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Essays on international trade and factor mobility in the presence of a public input Anwar, Sajid 1992

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ESSAYS ON INTERNATIONAL TRADE AND FACTOR MOBILITY IN THE PRESENCE OF A PUBLIC INPUT by SAJID ANWAR M.Sc, Quaid-i-Azam University, 1982 M.A., McMaster University, 1984 A THESES SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Economics) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA March 1992 © Sajid Anwar, 1992 National Library of Canada Acquisitions and Bibliographic Services Branch 395 Wellington Street Ottawa, Ontario K1A0N4 Bibliothèque nationale du Canada Direction des acquisitions et des services bibliographiques 395, rue Wellington Ottawa (Ontario) K1A0N4 Your tile Votre rétérence Our file Notre rétérence The author has granted an irrevocable non-exclusive licence allowing the National Library of Canada to reproduce, loan, distribute or sell copies of his/her thesis by any means and in any form or format, making this thesis available to interested persons. L'auteur a accordé une licence irrévocable et non exclusive permettant à la Bibliothèque nationale du Canada de reproduire, prêter, distribuer ou vendre des copies de sa thèse de quelque manière et sous quelque forme que ce soit pour mettre des exemplaires de cette thèse à la disposition des personnes intéressées. The author retains ownership of the copyright in his/her thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without his/her permission. L'auteur conserve la propriété du droit d'auteur qui protège sa thèse. Ni la thèse ni des extraits substantiels de celle-ci ne doivent être imprimés ou autrement reproduits sans son autorisation. ISBN 0-315-79769-X C a n a d a In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of ^ Q i v ^ y ^ * ^ The University of British Columbia Vancouver, Canada Date a?-DE-6 (2/88) ABSTRACT Governments spend large sums of monies on various services provided to both firms and households. However, most open economy studies do not take government spending on industries into account. The present study deals exclusively with government spending on industries. This spending i s incorporated into n e o c l a s s i c a l production functions i n terms of a public input. The purpose of t h i s thesis i s three f o l d : (i) to investigate the impact of terms-of-trade changes i n a small public input economy; ( i i ) to explore the international transmission of government spending on pu b l i c inputs; and ( i i i ) to examine the rela t i o n s h i p between government spending on public inputs and the pattern of international trade. The thesis consists of three essays. In a three-period setting, the f i r s t essay examines the impact of terms-of-trade changes on the a l l o c a t i o n of resources i n a small open economy. The private sector of the economy produces two f i n a l goods by means of private inputs and a public input. The public input i s produced by the public sector. The a l l o c a t i o n of resources between the private and public sectors i s endogenous and the public input i s supplied with a lag of one period. The essay demonstrates that the timing of terms-of-trade changes i s c r i t i c a l . The impact of terms-of-trade changes i n the presence of labour unemployment i s also considered. The second essay develops a two-country, one-good, and two-factor general equilibrium model with a pure p u b l i c input and international factor mobility. International transmission of government spending on a pure public input and the implications of p o t e n t i a l international coordination are investigated i n the short-run and the long-run. The essay also considers the i n t e r n a t i o n a l transmission of government spending on a pure public input i n the context of a three-country model where two countries have formed an economic union. The t h i r d essay develops a two-country, two-good, and two-factor general equilibrium model with a congestible public input. The model i s used to investigate the r e l a t i o n s h i p between government spending on a congestible public input and the pattern of international trade. Contents Abstract Table of Contents Acknowledgments 1. Introduction 1 2. Terms-of-Trade Changes in a Public Input Economy 12 2.1 Introduction 12 2.2 Review of Related Literature 17 2.3 A Three-Period Model 25 2.3.1 Optimal Allocation of Resources 29 2.4 Comparative Statics 34 2.4.1 Terms-of-Trade Changes in Period One 34 2.4.2 Terms-of-Trade Changes in Period Two 39 2.4.3 Terms-of-Trade Changes in Period Three 41 2.4.4 Technological Progress in the Production of Final Goods 46 2.5 Terms-of-Trade Changes in an Underemployed Economy 49 2.6 Concluding Remarks 54 3. Government Spending on Industries, International Factor Mobility, and Policy Coordination 57 3.1 Introduction 57 3.2 A Short-Run Model 65 3.3 Transmission of Economic Policy and International Coordination in the Short-Run 73 3.4 A Long-Run Model 83 3.5 Transmission of Economie Policy and International Coordination in the Long-Run 87 3.6 International Transmission of Economic Policy in the Presence of an Economic Union 96 3.7 Concluding Remarks 103 Appendix 107 4. Government Spending on Industries and the Pattern of International Trade no 4.1 Introduction 110 4.2 Government Spending on an Impure Public Input and the Trade Pattern between Fully Employed Economies 116 4.2.1 The Pattern of Trade 122 4.3 Government Spending on an Impure Public Input and the Trade Pattern between Underemployed Economies 129 4.3.1 The Pattern of Trade 130 4.4 Concluding Remarks Appendix 5. Final Summary and Concluding Remarks References Acknowledgments I am greatly indebted to the members of my thesis committee, Brian Copeland (chairman), David Donaldson, and Ashok Kotwal, for comments and discussions that helped me to complete the present study. I am also g r a t e f u l for comments and suggestions of John Cragg, Erwin Diewert, Jon Kesselman, and Margaret Slade. CHAPTER 1 INTRODUCTION Government spending constitutes a s i g n i f i c a n t proportion of national incomes world wide.^ Such spending can be divided into two broad categories: spending on households, and spending on industries. In a l l r e a l economies, large proportions of government budgets are directed towards services provided to i n d u s t r i e s . However, most open economy studies do not take government spending on industries into account and consider the private sector exclusively. These studies appear to be consistent with the assumption that the a l l o c a t i o n of resources between the private and the public sectors i s exogenous. In fact, despite separate management, the private and the public sectors are highly interdependent i n most r e a l economies. Accordingly, domestic and foreign shocks are l i k e l y to influence the output of both private and public sectors. Examples of these shocks include (exogenous) technological progress i n the domestic private sector; an increase ^ 12% and 14% respectively was the share of government sector i n the gross domestic product of the USA i n 1950 and 1980. On the other hand, 20% and 7% respectively was the government's share of Japanese gross domestic product i n 1950 and 1980. The corresponding figures for the U.K. were 25% and 23%. See Summers and Heston (1984). in the price of imported raw materials; and an improvement i n the terms-of-trade. Although government spending on industries has not received much attention i n the t h e o r e t i c a l l i t e r a t u r e , i t s importance has long been recognised. Pigou (1932) used Sidgwick's famous lighthouse example i n t h i s regard: the services of a lighthouse are an input into shipping companies' production functions for sea transport. Other examples include transportation f a c i l i t i e s ( i . e . , roads, bridges, canals and harbours) and government financed s c i e n t i f i c research whereby information on new production techniques i s made available to a l l firms simultaneously. The present study exclusively considers government spending on industries. This spending i s incorporated i n open economy models i n terms of a public input. The private sector of an economy takes the supply of public inputs as given. However, for the society as a whole the supply of public inputs i s endogenous. The supply of public inputs i n an economy i s determined by the government as the re s u l t of an optimisation process, such as the national welfare maximisation. In the presence of a public input, the domestic and foreign shocks influence the output of the private sector through the following channels: (1) an increase i n the supply of public input influences the productivity of the private sector d i r e c t l y ; (2) an increase i n the production of public input leaves fewer resources for the private sector to work with; (3) induced factor mobility within the private sector due to domestic and/or foreign shocks. If the interdependence of the public and the private sectors i s assumed away, then domestic and foreign shocks a f f e c t the output of the private sector only through induced factor mobility. Most available open economy studies do not take into account the lag between the production and supply of public inputs. For example, government financed s c i e n t i f i c research conducted i n the present i s expected to benefit future users; production infrastructure u t i l i s e d by firms i n the present was b u i l t i n the past. Due to the lag between the production and supply of public inputs, the timing of domestic and foreign shocks i s c r i t i c a l . Economic p o l i c i e s of the government also influence the provision of public inputs i n an economy. For example, i f the government uses t a r i f f s to promote domestic import-competing industries, i t i n d i r e c t l y raises the demand for the relevant public inputs. Similar arguments can be made regarding the formation of Trade Development Zones and the Export Promotion Zones established by governments i n some developing and developed countries. It i s therefore desirable to investigate the impact of domestic and foreign shocks on the government and non-government sectors. This task can be accomplished only i n the context of a multi-period model where the a l l o c a t i o n of resources between the private and public sectors i s endogenous. The presence of public input within production functions allows one to consider the international transmission of government spending on industries.^ Government spending on in d u s t r i e s i s p a r t i c u l a r l y important for economies engaged i n tough competition in the international market. Abe (1990), Manning and McMillan (197 9), and McMillan (1978) have shown that government spending on public inputs can influence the comparative advantage of an economy. Barro (1990) has shown that a po s i t i v e relationship e x i s t s between the rate of economic growth and government spending on public inputs. The s t a t i s t i c a l estimates obtained i n a cross country study by Ram (1986) support the view that government size has a p o s i t i v e e f f e c t on economic performance and growth. The size of the government i s measured by the output of the government sector. The private sector uses the output of the government sector as an input. Yamamura (1986) i n his discussion of Japanese i n d u s t r i a l p o l i c y indicates that from 1966 to 1980, the ministry of international trade and industry (MITI) provided services worth 663.1 m i l l i o n U.S. d o l l a r s to semiconductors and the computer industry alone. In general, government spending on the provision of public inputs affects the marginal productivity of private inputs ^ Frenkel and Razin (1987), Devereux (1988), and Durlauf and Staiger (1990), among others, have examined the international transmission of government spending on households. Government spending on households i s included i n the u t i l i t y functions i n terms of a public good. and thus influences the pattern of international trade and f a c t o r mobility. The purpose of t h i s thesis i s three f o l d : (i) to examine the implications of terms-of-trade changes i n a small open economy, where a public input i s supplied by the government with a l a g of one period; ( i i ) to explore the international transmission of government spending on public inputs and evaluate the implications of p o t e n t i a l international economic p o l i c y coordination; and ( i i i ) to investigate the re l a t i o n s h i p between government spending on public inputs and the pattern of international trade. S i g n i f i c a n t labour unemployment exists i n most re a l economies. The present study also examines the extent to which the r e s u l t s derived i n t h i s thesis are sens i t i v e to a relaxation of the f u l l -employment assumption. The thesis consists of three essays, each of which i s concerned with a s p e c i f i c issue outlined above. The f i r s t essay examines the impact of terms-of-trade changes on the a l l o c a t i o n of resources i n a small open economy. The private sector of the economy under consideration produces two f i n a l goods by means of labour, public input and some fixed factors, whereas the public sector produces a public input by means of labour which i s f u l l y mobile between the two sectors. The a l l o c a t i o n of resources between the private and public sectors i s therefore endogenously determined. The public input, which i s produced by the p u b l i c sector, i s made available to the private sector free of charge. In order to capture the ef f e c t s of lags i n the production and supply of public inputs, a three-period model i s u t i l i s e d . In period one, the private sector u t i l i s e s the pre-e x i s t i n g stock of the public input, whereas the public sector produces a public input. In period two, the private sector uses the p u b l i c input produced i n period one, whereas the public sector produces a public input which i s made available to the private sector i n period three. There i s no public production i n period three. In order to bring the role of lags i n the supply of a public input into sharp focus, private investment i s assumed away. It i s shown that an improvement i n the terms-of-trade i n period one decreases (increases) the production of public input i n period one (two). Whereas, an anticipated improvement i n the terms-of-trade i n period two increases (decreases) the production of public input i n period one (two). F i n a l l y , an anticipated improvement in the terms-of-trade i n period three decreases (increases) the output of public input i n period one (two). Due to intertemporal l i n k s , terms-of-trade changes i n one period also influence the production of f i n a l goods i n another period. It i s shown that an improvement i n the terms-of-trade i n period one decreases (increases) the output of both f i n a l goods i n period two (three). Whereas, an anticipated improvement i n the terms-of-trade in period two decreases the output of both f i n a l goods i n period one and three. F i n a l l y , an anticipated improvement i n the terms-of-trade i n period three increases (decreases) the output of both f i n a l goods i n period one (two). The implications of labour unemployment in period one are also considered: i t i s shown that the output of public input i n e i t h e r period i s not influenced by the terms-of-trade changes i n period one. Consequently, terms-of-trade changes i n period one have no impact on the output of either f i n a l good i n period two and three. In addition, anticipated terms-of-trade changes i n period two and three have no influence on the output of both f i n a l goods i n period one. However, an increase i n the minimum wage rate i n period one influences both private and public sectors in each period. The essay e x p l i c i t l y considers a pure public input. However, afte r some modification, the r e s u l t s derived can also be extended to include an impure public input. The focus of the second essay i s the international transmission of government spending on public inputs and p o t e n t i a l i n t e r n a t i o n a l economic p o l i c y coordination. The analysis i s conducted by means of a two-country, one-good general equilibrium model with international factor mobility.^ Both countries produce an i d e n t i c a l f i n a l good by means of c a p i t a l , labour, and a pure ^ For a n a l y t i c a l s i m p l i c i t y , the lags between the production and supply of public inputs are ignored i n the rest of the t h e s i s . public input. In the short-run, c a p i t a l i s f u l l y mobile across i n t e r n a t i o n a l boundaries and labour i s f u l l y u t i l i s e d i n one country only. Whereas, i n the long-run, both labour and c a p i t a l are f u l l y mobile across international boundaries and a l l resources are f u l l y u t i l i s e d i n both countries. By means of a comparative s t a t i c s exercise, the international transmission of government spending on a pure public input i s considered. It i s shown that i n the short-run equilibrium, the production of public input i n a country where labour i s f u l l y u t i l i s e d has no impact on the equilibrium rate of return on the i n t e r n a t i o n a l l y mobile factor. On the other hand, the production of public input i n a country where labour i s not f u l l y u t i l i s e d influences the equilibrium rate of return on the i n t e r n a t i o n a l l y mobile f a c t o r . In addition, an increase i n the supply of public input i n the country which f u l l y u t i l i s e s i t s resources can decrease labour employment in i t s trading partner. Furthermore, from the point of view of the country which f u l l y u t i l i s e s i t s resources i n the short-run non-cooperative solution, the underemployed country spends too much ( l i t t l e ) on the public input i f i t exports (imports) c a p i t a l . In the short-run coordinated solution, the underemployed country spends too l i t t l e (much) on the public input from the point of view of i t s residents i f i t exports (imports) c a p i t a l . In the long-run, the production of public input i n both countries affects equilibrium factor prices. The results depend on r e l a t i v e c a p i t a l i n t e n s i t y of the two countries. It i s shown that in the long-run, non-cooperative solution both countries spend too much on public input from the point of view of each other; i f the c a p i t a l intensive country exports c a p i t a l . On the other hand, i n the long-run coordinated solution, both countries spend too l i t t l e on the public input from the point of view of t h e i r residents; i f the c a p i t a l intensive country exports c a p i t a l . The model i s further extended to include a t h i r d country c a l l e d the rest of the world, which i s linked with the other two countries through i n t e r n a t i o n a l c a p i t a l mobility. It i s shown that although c a p i t a l i s f u l l y mobile across international boundaries and resources are f u l l y u t i l i s e d everywhere, the supply of public input i n the rest of the world has no influence on the equilibrium rate of return on c a p i t a l . Economic po l i c y coordination within the economic union i s therefore desirable i n order to exploit the rest of the world. The t h i r d essay explores the l i n k between government spending on public inputs and the pattern of trade i n the context of a two-country, two-good general equilibrium model. Both goods are produced by means of c a p i t a l , labour and a public input. Abe (1990) has considered the relationship between the supply of a pure public input and the pattern of international trade. The purpose of the t h i r d essay i s to extend Abe's work in two d i r e c t i o n s : (1) to consider the relationship between the supply of an impure public input and the pattern of trade, and (2) to consider the pattern of trade between underemployed economies. Pure public inputs are non-congestible. On the other hand, impure public inputs are congestible within industries and among firms across industries. Congestion among firms across ind u s t r i e s i s inter-industry congestion. Due to t h e i r c o n g e s t i b i l i t y , differences i n the production of impure public inputs can also influence the pattern of international trade. The pattern of trade between two economies where a l l resources are f u l l y employed i s considered f i r s t . It i s shown that the country that produces more impure public input exports (imports) the output of the industry which causes more (less) congestion i n the other industry, i f the public input i s equally congestible within each industry. Furthermore, i f the congestion created by each industry i n the other i s symmetric, then the country which produces more public input exports (imports) the output of the industry i n which the public input i s r e l a t i v e l y less (more) congestible. In other words, Abe's result can be extended to include an impure pubic input only i f (a) congestion caused by each industry i s symmetric, and (b) public input i s equally congestible across industries. F i n a l l y , the r e l a t i o n s h i p between government spending on an impure public input and the pattern of trade between underemployed economies i s considered. It i s shown that even i f both i n d u s t r i e s derive equal benefits from an impure public input which i s equally congestible across industries, and the congestion caused by each industry i s symmetric, the pattern of international trade can s t i l l be influenced by i t s supply. S p e c i f i c a l l y , i f two underemployed countries have i d e n t i c a l preferences, production