THREE ESSAYS ON NORTH-SOUTH TRADE, GROWTH, AND DEVELOPMENT by CHAYUN TANTIVASADAKARN B.A., Thammasat University, 1981 M.A., Thammasat University, 1985 M.A., The University of British Columbia, 1989 A THESIS SUBMIITED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATh STUDIES Department of Economics We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA December 1994 © Chayun Tantivasadakarn, 1994 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. (Signature) Department of EwncnmCS The University of British Columbia Vancouver, Canada Date DE-6 (2188) -Qc j 1?f- ABSTRACT This thesis focuses on three issues pertaining to growth, development, and trade between developed and developing countries. The first essay develops an endogenous growth model that incorporates Engel’s law into the preferences. The model shows that the initial distribution of income is crucial to the outcome. A closed-economy country where most of its population is poor experiences a low rate of innovation. Income transfers from the rich to the poor can increase the effective labour supply, thereby enhancing the rate of innovation. Under free trade, only the rich benefit from trade. The poor are indifferent unless they already can afford to consume the minimum requirement of food before trade or the minimum requirement becomes affordable after trade by cheaper imported food. The initial distribution of income influences the trade patterns. Moreover, income redistribution in a free trade environment also increases the growth rate. The second essay extends the first one by assuming that the marginal product of labour of the food sector is decreasing. It shows that an increase in population may decrease the growth rate if the initial population is large relative to the productivity of the food sector. Moreover, an increase in one country’s population may reduce that country’s production share of the world’s innovation and increase its dependency on imported technology. The last essay analyzes the welfare impact of minimum-export requirements (MERs) imposed on foreign direct investments. This essay shows that MERs can be Pareto improving measures to both the source and the host countries. When offshore plants are used by parent firms to compete with domestic firms in the source country, MERs can improve the host country’s welfare by inducing the total sales in the source country to rise, thereby reducing the distortion generated by imperfect competition. 11 The MERs can simultaneously improve the welfare of the host country by shifting profits of the foreign firms toward the local firms. If the local firms are absent, the host’s welfare may still be improved if sufficient profits from foreign operations are retained in the host country. 111 TABLE OF CONTENTS ABSTRACT ii TABLE OF CONTENTS iv LIST OF FIGURES vii ACKNOWLEDGEMENT viii I IITRODUCTION 1 II NORTH-SOUTH TRADE AI1) THE RICARDIAN GROWTH MODEL 7 1. Introduction 7 2. Autarky Model 10 2.1 Consumer’s intertemporal maximization problem 12 2.2 Firm’s Problem 16 2.3 Steady State Equilibrium 21 2.4 Redistribution of income and growth 27 3. Free Trade Model 30 3.1 Trade Patterns 31 3.2 Consumers 34 3.3 Trade Equilibrium 36 4. Redistribution of income under free trade 50 5. Comparative Steady-state Analyses 54 5.1 Changes in productivity of the manufacturing sector 54 5.2 Changes in productivity of the R&D sector 57 5.3 Changes in productivity of the grain sector 58 5.4 Changes in labour endowment 65 6. Conclusion 67 Appendix 68 iv Ill NORTH-SOUTH TRADE AND GROWTH: WITH DIMINISHING MARGINAL PRODUCTIVITY 80 1. Introduction 80 2. Autarky: 81 2.1 Country size, population mix, and growth 88 2.2 Redistribution of income and growth 95 3. Free Trade 98 3.1 Consumers 99 3.2 Trade patterns 99 3.3 Trade equilibrium with both countries producing R&D 103 4. Comparative Steady State Analyses: Trade model 112 5. Conclusion 119 Appendix 120 IV MINIMUM EXPORT REQUIREMENTS: PARETO IMPROVING MEASURES 126 1. Introduction 126 2. Structure of the Model 130 2.1 Minimum-Quantity-Export Requirement (QER) 131 2.2 Export-Share Requirement (ESR) 135 3. Optimal MERs 148 3.1 Optimal quantity-export requirement 149 3.2 Optimal export-share requirement 152 4. Multiple-duopoly Case 153 4.1 Minimum-quantity-export requirements 153 4.2 Minimum-export-share requirements 154 5. Conclusion 160 V Appendix 162 REFERENCES 164 vi LIST OF FIGURES Figure 2.1 Balance of Payments Schedule 40 Figure 2.2 Steady State Equilibrium 41 Figure 2.3 Effect of the Change in Relative Labour Productivity in Manufacturing Goods 56 Figure 2.4 Effect of the Change in the South’s Grain Productivity 63 Figure 2.5 Effect of the Change in the North’s Grain Productivity 64 Figure 3.1 Balance of Payments Schedule 105 Figure 3.2 Patterns of Manufacturing and R&D Production 109 Figure 3.3 Steady State Equilibrium 113 Figure 4.1 Market Structures and trade flows 132 Figure 4.2 Effect of Minimum Export Share Requirements 141 Figure 4.3 Effect of Optimal Quantity Export Requirements 151 vii ACKNOWLEDGEMENTS It has been my very good fortune to have worked under the supervision of Brian Copeland. I am deeply indebted to him for his guidance, patience and support. I cherish the opportunity I have had to work with him and the example he has set as a teacher and a supervisor. I wish to express my gratitude and thanks to Scott Taylor, my thesis committee, who has devoted efforts to a far greater extent than the normal involvement of a committee member. His invaluable insights on endogenous growth models are greatly appreciated. Mukesh Eswaran, the remaining member of my committee, contributed comments and suggestions that brought fresh perspectives to my work. My appreciation also goes to my department examiner, Ashok Kotwal, and my university examiner, James Brander, for their thorough reading of a draft of this thesis and valuable comments. My studies at the University of British Columbia have been made possible by a scholarship from the Canadian International Development Agency and by awards of Teaching Assistantships from the Department of Economics. I am grateful to the Faculty of Economics of Thammasat University for granting me the required study leave. My appreciation also goes to my friend, Alison Gear, for her warm friendship throughout my stay in Canada and for her thorough editing of this dissertation. Finally, my love and admiration goes to my family, especially my wife Patchara, who has stood by me all this time throughout all frustrations and achievements with patience and love. viii CHAPTER I INTRODUCTION Economic development and growth are among the most important goals of all nations especially the less developed countries (LDCs). Economic history has revealed phenomena of a large variation in the growth experiences and long sustenance of growth rates in many countries. These phenomena are believed to be attributed to different economic environments and government policies. Several studies have tried to identify the key factors that sustain and stimulate economic growth. By the globalization trend and the success of the “outward oriented” policy of the “Four Asian Dragons”, the factor that seems to get the most attention is the trade orientation that one country takes. At least two studies confirm this connection between the trade orientation and the growth performances. The studies by World Bank (1987) and by Syrquin and Chenery (1989) conclude that the countries with the “outward trade orientation” outperformed those countries with the “inward trade orientation ’. 11 These findings have prompted theorists to construct models that can explain the linkage of trade to the growth performances, e.g., Grossman and Helpman (1992), Taylor (1994b). In these types of models, growth is a result of technological breakthrough that is achieved by research and development (R&D) of profit seeking entrepreneurs. The economic environments (including the trade orientation) can influence the incentives of the R&D, thereby affecting the growth outcomes. The World Bank reports that during 1973-85 the growth rate of real GDP of the strongly outward-oriented countries was 7.7 percent per year while it was 2.5 percent for those of the strongly inward oriented countries. In Syrquin and Chenery (1989), the average output growth rate (1952-83) of the countries with the outward trade orientation is 5.22 percent per year versus 4.28 percent for those of the countries with the inward trade orientation. 1 These types of models have provided many important lessons about trade, growth and development especially for the developed countries (DCs). However, there are some important characteristics of the LDCs that should be incorporated so that we can better explain the situations of the LDCs. There are at least three aspects about the LDCs that need special attention. First, the LDCs have serious income distribution problems. With a very skewed distribution of income, most people in the LDCs are not wealthy enough to demand industrial products. This insufficient demand may inhibit the ability of the LDCs to support R&D necessary for industrialization especially when the economy is closed by protection. If the problems of income distribution are reduced, the LDCs should have higher capability to engage in R&D and achieve higher growth. Second, the agricultural sectors of the LDCs are still the major sectors of their economies and most of the LDCs’ labour forces concentrate in these sectors. Thus, output of their agricultural sectors tends to suffer from the problem of diminishing marginal productivity of labour. The problem is more severe for the LDCs with scarce land and rapid population growth. Thus, a diminishing marginal productivity (DMP) assumption may be more appropriate for the LDCs. The DMP assumption is important not only because of its ability to fit the production pattern of the LDCs, but also because of its implication on the growth performance. In the country in which land is scarce, an increase in food production to serve the larger population would cause the agricultural sector to be less and less productive due to the DMR Hence, it has to draw resources increasingly from other sectors. Consequently, the more the population grows, the fewer resources will be available for R&D. This could decrease growth. 