlier ve rsion of this paper was presented at the Canadian Economics Association Annual Meetings, Unive rsity of Prince Edwa rd Island, June I would like to thank A. Thompson, I. Wooton and the participants of the CEA meeting fo r helpful comments. Responsibility for any remaining errors and omissions is mine. 1 See for example, Ishizawa (1988), Okamoto (1985), Tawada (1980, 1982), and Tawada and Abe (1984). Khan (1980, 1983) has considered the validity of some trade theorems in the presence of a pure public input.

2 76 SAJID ANWAR h ave identical homothetic pre fe rences, production tech n o l ogy, factor supplies and the factor intensity of the public sector is the same as that of private sectors, then the country t h at produces more public input ex p o rts (imports) the output of the industry wh i ch derive s m o re (less) benefits from its supply. This implies that, when both industries derive equal b e n e fits from the supply of a pure public input and the other conditions stated ab ove also h o l d, diffe rences in the production (and hence the supply) of a pure public input cannot i n fluence the pat t e rn of intern ation tra d e. Clarida and Fi n d l ay (1991) have considered the role of a pure public input and a public good in the context of a specific factor model. A n war (1992) has examined the role of the supply of a pure public input in determ i n i n g the pat t e rn of trade between undere m p l oyed economies. A significant pro p o rtion of gove rnment ex p e n d i t u re is directed towa rds the provision of impure public (or semi-public) inputs in most real economies. Examples of such public inputs include roads, canals, bri d ges and harbours. The re l at i o n s h i p between government spending on impure public inputs and the pattern of international trade, however, has not been adequately analysed. An important difference between pure and impure public inputs is their availability to fi rms. The entire supply of a pure public input can be utilised by all fi rm s s i mu l t a n e o u s ly. Consequently, a pure public input is non-conge s t i ble both acro s s industries and among firms within each industry. On the other hand, the entire supply of an impure public input cannot be utilised by all fi rms simu l t a n e o u s ly. In other words, an impure public input is congestible within industries and among firms across i n d u s t ries. Due to this asymmetry, the supply of pure and impure public inputs influences the pattern of trade differently. For a given supply of impure public input, the entry of an ex t ra fi rm not only i n c reases congestion within the re l evant industry, but also increases the level of congestion in the other industries. Congestion affects the size of benefits derived by each industry from the use of an impure public input. An impure public input may not be equally conge s t i ble across industries. In addition, each industry is like ly to contribute in different ways to the degree of congestion. The pattern of international t rade is there fo re also influenced by (a) intra - i n d u s t ry congestion and (b) interindustry congestion. The purpose of the present study is to consider the relationship between the supply of a conge s t i ble public input and the pat t e rn of tra d e. The paper develops a two - c o u n t ry, two - good and two - factor ge n e ral equilibrium model with gove rn m e n t spending on a congestible public input. The private sector produces two final goods by means of capital, labour and the public input. The public input is produced by means of capital and lab o u r. Marshallian ex t e rnalities cause the congestion of the public input. The relationship between government spending on a congestible public input and the pattern of trade is discussed in section two. Both intra-industry and inter-industry c o n gestion are ex p l i c i t ly taken into account. It is shown that Abe s result can be extended to include an impure public input only if (i) the public input is equally congestible across industries, and (ii) congestion created by one industry in the other