technology, primary factor supplies, the public input i s equally congestible across industries and the congestion caused by each industry i s symmetric; then the country that produces more public input exports (imports) the output of the industry that i s r e l a t i v e l y labour (capital) intensive. Each of the following three chapters constitutes a s e l f contained essay. The l a s t chapter i s the f i n a l summary of a l l the essays. CHAPTER 2 TERMS-OF-TRADE CHANGES IN A PUBLIC INPUT ECONOMY 2.1 Introduction Most open economy studies [for example Bhagwati and Srinivasan (1983), D i x i t and Norman (1980), and Woodland (1982)] do not take government spending into account and consider the private economy exclusively. These studies provide an excellent survey of the alternative theories of international trade but do not e x p l i c i t l y consider either public goods or public inputs. These studies appear to be consistent with the assumption that the resource a l l o c a t i o n problems of the private and public sectors are independent. In fact, despite separate management, the private and public sectors are highly interdependent i n a l l mixed economies. The assumed independence of resource a l l o c a t i o n problems of the private and public sectors implies that neither domestic nor foreign shocks, which a f f e c t the private sector d i r e c t l y , influence the supply of public goods or public inputs i n an open economy. Examples of these shocks include (exogenous) technological progress in the domestic private sector; an increase i n the p r i c e of imported raw materials; and an improvement i n the terms-of-trade. Governments spend large sums of monies on various services provided to firms and households in a l l mixed economies. Nevertheless, t h e o r e t i c a l studies which take government spending into account often assume that such spending enters into household u t i l i t y functions but not into production functions [see for example; Devereux (1988), Durlauf and Staiger (1990), Frenkel and Razin (1986a, 1986b, 1987), and Svensson (1987)]. These studies also assume that the u t i l i t y functions are strongly separable i n the public and private g o o d s . T h e present study considers government spending on public inputs exclusively. Examples of these inputs include government financed s c i e n t i f i c research whereby information on new production techniques i s simultaneously made available to a l l firms, and production infrastructure. Most open economy studies which include government spending on public inputs do not take into account the lag between the production and supply of these inputs. For example, government financed s c i e n t i f i c research conducted i n the present i s expected to benefit future users; production infrastructure u t i l i s e d by firms i n the present was b u i l t i n the past. Very often s i g n i f i c a n t •'• An i n t e r e s t i n g example i n t h i s regard i s Devereux (1988) where optimal government spending i s zero. repairs of the e x i s t i n g i n f r a s t r u c t u r e involve a long period of time. Therefore, lags between the production and supply of p u b l i c goods cannot be ignored. These lags can only be taken into account in a multi-period s e t t i n g . E x i s t i n g t h e o r e t i c a l studies which include government spending on industries, where the a l l o c a t i o n of resources between the private and public sectors i s endogenously determined, are almost e n t i r e l y s t a t i c i n nature. In addition, these studies do not examine the impact of either t a r i f f s or terms-of-trade changes on the provision of public inputs. It i s well-known that changes i n the terms-of-trade d i r e c t l y a f f e c t the private sector. However, i n a mixed economy, terms-of-trade changes also affect the p r o v i s i o n of public inputs which affects the private sector i n d i r e c t l y . The purpose of t h i s essay i s to develop a simple three-period perfect foresight model of "productive" government, i n which the a l l o c a t i o n of resources between the public and private sectors i s endogenously determined i n a system that includes behavioural hypotheses about the agents exercising the power of the government to tax and spend. The small open economy under consideration produces two f i n a l goods by means of private inputs and a public input. The public input i s produced by means of private inputs. The producers of f i n a l goods take the supply of public input as given, but i n the f u l l equilibrium the supply of public input i s endogenous. The a l l o c a t i o n of resources between the private and public sectors i n the small open economy i s therefore endogenous. The model also takes into account lags between the production and supply (or the a v a i l a b i l i t y to firms) of the public input. Through a comparative s t a t i c exercise, the present study examines the impact of terms-of-trade changes on the provision of the public input and hence the production of f i n a l goods. There are intertemporal production l i n k s due to a lag between the production and supply of public input. These lin k s provide a mechanism whereby terms-of-trade changes i n either period are transmitted to the other periods. It i s shown that an improvement i n the terms-of-trade i n period one decreases the supply of public input i n the second period, but the supply i n period three increases. An anticipated improvement i n the terms-of-trade i n period two increases the supply of public input i n the second period but the supply i n the t h i r d period decreases. F i n a l l y , an anticipated improvement i n the terms-of-trade i n period three decreases the supply of public input i n the second period, but the supply i n the t h i r d period increases. Changes i n the terms-of-trade influence the production of f i n a l goods both d i r e c t l y , and i n d i r e c t l y ; through t h e i r impact on the supply of public input. An improvement i n the terms-of-trade i n period one decreases (increases) the production of both f i n a l goods i n the second (third) period. An anticipated improvement i n the terms-of-trade i n the second period decreases the production of both f i n a l goods i n the f i r s t and t h i r d period. F i n a l l y , an anticipated improvement i n the terms-of-trade i n the t h i r d period increases (decreases) the production of both f i n a l goods i n the f i r s t (second) period. The timing of terms-of-trade changes i s therefore c r i t i c a l . An increase i n the cost e f f i c i e n c y of producing the f i n a l goods i s also considered. Si g n i f i c a n t unemployment exists i n ipost re a l economies. The model i s therefore extended i n section f i v e to include unemployment in period one. The comparative s t a t i c response of the private and public sectors i s shown to be s i g n i f i c a n t l y influenced by the presence of unemployment. The essay i s organised as follows. Some related studies are b r i e f l y reviewed i n section two. Section three develops a simple model of a small open economy. The e f f e c t of terms-of-trade changes on the private and public sectors i s examined in the fourth section. The model developed i n section three i s extended i n section f i v e to include labour unemployment due to economy-wide r i g i d wages i n period one. Section six contains a summary and concluding remarks. 2.2 Review of Related Literature A s i g n i f i c a n t proportion of government spending i s d i r e c t e d towards the provision of public inputs i n a l l mixed economies. Public inputs are intermediate goods and services which are non-r i v a l i n use. Due to t h e i r c o l l e c t i v e nature, the private p r o v i s i o n i s subject to market f a i l u r e . However, the problem i s less severe compared to the provision of public goods. Meade (1952) distinguished two types of public inputs. He refers to these as "creation of atmosphere", and "unpaid factors of production" respectively. The "creation of atmosphere" i s i n fact the production analogue of the pure public (consumption) good as defined by Samuelson (1954) . The use of the public input by one firm does not reduce the amount available for the other firms to use. Constant returns to scale has a very d i f f e r e n t meaning i n such a case. Following Meade (1952), many authors {for example, Negishi (1973), Manning and McMillan (1982)} have indicated that the appropriate d e f i n i t i o n of constant returns to scale i s a production technology l i n e a r l y homogeneous i n the private factors of production alone. Manning et a l . (1985) have shown that i n the presence of a pure public input, constant returns to scale i n the private factors alone means that placing user charges on firms, e.g., Lindahl p r i c i n g , i s not f e a s i b l e . A pure public input gives r i s e to increasing returns to scale which can result i n a non-convex production set. In the relevant l i t e r a t u r e , government financed information on new production techniques has been widely c i t e d as an example of pure p u b l i c input. Feehan (1989) refers to the pure public input as the f a c t o r augmenting public input. Unlike the pure public inputs which are non-congestible both across industries and among firms within each industry, Meade's second type of public inputs, the unpaid factors of production, are congestible. These are therefore the production analogue of the impure public (consumption) goods. In the presence of an impure public input, doubling the amount of each private factor of production used i n the industry leaves each unit of private factor with less public input to work with than before. An unpaid factors type public input i s c l e a r l y a l i m i t i n g input. Constant returns to scale i n such a case means a production function l i n e a r l y homogeneous with respect to a l l inputs, including the public input. Such public inputs include production infrastructure, for example, roads, bridges, canals, and harbours. Kaizuka (1965) and Sandmo (1972) derived rules for the e f f i c i e n t provision of public inputs i n a single period s e t t i n g . Laffont (1975) and Pestieau (1976) extended these optimality rules to encompass technological uncertainty and distortionary taxes, respectively. Thompson (1968) and Negishi (1973) demonstrated that competitive markets can achieve the e f f i c i e n t outcome. Most t h e o r e t i c a l studies i n the l i t e r a t u r e on international trade consider the private economy exclusively. These studies appear to be consistent with the assumption that the a l l o c a t i o n of resources between the production of private and public goods i s exogenous. Some studies where the a l l o c a t i o n of resources between private and public sectors i s endogenous are reviewed i n the remainder of t h i s section. Manning and McMillan (1979), Tawada (1980), Tawada and Okamoto (1982), Manning and McMillan (1982), Tawada and Abe (1984), and Altenburgh (1987) mainly address the shape of the production p o s s i b i l i t y curve i n the presence of a public input. In the context of a two-good, two-private and one public input model, i t i s shown that i n the presence of an impure public input, the production p o s s i b i l i t y curve can be concave to the o r i g i n . However, i n the presence of a pure public input, the production p o s s i b i l i t y curve can be concave to the o r i g i n only i f the e l a s t i c i t y of both goods with respect to the public input i s i d e n t i c a l . R i e s l i n g (1974), Khan (1980), and Tawada and Okamoto (1983) are some of the few attempts to re-examine various theorems i n international trade theory i n the presence of a public input. Manning and McMillan (1979), Okamoto (1985), Tawada and Abe (1984), Ishizawa (1988) and Abe (1990) examine trade patterns i n the economy with a public input. Pugel (1982) considers technology transfer in the context of a Ricardian model incorporating Meade's f i r s t type of public input. He uses a two-country model where each country completely sp e c i a l i s e s i n the production of a private good. The home country produces a pure public input (e.g., an improved production management technique). The home country cannot exclude the foreign country from using the new technique. However, the foreign country (through some sort of binding i n t e r n a t i o n a l agreement) can be made to pay a royalty. Pugel derives and compares three d i f f e r e n t r o y a l t i e s for the foreign country: (1) a royalty which maximises the u t i l i t y of the home country only, (2) a royalty which maximises the u t i l i t y of the foreign country only, and (3) a royalty which maximises the aggregate u t i l i t y of the two countries. The framework of the studies mentioned above i s s t a t i c ; public inputs are produced by means of private factors and these factors are f u l l y mobile between the public and private sectors. In addition, a l l resources are f u l l y u t i l i s e d . What follows i s a b r i e f review of the relevant dynamic studies. McMillan (1978) deals with the optimal supply of public input i n a small open economy. The economy produces two private goods by means of labour and a public input. The public input i s produced by means of labour which i s f u l l y mobile within national boundaries. There i s no private investment i n the economy. Private good production functions are l i n e a r i n labor,^ and consequently the underlying production p o s s i b i l i t y curve i s s t r i c t l y convex to the o r i g i n . McMillan (1978) derives the e f f i c i e n c y conditions for the supply of public input i n t h i s economy. The properties of the optimal t r a j e c t o r y are discussed and i t i s shown that despite one private factor of production, the comparative advantage of the small open economy i s endogenously determined. Barro (1990) introduces a public sector into a simple constant-returns model of economic growth. He considers a closed economy, where the private sector produces a f i n a l good by means of private and public inputs. The production of public input i s financed by a proportional tax on domestic income: government converts i t s tax receipts into public input without additional cost. The rate of depreciation of the public input i s 100%. Using a s p e c i f i c functional form for the production and u t i l i t y functions, the steady state growth and saving rates are shown to depend on the proportional tax rate. Devereux and Mansoorian (1989) develop a two-country, two-good model with a public good which i s used by both consumers and producers. Each country i s assumed to s p e c i a l i s e i n the production of one good i n an i n f i n i t e - h o r i z o n setting. Their model i s similar to Barro (1990) . They are concerned with the implications of ^ In other words, McMillan (1978) considers Meade's f i r s t type of public intermediate good. international f i s c a l cooperation for the growth rates of the two countries. Using Cobb-Douglas production and logarthamic u t i l i t y functions, Devereux and Mansoorian (1989) argue that "the gains from international f i s c a l coordination w i l l i n general e n t a i l higher growth rates for each country". None of the studies mentioned above explores the l i n k between terms-of-trade changes and the provision of public inputs. Tawada and Okamoto (1983), and Okamoto (1985) re-investigate the v a l i d i t y of the Stolper-Samuelson theorem i n the presence of a public input. However, they do not e x p l i c i t l y consider the impact of a t a r i f f on the supply of public inputs. In addition, the studies mentioned so far do not take the lags i n the production and supply of public inputs into account. These lags can be best considered i n a multi-period framework. Government economic p o l i c i e s which are designed to influence the production of private goods also a f f e c t the demand for and hence the supply of public inputs i n d i r e c t l y . The present study e x p l i c i t l y considers the impact of terms-of-trade changes on the public sector which i n d i r e c t l y influences the private sector. In Anwar (1991), I developed a two-period, two-good, and two-country model with a durable public input. The public input which i s used i n the production of both f i n a l goods i s produced by means of labour i n period one. The two f i n a l goods produced are i n d u s t r i a l and primary goods. The i n d u s t r i a l good i s produced by means of c a p i t a l and public input while the primary good i s produced by means of labour and public input. Private investment therefore takes place i n the i n d u s t r i a l sector only. In period one, labour i s mobile within each country but international labour mobility i s r e s t r i c t e d . The two countries are linked through perfect international labour mobility i n period two. I have considered the implications of the introduction of a t a r i f f by either country, i n either period, on private and public investment. Due to anticipated perfect labour mobility i n period two, the introduction of a t a r i f f by either country affects private and public investment i n both countries. The timing of the introduction of a t a r i f f i s shown to be c r i t i c a l . An increase i n the cost e f f i c i e n c y of producing the public input i s also considered. However, I have not taken into account the lag between the production and provision of a public input. In addition, I have not e x p l i c i t l y considered the impact of a t a r i f f on the production of f i n a l goods. During the l a s t few decades trade among nations has increased s i g n i f i c a n t l y . Economic po l i c y changes i n any country i n a quickly integrating world economy are therefore l i k e l y to influence both public and private sectors of a l l countries involved. The present study develops a simple model, where the a l l o c a t i o n of resources between the private and public sectors i s endogenous and lags i n the production and supply of public inputs are taken into account. The model i s used to study the e f f e c t s of temporary changes i n the terms-of-trade on both private and public sectors. 2.3 A Three-Period Model The purpose of t h i s section i s to develop a simple framework where the a l l o c a t i o n of resources between the private and public sectors i s endogenous and which allows an investigation of the e f f e c t s of terms-of-trade changes on the two sectors. The present study e x p l i c i t l y deals with government spending on a pure public input. However, after some minor modifications, the results presented i n t h i s study can also be extended to include an impure public input. There are three periods, indexed t = 1, 2 and 3, which can be interpreted as the past, the present, and the future respectively.^ In each period, the private sector produces two f i n a l goods by means of labour, a public input, and other s p e c i f i c factors. The government provides the public input, produced by means of labour, free of charge to the private sector. The pure public input under consideration i s u t i l i s e d by the producers of both f i n a l goods. Examples of such a public input, which i s non-congestible both within an industry and across industries, include information on ^ The results presented i n the present study can be generalised to any f i n i t e number of periods. However, a three-period s e t t i n g captures the important role played by the lag in the production and eventual provision of public input without much mathematical complexity. improved production management techniques. In the f i r s t period, private producers use the pre-existing stock of public input, whereas the government produces a p u b l i c input which i s made available to the private sector i n the second period. In the second period, the government produces a p u b l i c input which i s made available to the private sector i n the t h i r d period. The public input can be used for only one period. In other words, the public input i s durable but i t s rate of depreciation i s 100%. This implies that the private sector u t i l i s e s only the most recent information on production management techniques.* There i s no private investment. The purpose of t h i s assumption i s to bring the role of lags i n the supply of public input into sharp focus. The supply of labour i n each period i s fixed and there i s perfect labour mobility between the private and public sectors. In each period, the two f i n a l goods (X and Y) are traded at * In the case of an impure public input, the assumption regarding the depreciation ensures that the p r o f i t i n the l a s t period i s not unlimited. 100% depreciation, however, s i m p l i f i e s the algebra of the comparative s t a t i c s considerably. A sim i l a r assumption i s widely used i n the rela t e d l i t e r a t u r e ; see for example, Devereux (1988), Devereux and Mansoorian (1989), Durlauf and Staiger (1990), Frenkel and Razin (1986a, 1986b, 1987), and Barro (1990). r e l a t i v e prices set by the rest of the world. The open economy under consideration can also borrow and lend from the rest of the world at a fixed rate of i n t e r e s t . In other words, the economy under consideration i s small i n both goods and credit markets. Demand conditions therefore have no role to play i n the present study. Good X i s the numeraire and the public input i s also measured i n i t s units. The economy under consideration exports good Y . As indicated e a r l i e r , t h i s study e x p l i c i t l y deals with a pure public input, the f i n a l good production functions are therefore assumed to exhibit constant returns to scale for a given l e v e l of public input. The private and public good production functions f o r the economy under consideration are given below, where the s p e c i f i c factors are not e x p l i c i t l y included.