2 Third, the LDCs need to industrialize in order to achieve the desired economic development and growth. However, the LDCs usually lack both the capital and the technology to start their own industrialization. They have to rely on foreign direct investment (FDI). LDCs often design investment incentive packages which are attractive for the foreign investors yet still have some mechanisms to control the benefits of FDI. These control mechanisms or Trade Related Investment Measures (TRIMs) are opposed by the DCs who are the source of the FDIs on the ground that they restrict trade, and therefore, generate adverse effects on the DCs’ welfare. However, certain kinds of TRIMs, particularly minimum export requirements (MERs), may be beneficial for the source countries for the following reasons. The market structures of the industries that use FDI are often highly concentrated. Producers do not need to sell as much as they would if they were in perfectly competitive industries. As a result, the prices will be higher than the marginal costs which give rise to distortions. The MERs imposed by the host countries may increase the total sales of the source countries. This increase of sales reduces the gap of prices and marginal costs which, in turn, decreases the distortion in the source countries; and improves their welfare. This thesis consists of three essays, which deals respectively with each of the issues outlined above. They are presented in Chapter II to W The first two essays are closely related and deal specifically with growth and development under free trade environments. The last essay concentrates on development and trade with intervention. Thus, the three essays may be united under the common theme of North-South trade, growth and development. The main objective of the first essay is to study how a redistribution of income affects growth, trade patterns, and welfare. growth model is used. To attain this objective, an endogenous Most of the existing endogenous growth models assume that 3 preferences are homothetic which inhibits their abilities to analyze problems pertaining to changes in income distributions. Thus, to analyze the effect of income redistribution, the model incorporates Engel’s law into the preferences. It employs two types of consumers: the capitalists and the workers. Workers represent the poor who suffer from malnutrition and therefore can supply fewer effective units of labour than the capitalists. The economy has two final goods: grain and manufactured goods. The technology of the grain sector is time invariant while the processing technology of the manufacturing sector can be improved by R&D. The intensity of R&D determines the speed that the processing technology advances which in turn influences the utility growth rate and welfare. A wealth redistribution from capitalists to workers will allow these workersturned-capitalists to consume manufactured goods and increase the aggregate demand. The higher aggregate demand then raises the expected profits of R&D, thereby, stimulating the growth rate and welfare. Moreover, these worker-turned-capitalists will no longer have malnutrition problems, so their effective units of labour will rise. With larger labour supply, R&D increases, which in turn raises growth and welfare. The second essay deals with the issue of DMP in the agricultural sector. The structure of the model follows the format of the first essay, except that the grain sector is now subject to DMP. The objective is to determine how the results from the first essay change with the DMP assumption. An increase in population may increase or decrease R&D and growth. On the one hand, the increase in population adds labour supply to the economy (endowment expansion effects). On the other hand, the increase in population also raises the demand for grain which draws labour resources from the R&D sector because of the diminishing marginal productivity (diminishing marginal productivity effects). The endowment expansion effects increase R&D while the diminishing marginal productivity effects 4 decrease R&D. An increase in population from an initially low level would generate small diminishing marginal productivity effects; thus, R&D would rise. A continued increase in population, however, generates increasingly stronger diminishing marginal productivity effects which will eventually overtake the endowment expansion effects. Therefore, R&D would eventually reduce. A redistribution of wealth from capitalists to workers, under DMP assumption, also suffers the same phenomenon. Hence, it only works for an initially small population level. In the first two essays, it is assumed that multinational corporations (MNCs) from DCs are free to choose where to apply their processing technology: domestic or abroad. If they find that it is more efficient to apply their technology in LDCs, they can establish subsidiary firms in LDCs and supply the world demand from these firms. The first two essays also assume that these activities are free from intervention. However, some forms of TRIMS are often applied to FDI. The last essay studies the effects of Minimum Export Requirements (MERs) which are one of most popular TRIMs. The third essay does not deal directly with the growth issues, but concentrates on the issues related to FDI which are the means for LDCs to attain economic growth. It focuses on the strategic interactions between firms in the source and host countries caused by the imposition of MERs. Therefore, the model departs from the endogenous growth framework and adopts the static partial equilibrium framework commonly used in this type of literature for analyzing trade issues with strategic interactions. The main objective of the last essay is to show that MERs are not always harmful to the source countries as are normally believed. In fact, they can lead to a Pareto improvement for both the source and the host countries. The MERs can improve the welfare of the source country because they help the MNCs to make a commitment to sell to a greater extent than they normally would in the source countries. This raises the total 5 outputs and reduces the price. The gap of the price over the marginal cost and its economic distortion are, therefore, reduced. The MERs can simultaneously improve the welfare of the host countries by shifting the profits of the MNCs toward the local firms in the host countries. Even when local firms do not exist, the MERs can still improve welfare of the host countries if the MERs are tied with other measures such as minimum share of profits that the MNCs must retain in the host countries. 6 CHAPTER II NORTH-SOUTH TRADE AND THE RICARDIAN GROWTH MODEL 1. Introduction One of the recent developments in the endogenous growth model was originated by Romer (1986, 1987). It has been popularized and developed into trade models by Grossman and Helpman (1989, 1990, 199 Ia, b), and Taylor (1993, 1994a, b). Unlike the neoclassical growth model developed by Solow (1956) and by Swan (1956), growth in these approaches is generated by the profit-maximizing behaviour of firms which choose the optimum level of research and development (R&D) either to develop new varieties of goods (variety approach) or to improve an existing set of goods (quality ladder approach). Any changes in the economic environments (e.g., trade policies, incentives for R&D) can affect the optimum level of R&D chosen by the firm, thereby changing the growth rate. These endogenous growth models are very useful in tackling many questions relating to long-run growth and international trade. But most of these models assume homothetic preferences. Although the homothetic assumption has helped economists by simplifying the demand side of the model so that they could concentrate on problems of the supply side, some economists have started to express concern about this simplifying assumption. Their concerns come from two sources. First, homothetic preferences deny Engel’s law. When homothetic preferences are assumed, we force the consumption patterns of the rich and the poor to be the same which may be acceptable for the case of developed countries (the North). This assumption is rather unrealistic for developing countries (the South) where income distributions are quite skewed. In addition, when we consider economic problems pertaining to the South, we might want to distinguish between the impact of some changes on the welfare of the rich and the poor. The 7 homothetic assumption, nevertheless, does not allow us to do so because anything that affects the consumption patterns of the rich also proportionately affects those of the poor. The second problem of the homothetic assumption is its inability to fit the data. Many empirical studies in international trade [e.g., Ballance, Fostner, and Murrey (1985), Hunter and Markusen (1988), Hunter (1991)] have rejected the homothetic preference hypothesis. Consequently, if we are going to use an endogenous growth model to analyze problems pertaining to North-South issues, we need to abandon the homothetic assumption. A simple yet powerful way to incorporate Engel’s law is to assume a “hierarchical preference structure” as in Eswaran and Kotwal (1993), and Murphy, Shliefer, and Vishny (1989). The idea of these preferences is that goods are consumed according to their ranking in the hierarchy of needs; i.e., people try to fulfil a minimum need of food before starting to consume manufactured products. Inspired by these pioneering works, this paper combines the hierarchical preferences of Eswaran and Kotwal (1991, henceforth E-K) with the dynamic Ricardian trade model of Taylor (1993, 1994a, b henceforth Taylor). As a result, the model used in this paper inherits the features of the endogenous growth model but employs the non-homothetic preferences which rectify the problems mentioned above. Before moving on, it may be appropriate to discuss why these two models were chosen. Taylor’s model shares several parallel properties to the quality ladder model of Grossman and Helpman. However, growth in Taylor’s model is generated by investment in R&D to reduce unit labour requirements of production. His approach is also very tractable since labour is the only input of production; hence, many questions can be answered simply by graphical methods. Moreover, the factor prices are not generally equalized between trade partners. This is a suitable property for North-South trade where factor prices are not often equalized. The paper by E-K explains how patterns of consumer demand which behave according 8 to Engel’s law can affect real wages and hinder the benefits of industrialization from “trickling down” to the poor. Although their approach of incorporating Engel’s law into the preferences is “stark”, the underlying logic and their results would still hold if the substitution effect between food and manufactured products for the poor was sufficiently small. Now let us continue on the structure of the model in this paper. The supply side of the model relies heavily on Taylor’s framework and the following modifications have been made. First, apart from the manufacturing sector, an agricultural sector called grain (representing food products) with a perfectly competitive market structure and time-invariant technology is added. Second, the original functional form of preferences is modified to incorporate grain consumption and reflect the hierarchical nature based on E-K’s idea. Third, instead of homogeneous consumers, there are now two classes of people, workers and capitalists. Capitalists, with higher income than workers, can consume both grain and manufactured products. Workers, however, may consume only grain when their income is too low. Finally, the model concentrates on North-South trade instead of North-North trade. North is considered to be a developed country, with its population sated with