3 DETERMINANT OF TRADE 77 is symmetric. Section three contains a summary and concluding remarks. 2. GOVERNMENT SPENDING ON AN IMPURE PUBLIC INPUT AND THE PATTERN OF TRADE A simple two - c o u n t ry, two - good fra m ewo rk s utilised in wh i ch the re s p e c t ive gove rnments supply an impure public input for use within national boundari e s. Examples of impure public inputs include production infra s t ru c t u re: roads, bri d ge s, canals, dams and harbours. The public input is cooperative with private inputs in the p roduction of both goods. The economies under consideration fully utilise their resources. The two countries are assumed to be identical in every respect, except for differences in the supply of a congestible public input. The autarky equilibrium of a representative economy is considered in the following. Consider a self sufficient economy that produces two final goods (X and Y) by means of two pri m a ry inputs and an impure public input. The pri m a ry inputs are capital and labour which are fully utilised. The public input is produced by means of capital and labour. The supply of labour and capital in the economy is fixed. The p u blic input is provided free of ch a rge by the gove rnment. The cost of publ i c p roduction is financed by a pro p o rtional income tax. The final good X is the nu m é ra i re. All markets are competitive and private pro d u c e rs take the supply of public input as given. Given an inter- and intra-industry congestible public input and that firms in each industry are assumed to be identical, it follows that congestion caused by each firm within an industry is identical. Howeve r, the public input may not be equally c o n ge s t i ble across industries. In addition, each industry is like ly to contri bute in d i ffe rent ways to the degree of congestion. In other wo rds, congestion caused by d i ffe rent industries is unlike ly to be symmetri c. Congestion is assumed to be p o s i t ive ly re l ated to the output of each industry. Accord i n g ly, when an industry expands, the resulting congestion decreases the usefulness of the public input to all i n d u s t ries. In the present study, congestion is modelled as a negat ive ex t e rn a l i t y. Each industry consists of a large number of identical firms. The production functions of the ith firm in industry X and Y are the following: X i = s x (G, X, Y) f(k x, L x ); X = n x X i (i = 1, 2,., n x ) Y i = s y (G, X, Y)h(K y, L y ); Y = n y Y i (i = 1, 2,., n y ) where X i is the output of firm i in industry X; n x is the number of firms in industry X; G is the supply of impure public input; and K x, and L x are respectively capital and labour used in the production of X i. Each firm takes G, X, and Y as given. f(.) and h(.) are linearly homogeneous. s x (.) and s y (.) measure the contribution of the public input to production. For a given X and

4 78 SAJID ANWAR Y, an increase in G reduces the congestion. In other words, s x (.) and s y (.) are positively re l ated to the supply of conge s t i ble public input. Howeve r, for a given supply of p u blic input, an increase in the output of either or both industries incre a s e s c o n gestion. In other wo rds both s x (.) and s y (.) are negat ive ly re l ated to X and Y. However, s x (.) and s y (.) are concave. 2 The above production functions are separable in the private and the public inputs. Consequently, an increase in the supply of impure public input affects the output of the two industries in a Hicks neutral fashion. For the sake of algebraic simplicity the following functional forms for s x (.) and s y (.) s x (.) = G α X γ Y λ ; 1 > α > 0, γ > 0, λ > 0 s y (.) = G β Y ζ X µ ; 1 > β > 0, ζ > 0, µ > 0 are used. where γ is the congestion rate in industry X; ζ is the congestion rate in industry Y;λ is Y i n d u s t ry s contri bution to congestion in industry X; and µ is X i n d u s t ry s contri - bution to congestion in industry Y. For a given G, X, and Y, the cost functions for the ith firm in industry X and Y can c x (r, w)[x i /s x (.)]=Min [wl x +rk x : X i / s x (.)= f(k x, L x )] with respect to L x and K x. c y (r, w)[y i /s y (.)] = Min [ wl y +rk y : Y i /s y (.)= h(k y, L y )] with respect to L y and K y. be derived as follows: where w and r are respectively the wage rate and the rate of return on capital. Since all firms in both industries are identical, the industry cost functions can be c x (r, w)[x /s x (.)] c y (r, w)[y / s y (.)] derived by aggregating the cost functions of the firms as follows: The tech n o l ogy for public production is the fo l l ow i n g, wh e re g(.) is linearly G = g(k g, L g ) The corresponding cost function is the following : Gc g (r, w) = Min [ wl g + rk g : G = g(k g, L g )] with respect to L g and K g. 2 In the present study, congestion of public input is caused by Marshallian externalities.