^ X i = Y i x G o " ' F i ( L i „ T i J / 1 > a > 0 Y i = YiyGo^'Hi ( L , „ Tiy) ; 1 > P > 0 G i = Yig L i g ^2 = YzxGi^^Fj (Ljx, Tjx) ^ The subscripts 1, 2, and 3 refer to the f i r s t , the second, and the t h i r d period respectively. Y2 = YzyGi^ 'Ha (L2y, T^ )^ Gz = Y2g ^3 = YsxGa^ F^s (L3X, Tax) Y3 = Y3yG2^ 'H3 (L3y, T3y) where X^ : production of importable good i n period t . {t = 1, 2, 3} Y^ : production of exportable good i n period t. {t = 1, 2 , 3} G^ : public input produced i n period t . {t = 1, 2} Lt^: labour employed i n the production of X f Lty: labour employed i n the production of Y^ . LtgZ labour employed i n the production of Gf T: fix e d factors. at and Pt are the e l a s t i c i t y of X and Y with respect to G i n period t respectively. Ytx^  Yty/ Ytg capture the e f f e c t of exogenous technological progress. The functional form of the above production functions implies that the public input i s cooperative with private inputs i n the production of both f i n a l goods.® The labour-market cl e a r i n g ^ The private production functions are separable i n the public and the private inputs. The r e s u l t s of t h i s and the next essay do not depend on t h i s assumption. conditions are given below where Nt refers to the supply of labour in period t : L i g + L i , + = N i (1) (2) L3, + = N3 (3) Equations (1) to (3) indicate that the entire labour force i s f u l l y u t i l i s e d i n each period. The conditions for the optimal a l l o c a t i o n of resources are derived i n the following section. 2.3.1 Optimal Allocation of Resources E f f i c i e n c y conditions for the small open economy under consideration can be derived by maximising the present value of the f i n a l goods produced by the private sector. For the sake of si m p l i c i t y , the relevant intertemporal discount factors are assumed to be unity. In other words, the rate of inter e s t on foreign borrowing and lending i s assumed to be zero. In addition, for s i m p l i c i t y 7txf Yty/ and Ytg are i n i t i a l l y assumed to be unity.^ The An increase i n these parameters from unity can be interpreted as technological progress. optimisation problem of the central planner i s the following: Max {Go"^Fi(Li,, TiJ + Pi GoP^Hi(Liy, T^ y) } + {Gi«2F2(L3,, T 2 J + P2 G i P 2 H 2 ( L 2 y , T2y) } + { G 2 " ^ F 3 ( L 3 , , T 3 J + P 3 G 2 P ^ H 3 ( L 3 y , T 3 y ) } subject to f u l l employment conditions (1) to (3). Gi, G2, Liy, Lij,/ L 2 y , L 2 X / Lay, and L3j( are the choice variables and Pt i s the price of good Y (determined by the rest of the world) in terms of X i n period t . {t = 1, 2, 3} The above constrained optimisation problem, by proper substitution, can be reduced to the following unconstrained problem: Max {Go"^Fi(Ni - Gi - Liy, T^J + P^  GoP^Hi(Liy, Tiy) } + {Gi"^F2(N2 - G2 - L 2 y , T 2 J + P2 G i P 2 H 2 ( L 2 y , T2y) } + { G 2 " ^ F 3 ( N 3 - L 3 , , T3y) + P 3 G 2 P ^ H 3 ( L 3 y , T 3 y ) } with respect to Gi, Gg, L^ y, L2y, and L3y. The f i r s t order conditions of the above optimisation problem are given below where for s i m p l i c i t y Gq i s assumed to be unity; FiL(Ni-Liy-Gi, TiJ = a 2 G r ' F 2 ( N 2 - L 2 y - G 2 , T 2 J + P2 p2Gp ' 'H2(L2y, T2y) (4) GfF2 ,(N2-L2y-Gi, T 2 J = a3G2°^ -^ F3 (N3-L3y, T3J + P3 P3Gf-%(L3y, T3y) (5) FiL(Ni-Liy-Gi, TiJ = Pi HiL(Liy, T^ ,) (6) Gf-^'F2^{U2-L,^-G„ T 2 J = P2 H 2 , ( L 2 y , T2y) (7) Gf-P3F3L (N3-L3y, T3J = P3 H3,(L3y, T3y) (8) where (. ) : marginal product of labour i n the production of Y i n period t . FtL (. ) : marginal product of labour i n the production of X i n period t, atGt^'^Ft (. ) : marginal product of pure public input i n the production of X i n period t . j3tGf*^ "^ Ht (. ) : marginal product of pure public input i n the production of Y i n period t . The economy described by equations (4) to (8) i s a public input economy.® There are f i v e e f f i c i e n c y conditions [equations (4) to (8)] i n f i v e endogenous variables: G^ , G2, L^ y, Ljy, and L3y. Equations (4) and (5) are the conditions for the optimal provision of public input i n period two, and three respectively. The r i g h t -hand side of these equations i s the present value of marginal ® The term "public input economy" has been used by Abe (1990) . benefits to the f i n a l good producers from an additional unit of public input, whereas the left-hand side i s i t s marginal cost.' Equations (6) to (8) indicate the implications of perfect labour mobility within the private sector i n each period. Equations (4) and (5) i n conjunction with (6) and (7) also demonstrate the implications of perfect labour mobility between the private and public sectors i n the f i r s t and second period: the wage rate i n both sectors i s i d e n t i c a l . I f the firms behave competitively and the government supplies the optimal l e v e l of public input at market wages, the s o c i a l planning optimum, described by equations (4) to (8) above, can be decentralised. The equilibrium can be interpreted as a perfect foresight equilibrium over time. The present study e x p l i c i t l y assumes that the producers of f i n a l goods do not pay for the use of the pure public input. The reward of public input i s captured by the private factors. The government uses a f l a t rate income tax to recover the cost of the public input. Since a l l agents and the government have access to the world credit market, the timing of these taxes does not matter. The government can also use a per-unit output tax to finance the public production but the tax rate must be i d e n t i c a l across industries and time. ' These conditions are si m i l a r to those derived by Kaizuka (1968), and Sandmo (1972) i n a single period s e t t i n g . In the case of an impure public input, the reward of p u b l i c input accrues to the owner of the firm. The government can therefore use a Lindahl p r i c i n g scheme to finance the cost of public production. Under t h i s scheme the price paid by each producer, i n each period, equals the marginal product of p u b l i c input. The Lindahl p r i c i n g scheme i s plausible because by observing the p r o f i t s of the private producers i n each period, the government can determine the benefits of public input to each industry. ^ ° In the next section comparative s t a t i c properties of the model are explored. The r e s u l t s are derived by d i f f e r e n t i a t i n g the equilibrium conditions (4) to (8) with respect to various exogenous variables. °^ The true marginal p r o d u c t i v i t i e s of public input can also be determined by using a mechanism suggested by Groves and Loeb (1975) . 2.4 Comparative Statics The purpose of t h i s section i s to investigate the impact of temporary terms-of-trade changes on the private and p u b l i c sectors. Svensson and Razin (1983) and Marion and Svensson (1984) define a temporary improvement i n the (temporal) terms-of-trade as dPt > 0 for only one t = {1, 2, 3}. The impact of technological improvement i n the production of f i n a l goods i s also considered. The public input and labour are cooperative i n the production of both f i n a l goods. In the present study, the private and public sectors are linked through unrestricted labour mobility i n period one and two. The comparative s t a t i c s r esults presented i n the following are derived under the assumption that = Pt/ which implies that the direc t benefits of the public input to both industries are i d e n t i c a l . This allows one to focus on the role of in d i r e c t benefits of a public input. The impact of terms-of-trade changes i n period one i s discussed i n the following. The res u l t s are derived by using equations (4) to (8), where for algebraic s i m p l i c i t y Gq i s i n i t i a l l y assumed to be unity. 2.4.1 Terms-of-Trade Changes in Period one The following equations describe the impact of a temporary change i n the terms-of-trade (in period one) on the optimal d , G2, Liy/ l'2y, and Lsyi aci/aPi = (. ) Fi,, (. ) [P2H2LL (. ) F2LL ( • ) + (P2-l)G2-^GfF2i,(.) {P2H2LL(.) + F2LL(.)}]/H < 0 (9) 9G2/aPi = a2Gf-^[F2L(.)Fii,L(.) ] [P2H2LL(-) + FJLL ( . ) ]/H > 0 (10) 8Liy/aPi = - [HiL(.)+Fii,L(.)aGi/dPJ/[FiLi,(.)+PiHii,L(.)] > 0 (11) aL2y/aPi = - [F2LL(-)/[F2LL(-)+P2H2LL(-)] [OGz/aPJ < 0 (12) aL3y/aPi = 0 (13) H = bib2 - bab^ > 0^ ^ bi = PiHiLi (.) FILL (.) +(«1-1 ) G-\F (.) [PIHII.L(.)+FILL(.) ] > 0 b2 = P2H2LL ( . ) F2LL ( . ) + («2-1 ) G-SG°^ 2F2L ( • ) [P2H2LL ( • ) +F2LL ( • ) 1 > 0 ba = - ttiG"^-^ F2L(.) [PIHILL(.)+FII.L(.) ] > 0 h , = - ttiG"^-^ F2L(.) [P2H2LL(.)+F2LL(-) ] > 0 Equation (9) shows that an improvement i n the terms-of-trade in period one leads to a decrease i n the production of public input. This result can be explained by using e f f i c i e n c y conditions (4) and (6). According to equation (6), an improvement i n the H i s po s i t i v e because the production functions are assumed to be s t r i c t l y concave. terms-of-trade i n period one increases the wage rate i n the private sector. Due to perfect labour mobility between the private and public sectors, an improvement i n the terms-of-trade leads to labour outflow from the public sector which increases the marginal cost of the public input above i t s marginal benefits i n the second period. According to the e f f i c i e n c y condition (4), the production of public input i n period one must f a l l . Equation (10) shows that an actual improvement i n the period one terms-of-trade results i n an increase i n the output of public input i n period two. This r e s u l t follows from e f f i c i e n c y condition (5). An improvement i n the terms-of-trade i n period two decreases the output of the public input i n period one and therefore decreases i t s marginal cost i n period two [ i . e . , Gf^ FgL (. ) ] below i t s marginal benefits. Therefore, the optimal output of the public input i n the second period must increase. Equation (11) shows that the presence of a public input i n the model strengthens the expected r e s u l t . E q u a t i o n (12) shows that an improvement i n the terms-of-trade i n period one lowers employment i n the production of ¥ 3 . This follows from the fact that an improvement i n the terms-of-trade increases the output of public input, which i s produced by means of labour. Consequently, fewer If the a l l o c a t i o n of resources between the private and public sectors were exogenous, dG^/dP^, and dGz/B^t would be zero for a l l t = {1, 2, 3}. workers w i l l be available for employment i n the private sector. Equation (13) can be explained i n the following way. Public input i s not produced i n period three, therefore a l l workers are available for employment i n the private sector. A change i n the terms-of-trade therefore does not aff e c t employment within the private sector. The impact of terms-of-trade changes i n period one on the output of the private sector i s discussed i n the following: aXi/aPi = ( . ) [HiL ( . ) -PiHiLL ( . ) 5GI/8PJ / [PiHiLL ( • ) +FiLL ( • ) ] ? (14) aYi/8Pi = R ^ ^ i . ) [8Liy/aPJ > 0 (15) ax2/aPi = a2Gf-^F2(.) [aoi/dpi] -Gf [P2H2LL(.)F2L(.)/[P2H2LL(.)+F2LL(-) ] [aG2/aPi] <0 (16) dY^/dPi = p2Gp-'H2(.) [aci/apj + gPh2L(.) [aL2y/aPi] < o (iv) axj/aPi = a3Gf-'F3(.) [aGz/apj > o (is) aYa/aPi = p3Gf-^H3(.) [aG2/aPi] > o (i9) Equation (15) shows that the incorporation of public spending in the production function strengthens the expected r e s u l t : an improvement i n the terms-of-trade i n period one leads to an increase in the production of Y^ . However, i t s e f f e c t on the production of i s ambiguous because the sign of dL^Jd^^ i s ambiguous. If the public input were absent from the model or i f i t were produced by s e c t o r - s p e c i f i c labour, then the sign of equation (14) would be unambiguously negative. But i n the present case the production of public input decreases i n response to an improvement in the terms-of-trade. Labour i s released from the production of public input, but i t i s not clear i f a l l of t h i s labour finds employment in the production of Yi. If i n the new equilibrium a l l the labour released by the public sector i s absorbed i n the production of Yi, then there w i l l be no change i n the production of Equations (16) to (19) show that the impact of an improvement in the terms-of-trade i n period one i s transmitted to periods two and three through i t s e f f e c t on the supply of the public input. According to equations (16) and (17), i t s e f f e c t on production i n the private sector i n period two i s negative whereas equations (18) and (19) indicate that the private sector i n period three benefits. It i s noticeable that i f the public input was not included i n the model then an improvement i n the terms-of-trade i n period one w i l l not a f f e c t the output of the private sector i n periods two and three. An improvement i n the terms-of-trade i n period one leads to a decrease i n the output of the private sector i n period two because i t r esults i n a decrease i n the production of public input i n period one (i . e . , Gi) which i s used by the private sector i n period two. However, i t leads to an increase i n the production of public input i n period two (i. e . , Gj) which i s used by the private sector in period three. This implies that less labour w i l l be available to the private sector i n period two, which reinforces the eff e c t of a decrease i n the supply of public input i n period two. The e f f e c t of an improvement i n the terms-of-trade i n period one on the output of the private sector i n period three i s p o s i t i v e because i t results i n an increase i n the supply of public input without a f f e c t i n g the supply of labour to the private sector. 2.4.2 Terms-of-Trade Changes in Period Two The model developed i n the previous section i s a perfect foresight model. The following equations describe the impact of a change i n the terms-of-trade, i n period two, on the optimal Gi, Gj, Liy/ L2y/ Lay. This change was anticipated i n the beginning of period one: 8Gi/aP2 = -a2Gf-^[FiLL(.)+PlHiLL(.) ] [P2H2LL(.)F2LI,(.)H2 + (a2-l ) Gj'Gf ( . ) { P2H2LL ( . ) +F2LL ( . ) } -GfF2,(.)H2L(.)F2i,L(.) ]/H > 0 (20) aCz/aPj = Gf F2LL ( . ) ( . ) [FILL ( • ) PIHILL ( • ) + G f - ^ { FILL ( • ) +PIHILL ( • ) ) [ («i"! ) F^ L ( • ) " aiGriF2L(.)H2(.) {P2H2:,I,(.)+F2LL(.) }]/H < 0 (21) aLiy/aP2 = - {FILJ,(.)/[FII,:,(.)+PIHILL(.) ] }{9Gi/aP2} < 0 (22) aL2y/aP2 = -[H2L(.)+F2LL(.)5G2/8P2]/[F2LL(.)+P2H2I,L(.) ] > 0 (23) aL3y/aP2 = 0 (24) Equations (20) and (21) indicate that an anticipated improvement i n the terms-of-trade i n period two increases the production of public input i n period one, but i t results in a decrease i n the production of public input i n period two. An anticipated improvement i n the terms-of-trade i n period two increases the anticipated marginal cost of the production of public input i n period two ( i . e . , G2) above the present value of i t s marginal benefits i n period three. The optimal production of public input i n period two therefore decreases. This however increases the marginal benefits of the public input supplied i n period two (i . e . , Gi) above i t s marginal i n period one. An anticipated improvement i n the terms-of-trade i n period two therefore leads to a increase i n the production of public input i n period one. An anticipated improvement i n the period two terms-of-trade also a f f e c t s the demand for labour i n the production of f i n a l goods i n periods one and two. Equation (22) shows that the demand for labour i n the production of decreases, whereas the demand for labour i n the production of Y2 increases {see equation (23)}. Equation (24) shows that the demand for labour i n the production of X 3 and Y 3 i s unaffected by anticipated changes i n the terms-of-trade in period two. The following discussion pertains to the impact of an anticipated improvement i n the terms-of-trade i n period two on production by the private sector: a X i / a P 2 = -[FIL(.)PIHILL(-) ]/[PIHILL(.)+FILL(-) ] [ a G i / 8 P 2 ] < 0 (25) aYi / a P 2 = HIL(.) [BL^y/B^z] < 0 (26) aX2/aP2 = F 2 L ( . ) { [H2L ( . ) - P 2 H 2 L L ( . ) aG2/aP2] / [PZHZLL ( . ) +F2LL ( • ) ] > + [ a 2 G f - ^ F 2 ( . ) ] [ d G i / a P z ] ? (27) aY2/aP2 = [gPh2L(.)] [ a L 2 y / a P 2 ] + [p2Gp - 'H2(.)] [aGi/ a P 2 ] > o (28) ax3/aP2 = a 3 G f - ^ F 3 ( . ) [ a G 2 / a P 2 ] < o ( 2 9 ) aY3/aP2 = p3Gf - ' H 3 ( . ) [ a G 2 / a P 2 ] < 0 o o According to equations (25), (26), (29), and (30), an anticipated improvement in the terms-of-trade i n period two leads to a decrease i n the output of both f i n a l goods i n period one and period three. The eff e c t on the output of i s ambiguous whereas the output of Y2 increases. 2.4.3 Terms-of-Trade Changes in Period Three The following equations describe the impact of an improvement in the terms-of-trade, i n period three, on the optimal G^ , Gg, L^ y, L2y, and Lay. This improvement was anticipated i n the beginning of period one: aGi/8P3 = [-a2a3G2"'-'Gf-^ F2L ( . ) H3 ( . ) ] [P2H2L1, ( . ) +F2LL ( • ) ] [PIHILL(.)+FILL(-) ]/H < 0 (31) aG2/9P3 = { [ -a3G2"'-^ H3 ( . ) ] [P2H2LL ( . ) +F2LL ( • ) ] [ (ai-l)Gr^FiL(.) ] [PIHILL(.)+FILL(-) ] }/H > 0 (32) aLiy/aP3 = - {FiLL(.)/[FiLi,(.)+PiHi:,L(.)]}{aGi/aP3} > o (33) 8L2y/aP3 = - {F2LL(.)/[F2l,L(.)+P2H2LL(.)]}OG2/aP3} < 0 (34) 9L3y/aP3 = - {H3L(.)/[F3LL(.)+P3H3LL(.) ] } > 0 (35) Equation (3'^ ) shows that an anticipated improvement i n the terms-of-trade, in period three, leads to a increase i n the public input produced i n period two. This result can be explained by using equation (5) which shows that an anticipated improvement i n the terms-of-trade i n period three d i r e c t l y increases the marginal benefits of public input above i t s marginal cost. Consequently, the output of public input i n period two ( i . e . , G2) increases. An anticipated increase i n the production of public input i n period two leads to a decrease i n the marginal benefits of the public input produced i n period one below i t s marginal cost [see the right-hand side of equation (4)] . The output of the public input i n period one ( i . e . , Gi) therefore decreases. Equation (33) shows that an anticipated improvement i n the terms-of-trade i n period one, due to i t s negative e f f e c t on the optimal G i , leads to an increase i n labour employed i n the production of Y^ . On the other hand, the employment of labour i n the production of Y2 decreases, as indicated by equation (34) . Equation (35) i s independent of the supply of public input; i t shows that the demand for labour i n the production of Y3 increases, which i s not surprising. The impact on private sector production of an anticipated improvement i n the terms-of-trade i n period three i s discussed i n the following; axi/aP3 = -{FIL(.)PIHII,L(.)/[PIHILL(-)+FUL(.)]}{aGi/aP3} > 0 (36) 8YI/8P3 = Hii,(.) [dL^JdP,] > 0 (37) aXj/aPa = -[GfF2(.) ] {F2L(.)P2H2I,L/[P2H2LL(-)+F2LL(-) ] }{8G2/aP3} + [aiGf-^F2(.) ] [aCi/aPs] < 0 (38) aY2/aP3 = [gPh2L(.)] [aL2y/aP3] + [p2Gp-'H2(.)] [aGi/aP3] < o (39) ax3/aP3 = [a3G2"^ -^ F3(.)] [aG2/aP3] - [G2"'f3L(.)i [aL3y/aP3] ? (40) aY3/aP3 = [p3Gf^-%(.)] [aG2/aP3] + [Gi'E,^(.)][dh^^/dp,] > o (4i) Equations (36) and (37) indicate that an anticipated improvement i n the (temporal) terms-of-trade i n period three results i n an increase i n the output of both f i n a l goods produced i n period one. On the other hand, equations (38) and (39) indicate that the output of both f i n a l goods i n the second period decreases. The above results depend e n t i r e l y on the response of the public sector, i . e . , the sign of dG^/dP^, Equation (40) shows that the presence of a public input i n the model strengthens the expected res u l t , whereas the impact on the output of X3 i s ambiguous. The results presented i n t h i s section c l e a r l y indicate the importance of the timing of terms-of-trade changes. These results also demonstrate the important role played by lags in the production and supply of public inputs. The public and private sectors are linked through unrestricted labour mobility. In other words, the a l l o c a t i o n of resources between the two sectors i s endogenous. Accordingly, terms-of-trade changes influence the private sector d i r e c t l y , as well as i n d i r e c t l y through t h e i r impact on the supply of public input. The purpose of using a three period model i s to s p e l l out the transmission of terms-of-trade changes from one period to another. The pattern which emerges i s the following. In an n-period setting, i t can be shown that the sign of 8Gt/3Pi w i l l be negative for t = 1, 3, 5, 7, ... and p o s i t i v e for other values of t . The e f f e c t on the output of w i l l be ambiguous whereas the output of w i l l increase. The output of both f i n a l goods w i l l decrease (increase) for t = 2, 4, 6, (t = 3, 5, 7, . . . ) . As indicated e a r l i e r , the framework of the present study also allows one to examine the impact of domestic shocks on the output of private and public sectors. An example of such shocks i s exogenous technological progress i n the private sector. The impact of exogenous technological progress on the output of public sector i s discussed i n the following section. The results derived i n the next section indicate that technological progress i n the production of either good i n either period has implications for the supply of the public input. In the case of an impure public input, the reward of the public input i s captured by the owner of the firm. The timing of technological progress therefore has implications for the p r o f i t s of firms. 