grain; South is considered less developed and only its capitalists are sated with grain. With these modifications, the model is different from its predecessors in the following ways. First, the hierarchical preferences allow us to analyze the effects of a redistribution of income on R&D, growth, trade patterns, and welfare. These analyses are not possible under the homothetic preferences. Second, this functional form does not restrict the consumption units (of manufactured products) to be discrete as the one used in Murphy, Shliefer, and Vishny (1989, henceforth M-S-V)’. Third, as in E-K and M-S-V the model shows that when food is the first priority in the hierarchy of needs, a technological improvement in the agricultural sector creates In M-S-V, the consumption unit of each manufactured good is either 1 when it is consumed or 0 when it is not. 9 static spilover effects in the manufacturing sector. Besides those static effects, this paper can capture dynamic effects which are not presented in the static framework. Some similarity and differences of the approach used in this paper from other studies on ’ redistribution of income should be pointed out. Chou and Talmain (1991) use a similar endogenous growth model with R&D in intermediate inputs and with variable labour supply . When the labour Engel curve is concave, a redistribution of income increases the growth rate in their model by reducing leisure consumption which in turn raises the aggregate labour supply . The result in this paper also relies on the supply side. However, the labour supply is inelast ic since consumers in this paper do not consume leisure. Redistribution of income increas es the labour supply and growth because it alleviates malnutrition problems of the poor. Furthe rmore, Chou and Talmain study only the case of a closed economy while this paper studies both autarky and free trade cases. Fischer and Sega (1992) employ a trade model with externalities of human capital to show the negative relationship between inequality and growth. They also conclu de that inequality decreases over time. However, this paper reveals that it persists. The poor are trapped in poverty while the rich prosper and the gap, in terms of welfare, grows wider over time. The organization of the paper wifi be as follows: Section 2 lays down the structure of the model for a closed economy. Section 3 extends the model in section 2 with Ricardian technology to a free trade model. The impacts of a redistribution of income and comparative steady-state analyses for the free trade model are provided, respectively, in section 4 and 5. Finally, section 6 gives the conclusion and suggests some extensions. 2. Autarky Model Consider an economy with two sectors: grain and a continuum of manufactured goods. Their respective quantities are denoted by g and x(z), where z is the index of commodities on an interval [0,1]. The grain sector represents a traditional sector with no technological progress 10 while the manufacturing sector depicts the advanced sector with technological progress. The total population (L) is fixed consisting of L workers and L capitalists, where L Consumers in each group are homogeneous. = IL, 0 <1 < 1. All consumers share identical hierarchical preferences. The consumption pattern derived from these preferences depends on the income level y, where i e {w=worker, c=capitalist}. Consumers will not demand any manufactured products if their incomes are insufficient to consume a minimum biological need of grain (g). However, if they earn sufficient income to consume §, no further grain will be consumed. They will spend the remaining income on manufactured products only . 2 It is assumed as in Dasgupta and Ray (1986, 1987) that people who are not sated with grain suffer from malnutrition and, therefore, have less labour power than those who are sated . 3 Normalize the unit of labour of any person who is sated with grain to 1 and denote the labour power of any individual who is not sated with grain as a, where 0 <a < 1. Leisure is assumed to generate no utility to consumers, so everyone supplies all of his or her labour inelastically. Apart from labour, each capitalist is endowed with q unit of equities which yields an interest rate of r per period. Since we are interested in the case where income distribution is sufficiently skewed so that people in different groups demand different consumption shares of grain and manufactured goods, the following assumptions are made. Income generated from the equities and wages allows capitalists to be sated with grain, however, wage income that workers earned does not. Denote the wage rate per unit of labour productivity as w and the price of grain as p. Then, this last assumption, henceforth Satiation Assumption, implies that each capitalist’s income: y, 2 = w + rq is greater than the expenditure for i which, in turn, is greater than each See justifications of these preferences in E-K, section 4. The theoretical implications of the link between productivity and consumption date back at least to Leibenstien (1957). Also see Rodgers (1975), Mirrlees (1976), Stiglitz (1976), and Bliss and Stern (l978a,b) analyses of efficiency wages. 11 worker’s income: y = ctw, i.e., y, > p> y. Goods are assumed to be produced according to Ricardian technology with labour as the only input. The grain sector is perfectly competitive and its technology is fixed over time. Firms in the manufacturing sector have two activities: conducting R&D to discover new technology and then producing goods using this technology. The leader firm which discovers the newest technology of industry z receives an infinite life patent. However, the know-how generates spillover effects on the public knowledge upon which the subsequent generations of technologies will be built. Therefore, the overall manufacturing activity exhibits dynamic increasing returns to scale. With the exclusive right on the best production technology, the leader uses limit pricing to capture the whole market of its industry and earns monopoly profits. The monopoly power continues until the next generation of technology is discovered; then the new leader becomes the monopolist. The cost of discovering the next generation of technology is incurred only once and the up-front cost of R&D is fixed to production activity. Each firm funds its risky R&D by seffing equities to the public. Successful R&D increases labour productivity by reducing the unit labour requirement which, in turn, reduces prices of manufactured goods and generates utility growth. With the above general idea of the model, the rest of this section describes the formal model and provides analyses. 2.1 Consumer’s intertemporal maximization problem All consumers have an identical, time separable, expected intertemporal utility function. Denote the price of grain and the expected prices of manufactured goods at time t as p(t) and p(z,t), z E [O,lj respectively. Given these prices and income, a representative consumer i {w,c) chooses consumption of g(t) and x(z,t) to maximize See the proof in footnote 18. 12 E W fe-Pt = st. q = y ( 1 t) 1nudt — } (2.1) e(t). (2.2) where E 0 is the expectation taken at time t=O conditional on the current information; p is the subjective discount rate; and lnu (t) represents the instantaneous utility at time 1 t. The constraint (2.2) indicates that the rate of change of investment in equities q dq/at is equal to the income leftover from consumption expenditure, where 1 y ( t) is the total income and e.(t) is the total consumption expenditure. The instantaneous utility function is assumed to take a form given by 3 y ( 1 t) pj lnu(t) 1 = ma + f (2.3) ln[x ( 1 z,t)J d, 1 y ( t) >pj, Each worker has only y(t) = aw(t) as income which, by Satiation Assumption, is less than p(t) Thus, the top part of (2.3) is used for the worker. Solving for each worker’s per period demand for grain gives: g(t) = ciw(t)Ip(t). It is assumed that workers will not survive if they cut back their consumption in order to save. Therefore, workers do not invest in any asset if they are not sated with grain . 6 The income of each capitalist is y(t) = w(t) + rq(t), where q(t) = Q(t)ILQ and Q(t) is the The preferences are adapted from E-K’s idea. They are lexicographic since they are not continuous at the point where y = pg. However, the preferences are continuous in the range of (O,p) and (pjoo). Therefore, we can order the utility of an individual within each income range, but not between the two ranges of income. Throughout this paper, these preferences are used for welfare comparison only for the change of income within each income range. Although the functional form of the preferences used here is lexicographic, it is needed for solving the consumer’s optimization problem. A similar functional form which is also lexicographic is used by M-S-V. 6 save. Bertola (1991), using a similar endogenous growth model, shows that wage earners do not 13 total equities held by the capitalist. Recall that yç(t) > p(t) by Satiation Assumption; hence, the relevant instantaneous utility function for the capitalist is the bottom part of (2.3). It has a Gorman polar form ; thus, it is quasi-homothetic and the Engel’s curves are straight lines. 7 Therefore, aggregation across capitalists is allowed. Furthermore, solving each individual maximization problem and then aggregating the results up is equivalent to solving the maximization problem of the representative capitalist who has the aggregate income and requires an aggregate minimum grain consumption of the group. The latter method is used by giving an income of Y(t) capitalist who has a minimum grain requirement of G the aggregate variables of the people in group i E = y(t)L to a representative . (Note that, throughout the paper, 7 g {w,c) are denoted by capital letters and they are defined by the product of their corresponding individual variables and population). Then, using the fact that the utility is quasi-homothetic and time separable, the interte mporal maximization problem of the representative capitalist can be solved in two stages. The proble m in the second budgeting stage will be solved first, then the result is used for solving the problem in the first budgeting stage. In the second budgeting stage, the representative capitalist chooses per period consumption of grain and manufactured goods, Gjt) and X(z,t), to maximize lnu(t) given prices and EQ) = eQ)L. Since land x(z,t) are separable in (2.3), the expenditure for x(z,t) is just the expenditure left over from capitalist as MçQ) [e(t)-p(t).L. Define this aggregate manufacturing expenditure of the Then, the capitalist’s per period demand for grain and manufactured goods 8 is: See Gorman (1961, 1976). The sub-utility function for the manufactured goods is Cobb-Douglas; hence the deman d of good z takes the familiar form of a share of total budget divided by its price. Notice that the budget share for every good z is equal to 1. 