5 DETERMINANT OF TRADE 79 homogeneous. By using the properties of cost functions, the factor market clearing conditions can L e = [X/s x (.)] c wx (.) + [Y/s y (.)] c w y (.) + Gc w g (.) K e = [X/s x (.)] c rx (.) + [Y/s y (.)] c r y (.) + Gc r g (.) (1) (2) be written as follows: where [X/s x (.)]c w x(.) and [X/s x (.)]c r x(.) are labour and capital used in the production of X; Gc w g(.) and Gc r g(.) are labour and capital used in the production of G; K e is supply of capital; and L e is supply of labour. Due to unrestricted factor mobility within the economy, the wage rate and the rate of return on capital in the private and the public sectors is identical. The zero profit c x (r, w)/[s x (.)] = 1 c y (r, w)/[s y (.)] = p (3) (4) conditions for industry X and Y are the following: For a given supply of the conge s t i ble public input (G) and the autarky re l at ive goods price ratio (p), equations (1) to (4) determine the equilibrium w, r, X and Y. The autarky price ratio in the economy is determined by the interaction of supply and demand. On the demand side, preferences are assumed to be homothetic. The relative demand for the two goods in the economy therefore depends on the relative price ratio Y/X = φ(p) (5) alone. Market equilibrium for the final goods can be written as: where φ(p) is relative demand of the two final goods and φ(p)/ p is negative. For a given supply of G, equilibrium of the private sector can be characterised by equations (1) to (5). In five equations there are five endogenous variables; w, r, p, X and Y. These variables are determined as the function of the supply of public input. As indicated earlier, the cost of public production is financed by means of an income tax. The budget constraint of the government is given in the following, where t is the t{wl e +rk e } = Gc g (w, r) (6) income tax rate. 3 The right hand side of the ab ove equation is the total cost of the public input; 3 The budget constraint of the representative consumer is: (1 t){wl e + rk e } = X + px.

6 80 SAJID ANWAR whereas the left hand side is government tax receipts. For the purposes of the present study, the supply of public input does not have to be optimal. The full equilibrium of the closed economy under consideration is given by equations (1) to (6). These are six equations and six endogenous variables: w, r, p, X, Y, and t. This completes the description of a representative closed economy. The relationship between the supply of an impure public input and autarky terms of trade is discussed in the following. For a given supply of impure public input, equations (1) to (5) describe the autarky equilibrium of the private sector of an economy. Consider two such economies. If the t wo countries are identical in eve ry respect, then there is no basis for intern at i o n a l trade, since the autarky price ratio in the two countries will be identical. However, differences in the supply of public input can lead to differences in the autarky price ratio. The supply of an impure public input influences the autarky goods price ratio (p) through the following channels: (i) for a given wage and rate of return on capital, an i n c rease in G i n fluences p t h rough a reduction in the cost of production of both industries. This is the direct effect of an increase in the supply of impure public input; (ii) an increase in G also increases the costs of both industries through its positive impact on wages and the rate of re t u rn on capital. This is the indirect effect of an i n c rease in the supply of an impure public input; and (iii) the public input is congestible within industries and among firms across industries. In general the public input is not like ly to be equally conge s t i ble across industries. In addition, the congestion caused by each industry for the other is also not likely to be symmetric. Accordingly, for a given wage rental ratio, an increase in G directly affects the output of both industries and hence the autarky price ratio. In the case of a pure (i.e., non-congestible) public input, Abe (1990) has shown that the pattern of international trade is not influenced by differences in the production of public input if (i) both industries derive equal benefits from its supply, i.e., α is equal to β in terms of the present study 4 ; and (ii) the factor intensity of the public sector is the same as that of the private sectors. The present study deals with an impure (i.e., congestible) public input. In order to facilitate comparison with the results derived by Abe, it is assumed that (1) α is equal to β, and (2) the factor intensity of the public and the private sectors is the same. In other words, the present study exclusively examines the role of congestion in determining the pattern of trade. The relationship between the supply of an impure public input and the pattern of t rade can be examined by means of the fo l l owing derivat ive, wh i ch describes the impact on the autarky price ratio of a country when its supply of public input p/ G = (p/g)[( λ µ ) + (γ ζ)[ H 1 / H d ] (7) 4 U n l i ke the present study, in Abe (1990) the elasticity of X and Y with respect to G i s variable. 5 P ro p e rties of the cost functions are used in the derivation of equation (7), see Diewe rt (1974).