2.4.4 Technological Progress in the Production of Final Goods The impact of exogenous technological progress (in the production of f i n a l goods) on the production of public input i s discussed below, where k = x and y 8Gi/dYik > 0 (42) 8G2/dYik < 0 (43) 5Gi/d72k < 0 (44) 8G2/dY2k > 0 (45) aCi/dYsk > 0 (46) 3G2/dY3k < 0 (47) Equation (42) and (43) respectively indicate that, due to perfect labour mobility within the private sector, exogenous technological progress i n the production of either or (or both) increases the production of public input i n period one but, decreases the production of public input i n period two. The explanation for t h i s r e s u l t i s simple: exogenous technological progress i n the private sector reduces the marginal cost of public input below i t s marginal benefits i n the second period, so i t i s appropriate to produce more public input i n period one. Similar reasoning applies to other r e s u l t s presented i n t h i s section. Equations (44) and (45) indicate that anticipated technological progress i n period two decreases (increases) the output of public input i n period one (two). Whereas equations (4 6) and (47) demonstrate that anticipated technological progress i n period three increases (decreases) the output of public input i n period one (two). Due to a lag i n the production and supply of public input, the eff e c t of technological improvement i n either period i s transmitted to the other periods. It can be shown that technological improvement i n the production of either or both f i n a l goods i n period one increases (decreases) the output of both f i n a l goods i n period two (three). Also, anticipated technological improvement i n the production of either or both f i n a l goods i n period two increases the output of both f i n a l goods i n periods one and three. F i n a l l y , anticipated technological improvement i n the production of either or both f i n a l goods i n period three decreases (increases) the output of both f i n a l goods i n period one (two). The results derived so far depend on the assumption that a l l resources are f u l l y u t i l i s e d i n the small open economy under consideration. However, s i g n i f i c a n t labour unemployment exists i n most rea l economies. In the next section, the f u l l employment assumption i s relaxed. 2.5 Terms-of-Trade Changes in an Underemployed Economy The model developed i n section 2.3 i s based on the assumption that labour i s f u l l y u t i l i s e d i n each period. However, s i g n i f i c a n t unemployment i s often present i n re a l economies. The purpose of t h i s section i s to re-examine the results presented i n section 2.4 when labour i s not f u l l y u t i l i s e d . Labour unemployment i n the present study i s assumed to be due to economy wide r i g i d wages i n period one. Several alternative reasons can be found for downward r e a l wage r i g i d i t y : the re a l wage may be indexed i n s t i t u t i o n a l l y ; the e f f i c i e n c y wage theory, as expounded by Shapiro and S t i g l i t z (1984), Wiess (1980) and Yellen (1984) provides a mechanism whereby the real wage becomes downward r i g i d . This assumption i s often adopted i n the l i t e r a t u r e on international trade, see Bhagwati and Srinivasan (1983), Itoh and Negishi (1989) for an elegant survey. One can also appeal to the idea of "Surplus Labour" developed by Lewis (1954) to explain unemployment i n period one. The present study does not attempt to explain why wages are r i g i d . The focus of the present study i s on the outcomes when unemployment i s present. Due to the r i g i d i t y of the re a l wage rate i n period one, labour cannot be f u l l y u t i l i s e d and therefore the a l l o c a t i o n of resources cannot be optimal. A competitive equilibrium can be characterised by the following conditions: ^1 = a^Gf^-^Fz ( N 2 - L 2 y - G 2 , T 2 J + P 2 p 2 G p - % ( L 2 y , T2y) (48) G f F 2 L ( N 2 - L 2 y - G i , T 2 , ) = a3G2"^ -^ F3 ( N 3 - L 3 y , T3,) + P 3 p 3 G f - ^ H 2 (L3y, T3y) (4 9) «^FiL(Lie-Liy-Gi, TiJ = % (50) PPH , , (Liy, Tiy) = (51) G r P 2 F 2 L ( N 2 - L 2 y - G 2 , T 2 J = P 2 H 2 L ( L 2 y , T2y) (52) G2"^-P^F3,(N3-L3y, T3,) = P 3 H 3 , ( L 3 y , T3y) (53) Where ^ 1 : i n s t i t u t i o n a l l y f i x e d minimum wage rate i n period one. Lie = + Liy + L i j , : labour employed i n period one. Equations (48) to (53) are six equations i n six endogenous variables; G i , G 2 / L^e/ L^y, L 2 y , and Lsy. Equation (48), i n conjunction with other conditions, determines the equilibrium Gi i n the presence of unemployment i n period one. The left-hand side of th i s equation, W^ , i s the marginal cost of public input i n period one. Inefficiency i n the present formulation arises from the fact that the wage rate i n period one, ^ i , i s fixed above i t s market clearing value. Equilibrium conditions (48) to (53) can be used to derive the impact of terms-of-trade changes on the public and private sectors of an underemployed economy 8GI/8PI = 0 (54) aCa/aPi = 0 (55) aYt /aPi = 0 for t = {2, 3} (56) aXt/aPi = 0 for t = {1, 2, 3} (57) aYi/aPt = 0 for t = {2, 3} (58) aXi/aPt = 0 for t = {2, 3} (59) Equation (54) shows that an improvement i n the terms-of-trade i n period one does not influence the production of the public input, Gi, i n period one. This implies that terms-of-trade changes Some comparative s t a t i c r esults presented i n section four are not affected by the presence of unemployment i n period one. These re s u l t s are not included i n t h i s section. i n period one w i l l not be transmitted to periods two and three, see equations (55) to (57). An improvement i n the terms of trade leads to an increase i n demand for labour i n the production of Y^ . However, the wage rate i n period one i s r i g i d ; there i s no outflow of labour from the public sector. The public sector i s therefore insulated from terms-of-trade changes i n period one. Additional workers are hired from the e x i s t i n g pool of unemployed workers. The output of Xi also does not depend on P^ , which i s a standard result under r e a l wage r i g i d i t y . Equations (58) and (59) also indicate that anticipated terms-of-trade changes i n the second and the t h i r d periods have no influence on the output of the private sector i n period one. An anticipated improvement i n the terms-of-trade i n period two leads to an increase i n the production of public input i n period one. However, additional workers required i n the public sector can be hired from the ex i s t i n g pool of unemployed. Consequently, the output of the private sector i s not affected. Similar reasoning applies to the resu l t given by equation (59). In most r e a l economies, unions often demand an increase in the re a l wage. The implications of such a p o l i c y change are discussed in the following: aCi/ a^i < 0 (60) BGa/B^i > 0 (61) aYi/aiATi < 0 (62) aYz/a^i < 0 (63) dX^/d^^ < 0 for t = {1, 2} (64) dY^/d^^ > 0 (65) dX^/d^^ > 0 (66) Equations (60) and (61) respectively indicate that an increase in the minimum wage, i n period one, decreases the production of public input i n period one, but increases the production of public input i n period two. An increase i n the minimum wage also a f f e c t s the output of both f i n a l goods i n each period: the output of f i n a l goods i n period two (three) decreases (increases) . An increase i n the minimum wage rate increases the marginal cost of the public input produced i n period one, which explains the results presented i n t h i s section. 2.6 Concluding Remarks The present study develops a three-period perfect foresight model of a small open economy. The model i s used to demonstrates that terms-of-trade changes i n either period a f f e c t both private and public sectors of an economy, i n that period, and lags i n the production and supply of a public input transmit these effects to the other periods. The economy under consideration produces two f i n a l goods by means of a public input, labour and other fixed factors. The public input i s produced by means of labour which i s f u l l y mobile between the private and public sectors. The a l l o c a t i o n of resources between the private and public sectors i s therefore endogenous. The public input produced i n period t i s made available to the f i n a l good producers i n period t+1. In other words, lags i n the production and supply of public inputs are e x p l i c i t l y taken into account. The model i s used to investigate the impact of terms-of-trade changes, i n either period, on the private and public sectors. The resu l t s presented i n section four demonstrate the important r o l e played by the timing of a change i n the terms-of-trade. It has been shown that an improvement i n the terms-of-trade i n period one leads to a decrease (increase) i n the production of public input i n period one (two). On the other hand, an anticipated improvement i n the terms-of-trade i n period two leads to a increase (decrease) i n the production of public input i n period one (two) . F i n a l l y , an anticipated improvement i n the terms-of-trade i n period three leads to a decrease (increase) i n the production of public input i n period one (two). Due to a lag i n the production and supply of public input, the ef f e c t of terms-of-trade changes i n either period i s transmitted to the other periods. An improvement i n the terms-of-trade i n period one results i n a decrease (increase) i n the production of both f i n a l goods i n period two (three). On the other hand, an anticipated improvement i n the terms-of-trade i n period two res u l t s in a decrease i n the production of both f i n a l goods i n period one and three. F i n a l l y , an anticipated improvement i n the terms-of-trade i n period three r e s u l t s i n an increase (decrease) i n the production of both f i n a l goods i n period one (two). The presence of labour unemployment i n period one, due to economy wide r i g i d wages, breaks the intertemporal production l i n k s . A change i n the terms-of-trade i n period one does not change the production of public input i n either period. It therefore does not influence the production of f i n a l goods i n the second and t h i r d period. In addition, anticipated changes i n the terms-of-trade i n period two and period three do not influence the production of f i n a l goods i n period one. The impact of a change i n the minimum wage rate i s also considered: i t has been shown that a small decrease i n the minimum wage leads to an increase (decrease) i n the production of public input i n period one (two). Consequently, the production of both f i n a l goods in period two (three) increases (decreases). The model can be extended further to include uncertainty about the future provision of the public input and the future terms of trade. CHAPTER 3 GOVERNMENT SPENDING ON INDUSTRIES, INTERNATIONAL FACTOR MOBILITY, AND POLICY COORDINATION 3.1 Introduction In a l l rea l economies, governments spend large sums on services provided to households and industries i n a l l rea l economies. A change i n government spending i n a large open economy, l i k e the United States or Japan, affects not only the domestic economy but also the economies of trading partners. Concerns of a similar nature led to the formation of the so c a l l e d G-7 (group of seven), an important objective of which i s to coordinate monetary and f i s c a l p o l i c i e s . Frenkel and Razin (1986a, 1986b, 1987), Svensson (1987), Devereux (1988), and Durlauf and Staiger (1990), among others, have discussed the international (indirect) s p i l l o v e r s of government spending i n an economy. However, these and most other relevant studies do not consider government spending on industries.^ In addition, these studies have not investigated the implications of p o t e n t i a l international economic p o l i c y coordination. The idea of international f i s c a l coordination has not received much attention i n the t h e o r e t i c a l l i t e r a t u r e . Kehoe (1987, 1989) i s concerned with government spending on households only. Using a Cobb-Douglas s p e c i f i c a t i o n f o r the u t i l i t y function, Kehoe (1987) argues that i n a world economy i n which a l l countries are small, equilibrium under international f i s c a l cooperation may not coincide with the non-cooperative equilibrium. Kehoe (1989) presents a counter-example to the b e l i e f that f i s c a l cooperation among benevolent governments i s desirable. His r e s u l t i s p a r t l y driven by the time inconsistency problem. Using a logarithmic s p e c i f i c a t i o n of the u t i l i t y and Cobb-Douglas production functions, Devereux and Mansoorian (1989) argue that the gains from international f i s c a l coordination may e n t a i l higher growth rates for the countries involved. In Anwar (1992), I have considered government spending on what Meade (1952) described as "atmosphere e x t e r n a l i t i e s " . This spending ^ The importance of t h i s i s examined by Abe (1990), Manning and McMillan (1979), and McMillan (1978), who suggest that government spending on industries can influence the d i r e c t i o n of international trade. i s incorporated into a one-good, two-country, and two-factor general equilibrium model i n the form of a pure public input. The public input i s available to a l l firms i n the industry. Under competitive conditions, each country produces an i d e n t i c a l consumption good by means of labour, c a p i t a l , and a non-traded pure public input. The two countries are linked through international factor mobility: i n the short-run, only one private factor i s f u l l y mobile across international boundaries; whereas i n the long-run, both private factors are f u l l y mobile. In addition, both factors are f u l l y u t i l i s e d i n the short-run and the long-run. International transmission of government spending on a pure public input and pol i c y coordination are examined i n the short-run and the long-run. In the short-run, an increase i n the supply of public input i n either country increases the reward of the f u l l y mobile factor. On the other hand, i n the long-run, the impact of an increase i n the supply of public input i n eithe r country on the equilibrium wage rate and the rate of return on c a p i t a l depends on the r e l a t i v e c a p i t a l i n t e n s i t y . In the short-run non-cooperative solution, a country which exports the mobile factor spends too much on i t s industries from the point of view of the i t s trading partner. Whereas, i n the long-run non-cooperative solution, both countries spend too much ( l i t t l e ) on t h e i r industries from the point of view of each other, i f the c a p i t a l (labour) intensive country exports c a p i t a l . On the other hand, i n the short-run cooperative solution, a country which exports the mobile factor spends too l i t t l e on i t s industries from the point of view of i t s residents. Whereas, i n the long-run cooperative solution, both countries spend too l i t t l e (much) on t h e i r industries from the point of view of t h e i r residents, i f the c a p i t a l (labour) intensive country exports c a p i t a l . This study extends my e a r l i e r work in the following di r e c t i o n s : (1) international transmission of government spending on industries i n the presence of labour unemployment i s considered; (2) a three-country model i s developed at the end of the essay which allows an investigation of international transmission of government spending when two countries have formed an economic union. The present study extends and generalises the r e s u l t s derived i n my previous study [Anwar (1992)] . The present study incorporates a pure public input into a two-country, one-good, two-factor general equilibrium model. Under competitive conditions, each country produces an i d e n t i c a l consumption good by means of labour, c a p i t a l , and a pure public input. The public input i n each country i s provided free of charge by the government. Both governments use an income tax to finance the cost of public production. The two countries are linked through international factor mobility. This study focuses on the implications of public inputs across international boundaries. The public inputs do not s p i l l o v e r d i r e c t l y , but because of t h e i r implications for r e l a t i v e p r i c e s , there are impacts on countries which have integrated economies. These impacts are examined under the following alternative assumptions regarding factor mobility and labour employment: (1) c a p i t a l i s f u l l y mobile across international boundaries but labour mobility i s r e s t r i c t e d , while labour i s not f u l l y employed i n one country due to r i g i d wages; (2) both private factors, i . e . , labour and c a p i t a l , are f u l l y mobile across international boundaries and a l l factors are f u l l y employed. These two cases can be interpreted as the short-run and the long-run respectively.^ The model developed i n the next section i s also used to compare the coordinated p o l i c y outcome to the uncoordinated one. In the short-run, the supply of the public input i n a country where wages are f u l l y f l e x i b l e does not influence the equilibrium rate of return on c a p i t a l , which i s f u l l y mobile across international boundaries. On the other hand, the supply of public input i n a country where wages are r i g i d can influence the equilibrium rate of return on c a p i t a l . The supply of public input i n a country which does not f u l l y u t i l i s e labour can also influence the equilibrium wage rate i n the country which f u l l y u t i l i s e s i t s labour. Consequently, i n the absence of international p o l i c y ^ The long-run model i s i d e n t i c a l to the one presented i n Anwar (1992). However, the present version e x p l i c i t l y considers the existence and s t a b i l i t y of the i n t e r i o r solution. coordination, a country which exports (imports) c a p i t a l and where wages are r i g i d spends too much ( l i t t l e ) on i t s industries from the point of view of the other country where wages are f u l l y f l e x i b l e . On the other hand, in the absence of international p o l i c y coordination, a country which does not f u l l y u t i l i s e labour spends too much on i t s industries from the point of view of the country which f u l l y u t i l i s e s i t s labour ir r e s p e c t i v e of the di r e c t i o n of international c a p i t a l mobility. In the long-run, the supply of public input i n both countries determines a l l factor p r i c e s . A r e l a t i v e l y c a p i t a l (labour) intensive country can increase the equilibrium rate of return on c a p i t a l (labour) by increasing i t s supply of public input. In the absence of international p o l i c y coordination, each country spends too much on i t s industries from the point of view of the other country, i f the production technologies are such that the c a p i t a l (labour) intensive country exports c a p i t a l (labour). On the other hand, under international p o l i c y coordination both countries spend too l i t t l e on t h e i r industries from the point of view of t h e i r residents, i f the c a p i t a l (labour) intensive country exports c a p i t a l (labour). The model i s further extended to include a t h i r d country c a l l e d the rest of the world. A three-country model allows an investigation of international transmission of government spending on industries when two countries have formed an economic union. Capital i s f u l l y mobile across international boundaries, including the rest of the world. On the other hand, international labour mobility i s r e s t r i c t e d : labour i s f u l l y mobile between the other two countries only. The other two countries can therefore be considered as members of an economic union, such as the European Economic Community. A l l resources are f u l l y u t i l i s e d i n each country. It i s shown that despite free international c a p i t a l mobility and f u l l u t i l i s a t i o n of resources, the supply of the public input i n the rest of the world does not influence the equilibrium rate of return on c a p i t a l . In addition, the supply of public input i n the rest of the world does not influence the equilibrium wage rate i n the economic union. The rest of the world therefore cannot influence the consumption of the members of the economic union through i t s supply of public input. On the other hand, the supply of public inputs i n the economic union can influence the equilibrium rate of return on c a p i t a l and the wage rate i n the rest of the world. Policy coordination within the economic union i s therefore desirable i n order to exploit the rest of the world. The essay i s organised as follows. The next section develops a simple two-country, two-sector general equilibrium model with a pure public input and international c a p i t a l mobility. Due to economy wide r i g i d wages, labour i s not f u l l y u t i l i s e d i n one country. International transmission of economic p o l i c y and the implications of p o t e n t i a l international p o l i c y coordination in the short-run are explored i n section three. A long-run model i s developed i n section four, where both private factors are f u l l y mobile across international boundaries and there i s no unemployment. In the f i f t h section, international transmission of economic po l i c y and the ramifications of international economic pol i c y coordination are examined i n the long-run. A three-country model i s developed i n section six, where two countries have formed an economic union. The model i s used to re-investigate the international transmission of government spending on industries. The l a s t section contains concluding remarks. 