14 M(t) G(t) X(z,t) = respectively, where G In U(t) (2.4) zE[O,1], Substituting these demands into the bottom part of (2.3) yields: mG = p(z,t) InM(t) + - (2.5) flnp(z,t)dz. Then set w(t)=l as a numeraire and rewrite constraint (2.2) as = rQ(t) + [1-p(t)g7L - Q— where i(t) + - + p(t)gL M(t). Now reformulate the first stage problem as the one of choosing M Q 0 ) and Q(t) to maximize the current Hamiltonian: H = 1nU(t) H = mG [1+rq(t) ]L M(t) 1nM(t) — fhw(z,t)dz + IL(t){rQ(t) + + p(t)Q or [1 —p(t)jJL —M(t)J, (2.6) is the current value multiplier. From the optimal control theor9, the solution to (2.6) is characterized by the following necessary conditions: — = = pi.(t) lim (t)Q(t) (t) = M(t) — = HQ = 0, (2.7) [p—r](t), (2.8) 0, (2.9) t-. Q where = rQ(t) ÷ [1 PgGILc — (2.10) M(t), denotes the derivative of H with respect to k E {M,Q} and u(t)/t is the rate of change of the shadow price of assets. Differentiate (2.7) with respect to time to derive: MJM = pIn. Then using this in (2.8) and (2.9) gives the differential equation of manufacturing - See Kamien and Schwartz (1981), Part II, Section 2. 15 expenditure and the transversality condition: r-p, = Q(t) M(t) = (2.11) 0, (2.12) respectively. These two conditions with the intertemporal budget constraint (2.10) govern the dynamics of the economy. The intuition for these conditions is as follows. To smooth manufacturing expenditure, the capitalist has to decide whether to consume or invest. Condition (2.11) guarantees that each period utility is maximized. This maximization occurs when the growth rate of the marginal utility of manufacturing expenditure cost of spending’°, (r-p). () is equal to the opportunity The intertemporal budget constraint (2.10) then ensures that the increase in the asset investment does not exceed the income left over from consumption expenditure. The transversality condition (2.12) makes sure that the shadow value of assets is equal to zero at the terminal time and the Hamiltonian function is indeed maximized. To simplify the notation, from now on the time index t will be omitted unless it is needed for clarity. 2.2 Firm’s Problem 2.2.1 Grain sector: The technology of this sector is time invariant and the market structure is perfectly competitive. Thus, every firm in the grain sector earns zero profits and must charge p = ag, where ag is its unit labour requirement. 10 If the manufacturing expenditure were used to invest in equities, it would earn a net return of r-p. 16 2.2.2 Manufacturing sector: 1’ It is possible to improve the technology of this sector over time. At any moment in time, the newest generation of technology, denoted by defines j, the state of the art of z production process. With generation j technology employed in industr y z E [0,1], the unit labour requirement is denoted by a(z,j) which is defmed as: a(j,z) = a(z)4(j), je(0,1,2,...), z E (2.13) [1,0], where a(z) is a pure labour requirement component and is time invariant; 4(j) represents a technology component. Potential competitors race to discover the next generation of technology in every industry by exploiting the existing know-how accumulated in the previous generation of technology. If a technological breakthrough has been made for industry z, its state of the art jumps by one generation. This breakthrough is represented by a reduction in 4(j) = [1-n](j—1), 1 > n : 12 4 which evolves according to (2.14) 0. where n is the inventive step’ . In other words, labour productivity in the manufacturing sector 3 is rising over time. The new technology of each industry z is assumed, for simplicity, to genera te know-how spilover only on the subsequent innovation of its own industry. An exclusive infinite-life patent is granted to the inventor who succeeds first in discovering the next genera tion of technology. Therefore, imitation by rivals is prohibited. “The structure of this sector is adapted from Taylor. 12 For simplicity p(j) and n are assumed to be the same for all industries though in the original Taylor model they are industry specific. The interpretation of technological improvement used here is interchangeable with the one used in Grossman and Helpman (1991a) in which the innovation purpose is to improve produc t quality instead of cost cutting. Thus, there are many characteristics shared by both models . In this paper, these facts will be used in reference to some of the proofs that have already been done in their paper. 17 Denote the firm which owns the newest generation of technology of industry z as the leader and denote the firm which owns the technology one generation behind as the follower. It is assumed that both firms engage in price competition. In the Bertrand solution, the follower sets a price equal to its unit cost while the leader charges a price minutely below its competitor’s price. This solution can be understood by the following reasons. The follow er would not set a price higher than its unit cost, a(z)4(j-1), since the leader who has the lowest unit cost can always undercut the price. Nor would the follower charge a price lower than its unit cost since it would incur losses. Thus, the optimal response for the follower is to set the price equal to a(z)(j-l) and earn zero profits. ‘With this price, the leader also would have no incentive to set a price higher than a(z)4(j-l) since its demand and profit would be zero, nor the leader would have any incentive to charge a price discretely below a(z)c(j-l). This is because the manufactured demand is unit elastic and the total revenue is always consta nt, but the leader incurs higher total cost. As a result, the leader uses limit pricing to capture the entire market. This limit pricing is given by the unit cost of the follower: p(j,z) = a(z)4(j—1), z e [0,1], (2.15) Since unit cost of the leader is equal to a(z)4(j), its per-unit profit margin is the difference between the price and its unit cost: = a(z)[4(j—1)—(J)] = na(z)(j—1), ze[O,1]. (2.16) Consequently, the aggregate profits are the product of the per-unit profit margin in (2.16) and the aggregate demand X(z) = MJp(j,z): 18 U(j,z) 1t(J,z)M na(z)4(j—1)M p(j,z) a(z)(/-1) = nM, z e[O,1]. (2.17) Note that these profits are the same for ever y industry z and are independent of and will j henceforth be denoted by just 11. 2.2.3 Innovation sector: As in Grossman and Helpman (1991a, henceforth G-H), the existing leaders do not conduct R&D to acqu ire the technological lead for more than one generation’ To show this, consider a leader firm . 4 which succeeds in discovering two inventive steps over its nearest competitor. It would have a unit cost: a(z)(j+l) = a(z)4(j-l) 2 [1-n] and would earn profits H(j+l,z) = a(z)[ Ø(j-1)-Ø(j+l)jX(z) = n[2-n]a(z)(j-l)X(z) = n[2-n ]Mç. However, if the leader firm refrains from cond ucting further R&D, it earns profits H(J,z) = nM. Thus, the incremental benefit accrued to the existing leader firm is {n[2-n]-n)M = n[l-n]M <nMç. In other words, this incremental reward of discovering technology j+l is strictly less than the incremental reward of discovering the techn ology j. Hence, only non-leader firms undertake R&D to discover the technology j+l since the incremental reward accrued to them is higher than that of the leader firm. Potential innovators that are non-leaders can target any product z to discover the next generation of technology. Since profits, as shown in (2.17), are independent of z and the expected duration of leadership in all z’s is assu med to be equal, all industries are targeted at the same aggregate degree. A potential innovator, contemplating the disco very of the next generation of technology in industry z, recognizes that if the innovatio n succeeds, it will capture the whole market of industry z and start to earn a flow of profits asso ciated with industry leadership of z. These profi t flows will be reflected in the value of equi ty stocks that the firm issues to finance its R&D. 14 This paper abstracts from the possibility that the leader may conduct R&D to deter entry. 19 Denote the stock market value of an industry-leading firm as V. The innova tors devote an aggregate R&D at intensity I for a period of time dt. Each unit of I requires a, unit of labour. The R&D operation is risky and the probability of discovering generation j+l technology is assumed to follow Poisson distribution with an average success rate of Idt. The innovators finance the up-front cost of innovation by issuing equities that pay nothing if the R&D efforts fail but pay dividends if the efforts succeed. The market is perfectly compe titive; hence, free entry will guarantee that the stock market value of each firm must equal the expected cost of market entry; i.e., V = Wa, when I> 0. In a time interval of length dt, the successful firm pays dividends Hdt. If all the R&D efforts targeted at the firm’s product fail, the equity shares will appreciate by Vdt with probability [1-Idt]. The firm will also run a risk of capital loss of V with a probability of Idt if the next generation of technology is discovered. Hence, the expected rate of returns on equity stocks, ignoring terms of order (dt) , is [H 2 + V - 1V]dt/V. The rate of returns is uncertain but the risk is assumed to be statistically independent. Therefore, stock market arbitraging will reduce the gap between the expected rate of returns from R&D and the risk free rate of returns (r) until they are equal’ , or 5 {n+r.’—vi] r (2.18) V By setting w r = 1, V = a, and V= 0. Using these and H = nM, equation (2.18) becomes (2.19) a, Substituting (2.19) in (2.11), the differential equation for M becomes 15 See the discussion on this point in Grossman and Helpman (1991a, page 48) and in Taylor (1993a, footnote 7). 20 (2.20) = 1 a This is the condition that ensures consumer and capital market equilibrium. Finally, to close the model, we need to ensure that the labour market clears. The supply of labour is N a(z)(j)MJp(zj) aL = = + . 6 L Employment in the manufacturing sector is a(z)4(j)X . Employment in the grain sector is 16 [l-n]M Lastly, employment in the innovation sector is 1 a ! . ag[aLw/p+g7c] = = cth--aL. Equating the labour supply to total employment and rearranging gives: [1 —a1]L = [1 —n]M + a/. (2.21) 2.3 Steady State Equilibrium The differential equation (2.20) and the resource constraint (2.21) are two equations in M and I which characterize the steady state equilibrium for the autarky economy. As in Taylor (1993), they are analogous to equations (10) and (11) in 0-H. The two systems of equations wifi be identical if preferences are homothetic and 1-n = iD. where . is the common step of quality ladders in their model. The solution to (2.20) and (2.21) also immediately jumps to the steady state as in 0-H for the following reasons. If M is larger than the steady state value, the differential equation (2.20) indicates that ? > 0; hence, M will grow without bounds. From (2.21), if M keeps increasing, I will eventually be zero. This contradicts profit maximization by the firms since H = nM> 0, but no one conducts R&D. Conversely, if M is smaller than the steady state value, it will decrease and eventually be zero. But this means Q(t)IM(t) violate the transversality condition (2.12). 