7 DETERMINANT OF TRADE 81 where H 1 = K g {L x a xw +L y a gw + L g a gw } + L g {K x a xr +K y a yr +K g a gr } < 0 a yr = (r/c y r (.)[ c y r (.)/ r]< 0; a xw = (w/c wx (.)[ c wx (.)/ w] < 0 a xr = (r/c rx (.)[ c rx (.)/ r]<0; a yw = (w/c y w (.)[ c y w (.)/ w] < 0 a gw = (w/c g w (.)[ c g w (.)/ w]<0; a gr = (r/c g r (.)[ c g r (.)/ r] < 0 H d < 0 increases by a small amount. 5 E q u ation (7) is derived by using equations (1) to (5) and conditions (i) and (ii). The sign of the ab ove derivat ive depends on: (a) the re l at ive size of inter- i n d u s t ry congestion (µ λ); (b) the relative size of congestion within each industry (r ζ); and (c) the sign of H d. H d is negative provided the equilibrium is stable. 6 If the impure public input is equally congestible within each industry (i.e., γ = ζ) and the congestion caused by each industry is symmetric (i.e., λ = µ), then the above derivative is zero. This implies that both pure and impure public inputs influence the pat t e rn of i n t e rn ational trade symmetri c a l ly. If the congestion caused by each industry in the other is symmetric (i.e., λ = µ), then the following proposition follows from equation (7): P ROPOSITION 1. When two countries have: (i) identical homothetic pre fe re n c e s, production technology and factor supplies; (ii) both industries derive equal benefits from the impure public input; (iii) the factor intensity of the public sector is the same as that of the private sectors and (iv) the congestion caused by each industry in the other is symmetric; then the country that produces more public input exports (imports) the output of that industry in wh i ch the public input is re l at ive ly less (more ) congestible. An increase in the supply of public input increases the output of both industries. Suppose that the public input is relatively more congestible in X industry as compared to Y in the sense that ex t e rnal diseconomies wo rk re l at ive ly more intensive ly in X industry. Hence if G increases, the relative cost of X industry would decline, since the same percentage decrease in the production levels would alleviate the congestion by a greater amount in X industry. This effect will bring an increase in the relative supply of good X for any relative price of private goods which, in turn, would decrease the re l at ive price of good X in the autarky equilibrium. Th e re fo re, the country that p roduces more public input will ex p o rt the output of the industry wh e re the publ i c input is relatively more congestible. 6 Stability condition is discussed in the appendix. Okamoto (1985) has also derived a similar stability condition.

8 82 SAJID ANWAR If the public input is equally congestible within each industry (i.e., γ = ζ), then the following proposition follows from equation (7): P ROPOSITION 2. When two countries have: (i) identical homothetic pre fe re n c e s, production technology and factor supplies; (ii) both industries derive equal benefits from the impure public input; (iii) the factor intensity of the public sector is the same as that of the private sectors and (iv) the public input is equally congestible within each industry; then the country that produces more public input exports (imports) the output of that industry which causes more (less) congestion in the other industry. The ab ove propositions are based on the assumption that both industries derive equal direct benefits from the public input (i.e., α = β). On the other hand wh e n overall congestion in the two industries is identical (i.e., λ + γ = µ + ζ), but the direct benefits derived from the public input are not identical, the pattern of trade is solely determined by the relative size of the direct benefits. P ROPOSITION 3. When two countries have: (i) identical homothetic pre fe re n c e s, production technology and factor supplies: (ii) the overall congestion cost is identical (i.e., λ + γ = µ + ζ) and (iii) the factor intensity of the public sector is the same as that of the private sectors; then the country that produces more public input exports (imports) the output of that industry which derives more (less) benefits from the public input. The ab ove proposition ge n e ralises Abe s result. Abe has considered a nonc o n ge s t i ble public input, there fo re in his model para m e t e rs λ, γ, µ, and ζ a re ze ro. A c c o rd i n g ly, condition (ii) in proposition 3 is automat i c a l ly sat i s fi e d. However in proposition 3, congestion parameters are not required to be zero. Hence Abe s result is a special case of proposition 3. In addition to generalising and extending the existing results, the present analysis also suggests that the introduction of congestion costs can reverse Abe s result where the pat t e rn of trade is solely determined by the re l at ive size of the direct benefi t s derived from the supply of a public input. Consider proposition 3 where the relative congestion cost is identical and the output of the industry which derives more direct b e n e fits from the public input is ex p o rt e d. Suppose that for some reason ove ra l l c o n gestion costs in the industry wh i ch derives more direct benefits from the publ i c input increase suffi c i e n t ly as compared to the industry wh i ch derives less dire c t benefits. This increase in overall congestion cost will reverse the pattern of trade in the sense that the output of the industry which derives more direct benefits from the s u p p ly of the public input will now be imported because the net benefits from the public input are relatively lower. The p a ra m e t ric conditions re q u i red for the reve rsal of the pat t e rn of trade are (i) β α is positive (negative) and (ii) β α + [β(ζ + µ) α(λ + γ )] is negative (positive). Condition (i) measures the re l at ive direct benefits only, wh e reas (ii) measures the