3.2 A Short-Run Model The purpose of t h i s section i s to develop a simple two-country model which allows an investigation of international transmission of government spending on public inputs. There are no international s p i l l o v e r s of public inputs d i r e c t l y , but because of t h e i r implications for factor prices, a change i n the supply of a public input i n either country can influence the consumption of both countries. The two countries under consideration are home and the foreign countries.^ Each country produces a f i n a l good by means of a pure public input (G) , c a p i t a l , and labour. A l l inputs are ess e n t i a l i n the production of the relevant goods. The pure public input i s provided free of charge by the government of each country. A widely c i t e d {see for instance, Laffont (1975), Negishi (1973), and Sandmo (1972)} example of such pure public input i s government financed applied s c i e n t i f i c research whereby information on new production techniques i s made available to a l l firms simultaneously. Each country has a f i x e d endowment of private factors, i . e . , c a p i t a l and labour. Capital i s f u l l y mobile across international boundaries. On the other hand, there are b a r r i e r s to free ^ Throughout the paper, the foreign variables w i l l be distinguished by an asterisk (*). international labour mobility. S i g n i f i c a n t labour unemployment exists i n many real economies. In addition, international rates of labour unemployment d i f f e r considerably. Unemployment i n most open economy studies i s assumed to be due to r i g i d wages, Bhagwati (1883) and Batra and Beladi (1990) for example. The countries under consideration (in the short-run) are therefore assumed to be asymmetric: wages are f u l l y f l e x i b l e i n the foreign country, whereas wages are r i g i d i n the home country. Consequently, home labour i s not f u l l y u t i l i s e d . In other words, the home country i s a labour surplus economy. Batra and Beladi (1990) have considered the pattern of trade between two asymmetric economies. The f i n a l good i s the numéraire and public input i s also measured i n i t s units. Since the public input i s measured i n the units of the f i n a l good, the marginal rate of transformation between the two i s constant. Public production i s financed by means of a f l a t rate tax on domestic income. The government receives taxes i n terms of the numéraire good which are converted into a pure public input without additional cost: these are assumptions widely used i n the e x i s t i n g l i t e r a t u r e , see Barro (1990) and Devereux and Mansoorian (1989) for instance.'' In the case of a pure public input, the p o s s i b i l i t y of * This i s e s s e n t i a l l y a simplifying assumption. The results presented i n t h i s essay continue to hold even i f the public input i s produced by means of ( f u l l y mobile) primary factors. congestion i n use does not ar i s e . Constant returns to scale therefore has a very d i f f e r e n t meaning. Following Meade ( 1 9 5 2 ) , many authors {for example, Negishi ( 1 9 7 3 ) , Manning and McMillan ( 1 9 8 2 ) } have indicated that the appropriate d e f i n i t i o n of constant returns to scale i s a production technology l i n e a r l y homogeneous i n the private factors of production alone. Consequently, the f i n a l good production function exhibits increasing returns to scale as a whole. If for a given l e v e l of pure public input, the f i n a l good technology i s homogeneous of degree one i n private inputs then there i s no economic p r o f i t under competitive conditions because the entire output i s exhausted by payments to the private factors. In other words, the reward for the pure public input (which i s supplied free of charge by the government) i s appropriated by the private factors of production. The production functions for the f i n a l good for the home and the foreign countries are given below: Y = G" F (Ky, Ly) ; 1 > a > 0 Y = GP F (Ky, Ly) ; 1 > p > 0 where a and P are constants. G: supply of pure public input in the home country. Ky: c a p i t a l used i n the production of the f i n a l good i n the home country. Ly: labour used i n the production of the f i n a l good in the home country, The functional form of the above production technologies implies that the public input i s cooperative with private inputs i n the production of Y and R and there are diminishing returns with respect to the public input. Competitive firms i n both countries take the supply of public input as given. F(.) and F(.) are l i n e a r l y homogeneous with respect to the relevant inputs. The production functions for the home and the foreign country described above are therefore the industry production functions. There are economies of scale i n the present case but these economies are external to both the firm and the industry. Due to the Marshallian nature of economies of scale the market structure i s assumed to be competitive. An increase i n the supply of the public input i n the present study can also be interpreted as an improvement i n the respective production techniques. However, such a technological improvement can be achieved only by an increase i n the relevant tax rate. In other words, technological progress i s endogenous. The relevant cost functions for the home and the foreign countries are derived below: Y C(r, wJ/G" = Min [w^ Ly + rK^ : Y = G" F (Ky, Ly) ] with respect to Ly, and Ky. Y C(r, w)/GP = Min [wLy + rKy : Y = G^ F (Ky, Ly) ] with respect to Ly, and Ky. where w^ : minimum wage rate i n the home country. r: rate of return on c a p i t a l i n the home and foreign country. C(r, WQ)/G": home country's unit cost function for the f i n a l good. Due to unrestricted international c a p i t a l mobility, the rate of return on c a p i t a l i n the two countries i s i d e n t i c a l . The zero p r o f i t conditions for the home and the foreign country respectively are given below: C(r, wj / G « = 1 (1) C(r, W)/GP = 1 (2) For a given supply of the pure public input, the above zero p r o f i t conditions determine the equilibrium factor prices independent of factor market clearing conditions. However, in a f u l l equilibrium, only those values of G and G are considered for which the economy's minimum wage constraint i s binding. The factor market cl e a r i n g conditions given below ac t u a l l y determine the output of the f i n a l good i n the two countries and labour employment in the home country: + K3 = y {C,(r, wJ/G"} + Y {C,(r, w)/G^} (3) L = Y {C„(r, wJ/G«} (4) N3 = Y {C„(r, W)/GP} (5) where Kg: c a p i t a l endowment of the home country. L: labour employed i n the home country. N^ : labour supply i n the foreign country. C r ( . ) / G " : c a p i t a l requirement per unit of Y i n the home country. C „ ( . ) / G " : labour requirement per unit of Y i n the home country. Equation (3) i s the international c a p i t a l market c l e a r i n g condition. Equation (4) i n conjunction with other equations determines the labour employment i n the home country. Whereas, equation (5) determines the labour market cl e a r i n g wage rate i n the foreign country. (1) and (2) are equations i n two endogenous variables, r and w. Once _ie optimal r and w are determined the output of f i n a l good in the two countries and labour employment i n the home country can be determined from equations (3) to (5). Clearly, the optimal r and w are influenced by the supply of the public input in both countries. This completes the discussion of the production side of the model. Because both countries produce an i d e n t i c a l f i n a l good (which i s also the numéraire), supply determines demand in the present model.^ The net consumption of the home and the foreign country (c and c respectively) i s given below, where gross national product i s used as the tax base: c = [rKe + WoL] - G (6) c [rKe + wNJ G (7) The government i n each country determines the l e v e l of public input. In other words, each government acts as a monopolist i n i t s provision of public input within national boundaries. The provision of public input by the two governments can be modelled as a standard two person game where the following solutions can be adopted: (1) a non-cooperative solution where each government passively observes the other and takes i t s supply of public input as given, then determines i t s own supply; (2) a cooperative solution which involves international economic p o l i c y coordination. ^ In other words, Walras' law ensures that the market for consumption goods clears i n both countries. The supply of public input i n the home and the foreign countries (i.e . , G and G respectively) enter as parameters i n the reduced form solutions of r and w. Consequently, a change in the supply of public input i n either country influences the relevant variables and hence the net consumption of both countries. In the present study, the e f f e c t s of a change in the supply of p u b l i c input i n one country are transmitted to another through international factor mobility. These ef f e c t s and the p o s s i b i l i t y of international economic p o l i c y coordination are examined in the next section. The public input i n the present study can also be considered as a l o c a l public (intermediate) good. In such a case, the model l a i d out i n t h i s section describes two regions i n a closed economy where c a p i t a l i s f u l l y mobile between the two regions but labour mobility i s r e s t r i c t e d . Also, the earnings of the mobile factors are repatriated. Each region i s managed by a separate government which provides a pure public input for use within i t s own j u r i s d i c t i o n . ^ The r e s u l t s presented i n t h i s essay can e a s i l y be reinterpreted. ^ See Mera (1973) for an empirical investigation of the role of infrastructure investment i n r a i s i n g the income l e v e l of various regions i n Japan. 3.3 Transmission of Economie Policy and International Coordination in the Short-Run The purpose of t h i s section i s to demonstrate that due to i t s implications for factor prices, a very small change i n the provision of public input i n either country can s i g n i f i c a n t l y influence the welfare l e v e l of i t s trading partner. Accordingly, there i s a need for international economic po l i c y coordination. In the rest of t h i s section, the implications of such coordination are analysed by means of a comparative s t a t i c exercise. The countries considered i n t h i s section are asymmetric: wages are r i g i d i n the home country, whereas wages are f u l l y f l e x i b l e i n the foreign country. The impact of a small change i n the provision of public input i n e i t h e r country on the optimal r and w i s considered below. These results are derived by d i f f e r e n t i a t i n g equations (1) and (2): dr/dG = aG"-VC^(.) > 0 (8) dr/dG = 0 (9) hl/dG = - [C^(.)/C„(.) ] [ar/ac] < 0 (10) aw/dG = pG^-VC„(.) > 0 (11) Equation (8) shows that a small increase i n the supply of public input i n the home country increases the equilibrium rate of return on the in t e r n a t i o n a l l y mobile factor, c a p i t a l . Whereas, a small increase i n the supply of public input i n the foreign country does not influence the equilibrium rate of return on c a p i t a l , see equation (9) . These results can be explained by means of equations (1) and (2) : for a given G, wage r i g i d i t y implies that the equilibrium rate of return on c a p i t a l does not depend on the supply of public input i n the foreign country. In other words, the equilibrium international rate of return on c a p i t a l coincides with the home country's pr e - c a p i t a l mobility rate. Equation (10) shows that a small increase i n the supply of public input i n the home country, through i t s impact on c a p i t a l mobility, decreases the equilibrium wage rate i n the foreign country. This re s u l t follows from equation (8): an increase in the supply of public input i n the home country increases the equilibrium rate of return on c a p i t a l i n the home country. Capital moves from the foreign country to the home country to take advantage of the higher rate of return. This leads to a situ a t i o n where there are too many workers per-unit of c a p i t a l i n the foreign country. The equilibrium wage rate i n the foreign country therefore f a l l s . On the other hand, equation (11) shows that a small increase i n the supply of public input i n the foreign country increases i t s equilibrium wage rate because such an increase d i r e c t l y increases the marginal productivity of foreign labour. Equations (4) and (5) can be used to eliminate Y and Y from equation (3). The r e s u l t i n g equation i s given below: Ke + Ke = L {C,(r, wJ/C„(r, wJ } + {C,(r, w)/C„(r, w) } In the following, the above equation i s used to determine the impact of a change i n the supply of public input on labour employment i n the home country. dh/dG > 0 (12) dh/dG = - [NJC\ ( . ) ] [C„ ( . ) /C^ (. ) ] [C^ ( . ) C„^ (. ) - C„(.)C„„(.) ] [dw/dG] < 0 (13) Equation (12) shows that the supply of public input i n the home country i s p o s i t i v e l y related to labour employment. This resu l t follows from the i m p l i c i t assumption that labour and the public input are cooperative i n the production of f i n a l good. On the other hand, equation (13) shows that an increase i n the supply of public input i n the foreign country, where labour i s f u l l y employed, decreases labour employment i n the home country due to i t s negative impact on the equilibrium wage rate. In a Cournot-Nash equilibrium ( i . e . , i n the absence of international economic p o l i c y coordination), each country takes the supply of public input i n the other country as given and determines i t s own supply such that the net consumption of i t s residents i s maximised. The following equations, which are derived by using equations (6), (7), and (9), determine the optimal supply of public input i n the home country and the foreign country respectively: Kg [Br/dG] + Wo [BL/BG] = 1 Ne OW /3G} = 1 The right hand side of the above equations i s the marginal cost of the provision of public input to tax payers whereas the l e f t hand side i s the net marginal benefit to the owners of the private factors.^ Clearly, the above rules ignore the in d i r e c t s p i l l o v e r s of public input across international boundaries due to international c a p i t a l mobility. The impact of a small change in the provision of public input on the net consumption of the two countries i s given below where the i n i t i a l supply of public input i n each country i s determined by using the above optimality conditions. These results are derived using equations (6) and (7): In the context of a closed economy model, Grossman and Lucas (1975) have derived a s i m i l a r condition. dc/dG = Ke {dr/dG} + {dw/dG} = [Ke - Ne C^(.)/C„(.) ] [dr/dG] = [Ke - K][ar /8G] (14) 8c/aG = Ke {8r/8G} + Wo {8L/aG} = w„ {dL/dG} < 0 (15) A small increase i n G has no f i r s t order e f f e c t on home consumption because i t i s optimally chosen. However, such an increase i n G can af f e c t foreign consumption as indicated by equation (14) above. The sign of dc/dG depends on the di r e c t i o n of international c a p i t a l mobility. I f i n the i n i t i a l Cournot-Nash equilibrium the foreign country exports c a p i t a l , then dc/dG i s po s i t i v e . In such a case, i t can be claimed that the home country spends too l i t t l e on i t s industries from the point of the foreign country. This follows from the fact that a small increase i n G does not change the net consumption of the home country, but increases the net consumption of the foreign country. Therefore, from the point of view of foreign country, the home country spends too l i t t l e on i t s industries.® On the other hand, i f the foreign country imports ® Negishi (1973) and Grossman and Lucas (1975) have used a sim i l a r argument to determine the excess of public spending in an economy. c a p i t a l then the sign of dc/dG i s negative which implies that from the point of view of the foreign country, the home country spends too much on i t s in d u s t r i e s . Equation (15) shows that the impact of an increase i n the foreign country's supply of public input on the net consumption of the home country i s negative, ir r e s p e c t i v e of the di r e c t i o n of international c a p i t a l mobility. An increase in the supply of public input i n the foreign country, where labour i s f u l l y employed decreases the net consumption of the home country through i t s adverse impact on the employment of labour. In other words from the point of view of the home country where labour i s not f u l l y u t i l i s e d , the foreign country spends too much on i t s industries i r r e s p e c t i v e of the d i r e c t i o n of c a p i t a l mobility. Since each country can influence the net consumption and therefore the welfare l e v e l of i t s trading partner by i t s choice of spending on industries, there i s a need for international policy coordination. Most available studies on international economic po l i c y coordination derive optimality rules by maximising the aggregate welfare of the countries involved; the present study follows the ex i s t i n g l i t e r a t u r e i n t h i s respect.* From a th e o r e t i c a l point of view, the joi n t welfare maximisation can also ' See for example Pugel (1982), Hamada (1985), and Koehe (1987, 1989) . be j u s t i f i e d i f lump-sum transfers between the two countries are allowed. However, the actual l e v e l of public spending would probably be the resu l t of international bargaining. The rest of th i s section deals with the implications of international economic pol i c y coordination. In the present framework, the welfare of each country i s measured by i t s net consumption of the f i n a l good. Consequently, the objective of international economic p o l i c y coordination i s to maximise aggregate net consumption of the two-country world. This problem i s formally stated i n the following: Max [r(Ke + Ke) + WQL + wN^  - G - G] with respect to G and G. The f i r s t - o r d e r conditions for a maximum are the following, where equation (9) has been used i n deriving condition (17): (Ke + Ke) {8r/aG} + WO{8L/8G} + Nei^w/BG} = 1 (16) WOOL/8G} + Ne{8w/8G} = 1 (17) Equations (16) and (17) state that the aggregate consumption of the two-country world w i l l be maximised when each government supplies a l e v e l of public input such that i t s net marginal benefit to the owners of private factors i n both countries equal i t s marginal cost to tax payers. The right hand side of the above equations i s marginal cost of the provision of public input to tax payers, whereas the l e f t hand side i s the net marginal benefit to owners of private factors i n the two countries. It can e a s i l y be shown that international economic p o l i c y coordination i n the above model i s not optimal either for the home or for the foreign country i n i s o l a t i o n . The following derivatives describe the impact on net consumption of the home and the foreign country when the respective governments increase supply of public input by a small amount. These are derived by d i f f e r e n t i a t i n g equation (6) with respect to G, and equation (7) with respect to G. Equation (9) has also been used i n deriving dc/dG: dc/dG = Ke{3r/dG} + ^n^{d^L/dG] - 1 8c/aG = Ne {dw/dG} - 1 The above equations, af t e r making use of equation (16) and (17) and further substitution, can be written as the following: ac/8G = - Ke {dr/dG} - ^^{dvi/dG] = - [Ke - Ne C,(.)/C„(.) ] [Br/BG] = - [Ke - K][ar / a c ] (18) dc/dG = - WO{8L/8G} > 0 (19) Since 3 C / 3 G and 9 C / 3 G are not zero, international economic pol i c y coordination does not maximise the net consumption of either country i n i s o l a t i o n . If i n the i n i t i a l equilibrium the home country exports c a p i t a l , then from the point of view of residents of the home country, the home government spends too l i t t l e on industries. On the other hand, i f the home country imports c a p i t a l , then from the point of view of the home residents t h e i r government spends too much on domestic industries. On the other hand, equation (19) shows that from the point of view of the residents of the foreign country, i t s government spends too l i t t l e on industries. This r e s u l t does not depend on the di r e c t i o n of international c a p i t a l mobility. The r e s u l t s presented i n t h i s section can be extended to include more than two (private) factors of production. However, these results are sensitive to the assumption that only c a p i t a l i s f u l l y mobile across international boundaries. The analysis conducted thus far can therefore be interpreted as the short-run analysis, where only one factor i s in t e r n a t i o n a l l y mobile and labour i s not f u l l y u t i l i s e d i n one country. In the next section, the international transmission of economic p o l i c y and the implications of p o t e n t i a l international p o l i c y coordination are re-investigated i n a long-run context where a l l private factors are free to move across international boundaries. 