16 This is because p(zj) = a(z)(f-i) and 4(J) 21 = [1-n]Ø(j-1). = oo. This event would To solve for the steady state equilibrium, multiply both sides of (2.20) by a 1 and set = 0 for steady state, then solve for a. Substituting the result in (2.21) and rearranging yields: M’ = A 1 = [1 — a, where a a p — (2.22) , 1 pa + = —-[[1-a]L+pa,] a, - (2.23) p, aj and the superscript “A” signifies the autarkic solution. With w = 1, equation (2.22) shows that the capitalist’s manufacturing expenditure consists of wage income after grain, 17 1 pa [w-a1L, and the profit income, . The steady state R&D intensity in (2.23) may take zero or positive value. The necessary and sufficient conditions that ensure positive 1 > a, and L > ! A 1 are. pa, (2.24) n [1-a] The first condition is obtained by rearranging (2.23) to get JA = 1 n[1-a]LJa - [1-nip. If 1 <a, both terms in the right hand side of the equation will be negative. This means that we have a A corner solution of 1 = 0. Thus 1 > . To get the second condition 8 a is the necessary condition’ in (2.24), set IA> 0, then rearrange for L using the fact that 1-a is positive. Suppose we interpret that F’ industrialization and fails when F’ = > 0 means the economy is successful taking off to 0. Then, (2.24) tells us that a closed economy needs several factors to succeed in “taking off.” First, it needs a sufficiently productive food sector (low a ) 8 to provide inexpensive food so that people are sated with the minimum need of food and start 17 The last term is profit income since kI equity stocks is V = a . 1 = 0 implies that r 18 = p and the present value of the It is necessary to ensure that the capitalists are sated with grain while the workers are not i.e., y, > p1> y. Recall that p = a , so p= a. By defmition y = M/L+p hence, y, = [1-a] 8 /L+a = 1+pa,/L. Since 1 > a by (2.24), y, > a = pg. To ensure that pj> y, it is assumed 1 +pa that a> cx because y,,, = cx. 22 consuming manufactured products. Second, it requires a sufficiently large number of capitalists (large U so that there is enough manufacturing demand to cover the fixed cost of R&D. A large L implies that there are enough people holding equities or the distribution of wealth is . 9 sufficiently even’ Third, it needs sufficient labour productivity in innovation (small a,) and fourth, a large inventive step (n) so that there is enough incentive for R&D. Lastly, it requires a sufficiently low rate of time preferences (p) so that the opportunity cost of capital is low since r=p. In the case where R&D intensity is positive, the prices of manufacturing goods will be reduced over time. This reduction in prices increases the amount of manufactured products that the capitalists consume, thereby raising their utilities. This growth rate of utility can be calculated as follows. Substitute X(z,t) = MJp(zj) and p(zj) = a(z)4(O)[l-n] into the bottom part of (2.3) to derive lnU(t) = luG + InM - flna(z)4(O)dz - E{In[1 -nf }, where E, is the expectation at time t conditional on current information. (2.25) Let Pr(j,t) be the probability that process technology of a given product will improvej step in a time interval t and each industry follows the same Poisson process with a mean of arrival equal to tI. Then, the utility growth rate of the capitalist can be calculated once the expected value of the technological improvement has been determined. Summing over all possible probabilities off, we have 19 These first and second factors are the same as in M-S-V. The differences are that, in this paper, once the growth process has started, it can be sustained forever instead of a once off phenomenon. 23 E{ In[1—nI } Prq,t) in[1—n] = = (2.26) tI In[1—n]. Substitute (2.26) into (2.25) to get lnU(t) = mG + 1nM - fln[a(z)4(O)]dz tIAln[1_n]. - (2.27) Differentiating (2.27) with respect to t gives the growth rate of utility pA where q(n) q(n)IA = -ln{1-n] > q(n) = —- 1 a [1—01 L — (2.28) [1—n] p 0. The last equality is obtained by substituting the value of aggregate innovation intensity from (2.23). The growth rate in this paper shares many common characteristics to those of its predecessor endogenous-growth models. From (2.28), the growth rate is faster the larger the inventive step (larger n), the greater the labour productivity in innovation (smaller 1 a ) , and the more patient the consumers (smaller p). Nonetheless, some results that are not present in the predecessor endogenous-growth models are worth noting. Before moving on to those results, it is helpful to calculate the welfare representations of the worker and the capitalist. Use (2.27) and the fact that lnU(t) = ctLw/ag in (2.1) and integrate the right hand sides to get I — pW = mG P ’ T w = lnaL + InM - - A fIn[a(z)(O)]dz + (2.29) Inag. Now we are ready to investigate three additional results attained from this model. First, in contrast to the “homothetic preferences with homogeneous consumers” formulation, only capitalists experience perpetual growth in utility and welfare. Workers’ welfare 24 exhibits no growth. This is true for two reasons. First, by the hierarchical preferences, workers do not substitute grain for manufacturing goods when their prices are reduced by the new technologies. Workers, who are not yet sated with grain, consume only grain whose price is ° by the technology (p=ag). Second, the division of labour among sectors and the real 2 fixed wage of workers remain unchanged though the prices of manufacturing goods keep declining by R&D. These result from the assumption that the demand for manufacturing goods has unitary price elasticity. A reduction in price will be matched by the same proportional increase in demand. Therefore, technological progress of the manufacturing sector does not draw more labour away from the grain sector. The demand for grain is also constant since the capitalists are already sated with grain. Thus, the amount of labour employed in the grain sector stays the same and so does the real wage in terms of grain. In summary, technological progress of the manufacturing sector improves the welfare of the capitalist, but the benefit does not “trickle down” to the worker when the worker is too poor . Furthermore, the change in the values of 21 n, a 1 and p have no effect on the utility of the worker. Second, an improvement in grain productivity (a reduce in ag) will enhance innovation in the manufacturing sector. This is because an improvement in grain productivity will reduce the price of grain. The capitalists who are already sated with grain will demand the same amount of grain but will pay less. Consequently, more expenditure can be spent on manufactured goods since [l-a]L is larger. As demand for manufactured goods increases, R&D and the growth rate of the capitalist’s utility are higher. 20 Even when the price of grain can vary, workers remain indifferent. Chapter ifi. 21 See details in This result may be interpreted as a dynamic version of Proposition 2 in Eswaran and Kotwal (1993). As also mentioned by them, if preferences are not exacting hierarchically in the real world, the benefits filtered down to workers would, nonetheless be modest as long as the magnitude of substitutability between the two groups of goods were sufficiently low. 25 Note that a rise in grain productivity strictly improves the welfare of all consumers in the closed economy. Workers are directly better off by the cheaper price of grain while capitalists are better off by a once-off increase in consumption of manufactured goods. These two channels of welfare improvement are shown in E-K. Moreover, the welfare of the capital ists, in this paper, is also improved through another channel by a higher R&D and growth rate. Lastly, in the endogenous growth model with the homothetic preferences, a change in population mix will not change the rate of innovation. This paper, however, will show that when preferences are hierarchical and workers are not sated with grain, an increas e in the number of capitalists will increase the rate of innovation. As the condition in (2.24) has shown, an economy needs a sufficiently large L to have a positive R&D intensity. Suppose, we compare two economies which are identic al in every way, except that one has LG lower than the second condition in (2.24) and the other economy has the required L. Clearly, the latter economy enjoys a positive growth while the former has no growth. For the economy which already has parameters that satisfy the conditions in (2.24), an increase in the value of L, will increase the growth rate even further. To demonstrate this, differentiate the growth rate given in (2.28) with respect to L to get 1 a > 0. (1.30) By (2.24), when I’ is positive, [1-a] is also positive; thus, the sign of (2.30) is positive and the country which has a higher 4, grows faster. Since different mixes of population can affect the growth rate, the immed iate policy implication is whether the redistribution of income that changed the popula tion mix also increased growth rate. The analysis in the next section provides the answer . 26 2.4 Redistribution of income and growth One of the widely known properties of the homothetic preferences is that a redistribution of income does not affect the aggregate consumption expenditure. Thus, an income redistribution cannot affect the R&D intensity or the utility-growth rate of the endogenous growth models with the homothetic preferences since these variables depend on the aggregate expenditure. However, the hierarchical preferences used here allow a redistribution of income to change the aggregate manufacturing expenditure. Therefore, the R&D intensity and the utility-growth rate would be affected by the redistribution. Note that here the redistribution of income means that a fraction of equity assets of capitalists are transferred to workers such that they have sufficient income to consume jand gain their labour force from cc to one, due to better nutrition, and therefore become capitalists. In effect, this type of redistribution of income is equivalent to an increase in the ratio of capitaliststo-total-population. To get the impact of income redistribution on the growth rate, substitute L 0 in (2.28) with 1L. Then, differentiating (2.28) with respect to 1 fixing L and rearranging yields = nq(n) {[1-a] -[a—c]}L 1 a > (1.31) 0. The terms in the first square bracket of the (2.31) represent the impact of the increase in the labour force of the worker-turn-capitalist from a to 1 due to a better nutrition. The terms in the second square bracket capture the effect of the increase in labour demanded in the grain sector to satisfy the higher demand for grain of the worker-turn-capitalist. The former effect stimulates R&D, but the latter effect reduces R&D. The net effect of the two terms is 1-a > 0. Therefore, a redistribution of income increases the growth rate of the capitalist’s utility. The increase in labour productivity from a to 1 is the key mechanism that drives the result here. If the model only incorporate the hierarchical preferences, the redistribution of 27 income would have reduced the growth rate since the workers must spend a part of the transferred