9 DETERMINANT OF TRADE 83 relative net benefits. 7 The relative net benefits are calculated by adding the relative direct, β α, and the relative indirect benefits, [β(ζ + µ) α(λ + γ)]. The indirect b e n e fits wh i ch are weighted by the direct benefits para m e t e rs measure the indire c t ove rall congestion cost. If Y i n d u s t ry derives more direct benefits from the publ i c input then β > α, however, the presence of sufficiently high indirect overall congestion cost can out weigh the relatively large direct benefits so that the overall net benefits in Y industry are less than X. In such a case, although Y industry derives more direct benefits from the public input, its output will be imported. 3. CONCLUDING REMARKS This paper examines how a congestible public input affects the trade pattern in an extended Heckscher-Ohlin model. The model consists of two-goods, two-factors and o n e - p u blic input incorp o rating the Marshallian ex t e rnalities wh i ch cause the c o n gestion of public input. The public input is conge s t i ble across industries and among firms within each industry. It is shown that when the public input is equally congestible within each industry but congestion caused by each industry in the other is not symmetric, then differences in its supply can determine the pattern of trade even if both industries equally benefit from its services and the factor intensity of the public and the private sectors are identical (or sufficiently close to each other). A country which produces more public input exports (imports) the output of that industry which creates less (more) congestion in the other industry. F u rt h e rm o re, when the congestion caused by each industry in the other is symmetric but the public input is not equally congestible within each industry, then d i ffe rences in its supply can determine the pat t e rn of trade even if both industri e s equally benefit from its services and the factor intensity of the public and the private sectors is identical: a country which produces more public input exports (imports) the output of that industry in which the public input is relatively more (less) congestible. On the other hand, if both industries benefit equally from the supply of the public input; if the congestion caused by each industry is symmetri c, if public input is e q u a l ly conge s t i ble within each industry and conditions (i) and (ii) hold, then d i ffe rences in the supply of an impure public input cannot influence the pat t e rn of i n t e rn ational tra d e. This implies that congestion can actually reve rse the re s u l t s derived by Abe (1990). If the public input is not congestible and the factor intensity of the public and private sectors is identical, then the country which produces more public input exports the output of the industry which derives more benefits from its s u p p ly. Howeve r, in the case of a conge s t i ble public input, the country wh i ch produces more public input may import the output of the industry which derives more benefits from its supply, if the public input is relatively less congestible in the relevant 7These conditions can be derived by re-writing the industry production function as X = (G α(1 + ζ) βλ F(.) (1 + ζ) H(.) λ } σ ; Y = {G β(1 + γ ) αµ F(.) µ H(.) (1 + γ) } σ ; where σ = 1/[(1 + γ)(1 + ζ) λµ].

10 84 SAJID ANWAR industry. APPENDIX: STABILITY CONDITIONS E q u ations (1) to (5) can also be used to derive the Routh-Hurwitz stab i l i t y dw/dt = a w [{ X / s x (.)} c wx (.) + [Y /s y (.)} c w y (.) + Gc w g (.) L e ] dr/dt = a r [{X / s x (.)} c rx (.) + {Y/s y (.)} c r y (.) + Gc r g (.) K e ] dx/dt = a x [1 c x (r, w)/{s x (.)}] dy/dt = a y [ p c y (r, w)/{s y (.)}] dp/dt = a p [φ( p) Y /X] conditions. The postulated dynamic adjustment process is described by means of the fo l l owing equations, wh e re the left hand side is the time derivat ive of the re l eva n t variable: where the relevant speeds of adjustment (a w, a r, a y, a x, a p ) are assumed to be positive constants. a 11 a 12 a 13 a 14 a 15 a 21 a 22 a 23 a 24 a 25 J = a 31 a 32 a 33 a 34 a 35 a 41 a 42 a 43 a 44 a 45 a 51 a 52 a 53 a 54 a 55 where a 11 = [{ X / s x (.)} c x ww y g (.) + {Y /s y (.)} c ww (.) + Gc ww (.)] a 12 = [{X/s x (.)} c x wr (.) + {Y/s y (.)} c y wr (.) + Gc g wr (.)] a 13 = c w x (.)[ Xs xx (.) s x (.)]/[ s x 2 (.)] c w y Ys yx (.)/ s y 2 (.) a 14 = c w y (.)[ Ys yy (.) s y (.)]/[ s y2 (.)] c wx Ys xy (.)/ s y2 (.); a 15 = 0 a 21 = [{X/s x (.)} c x rw (.) + {Y /s y (.)} c y rw (.) + Gc g rw (.)] a 22 = [{ X / s x (.)} c x rr (.) + {Y /s y (.)} c y rr (.) + Gc g rr (.)]