3.4 A Long-Run Model The purpose of t h i s section i s to extend the model developed i n the previous section by allowing unrestricted international mobility of both private factors. The modified framework allows an investigation of the international transmission of government spending on industries and potential international p o l i c y coordination i n the long-run. The countries under consideration are symmetrical. Each country produces a f i n a l good (Y). The f i n a l good i s produced by means of a pure public input (G) , c a p i t a l , and labour. A l l resources are f u l l y u t i l i s e d i n both countries. Both private factors ( i . e . , c a p i t a l and labour) are f u l l y mobile across international boundaries. In the present framework, due to the non-convexity associated with the o v e r a l l a l l o c a t i o n of c a p i t a l and labour, corner solutions are also possible with both private factors moving to one country or another depending on the production technologies and the l e v e l of public input provision. However, i n a two-country setting, the i n t e r i o r solution i s both i n t e r e s t i n g and relevant. Corner solutions are possible i f one country i s uniformly more productive than the other country i n the sense that F(z, v) = k F(z, v) for a l l z, v; where k i s some constant greater than unity. The implications of corner solutions are b r i e f l y examined towards the end of next section. The i n t e r i o r solution i s considered i n the following. The relevant zero p r o f i t conditions for the home and the foreign country are given below, where w i s the wage rate: Due to unrestricted international factor mobility, the wage rate and the rate of return on c a p i t a l i n the two countries are i d e n t i c a l . For a given supply of pure public input, the above zero p r o f i t conditions determine the factor prices independent of factor market cl e a r i n g conditions. The factor market clearing conditions given below determine the equilibrium output of the f i n a l goods i n the two countries: C(r, w) /G" = 1 (20) C{r, W)/GP = 1 (21) Ke + Ke = y {C,(r, w)/G"'} + y {C,(r, w)/G^ } (22) Ne + Ne = y {C„(r, w)/G"} + y {C„(r, w)/G^ } (23) where Kg: c a p i t a l endowment of the home country. Ng: labour supply of the home country. Cr(.)/G": c a p i t a l requirement per unit of Y i n the home country. C„(.)/G": labour requirement per unit of Y i n the home country. Equations (22) and (23) are the international market c l e a r i n g conditions for c a p i t a l and labour respectively. These equations indicate that both primary factors of production are f u l l y u t i l i s e d i n the present two-country world. The existence of an i n t e r i o r solution i s considered i n the following. For a given supply of pure public input i n the home and the foreign country, equations (22) and (23) can be solved for Y and Y, i f and only i f the determinant of relevant Jacobian matrix i s non-zero. The relevant determinant i s non-zero, i f the following condition holds G " G P [ C „ ( . ) C ^ ( . ) - C ^ ( . ) C „ ( . ) ] ^ 0 In other words, a unique i n t e r i o r solution i n which both Y and Y are po s i t i v e exists as long as (Ky/Ly) i s not equal to (Ky/Ly) . If (Ky/Ly) i s greater (less) than (Ky/Ly) then the foreign country i s r e l a t i v e l y c a p i t a l (labour) intensive. The res u l t s derived i n the next section depend on the r e l a t i v e c a p i t a l i n t e n s i t y of the home and the foreign country; therefore the foreign country i s assumed i n * * "^ For certain values of K^ , Ne, K^ , and Ne, the output of the f i n a l good i n the two countries may not be p o s i t i v e . The present study assumes away such values. to be r e l a t i v e l y c a p i t a l intensive. The s t a b i l i t y of the i n t e r i o r solution i s examined i n the appendix. Equations (20) and (21) are two equations i n two endogenous variables; r w. Once the optimal r and w are determined; the output of the f i n a l goods i n the two countries can be determined by equations (22) and (23) . Clearly, the optimal r and w are influenced by the supply of the public input i n both countries. This completes the discussion of production side of the model. The net consumption of the home and the foreign country (c and c respectively) are given below: c = [rKe + wNe] - G (24) * * * * C = [rKe + wNe] - G (25) The supply of public input i n the home and the foreign country (i . e . , G and G respectively) enter as parameters i n the reduced form solutions of r, w. Consequently, a change i n the supply of public input i n either country influences the relevant variables and hence the net consumption of both countries. In the present study, the ef f e c t s of a change i n the supply of public input i n one country are transmitted to another through international factor mobility. These ef f e c t s and the p o s s i b i l i t y of international economic p o l i c y coordination are examined i n the next section. 3.5 Transmission of Economie Policy and International Coordination in the Long-Run The purpose of t h i s section i s to re-investigate the international transmission of government spending on a pure public input i n the long-run. The results derived i n t h i s section are compared with those derived i n the short-run. The implications of potential international p o l i c y coordination are also examined by means of a comparative s t a t i c exercise. The impact of a small change i n the provision of public input i n either country on optimal r and w i s considered below. These results are derived by d i f f e r e n t i a t i n g equations (20) and (21): 8r/3G = - aG"-^C„(.)/H < 0 (26) dr/dG = pG C„(.)/H > 0 (27) dw/aG = aG"-^Cr(.)/H > 0 (28) dvj/dG = - pG^ ^ Cr(.) /H < 0 (29) H = [C„(.)C,(.) - C,(.)C„(.)] > 0 Clearly, the sign of the above comparative s t a t i c r e s u l t s depends on the sign of H. Since the foreign country i s assumed to be r e l a t i v e l y c a p i t a l intensive, H i s p o s i t i v e . In other words, * * (Ky/Ly) i s greater than (Ky/Ly) . Equations (26) and (28) respectively indicate that a very small increase i n the supply of public input i n the home country decreases the equilibrium rate of return on c a p i t a l and increases the equilibrium wage rate. This res u l t follows from the assumption that the foreign country i s r e l a t i v e l y c a p i t a l intensive compared to the home country. For a given rate of return on c a p i t a l , an increase i n G increases the wage rate i n the home country above i t s i n i t i a l equilibrium value. Consequently, labour moves from the foreign country to the home country to take advantage of higher wages. However, the foreign country i s less labour intensive compared to the home country. Consequently, not enough labour i s released from the foreign country. Accordingly, the equilibrium wage rate stays at a higher l e v e l . Also, due to outflow of labour, the foreign country ends up with too much c a p i t a l per unit of labour which puts downwards pressure on the equilibrium rate of return on c a p i t a l . In other words, during the adjustment period, both c a p i t a l and labour move from the foreign country to the home country, but too much c a p i t a l and too l i t t l e labour are released from the foreign industries. Therefore the equilibrium rate of return on c a p i t a l decreases and the wage rate increases. Equations (27) and (29) indicate that a small increase i n the supply of public input i n the foreign country results i n a higher rate of return on c a p i t a l and lower wage rate. This i s because the home country i s r e l a t i v e l y labour intensive compared to the foreign country. An increase i n the foreign supply of public input results in too much labour but too l i t t l e c a p i t a l inflow. The above results indicate that i n the present framework, a c a p i t a l (labour) intensive country can increase (decrease) the equilibrium rate of return on c a p i t a l , and decrease (increase) the equilibrium wage rate, by increasing i t s spending on industries. These results sharply d i f f e r from those derived i n section three where only c a p i t a l i s f u l l y mobile across international boundaries: when only c a p i t a l i s f u l l y mobile and wages are r i g i d i n the home country, the foreign country cannot influence the equilibrium rate of return on the mobile factor. In a Cournot-Nash equilibrium (i.e . , i n the absence of internat .1 economic p o l i c y coordination), each country takes the supply of public input i n the other country as given and determines i t s own supply such that the net consumption of i t s residents i s maximised. The following equations determine the optimal supply of public input i n the home and foreign country respectively: Ke {dr/dG} + Ne {9W/8G} = 1 Ke {dr/dG} + Ne {3W/8G} = 1 The right hand side of the above equations i s the marginal cost to tax payers of the provision of public input, whereas the l e f t hand side i s the net marginal benefits to owners of int e r n a t i o n a l l y mobile factors.•'^^ Clearly, the above rules ignore i n d i r e c t s p i l l o v e r s of the public input across international boundaries due to international factor mobility. The impact of a small change i n the provision of public input on the net consumption of the two countries i s given below, where the i n i t i a l supply of public input i n each country i s determined by using the above optimality conditions. These re s u l t s are derived by using equations (24) and (25) : ac/ a c = Ke {ar/ac} + Ne {aw/ao = Ne[(Ke/Ne) " (Ky/Ly) ] [Br/BG]/H < 0 (30) Since the home country i s r e l a t i v e l y labour intensive, the owners of domestic c a p i t a l w i l l prefer a lower l e v e l of public input. dc/dG = Ke {ar/ac} + {d^/dG} = Ne[(Ke/Ne) " (K^/L^) ] [dz/dG]/H < 0 A small change i n the supply of public input i n the home country does not change i t s consumption since the i n i t i a l l e v e l of G i s optimally chosen. Such an increase however has implications for foreign consumption as indicated by equation (30) . If the foreign country exports c a p i t a l and imports labour i n the i n i t i a l equilibrium, then both ac/ac and ac/ac are negative. Therefore, following Negishi (1973) , i t can be argued that each country spends too much on i t s industries from the point of view of i t s trading partner. This follows from the fact that a small increase i n G does not change the net consumption of the home country, but decreases the net consumption of the foreign country. Therefore, from the point of view of the foreign country, the home country spends too much on i t s industries. Consider the foreign country: a small increase i n i t s public spending does not change i t s own net consumption since G i s optimally chosen, but equation (31) shows that i t decreases the net consumption of the home country due to the s p e c i f i e d d i r e c t i o n of factor mobility. Accordingly, from the point of view It can e a s i l y be established that i f the foreign country exports c a p i t a l and imports labour, and H i s po s i t i v e , then the foreign country must be c a p i t a l abundant, i . e . , {Kg/Ng} > {Kg/Ng} . of the home country, the foreign country spends too much on i t s industries. Since each country can influence the net consumption and therefore the welfare l e v e l of i t s trading partner by i t s choice of spending on industries, there i s a need for international economic policy coordination. The rest of t h i s section deals with the implications of international economic p o l i c y coordination. The objective of int e r n a t i o n a l economic p o l i c y coordination i s to maximise the aggregate net consumption of the two-country world. This problem i s formally stated i n the following: Max [r(Ke + Ke) + w(Ne +Ne) - G - G] with respect to G and G. In other words, each government selects i t s spending such that aggregate net consumption i s maximised. The f i r s t - o r d e r conditions for a maximum are the following: (Ke + Ke){ar/aG} + (Ne + Ne){aw/aG} = 1 (32) (Ke + Ke){ar/aG} + (Ne + Ne){8w/aG} = 1 (33) Equations (32) and (33) state that the aggregate consumption of the two-country world w i l l be maximum when each government supplies a l e v e l of public input such that i t s net marginal benefit to the owners of private factors i n both countries equals i t s marginal cost to tax payers. It can e a s i l y be shown that international economic p o l i c y coordination i n the above model i s not optimal either for the home or for the foreign country i n i s o l a t i o n . By d i f f e r e n t i a t i n g equation (24) with respect to G, and equation (25) with respect to G dc/dG = Ke {dr/dG} + {d^/dG} - 1 8c/aG = Ke {dr/dG} + Ne {d^^/dG} - 1 The above equations, aft e r making use of equation (32) and (33) and further substitution, can be written as follows: ac/aG = - Ke {ar/ac} - Ne {aw/ac} = - Ne[(Ke/Ne) " (Ky/Ly) ] [Br/BG]/H > 0 (34) dc/dG = Ke {ar/aG} + Ne {d^/do.} = - Ne[(Ke/Ne) " (Ky/Ly) ] [Br/BG]/H > 0 (35) Since ac/aG and ac/ a c are not zero, international economic po l i c y coordination does not maximise net consumption of either country i n i s o l a t i o n . If the foreign country exports c a p i t a l and imports labour i n the i n i t i a l equilibrium, then both dc/dG and dc/dG are posi t i v e , which implies that by increasing t h e i r supply of public input, both governments can increase the net consumption of t h e i r respective countries. In other words, under in t e r n a t i o n a l economic policy coordination both governments spend too l i t t l e on th e i r industries. This re s u l t d i f f e r s sharply from the one derived in the short-run: i t has been shown that when labour i s not f u l l y mobile across international boundaries and wages are r i g i d i n one country, international p o l i c y coordination leads to a s i t u a t i o n where the country which f u l l y u t i l i s e s labour spends too l i t t l e on i t s industries, i r r e s p e c t i v e of the d i r e c t i o n of int e r n a t i o n a l c a p i t a l mobility. The analysis conducted so far exclusively considers the i n t e r i o r solution. As indicated e a r l i e r , corner solutions are possible when one country i s uniformly more productive than the other country. If the foreign country i s uniformly more productive compared to the home country, then both c a p i t a l and labour w i l l move to the foreign country. Consequently, the optimal supply of public input i n the home country w i l l be zero. In such a case, the net consumption of the two countries w i l l be the following: C = Kg r(0, G) + Ng w(0, G) * * * * * * C = Kg r(0, G) + Ng w(0, G) - G where w(.) and r(.) are respectively the equilibrium wage rate and the rate of return on c a p i t a l when both private factors move to the foreign country. In a non-cooperative solution, G w i l l be chosen such that the net consumption of the foreign country ( i . e . , c) i s maximised. Whereas, m a cooperative solution, G w i l l be chosen such that the aggregate consumption of the two-country world (i.e. , c + c) i s maximised. The analysis conducted thus far considers two countries only, where both private factors ( i . e . , c a p i t a l and labour) are f u l l y mobile across international boundaries. The above two-country framework i s therefore interpreted as the long-run. In the next section, the above model i s extended to include a t h i r d country: the rest of the world. The rest of the world i s linked with the home and the foreign country through unrestricted c a p i t a l mobility; labour i s f u l l y mobile between the home and the foreign country only. The three-country framework can be interpreted as the short-run, where the home and the foreign country are members of an economic union such as the European Economic Community (EEC). The modified framework allows an investigation of international transmission of government spending on industries, when two countries have formed an economic union. 3.6 International Transmission of Economic Policy in the Presence of an Economic Union The purpose of t h i s section i s to develop a simple three-country model, which allows an investigation of international transmission of economic p o l i c y i n the presence of an economic union. The home and the foreign country have formed an economic union, which i s linked with the rest of the world through unrestricted international c a p i t a l mobility. Capital i s f u l l y mobile within each country and across international boundaries. Labour i s f u l l y mobile within each country but i t s mobility across international boundaries i s r e s t r i c t e d : labour i s f u l l y mobile within the economic union but there i s no labour mobility between either the rest of the world and the home country, or the rest of the world and the foreign country. The rest of the model i s sim i l a r to the long-run model. The competitive producers i n the rest of the world take the supply of public input as given. The production functions for the rest of the world are given below :^'' Variables pertaining to the rest of the world w i l l be distinguished by ( A ) . Y = F (Ky, Ly) / 1 > s > 0 where Y: production of f i n a l good i n the rest of the world. A G: pure public input i n the rest of the world. Kyi c a p i t a l used i n the production of f i n a l good i n the rest of the world. A Lyi labour used i n the production of f i n a l good i n the rest of the world. The relevant cost functions for the rest of the world are derived below: A A A A A A A A A A A A Y C(r, w)/G^ = Min [wLy + rKy : Y = G^ F (Ly, Ky) ] A A with respect to Ly and Ky. where w: wage rate i n the rest of the world. For a given supply of public input, the corresponding zero p r o f i t condition i s the following: C(r, W ) / G 2 = 1 ( 3 6 ) For a given supply of public input i n each country, equations ( 2 0 ) , ( 2 1 ) , and ( 3 6 ) are three equations i n three endogenous variables: w, r, and w. These equations can determine the equilibrium factor prices independent of the relevant market clearing conditions. The re s u l t s presented i n t h i s section depend on the r e l a t i v e c a p i t a l i n t e n s i t y of the home and the foreign country only. Consequently, the foreign country i s assumed to be r e l a t i v e l y c a p i t a l intensive as compared to the home country. The present three-country model i s recursive: equations (20) and (21) determine the equilibrium w and r as a function of G and G only. Equation (36) can then be used to determine the equilibrium A W. Consequently, the equilibrium wage rate i n the rest of the world depends on the supply of public input i n a l l three countries. The recursive nature of the above model suggests that a change in the supply of public input i n the rest of the world (which i s linked with the economic union through c a p i t a l mobility) cannot influence the equilibrium w and r. However, by changing t h e i r supply of public input both home and foreign country can influence A the equilibrium w. The following factor market c l e a r i n g conditions determine the equilibrium output of f i n a l goods i n the three countries : K, + Ke + Ke = Y {Cr(r, w)/G°} + Y {C,(r, w)/G^} + Y {C,(r, W)/GS} (37) Ne + Ne = Y {C„(r, w)/G«} + Y {C„{r, w)/G^ } (38) Ne = Y {C„(r, w)/G«} (39) Equation (37) shows that c a p i t a l i s f u l l y mobile both within and across international boundaries. Whereas, equations (38) and (39) indicate that labour i s f u l l y mobile within each country but international labour mobility i s r e s t r i c t e d : labour i s inter n a t i o n a l l y mobile only between the home and the foreign country. The net consumption of the rest of the world (c) i s given below: The impact of a change i n the supply of public input on equilibrium factor prices i s discussed i n the following, where the foreign country i s assumed to be r e l a t i v e l y c a p i t a l intensive as compared to the home country: A A A A A A c = [rKe + wNe] - G dr/dG < 0 9 r / 3 G > 0 dr/dG = 0 (40) dw/dG > 0 9W/3G < 0 aw/ac = 0 (41) aw/ac > 0 (42) aw/ac < 0 (43) aw/ac > 0 (44) Equations (40) and (41) indicate that although the rest of the world i s linked with the home and the foreign country through perfect c a p i t a l mobility and the wage rate i s f u l l y f l e x i b l e , i t s supply of public input does not influence the equilibrium r and w. Equation (42) shows that an increase i n the supply of public input in the home country increases the equilibrium wage rate i n the rest of the world. On the other hand, equation (43) shows that an increase i n the supply of public input i n the foreign country decreases the equilibrium wage rate i n the rest of the world. An increase i n the supply of public input i n the rest of the world increases i t s equilibrium wage rate, see equation (44). The above results indicate that the supply of public input i n the rest of the world cannot influence the consumption of either the home or the foreign country. This implies that i n a Cournot-Nash equilibrium, from the point of view of these countries, spending on industries i n the rest of the world i s optimal. However, the supply of public input i n the home and the foreign country influences the consumption of the rest of the world. The following derivatives can be used to determine the impact of an increase i n the supply of public input on net consumption of the rest of the world: dc/dG = Kg {Br/aC} + Ng {8w/aG} = - [Ng][ (Kg/Ng) - (Ky/Ly) ] [ar/aG]/H (45) ac/ac = Ke {ar/ac} + Ng {aw/ac} = [Ng][ (Kg/Ng) - (Ky/Ly) ] [ar/aC]/H (46) Equation (45) indicates that an increase i n the supply of public input i n the home country decreases the consumption of the rest of the world, i f the rest of the world exports c a p i t a l i n the i n i t i a l equilibrium. On the other hand, equation (46) shows that an increase i n the supply of public input i n the foreign country increases the consumption of the rest of the world, i f the rest of the world exports c a p i t a l i n the i n i t i a l equilibrium. In other