income on grain so that they are sated before they start consuming manufactured goods. This can be seen by assuming that the labour force of the worker-turn-capitalist stay the same after the redistribution of income, the first square bracket would have been just [O-c]. Then, the combining result of the two square brackets would have been equal to -a. This would have caused the sign of (1.31) to be negative instead. The most striking result probably is that even with the effect of the hierarchical preferences working against the increase in labour productivity, the income redistribution is still able to generate a net increase in the growth rate. As the growth rate can be increased by the redistribution of income, the next logical question is whether it can improve the welfare of consumers, especially the existing capitalists. To answer this, we need to know the welfare of individual consumers. Note that each capitalist consumes i and x(z) = L}/p(z) and enjoys the same growth rate as that of the {[1-aJ+pa / 1 capitalist’s group, while each worker consumes only g=alag. The welfare of each person in each group can be written similar to (2.29) as 1 1n pw + 111m - A f1iazi0Idz + (2.29a) 0 PW IIIct = - lflL2g• Now differentiating W and W,. in (2.29) and w, and w. in (2.29a) give the impacts on the welfare: —1 = 8! a! p[l-!] = < o, (2.32) o, (2.33) 28 8W p— 81 = = + -____ pa, Ml (2.34) 0, > — pa 8w 81 1 1 ÷ fl17(fl’ ‘‘ ‘ [1-alL ÷ 1 pa 1 M — ‘[1—alL (2.35) The workers’ welfare in (2.32) is declined only because of the reduction in their members. However, the remaining workers are indifferent (as shown in (2.33)) since they are still not sated with grain and the price of grain is unchanged (p = ag). The worker-turned-capitalist now enjoys the benefits of innovation in manufactured goods and the existing capitalists gain a higher growth rate (as shown in (2.34)). Each original capitalist can be better off if the static losses, pa/Mi, , as shown in (2.35). The static losses measure 1 are smaller than the dynamic gains, nq(n){l-aJL/a a once-off reduction in the income of the existing capitalists used by income redistribution. The dynamic gains measure the increase in the growth rate of utility stimulated by a greater level of aggregate consumption from the worker-turn-capitalist. With some rearranging, (2.35) becomes nM 81 a, - a, 2 p q(n)[1 -o]L InM a, a, 2 p -p+p q(n)[l-a]L I + 1 a + [ and pa‘ l qQi) 0, [1—aJL where = 1 -a n L 1 .1 ‘1’. Il. (2.36) pM is the second-best optimal level of R&D intensity. The value of l is obtained by maximizing the welfare of the capitalist given in (2.29) subject to the resource constraint (2.21) (see Appendix 1). By condition (2.24) and the condition given in Appendix 1, both JA and are non-negative; thus, the sign of (2.36) is also non-negative. In other words, the existing 29 capitalist will always be better off by a redistribution of income. The following proposition recaps the result. Proposition 1: In a closed economy, a redistribution of income from capitalists to workers such that they become capitalists (i) raises the rate of innovation, (ii) increases the welfare of the existing capitalist while the remaining workers are indifferent. 3. Free Trade Model The preceding section has answered some questions pertaining to industrialization, redistribution of income, growth, and welfare for the closed economy. Although they are important, the answers will not be complete without considering the case of an open economy since more and more countries have been moving toward the trend of globalization. In this section, the autarky model is extended to a trade model between a developed country (North) and a developing country (South). It is found that a redistribution of income from Southern capitalists to its workers increases the growth rate as in autarky, however, its impacts on the consumer welfare depend on the trade patterns of grain. The gains from trade will not filter down to the Southern workers unless the South imports all of its grain from the North. Furthermore, the workers will remain un-sated with grain and experience no utility growth unless the imported grain is sufficiently inexpensive. The productivity improvement in the grain sector stimulates R&D and growth in all cases, unless both countries produce grain and the North is the net exporter of grain. The change in population mix may improve the South’s balance of trade, and affect the growth rate. Consider a world economy consisting of two countries: North and South. The North 30 represents the developed countries while the South represents the developing countries. Denote the South variables as before and the North variables by the superscript “*“• Consumers in both countries have identical preferences, but the population sizes are not necessarily the same. As normally observed, the income distribution is quite skewed in developing countries, but it is more evenly distributed in developed countries; thus it is assumed that the South’s population consists of capitalists and workers while all the Northern population is capitalist. Again, it is assumed that, before trade, Southern workers are not sated with grain, but all capitalists are. 3.1 Trade Patterns Each country is efficient in producing certain kinds of products depending on the relative labour productivity of the products and the equilibrium relative wage. Define the equilibrium relative wage rate between the North and the South as Co w=l. If Co w/w and retain the normalization is treated as given for the time being, the trade patterns (with no trade barriers and transportation costs) can be determined as follows. 3.1.1 Grain sector: Defme the relative grain productivity of the two countries as 0 ar/ag and for simplicity let 0 = 1 (a = ar). In other words, no one has an absolute advantage in the grain production . Then three possible trade outcomes can occur. If o <0, the South 22 has a lower production cost of grain (wag 0, the North will export grain. Finally, if o < wa) and it will export grain. Conversely, if co> = 0 both countries may import or export grain since they are equally efficient. Assuming that either of them has absolute advantage in grain production does not change the conclusions made in this paper, as long as ‘y < 0 <a7cc. 31 3.1.2 Manufacturing sector: The trade pattern for this sector can be determined similarly to the case of grain. At time t=0, let each country have its own pure unit labour requirement schedule, a(z), and its own patents on the technologies 4(j), for z E [0,1]. The generation of technology j for each industry may be different between countries, however, there is only one set of most advanced technology portion (j) for the whole world. It is assumed that the South own a of this most advanced technology (j) and the North own the remaining fraction 1-k. The firms which have access to the most advanced technology can either apply the technology domestically or become “multinational corporations” and apply the technology abroad. This assumption implies that cp(j) is the same for both countries and a relative labour productivity in manufactured goods can be defined as: A(z) a*(z)4(j,t=0) a*(z) a(z)(j,t=0) a(z) (3.1) z e [0,1]. Following the static Ricardian model by Dornbusch, Fischer and Samuelson (1977), z is indexed in the order of declining comparative advantage of the South. Therefore, A(z) is continuous and decreasing in z. For a given relative wage rate, the South will export any manufactured product z for which the labour cost [wa(z)] is less than or equal to the North’s labour cost [wa*(z)4]. In other words, w/w a(z)/a(z). On the other hand, the North will export the remaining z for which the labour costs are cheaper or wlw* must exist the competitive margin a() If o is known, a(z)/a(z). Hence, by the continuity of A(z) there () such that the North-South relative wage equates A(!): (3.2) A(f). can be solved from (3.2) and world production of manufactured goods wifi be divided into two sets. The South has a comparative advantage in z comparative advantage in z E [2,1]. 32 E [0,] and the North has a 3.1.3 Innovation sector: The North is assumed to have an absolute advantage in conducting R&D. Specifically, I assume 23 that a = , where 0 <y < 1, i.e., the North’s unit 1 ya labour requirement for R&D is strictly smaller than the South’s. By similar reasoning used in the case of grain, there are three possible trade outcomes depending on the values of co and The North is the sole producer of R&D when 0) (0 > <y and both countries conduct R&D when co , all R&D is undertaken by the South when = Since it is rare for developing countries to undertake all innovation activities, y will be assumed to be sufficiently small such that for all values of 0) considered in the model, Wa 1 > 1 wa and the North is always the sole producer of R&D. Henceforth, the South’s R&D intensity (1) is zero and the North’s R&D intensity (f) is the world’s R&D intensity (P). Although the North undertakes all the world’s R&D, the Northern firms apply only some of the next generation of their technologies domestically to serve world demand for products for which they have comparative advantage. For products for which the South has comparative advantage, the Northern firms become multinational corporations and license or “trade the technology with their Southern subsidiaries in return for royalty payments. This is because it is more profitable to implement the most advanced technology (j) in the country which has the lowest pure-unit-labour requirement a(z). This can be proved as follows. For products z E [0,!], if the next generation of technology is applied in the South, the profit margin will be given byp(zj)-a(zj) profit for this choice will be H(zj) = = na(z)4(j-l) as derived in (2.16). Thus, the aggregate na(z)Ø(j-1)WMIp(z,j) = nWM. Alternatively, if the next generation of technology is applied in the North, the profit margin will be p(zj)-wa(zj) = a(z)4(j-l) wa(z)4(j-l)[l-n] = a(z)(j-l){ 1 w*A(z)[1n]). The aggregate profit for this choice - - This is the assumption used in the “Footloose” R&D Version in Taylor (1994b). This is true when y [n/(1n)]{L7[Lca[Lc+L*]+paiJ). This assumption helps to simplify the balance of payments schedule that will be derived later. 33 will be IT(zj) = shows that H(zJ) {1 - - wA(z)[l-n] }WM. Taking the difference between these two alternatives lT(zj = [wa(z)-a(z)] [1-nj WM/a(z). It is positive since wa(z) > a(z) for z e [0,2]. Therefore, it is more profitable to apply the most advanced technology in the South for industry z E [0,2]. For products z E [2,1], if the next generation of technology is applied in the North, the profit margin will be nwa(z)4(j-l) and the aggregate profit for this choice will be lT(z,j) = nWM. On the other hand, if the next generation of technology is applied in the South, the profit margin will be p(zj)-a(zj) wa(z)(j-1)-a(z)4(j-1)[1-nj = aggregate profit for this choice will be H(zj) {1 = between these two alternatives shows that H*(zj) is positive since a(z) > w*a*(z) for z E - - = wa(zj){ 1-[1-n]O)/A(z)}. The [1-n]wIA(z) }WM. Taking the difference H(zj) = [a(z)-wa(z)][1-n]WM/[wa(z)j. It [2,1]. Hence, it is more profitable to apply the most advanced technology in the North for industry z E [2,1]. The Northern firms fund their R&D by issuing equity claims which must provide the same rate of returns as the risk free portfolio of equities. From equation (2.19) of the autarky model, we know that r = H/V - I = nMJwa, - I, where M represents the market size for the closed economy. By the same analogy, we have n[McfM*] — 1 Wa 1* = — 1*. 