11 DETERMINANT OF TRADE 85 a 23 = c rx (.)[ Xs xx (.) s x (.)]/[ s x2 (.)] c r y Ys yx (.)/s y2 (.) a 24 = c r y (.)[ Ys yy (.) s y (.)]/[ s y2 (.)] c rx Ys xy (.)/ s x2 (.); a 25 = 0 a 31 = c wx (.)/s x (.); a 32 = c rw (.)/s x (.) a 33 = c x (.)[ s xx (.)]/ s x2 (.) a 34 = c x (.)[ s xy (.)]/ s x2 (.); a 35 = 0; a 41 = c w y (.)/s y (.) a 42 = c r y (.)/s y (.); a 43 = c y (.)[ s yx (.)]/ s y2 (.) a 44 = c y (.)[ s yy (.)]/ s y2 (.); a 45 = 1; a 51 = 0; a 52 = 0; a 53 = Y /X 2 a 54 = (1/ X ); a 55 = φ'(p) One of the Routh Hurwitz stability conditions requires that ( 1) 5 J > 0, The economic meanings of the ab ove equations are obvious, there fo re the interpretation is not included here. The relevant Jacobian matrix, denoted by J is the J = H d following: where stands for the determinant. The determinant of the above Jacobian matrix is the following: The determinant condition is satisfied if H d is negative. REFERENCES Abe, K., Public Input as a Determinant of Trade, Canadian Journal of Economics, May 1990, A n wa r, S., Gove rnment Spending on Industries and the Pat t e rn of Trade betwe e n U n d e re m p l oyed Economies, Jo u rnal of Economic Integrat i o n, Autumn 1992, Clarida, R. and Findlay, R., Endogenous Comparative Advantage, Government, and the Pattern of Trade, NBER Working Paper No 3813, D i ewe rt, W., Ap p l i c ations of Duality Th e o ry, in M. Intri l i gator and D. Ke n ri ch, eds., Fro n t i e rs of Quantitat ive Economics Vol. II, Amsterdam: Nort h - H o l l a n d, I s h i z awa, S., Increasing Returns, Public Input and Intern ational Tra d e, A m e ri c a n Economic Review, September 1988, Khan, M. A., A Factor and Public Input Equalization Theorem, Economics Letters, Vol. 5, 1980, 1-6. Khan, M. A., Public Inputs and the Pure Theory of International Trade, Zeitschrift

12 86 SAJID ANWAR fur Nationalokonomie, Vol. 43, 1983, M a n n i n g, R. and McMillan, J., Public Inputs, Production Possibilities, and International Trade, Canadian Journal of Economics, May 1979, Okamoto, H., Production Possibilities and Intern ational Trade with a Public Intermediate Good: A Generalization, Economic Studies Quarterly, March 1985, Tawada, M., The Production Possibility Set with Public Interm e d i ate Goods, Econometrica, May 1980, Tawada, M., The Properties of the Set of Production Possibilities with Pure Intermed i ate Pro d u c t s, in M. Kemp, ed., P roduction Sets, New Yo rk: Academic Pre s s, Tawada, M., and Okamoto, H., International Trade with a Public Input, Journal of International Economics, February 1983, Tawada, M. and Abe, K., Production Possibilities and Intern ational Trade with a Public Intermediate Good, Canadian Journal of Economics, May 1984, Mailing Add ress: Pro fessor Sajid Anwa r, Faculty of Business, Nort h e rn Te rri t o ry University, Box 40146, Casuarina NT, AUSTRALIA 0811.