words, i n a Cournot-Nash equilibrium, the home country spends too much on i t s industries, whereas the foreign country spends too l i t t l e from the point of view of the rest of the world. Clearly, members of the economic union can exploit the rest of the world through p o l i c y coordination within the union. It i s i n the best interests of the rest of the world to join the economic union. However, the members of economic union are l i k e l y to oppose th i s since only the rest of the world may be gain from t h i s move. 3.7 Concluding Remarks This essay investigates the international transmission of economic p o l i c y i n a s t a t i c framework. The implications of potential international p o l i c y coordination are also examined. The purpose of international economic p o l i c y coordination i n the present study i s to maximise the aggregate consumption of a two-country world, where each country produces a f i n a l good by means of a pure public input, c a p i t a l , and labour. The two countries are linked through international factor mobility. International transmission of economic p o l i c y i s considered under the following alternative assumptions: (1) c a p i t a l i s f u l l y mobile across international boundaries but international labour mobility i s r e s t r i c t e d , and due to economy wide r i g i d wages i n one country, labour i s not f u l l y employed; (2) both c a p i t a l and labour are f u l l y mobile across international boundaries. These two cases can be interpreted as the short-run and the long-run respectively. In the short-run, the supply of public input i n a country where wages are f u l l y f l e x i b l e does not influence the equilibrium rate of return on the i n t e r n a t i o n a l l y mobile factor, i . e . , c a p i t a l . On the other hand, the supply of public input i n a country where wages are r i g i d can influence the equilibrium rate of return on c a p i t a l and the equilibrium wage rate i n a country where wages are f l e x i l e . Consequently, i n the absence of international economic pol i c y coordination, the country which exports (imports) c a p i t a l and where wages are r i g i d spends too much ( l i t t l e ) on i t s industries from the point of view of the other country, where wages are f u l l y f l e x i b l e . Whereas, a country where wages are f u l l y f l e x i b l e spends too much on i t s industries from the point of view of the country where wages are r i g i d i r r e s p e c t i v e of the d i r e c t i o n of international c a p i t a l mobility. On the other hand, under international p o l i c y coordination, the country where wages are r i g i d and which exports (imports) c a p i t a l spends too l i t t l e (much) on i t s industries from the point of view of i t s residents. Whereas, the country where wages are f u l l y f l e x i b l e spends too l i t t l e on i t s industries from the point of view of i t s residents, i r r e s p e c t i v e of the d i r e c t i o n of international c a p i t a l mobility. In the long-run, the supply of public input i n both countries determines a l l factor p r i c e s . A r e l a t i v e l y c a p i t a l (labour) intensive country can increase the equilibrium rate of return on c a p i t a l (labour) by increasing i t s supply of public input. Consequently, i n the absence of international coordination, each country spends too much ( l i t t l e ) on i t s industries from the point of view of the other country, i f the c a p i t a l (labour) intensive country exports c a p i t a l . On the other hand, under international p o l i c y coordination both countries spend too l i t t l e (much) on t h e i r industries from the point of view of t h e i r residents, i f the ca p i t a l (labour) intensive country exports c a p i t a l . The model has been further extended to include a t h i r d country: the rest of the world. The rest of the world i s linked with the home and the foreign country through unrestricted c a p i t a l mobility, whereas labour i s f u l l y mobile between the home and the foreign country only. The home and the foreign country can therefore be considered as members of an economic union. A three-country model allows an investi g a t i o n of international transmission of government spending on industries when two countries have formed an economic union. It i s shown that the supply of public input i n the rest of the world has no influence on the equilibrium rate of return on ca p i t a l , which i s f u l l y mobile across international boundaries. On the other hand, the supply of public input i n the home and the foreign country has implications for the equilibrium rate of return on c a p i t a l i n the rest of the world. Clearly, p o l i c y coordination within the economic union i s desirable i n order to exploit the rest of the world. This essay exclusively deals with the international transmission of government spending on a pure public input. In the case of an impure public input i t can be shown that both i n the short-run and the long-run, an increase i n the supply of public input i n either country increases the r e l a t i v e price of a l l inputs in the home and the foreign country. In the short-run, an increase in the supply of public input i n either country increases employment i n the underemployed country. In addition, i n the short-run uncoordinated equilibrium, the underemployed country spends too much ( l i t t l e ) on the impure public input from the point of view of the f u l l y employed country, i f i t exports (imports) c a p i t a l . On the other hand, i n the short-run coordinated equilibrium, the underemployed country spends too much on the impure public input. However, i n the long-run i n t e r i o r solution, where one country exports c a p i t a l and the other exports labour, unambiguous r e s u l t s cannot be derived. Appendix 3.1: Stability of the Interior Solution Equations (20) to (23) can also be used to show that the i n t e r i o r solution s a t i s f i e s Routh-Hurwitz s t a b i l i t y conditions. The postulated dynamic adjustment process i s described by means of the following equations, where the l e f t hand side i s the time derivative of the relevant variable: dY/dt = ay [1 - G-"C(w, r) ] dY/dt = by [1 - G-Pc(r, w) ] dw/dt = a^ [Y {C„(r, w)/G«} + Y {C„(r, w)/G^ } - Ng - N^] dr/dt = a, [Y {C,(r, w)/G"} + Y {C,(r, w)/G^ } - - KJ where the relevant speeds of adjustment (ay, by, a„, a,.) are assumed to be p o s i t i v e constants. The economic meanings of the above equations are obvious, therefore the int e r p r e t a t i o n i s not included i n t h i s essay. The relevant Jacobian matrix, denoted by J i s the following: J = 0 0 3l3 3l4 0 0 323 324 331 332 333 334 341 342 343 344 where 3l3 = - C„(.)G-° 3l4 = - C,(.)G-« 323 - C„(.)G-P 324 = - C,(.)G-P 331 = C„( . ) G-« 332 = C„ (. ) G-P 333 = [YC„„(.)G-" 334 = [YC„,(.)G-« 341 = (. ) G-° 342 = i(.)G-P 343 = [YC„,(.)G-" 344 = [YC„(.)G-« IG-One of the Routh-Hurwitz s t a b i l i t y condition requires that {-1)'|J| > 0 where "| |" stands for the determinant. The determinant of the above Jacobian matrix i s the following: | j | = G-2°G-2P {C«(.)C,(.) - C,(.)C„(.)}2 > 0 Clearly, the determinant condition i s s a t i s f i e d for a l l values of G and G. Also, the trace of the above Jacobian matrix i s negative. Hence, the i n t e r i o r solution i s stable. CHAPTER 4 GOVERNMENT SPENDING ON INDUSTRIES AND THE PATTERN OF INTERNATIONAL TRADE 4.1 Introduction One of the main objectives of international trade theory i s to explain the pattern of international trade. Explanations based on differences in production technologies led to the Ricardian Theorem, whereas explanations based on differences i n factor endowments resulted i n the Heckscher-Ohlin-Samuelson Theorem. More recent explanations consider the role of increasing returns and imperfect competition i n the world economy. However, the role of government spending on industries i n determining the trade pattern has not received much attention. Most open economy studies which e x p l i c i t l y include government spending on industries are mainly concerned with the shape of the production p o s s i b i l i t y curve.^ Khan (1980, 1982), Tawada and Abe (1984), Tawada and Okamoto (1983) have examined the v a l i d i t y of Heckscher-Ohlin-Samuelson Theorem, Factor Price Equalisation Theorem, Rybczynski Theorem, and Stolper-Samuelson Theorem i n the presence of government spending on public inputs. Diewert (1986) has proposed various measures of the economic benefits of public inputs. In the context of a one-factor and two-good model. Manning and McMillan (1979) have shown that the comparative advantage of an economy depends on the l e v e l of government spending on a pure input. In a multi-period setting, Barro (1990) and Devereux and Mansoorian (198 9) have shown that the growth rate of an economy depends on the l e v e l of government spending on public inputs. The empirical investigation by Ram (1986) also appears to support t h i s view. However, Abe (1990) i s the only available study where the relat i o n s h i p between government spending on industries and the pattern of international trade i s e x p l i c i t l y considered. Abe (1990) has incorporated government spending on a pure public input into a two-country general equilibrium model. Each country produces two f i n a l goods by means of c a p i t a l , labour, and a pure public input. The pure public input which i s supplied free ^ See for example, Ishizawa (1991), Okamoto (1985), Manning and McMillan (1982), Tawada (1980, 1982), and Tawada and Abe (1984) . of charge by the government i s produced by means of c a p i t a l and labour. The cost of the public input i s financed by means of an income tax. Both countries f u l l y u t i l i s e a l l resources. By means of a comparative s t a t i c s exercise, Abe has shown that when two countries have i d e n t i c a l homothetic preferences, production technology, factor supplies, and the factor i n t e n s i t y of public sector i s the same as that of private sectors, then the country that produces more public input exports (imports) the output of the industry which derives more (less) benefits from i t s supply. This implies that when both industries derive equal benefits from the supply of a pure public input and the other conditions stated above also hold, then differences i n the production (and hence the supply) of a pure public input cannot influence the pattern of international trade. A s i g n i f i c a n t proportion of government budget i s directed towards the provision of impure public (or semi-public) inputs i n most r e a l economies. Examples of such public inputs include roads, canals, bridges and harbours. However, Abe (1990) has not considered the rel a t i o n s h i p between government spending on impure public inputs and the pattern of international trade. An important difference between the pure and impure public inputs i s t h e i r a v a i l a b i l i t y to firms. The entire supply of a pure public input can be u t i l i s e d by a l l firms simultaneously. Consequently, a pure public input i s non-congestible both across industries and among firms within each industry. On the other hand, the entire supply of an impure public good cannot be u t i l i s e d by a l l firms simultaneously. In other words, an impure public input i s congestible within industries and among firms across industries. Due to t h i s asymmetry, the supply of pure and impure public inputs influences the pattern of trade d i f f e r e n t l y . For a given supply of impure public input, the entry of an extra firm not only increases congestion within the relevant industry, but also increases the l e v e l of congestion i n the other industries. Congestion a f f e c t s the size of benefits derived by each industry from the use of an impure public input. An impure public input may not be equally congestible across industries. In addition, each industry i s l i k e l y to contribute i n d i f f e r e n t ways to the degree of congestion. The pattern of international trade i s therefore also influenced by (a) congestion within the industries, and (2) inter-industry congestion. The above discussion pertains to those economies which f u l l y u t i l i s e a l l resources. However, s i g n i f i c a n t labour unemployment exits i n most real economies. It i s therefore desirable to investigate the v a l i d i t y of Abe's resu l t i n the presence of labour unemployment. In a recent study, Batra and Beladi (1990) have examined patterns of trade between underemployed economies, but they do not consider the ro l e of public inputs i n determining the comparative advantage. The underemployment i n Batra and Beladi (1990) refers to labour unemployment due to r i g i d wages. The purpose of t h i s essay i s to extend Abe (1990) i n two directions: (1) to consider the relationship between government spending on impure public inputs and the pattern of trade between economies which f u l l y u t i l i s e a l l resources; and (2) to consider the relationship between government spending on pure and impure public inputs and the pattern of trade between underemployed economies. The essay develops a two-country, two-good, and two-factor general equilibrium model with government spending on a public input. The private sector produces two f i n a l goods by means of c a p i t a l , labour, and the public input. The public input, which i s provided to firms free of charge, i s produced by the public sector. The cost of public production i s financed by means of a proportional income tax. The essay i s organised as follows. In section two, the relationship between government spending on an impure public input and the pattern of trade i s considered; the economies under consideration f u l l y u t i l i s e a l l resources. The public input i s congestible both across industries and among firms within industries. In other words, both congestion across industries and inter-industry congestion are e x p l i c i t l y taken into account. It i s shown that Abe's resu l t can be extended to include an impure public input only i f (i) the public input i s equally congestible across industries, and ( i i ) congestion created by one industry i n the other i s symmetric. Section three deals with the relationship between government spending on an impure public input and the pattern of trade between underemployed economies. It i s shown that even i f both i n d u s t r i e s derive equal benefits from an impure public input which i s equally congestible across industries and the congestion caused by each industry i s symmetric, the pattern of international trade can s t i l l be influenced by i t s supply: the country that produces more public input exports (imports) the output of the industry which i s r e l a t i v e l y labour (capital) intensive. The l a s t section contains concluding remarks. 4.2 Government Spending on an Impure Public Input and the Trade Pattern between Fully Employed Economies The purpose of t h i s section i s to investigate the relationship between government spending on an impure public input and the pattern of international trade between economies which f u l l y u t i l i s e a l l resources. A simple two-country, two-good framework i s u t i l i s e d i n which the respective governments supply an impure public input for use within national boundaries. Examples of impure public inputs include production infrastructure: roads, bridges, canals, dams, and harbours. The public input i s cooperative with the private inputs i n the production of both goods. The economies under consideration f u l l y u t i l i s e t h e i r resources. Since t h i s essay attempts to explore the rel a t i o n s h i p between government spending on industries and the pattern of trade i n goods, international factor mobility i s not considered. Consider a s e l f s u f f i c i e n t economy that produces two f i n a l goods (X and Y) by means of two primary inputs and an impure public input. The primary inputs are labour and c a p i t a l , which are f u l l y u t i l i s e d . The public input i s produced by means of c a p i t a l and labour. The supply of labour and c a p i t a l i n the economy i s fixed. The public input i s provided free of charge by the government. The cost of public production i s financed by a proportional income tax. Distortionary taxes are not considered i n t h i s essay: a distortionary tax (for example, a per-unit commodity tax) i n i t s e l f influences the trade pattern, see Melvin (1970) . The f i n a l good X i s the numéraire. A l l markets are competitive and private producers take the supply of public input as given. The present study considers an impure public input which i s congestible across industries and among firms within each industry. The firms i n each industry are assumed to be i d e n t i c a l . Consequently, congestion caused by each firm within an industry i s i d e n t i c a l . However, the public input may not be equally congestible across industries. In addition, each industry i s l i k e l y to contribute i n d i f f e r e n t ways to the degree of congestion. In other words, congestion caused by d i f f e r e n t industries i s u n l i k e l y to be symmetric. Congestion i s assumed to be p o s i t i v e l y related to the output of each industry. Accordingly, when an industry expands, the r e s u l t i n g congestion decreases the usefulness of the public input to a l l i n d u s t r i e s . In the present study, congestion i s modelled as a negative e x t e r n a l i t y . Each industry consists of a large number of i d e n t i c a l firms. The production functions of the i t h firm i n industry X and Y are given below: X, = S,(G,X,Y) F(Kix, L i J ; X = n ^ ( i = 1, 2, . . .nj Y, = Sy(G,X,Y) H(Kiy, Liy); Y = n^ Y^  ( i = 1, 2, . . .n^ ) where Xj.: output of firm i i n industry X. n^: number of firms i n industry X. G: supply of impure public input. Kix: c a p i t a l used i n the production of X^ . Li^: labour used i n the production of X^ . Each firm takes G, X, and Y as given. F(.) and H(.) are l i n e a r l y homogeneous. S^{.) and Sy(.) measure the contribution of the public input to production. For a given X and Y, an increase i n G reduces the congestion. In other words, S^{.) and Sy(.) are p o s i t i v e l y related to the supply of congestible public input. However, for a given supply of public input, an increase i n the output of either or both industries increases congestion. In other words both (. ) and Sy (. ) are negatively related to X and Y. However, (. ) and Sy(.) are concave. The above production functions are separable i n the private and the public inputs. Consequently, an increase i n the supply of impure public input affects the output of the two industries i n a Hicks neutral fashion. For the sake of algebraic s i m p l i c i t y the following functional forms for (. ) and Sy(. ) are used S^(.) = G"X-T^Y-*-; l > a > 0 , Y > 0 , X > 0 Sy(.) = Qpy-^ x-'^ ; 1 > | 3 > 0 , C > 0 , ^ > 0 a = [dX/dG] [G/X]: e l a s t i c i t y of X with respect to G. P = [dY/dG] [G/Y]: e l a s t i c i t y of Y with respect to G. y: congestion rate i n industry X. congestion rate i n industry Y. X: Y industry's contribution to congestion i n industry X. \i: X industry's contribution to congestion i n industry Y. For a given G, X, and Y, the cost functions for the i t h firm i n industry X and Y can be derived as follows: C='(r, w)[Xi/Sx(.)] = Min [wL^ + rK^ : X^/S^(.) = F (K^ , L J ] with respect to and K^ . a(r, w)[Yi/Sy(.)] = Min [wLy + rK^ : YjS^i.) = H (Ky, Ly) ] with respect to Ly and Ky. where w: wage rate. r: rate of return on c a p i t a l . Since a l l firms i n both industries are i d e n t i c a l , the industry cost functions can be derived by aggregating the cost functions of the firms as follows: C^(r, w) [X/S,(.) ] C^(r, w) [Y/Sy(.) ] The technology for public production i s the following, where g(.) i s l i n e a r l y homogeneous: G = g (Kg, Lg) The corresponding cost function i s derived i n the following: GC5(r, w) = Min [wL, + rK^ : G = g (Kg, Lg) ] with respect to Lg and Kg. By using the properties of cost functions, the factor market clearing conditions can be written as follows: Le = [X/S,(.) ]c\(.) + [Y/Sy(.) ]cy„(.) + Gc\(.) (1) Ke = [X/S^(.) ]c^(.) + [Y/Sy(.)]c\{.) + Gc\(.) (2) where [X/Sj, (. ) ] c\ (. ) : labour used i n the production of X. [X/Sx (. ) ] c^ 'r (. ) : c a p i t a l used i n the production of X. Gc^„ (. ) : labour used i n the production of G. Gc^r ( • ) • c a p i t a l used i n the production of G. Kg: supply of c a p i t a l . Lg: supply of labour. Due to unrestricted factor mobility within the economy, the wage rate and the rate of return on c a p i t a l i n the private and the public sectors i s i d e n t i c a l . The zero p r o f i t conditions for industry X and Y are the following: C M r , w)/[S,(.) ] = 1 (3) C M r , w)/[Sy(.) ] = p (4) For a given supply of pure public input (G) and the autarky r e l a t i v e goods pr i c e r a t i o (p) , equations (1) to (4) determine the equilibrium w, r, X and Y. The autarky price r a t i o i n the economy i s determined by the in t e r a c t i o n of supply and demand. On the demand side, preferences are assumed to be homothetic. The r e l a t i v e demand for the two goods i n the economy therefore depends on the r e l a t i v e price r a t i o alone. Market equilibrium for the f i n a l goods can be written as Y/X = D(p) (5) where D(p): r e l a t i v e demand of the two f i n a l goods. dD{p)/dp i s negative. For a given supply of pure public input, equilibrium of the private sector can be characterised by equations (1) to (5). In fi v e equations there are f i v e endogenous variables; w, r, p, X, and Y. These variables are determined as the function of the supply of public input. As indicated e a r l i e r , the cost of public production i s financed by means of income tax. The budget constraint of the government i s given i n the following, where t i s the income tax rate :^  t{wLe + rKe} = Gc9(w, r) (6) Right hand side of the above equation i s the t o t a l cost of public input; whereas the l e f t hand side i s government tax receipts. For the purposes of the present study, the supply of public input does not have to be optimal. The f u l l equilibrium of the closed economy under consideration i s given by equations (1) to (6). These are six equations i n 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 a pure public input and the pattern of trade i s examined i n the next section. 