1 Wa Notice that the term nWM is the aggregate profit, where WM M, + M is the world manufacturing expenditure consisting of both countries’ expenditure since each z is sold in both countries. 3.2 Consumers On the demand side, let us start with the determination of who will be sated with grain after trade. The proof below will show that if capitalists are sated with grain in autarky, they 34 also will be sated with grain after trade. Southern workers who are not sated with grain in autarky, however, may be sated with grain after trade if (0 a/ct. The superscripts “A” and “F” will be used, when necessary, to denote the autarkic and free-trade variables respectively. For the capitalists, take the case of the South as an example. Since capitalists with grain in autarky, to get WF> waj. 4 w > wAaj But p” wFag or 1 > agg. are sated Multiply both sides of this last inequality with w’ when the South exports grain. Hence, the Southern wage is always greater than the expense for Iwhenever it exports grain. If the South, however, imports grain, the import price of grain must be cheaper than wag. Thus, Southern capitalists also must be able to buy Iwith their post-trade wage income. Therefore, capitalists are always sated with grain after trade. Note that if Southern workers be rearranged to read: agict if w = are not sated with grain in autarky, wAaj> a/ct> 1. The inequality implies that a/ct> 9 since 9 a/ct, w must be greater than 0 and the South must import grain atp implies that ctw consume br they wai are = ctwA. This can = = 1. Then, wa. But w a/ct p i.e., the wage income of Southern workers is sufficient to sated with grain. Conversely, when (3 <w grain but workers are not sated. Lastly, if the South exports Therefore, workers will remain unsated after trade since < a/ct, the South still imports grain (o < 9), pF pA = ag. ct < Given these facts, only capitalists will demand for X(z) when 0) < a/cr., but all consumers will demand for X(z) if o> a/ct. Hence, the South’s consumer-optimization condition when its workers are not sated with grain after trade remains the same as in the autarky model. For the North, all consumers are capitalists; thus they above. are always sated with grain by the argument given So the North’s consumer-optimization condition is similar to that of the Southern capitalist. Therefore, in place of equation (2.11), we have the following differential equations: 35 iç r—p, = (3.4) = If, however, the South’s worker is sated with grain after trade (when o be replaced by M where M M + M and WM will become M + a/ce), the term Iv will M. 3.3 Trade Equilibrium With the information given in the previous sections, we are ready to describe the trade equilibrium in each case, starting from the case where (1) 0 > co > y, (2) a/cc> co> 8, (3) 0) = 0, and lastly (4) co> a/cc. 3.3.1 8 > co> For this case, the parameters indicate that the North conducts all R&D (since co > y); the South exports grain (since 0 (since > 0)); and Southern workers are unsated with grain 0) < a/CL). With this trade and consumption patterns in mind, the labour market clearing conditions can be written as: N = [1—][1—n]WM w* L* where N = (3.5) l1—n]WM ÷ aL÷a[L÷L], (3.6) + aL+L. The left hand side of each condition is the labour supply. The first term on the right hand side of each condition is the labour demanded by each country’s manufacturing sector. Recall from the autarky model that employment in the manufacturing sector is [1-n]M/w, where w=1. Thus, 2[1-n]WM is obtained by setting w=1 and using the fact that the South produces z [0,2] for the world market represented by WM E = M-i-M. The corresponding term for the North is calculated similarly by the fact that the North produces z € [2,1]. The terms ccL+a[L+L] measure the employment in the South’s grain sector since the South is the sole producer of grain. Similarly, aP measures the labour demanded in the North’s R&D sector 36 because the North conducts all R&D. To close the model, we must ensure that the balance of payments holds. This requires that JJ* +aL -[l-z9M = (3.7) fn[M÷M*] _Apaw*. The left hand side represents the South’s trade account. The terms M + aL are, respectively, the Southern export values of manufactured goods and grain. The term [l-!JM measures the Southern import value of manufactured goods. Terms on the right hand side of (3.7) depict the South’s service account which measures a net outflow of service payments abroad. The term zn[M+M] represents royalty payments of subsidiaries in the South to their Northern parent firms and paw quantifies Southern shares of the world profit income. Recall from (3.4) that ?v = r - p and lvi’ perfect-international-capital mobility, we have r = = - p. Then applying the assumption of r. Therefore, r’ can be substituted from (3.3) into (3.4) to obtain: flWM_JF_, C (3.8) * w *a 1 nWM_JF, (3.9) w Multiply both sides of (3.8) and (3.9) with w*a and add them up to get: wa[1’f 2 +1 = nWM — Now summing (3.5) and (3.6) yields the world resource constraint: L+w’L’-a[L-i-L’] + 3 10 w*a[IF+p], = [l-n]WM war. The differential equation (3.10) and this world resource constraint characterize the steady state equilibrium. They are analogous to differential equation (2.20) and constraint (2.21) in the autarky model. The economy also immediately converges to the steady state by similar 37 reasons given in the autarky modeP. The solution of the steady-state equilibrium is obtained by setting [A+M9= 0. To solve for the solution, using r = r in (3.4) yields fv =Af. Since [k-i-M]= 0, r r p. Next solving the world resource constraint for waF and substituting it into (3.10) yields w*a,*[1If +*1 = 2 Then setting [l’4÷M} WM = = w*[L* {wM + — pa;] — (3. 11 ) L+ 0 for the steady state gives the world manufacturing expenditure: + ] 1 pa + L — (3.12) a[L+L*]. Now rearrange (3.7) to obtain: M = aL + pw* + {1-n]WM and substitute [1-n]WM = [1-ajL-aL from (3.5) to get M = [1—a]L + (3.13) Xpaw. Deducting M from WM in (3.12) then gives M*F = [w _a]L* + [1_AJpaw*. (3.14) Both manufacturing expenditures of the North’s consumers and the South’s capitalists consist of income leftover from grain and a share of the world profit income. With the solution of WM from (3.12), set [M+M] = 0 in (3.10) to obtain F 1 = {Lc_o[Lc+L*]+w*[L*+pa;]} — p. (3.15) 1 w a To show this, replace the terms M with M+M, ?i with A-fM, and equation (2.21) with the world resource constraint in the argument given in Section 2.3. The term pwa represents world profit income since V = wa and p is equal to the steadystate rate of returns. Recall that Southern capitalists are assumed to own of the world’s most advanced technology and Northern consumers own the remaining [1-j share. 38 Finally, solve for WM from (3.5), then substitute the result in (3.12) and rearrange for l/w to gef: 1 = L + pa; z11—n l-z[1-n] L-a[L÷L] (3.16) Alternatively, this equation can be solved from the balance-of-payments condition by rewriting (3.7) to read ±[1-n]WM = M-aL-A,paw. Substituting the values of WM from (3.12) and M from (3.13), then solving for lIw* give the same result as shown in (3.16). Thus, (3.16) describes the combinations of 0 and that maintain the balance of payments. This equation describes segment AB of the BP(2) schedule corresponding to 2 E ,z in Figure 2.1. The values of z 1 [z J 1 and z 2 are given in Appendix 2. Note that the value A. plays no role in (3.16); i.e., the BP(2) schedule is independent of the distribution of asset ownership across countries. This is because all owners of the international assets have identical quasi-homothetic preferences. As a result, a change in the distribution of assets among them at the steady state leaves the world expenditure unchanged, and the world equilibrium unaltered. Appendix 3 shows that this segment of the BP(!) has a positive slope which can be understood as follows. Start at any point on the schedule and let 2 increase. The increase in! raises the South’s net exports and causes a current-account surplus. To maintain the balance of payments, 0) must increase so that net imports would rise and reduce the initial surplus in the South’s current account. Therefore, the BP(!) schedule slopes upward. Combining 0 of = BP(2), 2 E 2 , 1 [z ] z with = A(!) determines the steady state equilibrium and w, and starts the motion of the dynamic evolution of the world economy as shown in Figure 2.2. The A(z) schedule gradually rotates around the steady-state equilibrium as shown in For a positive value of o in (2.16), it is assumed that L > a[L-i-L9. 39 Figure 2.1 Balance of Payments Schedule Ct) BP(z) E (Tnx) : a :D a. 9 B S C 7.... 0 I zs 40 z Figure 2.2 Steady State Equilibrium 0) A(z;t>O) BP(z) Ct) A(z;t=O) A(z;t>O) z 0 z — 41 the figure because the next generation of technology for z and technology for z E E [O,] is applied only in the South [!,1] is applied only in the North. As the A() schedule rotates, nonetheless, the North-South relative wage, the geographic specialization pattern of world production, and R&D are left undisturbed. The balance of payments is also maintained in equilibrium. Then successful innovations improve the technologies in the manufacturing sector and propel growth. The dynamic evolution of the world economy of the cases presented below also follows the same characteristic just described so it will not be repeated for the following cases. 3.3.2 co = 0: The parameters in this case indicate that both countries diversify their fmal good production (grain and manufactured goods) and they are equally efficient at grain. The South’s workers remain unsated with grain while all capitalists are sated. The rate of returns for this case is similar to that of case 3.3.1., except that w since 0 = w = = 1 1. Tn place of the differential equations (3.8) and (3.9), we have nWM = — F 1 — a, nWM = - F 1 — P, (3.17) p. (3.18) a, Multiply both sides of (3.17) and (3.18) with a and add them up to get: = 2{nWM (3.19) — The BP() schedule corresponding to this case is given by segment BC in Figure 2.1. It will be shown below that BC is flat i.e., when co = 0, the balance of payments can be maintained by a set of and z 3 = E {aL 3 , 2 [z ] z . Appendix 2 shows that the end points are given by z 2 + L}/w, where N’ = [1-n] {[1-a][L+L]+pa). Since ciL+L = > 0 -a[L÷L] }/‘y, {L L-a[L,-i-L], z > 3 These characteristics of the steady state are first given in Taylor (1993), page 225. 42 ,z is not empty. 