4.2.1 The Pattern of Trade For a given supply of impure public input, equations (1) to (5) describe an autarky equilibrium i n the economy. Consider two ^ The budget constraint of the representative consumer i s the following: (1 - t){wL^ + rKe} = X + pY such economies. I f the two countries are i d e n t i c a l i n every respect, then there i s no basis for international trade, since the autarky price r a t i o i n the two countries w i l l be i d e n t i c a l . However, differences i n the supply of public input can lead to differences i n the autarky p r i c e r a t i o . The supply of an impure public input influences the autarky goods price r a t i o (p) through the following channels: (i) for a given wage and the rate of return on c a p i t a l , an increase i n G influences p through a reduction i n the cost of production of both industries. This i s the dire c t e f f e c t of an increase i n the supply of impure public input. ( i i ) an increase i n G also increases the cost of both industries through i t s p o s i t i v e impact on wages and the rate of return on c a p i t a l . This i s the i n d i r e c t e f f e c t of an increase i n the supply of an impure public input. ( i i i ) the public input i s congestible within industries and among firms across industries. In general the public input i s not l i k e l y to be equally congestible across industries. In addition, the congestion caused by each industry i n the other i s also not l i k e l y to be symmetric. Accordingly, for a given wage r e n t a l r a t i o , an increase i n G d i r e c t l y a ffects the output of both industries and hence the autarky price r a t i o . In the case of a pure (i . e . , non-congestible) public input, Abe (1990) has shown that the pattern of international trade i s not influenced by differences i n the production of public input i f (i) both industries derive equal benefits from i t s supply, i . e . , a i s equal to (3 i n terms of the present study^; and ( i i ) the factor i n t e n s i t y of the public sector i s the same as that of the private sectors, i . e . , [ (K^ +Ky) / (L^+Ly) ] i s equal to [Kg/Lg] The present study deals with an impure ( i . e . , congestible) public input. In order to f a c i l i t a t e comparison with the res u l t s derived by Abe, i t i s assumed that (1) a i s equal to (3, and (2) the factor i n t e n s i t y of the public and the private sectors i s the same. In other words, the present study attempts to examine the role of congestion i n determining the pattern of trade exclusively. The rel a t i o n s h i p between the supply of an impure public input and the pattern of trade can be examined by means of the following derivative, which describes the impact on the autarky price r a t i o of a country when i t s supply of public input increases by a small amount^ dp/dG = - (p/G)[(^l - >.) + (C - Y) ] [H1H2+H3HJ/Hd (7) ^ Unlike the present study, i n Abe (1990) the e l a s t i c i t y of X and Y with respect to G i s variable. ' This implies that Lg[LJ (K,/LJ - (Kg/Lg) }+Ly{ (Ky/Ly) - (Kg/Lg) } ] i s zero. In other words, the factor i n t e n s i t y of the public sector i s a weighted average of the factor i n t e n s i t y of the private sectors. ^ The properties of the cost functions are used i n the derivation of equation (7) . For an excellent survey of duality theory, see Diewert (1974) . where Hi = [ a K ^ + pKy] > 0 H2 = [L^a^„ + Lyay„ + L g E g j < 0 H3 = [ a K ^ + pKy] > 0 H4 = [Kxaxr + Kyayr + K^agrl < 0 ayr = (r/C\{.)) [ (dC\(.)/dr] < 0 axw ~ (w/C%(.) ) [ 0C\(.)/8w] < 0 axr = (r/C^(.)) [{dCM.)/dr] < 0 ayw ~ (w/C^„(.) ) [ OC^J.) /aw] < 0 agw = {w/C\(.)) [ (ac\(.)/aw] < 0 (r/C\(.)) [ (ac^,( .)/ar] < 0 Equation (7) i s derived by using equations (1) to (5) and conditions (i) and ( i i ) . The sign of the above derivative depends on: (1) the r e l a t i v e size of inter-industry congestion (jj. - X) ; (2) the r e l a t i v e size of congestion within each industry (y - C)/ and (3) the sign of H^ . i s po s i t i v e provided the equilibrium i s stable. If the impure public input i s equally congestible within each industry ( i . e . , y = and the congestion caused by each industry i s symmetric (i . e . , X, = |J, ), then the above derivative i s zero. This implies that both pure and impure public inputs influence the pattern of international trade symmetrically. If the congestion caused by each industry i n the other i s symmetric (i . e . , X = \i) , then the following proposition follows from equation (7). PROPOSITION 1. When two countries have (i) identical hcmothetic preferences^ production technology, 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 which the public input is relatively less (more) congestible. An increase i n the supply of public input increases the output of both industries. Suppose that the public input i s r e l a t i v e l y more congestible i n X industry as compared to Y. Hence i f G increases, then the output of X industry r i s e s r e l a t i v e l y less than Y. Consequently, the output of Y industry where the public input i s r e l a t i v e l y less congestible i s exported. The above proposition also implies that the c o n g e s t i b i l i t y can actually reverse the pattern of international trade based only on the size of the benefits of an impure public input across in d u s t r i e s . Suppose that i n the i n i t i a l equilibrium the public input i s equally congestible i n both industries, but the direc t benefits of the public input across industries are not symmetric. In such a case, a country which produces more public input exports the output of the industry which derives more benefits from i t s supply. However, i f the industry which derives more benefits from the supply of an impure public input i s also the industry where the public input i s r e l a t i v e l y more congestible, then i t may be cheaper for the country i n question to import the relevant good. If the public input i s equally congestible within each industry ( i . e . , y = C) / then the following proposition follows from equation (7). PROPOSITION 2. When two countries have (i) identical homothetic preferences, production technology, factor supplies, (ii) both industries derive equal benefits from the impure px2blic input, (Hi) 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 above resu l t can be explained as follows. Suppose that Y industry does not cause any congestion i n X, but X industry does cause congestion i n Y. In other words, X = 0 but [i > 0. Consequently i f G increases, then the output of X industry r i s e s r e l a t i v e l y more than Y (since X does not suffer from congestion). Hence, the output of industry X which causes congestion i n Y i s exported. The analysis conducted so f a r i s based on the assumption that a l l resources are f u l l y u t i l i s e d in both countries. However, s i g n i f i c a n t labour unemployment exists in most rea l economies. In the next section, the models used i n the previous sections are extended to include labour unemployment. 4.3 Government Spending on an Impure Public Input and the Trade Pattern between Underemployed Economies Although s i g n i f i c a n t labour unemployment exits i n most r e a l economies, most open economy models do not take unemployment into account. Batra and Beladi (1990) have considered the trade pattern between underemployed economies, but they do not consider the role of public inputs i n determining comparative advantage. The term underemployment refers to labour unemployment due to r i g i d wages. The purpose of t h i s section i s examine how the d i s t o r t i o n created by i n s t i t u t i o n a l l y f i x e d minimum wages influences the results derived i n the previous section. The s e l f s u f f i c i e n t economy under consideration produces two f i n a l goods (X and Y) by means of two primary inputs and an impure public input. The primary factors are labour and c a p i t a l , of which only c a p i t a l i s f u l l y employed. Due to economy wide r i g i d wages, labour i s not f u l l y employed. A l l other assumptions of section three are maintained i n t h i s section. The equilibrium conditions are the following, where L i s labour employment : L = [X/S,(.) ]c\(.) + [Y/S^{.)]c\{.) + Gc\i.) (8) Ke = [X/Sx(.) ]c\(.) + [Y/Sy(.) ]cy,(.) + Gc\{.) (9) C^(r, w)/[S,(.) ] = 1 (10) CUr, w)/[Sy{.) ] = p (11) y = D(p) X (12) For a given supply of impure public input, the above are f i v e equations i n f i v e endogenous variables: L, r, p, X and y. These equations determine the equilibrium of a representative closed economy. By means of a comparative s t a t i c s exercise, the pattern of international trade between two such economies i s considered i n the following section. 4.3.1 The Pattern of Trade The following derivative can be derived by using equations (9) to (12) . The two industries are assumed to derive equal benefits from the supply of an impure public input ( i . e . , a = P) , public input i s equally congestible across industries ( i . e . , y = C,) and the congestion caused by each industry i n the other industry i s i d e n t i c a l ( i . e . , |i = À) . 8p/aG = (p/G)T[a„ - a„J/H, •dd = [rw(P/G)T{c^„(.)c\(.) }/Hdd{cM.)cM.) }] [ (K,/LJ - (Ky/L^) ] (13) where T = [a(K^ + Ky) + (Y + |i)Kg] > 0 The sign of the above derivative depends on: (1) the r e l a t i v e c a p i t a l i n t e n s i t y (K^/L^ - Ky/Ly); and (2) the sign of H^ d. H^ d i s negative provided the equilibrium i s stable. The above derivative shows that even i f (1) the congestion caused by the two industries i s symmetric, (2) public input i s equally congestible within each industry, and (3) both industries derive equal benefits from the supply of public input; the pattern of trade can s t i l l be influenced by differences i n the supply of an impure public input. The wage rate i s fixed. However an increase i n G affects the equilibrium rate of return on c a p i t a l which increases the cost of production of both industries. The sign of the above derivative i s p o s i t i v e i f Y industry i s r e l a t i v e l y more c a p i t a l intensive. The following proposition follows from equation (13). PROPOSITION 3. When two countries have (i) identical preferences, production technology, factor supplies; (ii) a minimum wage rate; ( i i i ) both industries derive equal benefits from an impure public input; (iv) the congestion caused by each industry is symmetric; and (v) the public input is equally congestible within each industry; then the country that produces more public input exports (imports) the output of the industry which is relatively less (more) capital intensive. The wage rate i s fixed, but an increase i n G increases r through an increase i n the marginal productivity of c a p i t a l . Suppose that industry Y i s r e l a t i v e l y more labour intensive compared to X. If G increases, then the per unit cost of industry X r i s e s r e l a t i v e l y more than Y (since Y i s c a p i t a l i n t e n s i v e ) . Consequently, the output of labour intensive industry Y i s exported. The above r e s u l t d i f f e r s sharply from the one derived i n the previous section where i t was shown that when (i) both industries derive equal benefits from the supply of an impure public input, ( i i ) the factor i n t e n s i t y of the public and private sectors i s the same, ( i i i ) the congestion across the two industries i s symmetrical, and (iv) inter-industry congestion i s symmetrical; then the trade pattern i s not influenced by the differences i n the production of a public input. It can e a s i l y be shown that the above res u l t also holds i n the case of a pure public input. 4.4 Concluding Remarks Abe (1990) has shown that the differences i n the production of a pure public input alone can explain the pattern of trade between countries which f u l l y u t i l i s e t h e i r resources. This essay has attempted to extends Abe's work i n two d i r e c t i o n s : (1) the relationship between government spending on an impure public input and the pattern of trade between economies which f u l l y u t i l i s e t h e i r resources has been considered; and (2) the relationship between government spending on a public input and the pattern of trade between underemployed economies has been considered. In the context of a two-country and two-good general equilibrium model, the relationship between government spending on an impure public input and the trade pattern i s examined i n section two. A l l resources are f u l l y u t i l i s e d i n both countries. An impure public input i s congestible within industries and among firms across industries. Both types of congestion are considered. It i s shown that when the public input i s equally congestible within each industry but the congestion caused by each industry i s not symmetric, then the differences i n i t s production can determine the pattern of trade even i f both industries equally benefit from i t s supply and the factor i n t e n s i t y of the public and private sectors are i d e n t i c a l (or s u f f i c i e n t l y close to each other): a country which produces more public input exports (imports) the output of that industry which creates more (less) congestion i n the other industry. Furthermore, when the congestion caused i n each industry i s symmetric but the public input i s not equally congestible within each industry, then the differences i n i t s production can determine the pattern of trade even i f both industries equally benefit from i t s supply and the factor i n t e n s i t y of the public and private sector are i d e n t i c a l : a country which produces more public input exports (imports) the output of that industry i n which the public input i s r e l a t i v e l y less (more) congestible. On the other hand, i f both industries benefit equally from the supply of the public input, the congestion caused by each industry i s symmetric, public input i s equally congestible within each industry, and conditions (i) and ( i i ) hold, then differences i n i t s supply cannot influence the pattern of international trade. This implies that congestion can actually reverse the results derived by Abe (1990). If the public input i s not congestible and the factor i n t e n s i t y of the public and private sectors are i d e n t i c a l , then the country which produces more public input exports the output of the industry which derives more benefits from i t s supply. However, i n the case of a congestible public input, the country which produces more public input may import the output of the industry which derives more benefits from i t s supply, i f the public input i s r e l a t i v e l y more congestible i n the relevant industry. F i n a l l y , i t i s shown that the results derived i n section three are s i g n i f i c a n t l y influenced by the presence of labour unemployment: i f both industries benefit equally from the supply of a congestible public input, public input i s equally congestible within each industry, and the congestion caused by each industry i s symmetric, then the underemployed country which produces more public input exports the output of the r e l a t i v e l y less c a p i t a l intensive industry. Appendix 4.1: Stability Conditions Equations (5), and (8) to (11) can also be used to derive the Routh-Hurwitz s t a b i l i t y conditions. The postulated dynamic adjustment process i s described by means of the following equations, where the l e f t hand side i s the time derivative of the relevant variable: dw/dt = a„[{X/S^(.) }c\(.) + {Y/S^(.) }c\{.) + Gc\(.) - L,] dr/dt = a,[{X/S,(.) }c\(.) + {Y/Sy(.) }c^(.) + Gc^ (. ) - KJ dx/dt = a j l - C''(r, w) /{S,(.) }] dY/dt = ay[p - CMr, w)/{Sy(.) }] dp/dt = ap[D(p) - Y/X] where the relevant speeds of adjustment (a„, a^, a^, a^, a J are assumed to be p o s i t i v e constants. The economic meanings of the above equations are obvious, therefore the interpretation i s not included i n t h i s essay. The relevant Jacobian matrix, denoted by J i s the following: J = I a n a.21 aai a4i as i ai2 a32 a42 a52 ai3 323 a33 343 353 ai4 324 334 344 354 3 l 5 325 335 345 355 where 311= [ { X / S x ( . ) }c\„(.) + {Y/Sy(.) }cy„„(.) +Gc%„(.)] 312 = [ { X / S x ( . ) } c ^ , ( . ) + {Y/Sy(.) }cV(.) + Gc%,(.)] = c \ ( . ) [XS,,(.) - Sx(.) ] / [ S ^ ( . ) ] - cy„YSyJ.)/S\(.) = Cy„(.) [YSyy(.) - Sy(.) ] / [ S % ( . ) ] " C \ Y S ,y ( . ) / S ^  ( . ) 3l5 = 0 321= [ { X / S , ( . ) }c\„(.) + {Y/Sy(.) }cy,„(.) +Gc5,„(.)] 322 = [{X/SJ.)}c\,(.) + {Y/Sy(.) } c ^ , ( . ) + Gc\,{.)] a23 = c ^ ( . ) [XS,,(.) - S,(.) ] / [ S ^ ( . ) ] - c ^ Y S y , ( . ) / S % ( . ) = C^r(.) [ySyy(.) - Sy(.) ] / [ S % ( . ) ] - C ^ Y S , y ( . ) / S ^ ( . ) 325 = 0 331 = - c \ ( . ) / S , ( . ) ; a32 = - c \ ( . ) / S , ( . ) a33 = c='(.) [S,,(.) ] / S ^ ( . ) ; a34 = C (. ) [3,^ (. ) ] / S \ (. ) 335 = 0 341 = - c \ { . ) / S y { . ) ; a42 = - c y r ( . ) / S y ( . ) a43 = c M . ) [ S y , ( . ) ] / S % ( . ) ; a44 = c M . ) [S^^ (. ) ] / S % (. ) 345 = 1 351 = 0; 352 = 0; a53 = Y/X\- a^^ = - (1/X) / 355 = D' (p) One of the Routh-Hurwitz s t a b i l i t y condition requires that (-1)^|J| > 0 where "| |" stands for the determinant. The determinant of the above Jacobian matrix i s the following: J = - HH Clearly, the determinant condition i s s a t i s f i e d i f H^  i s p o s i t i v e . CHAPTER 5 FINAL SUMMARY AND CONCLUDING REMARKS This thesis consists of three essays. Each essay examines the role of government spending on industries i n open economies. Government spending on industries i s incorporated i n production functions i n terms of a public input. The public input i s cooperative with the private inputs i n the production of f i n a l goods. Add i t i o n a l l y , the public input i s provided to the firms by the government free of charge. Since each essay deals with a d i s t i n c t issue regarding public inputs i n open economies, d i f f e r e n t models are u t i l i s e d i n chapters 2 to 4. The purpose of the f i r s t essay (chapter 2) i s to investigate the impact of terms-of-trade changes i n a small public input economy. Lags i n the production and supply of public inputs are e x p l i c i t l y taken into account. These lags provide a mechanism whereby terms-of-trade changes i n either period influence the output of both private and public sectors i n other periods. Lags i n the production and supply of public inputs can only be taken into account i n the context of a multi-period model. A three period model i s therefore appropriate. The public input i s produced by means of labour, whereas the private goods are produced by means of labour, public input, and some fix e d factors. Labour i s f u l l y mobile between the public and the private sectors. The a l l o c a t i o n of resources between the public and private sector i s therefore endogenous. Because the focus of the essay i s on the role of public inputs, private investment i s assumed away. The model can further be extended to include uncertainty about the future terms-of-trade and the future provision of public inputs. Another possible extension i s to allow d i s t o r t i o n a r y taxes to finance the cost of public production. The second essay (chapter 3) examines the international transmission of government spending on public inputs i n the short-run and the long-run. The implications of po t e n t i a l international economic p o l i c y coordination are also considered. International i n d i r e c t s p i l l o v e r s of government spending on public inputs are possible only i f the countries under consideration are linked. International factor mobility provides one such l i n k . When the countries are linked through international factor mobility, a single f i n a l good model can be used. Accordingly, the analysis i s conducted by means of a two-country, one-good general equilibrium model with international factor mobility. The focus of the essay i s on international transmission of government spending on public inputs. For s i m p l i c i t y , the public input i s assumed to be produced out of the f i n a l good which i s also the numéraire. In the context of a three-country model, the essay also examines the international transmission of government spending on a public input when two countries have formed an economic union. The analysis i s conducted by means of a one-period model. A possible d i r e c t i o n for further research i s to consider a m u l t i -period model. Such a framework also allows one to consider the international transmission of f i s c a l d e f i c i t s . Abe (1990) considered the relationship between the supply of a pure public input and the pattern of trade. The t h i r d essay (chapter 4) examines the rel a t i o n s h i p between government spending on impure public inputs and the pattern of trade. An impure p u b l i c input i s incorporated into a standard two-country, two-good, two-primary-factor general equilibrium model. For s i m p l i c i t y , international factor mobility i s assumed away. Unlike pure public input, an impure public input i s congestible. 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