2 [z ] 2 and the set 3 z Three trade outcomes may result depending on where the A(z) schedule intersects this segment of BP() schedule. If the intersection point is exactly at point 5, trade in grain is zero or both countries are self sufficient in grain by producing the exact amount of grain needed for domestic consumption. If the intersection is in the range between B and S, the South will be the net exporter of grain. Conversely, if the intersection is in the range between S and C, the South will be the net importer of grain. The following sub-sections provide the solution for each case respectively. 3.3.2.(a) Self sufficiency in grain: Note that all capitalists are sated with grain while the Hence the corresponding resource constraints when both South’s workers remain unsated. countries are self sufficient in grain are: N L* = [1 -n] WM 3 z = O[1—zJ[1—n]WM + aL + aLe, + + (320) ar*P. where z denotes the competitive margin that causes both countries to be self sufficient in grain as shown in Figure 2.1. Henceforth, z, will be called the grain-self-sufficient margin. Using a = a, 0 = 1, and combining the two resource constraints with (3.19) as in section 3.3.1. yields a[?vfE ÷ME*] = WM-[1-o][L + L*] - 321 pa. Again, the steady-state solution requires that [?v-i-M] = 0. Set the left hand side of (3.21) equal to zero for the steady state and solve to obtain WM = [1 a][L ÷L*] — + (3.22) . 1 pa Since the net export of grain is zero, the balance-of-payments condition is just given by: zM [1-zjM zAWM ?pa. Rearranging this to read M - = z,[1-n]WM + - pa and using WM from (3.22) gives the solution for M. Use the result with (3.22) to give M. They can be written as 43 M M*F [1—a]L ÷ = Substituting WM from (3.22) into I” F 1 —{[1_a][L÷L*]} = = — [1.a]L* ÷ [1—]pa. = nWMIa - (3.23) p as in section 3.3.1. yields [1—n]p. (3.24) 1 a Finally, the solution of z can be calculated by equating WM = {[l-a]L}/{[l-n]z,}, from the South’s resource constraint, to the right hand side of (3.22) and rearranging: [1k, z where ‘P = (3.25) [1_n]{[1_a]{L÷L*]+ pa}. 3.3.2.(b) The South is the net exporter of grain: This case corresponds to the solution when A(z) intersects BP(!) between B and S in Figure 2.1. The South’s workers remain unsated with grain while all capitalists are sated. Both countries produce grain, but the North imports a fraction s of its grain consumption from the South. This fraction wifi be later called the South’s export share of grain. The resource constraints for this case are: Setting 0 = ccL + a[L +sL *1, O[1—f][1—n]WM ÷ [1_s]a*L* ÷ a,IF. [1 —ii] WM N L* = 1, a + (326) a, and combining the two resource constraints with (3.19) as before yield the solution of WM which is exactly the same as shown in (3.22). For a given schedule A(z), 2 is determined entirely by A(2) = o = 1; i.e., 2 = (o=1). Thus, the solution for s can be explicitly 1 A expressed as S = [1—a]L GL* z — (3.27) — = E , ]. 8 [;,z 2 Z-Z The first expression is obtained by equating WM = { [1 -aJL saLe }/{ [1-n)!), from the South’s - resource constraint, to the right hand side of (3.22) and solving for s. The second expression is obtained by using the definition z in (3.25) and the fact that z, 44 - 2 z = aL7’{’. The numerator of s is the difference between the grain-self-sufficient margin and the actual competitive margin. The denominator is the difference between the grain-self-sufficient margin and the end point of segment AB where the South serves the world demand for grain. Clearly, if A(z) and BP(!) intersect at S, =z, and s=0; the North’s net import of grain is zero. If they intersect at B, !=z 2 and s=l; the North imports all of its grain from the South. Any intersection point between B and S gives s E (0,1). Now we are ready to explain why the BP() schedule for co payments condition for this case is M* increase . - [1-JM + saLe = = e is fiat. The balance-of- nWM pa. Start from point B and - We can see that a current-account surplus generated by an increase in ! can be completely offset by a reduction in s without adjusting co to maintain the balance of payment as needed in section 3.3.1. This process of adjustment continues until s—() where the economy arrives at point S in the figure. Using the balance-of-payments condition given above with (3.26) and (3.22) also yields the same solutions of M and M as given in (3.23). The solution for the R&D intensity (?) is also the same as given in (3.24) since WM is the same. 3.3.2.(c) The South is the net importer of grain: This case corresponds to the solution when A(z) intersects BP(!) between S and C in Figure 2.1. Recall that all capitalists are sated with grain while the South’s workers remain unsated. Let s be the North’s export share of grain. It measures a fraction of Southern grain consumption imported from the North. The resource constraints for this case can be written as: [1 _s*][aLw N = zll —n]WM V = O[1 -][1 —n]WM Again, setting a = a’, 9 = + + aLe], ÷ s*[OaL ÷ a*L] + (3 28) + 1, and combining the two resource constraints with (3.19) yields the exact solution of WM given in (3.22). Hence, its solution of R&D intensity (P) is also the same as shown in (3.24). Moreover, the solutions for M and M can be calculated as in section 45 3.3.2.(a) by using the balance-of-payments condition (given below), (3.28) and (3.22). They are again the same as given in (3.23). To get the expression for s, equating WM = {N - [ls*][c,Lw+aLc]}/{[1nJ!}, from the South’s resource constraint, to the right hand side of (3.22) yields s* — [1—o]L = — z = aL+oL - , -; 3 z z e (3.29) ] 3 [z,z where the second equation is obtained by using the definition z, and the fact that z 3 z, - [xL+aLJ/’{’. The interpretation of s* is similar to that of s. If A(z) and BP(!) intersect at S, = 2=z. and s=0; the South’s net import of grain is zero. If they intersect at C, 2=z 3 and s=1; the South imports all of its grain from the North. Any intersection point between S and C gives? The balance-of-payments condition for this case is = E (0,1). 2nWM-&pa. The BP(2) schedule for the range between S and C is also flat by the similar reason given in section 3.3.2.(b). The balance of payments can be maintained without adjusting o by an increase in s when 2 increases beyond z,. The process of increase in 2 without an upward pressure on continues until s=1 and 2 = 0) . Then a further increase in 2 will eventually cause a surplus in 3 z the South’s current account and cause the BP(2) schedule to slope upward again (see next section). 3.3.3 okx> w> 0: The BP(!) schedule corresponding to this case is given by segment CD in Figure 2.1 and the boundary of this case is marked by 2 E ,z (see Appendix 2). The 3 [z ] 4 parameters for this case indicate that the North exports grain and the Southern workers are not sated with grain after trade. The North also exports R&D since 0 > y by assumption. Thus, the rate of returns in (3.3) and the differential equations in (3.10) are also applicable for this case. The labour market clearing conditions, reflecting the specified production and consumption, become: 46 N = L* z11—n]T4M, (3.30) [l_z1[1_n]WM÷1CLy+a[L+L*]+a*JF w* w* (3.31) The balance-of-payments condition for this case also must reflect the fact that the North exports grain. It can be written as f* _[1_Z9Mc_[OLw÷W*GLc] = n[M+M*] _Apaw*. (3.32) Combining differential equation (3.10) with the new labour market clearing conditions as before and setting WM = [Iv÷MJ 0 gives = w*{L* ÷ pa, - L7[Lc±L*]j + (3.33) L. The derivation of the remaining solution is analogous to that in section 3.3.1., so it will be explained only briefly. Rearrange the balance-of-payments condition in (3.32) to obtain: M = ?paw + [1-n]WM -[ciL+waLJ, then use (3.30) to get M as given in (3.34). Subtracting the result from (3.33), then yields M. To solve for F, substitute the value of WM from (3.33) into (3.10) and set [A-i-M] = 0 to get the result as shown in (3.35). Next, equate WM = NI[1-n]! from (3.30) to the right hand side of (3.33) and rearrange to get 0 as given in (3.36). M M*F = [1_W*a]Lc + )ptZ W, 1 w*{[1_a]L* + ‘ = {[L + w*[L* (334) — — [1—n]p, (3.35) w = zll-nl V + pa; N - — aL+L*] (336 z11-n]L The right hand side of (3.36) represents the BP(2) schedule for this case. It is depicted by segment CD in Figure 2.1. Appendix 3 shows that the slope of this segment of BP() is positive. 47 Combining (3.36) with 0 3.3.4 o = A(), then gives the equilibrium o and , for E 4 ,z 3 [z ] . a/a: The BP(2) schedule corresponding to this case is depicted by segment DE > in Figure 2.1. The boundary of this case is marked by ! E ,1] The trade pattern in this 4 [z . 29 case is the same as in section 3.3.3. However, the Southern workers are sated with grain and each of them now has one unit of effective labour productivity. The labour market clearing conditions become: L (3.37) I1—n]WM, = [1 —fJ[1—n]WM L* a[L ÷L*] + + aIF. (3.38) The balance-of-payments condition for this case must also reflect the fact that the South’s workers are sated with grain. It can be written as fM _[1_]M_w*aL n[M÷MJ _Apaw*. = (3.39) The procedure to solve the steady-state solution is the same as in the previous case. The solution is given as follows [1_w*a]L MF’ M*F F 1 = + w*[[1_o]L* ‘ = {L + )pa;w, ÷ (3.40) [1—.]pai], w*[L* — a[L+L*]]} — [1—nIp, (3.41) w — 41 -ii] 1-41-n] + pa; — oL ÷L*] (3.42) L where the right hand side of (3.42) depicts the last segment of the BP() schedule. The slope of 29 Appendix 2 provides the value of z 4 and shows that the endpoint of segment CD and the beginning point of segment DE are the same. 48 segment DE is also positive (see Appendix 3) and is steeper than the slope of segment CD (see Appendix 4). The schedule reaches its maximum value co(max) at = 1 with the South specializing in all manufactured production and the North specializing in R&D and grain (the value of co(max) is given in Appendix 2). Given the solution of R&D intensity in each case, the utility growth rate can be calculated as in the autarky model. Substituting the appropriate aggregate R&D intensity in f3F = q()JF gives the utility growth rate of the consumers who are sated with grain. Under free trade, their utility growth rates are identical because they consume the same set of goods at the same prices. Southern workers will be sated with grain and enjoy the same growth rate if the A(z) schedule intersects the last segment of the BP(2) schedule. However, if the A(z) schedule intersects other segments of the BP() schedule, Southern workers are not sated with grain, and will therefore experience no utility growth as in the autarky case. The welfare of consumers can also be calculated similarly to the autarky case. They can be written as W = InjL pW = 1ncL W = lnjL* p p where pF(zO) is a(zj=O) + frJF - ‘lnp Fcz,O) - + q(ii) F 1 (3.43) Inp, + flnpF(zo)o,z + j)JF 1 q( - for z E [0,!], and is w*a*(zj=0) for z e [2,1]. This completes the detail construction of the free trade model. Now we are ready to investigate the effects of the redistribution of income and other exogenous factors. 49 4. Redistribution of income under free trade In the autarky model, we have seen that a redistribution of income from capitalists to some workers enhances R&D and improves the welfare of capitalists when preferences are hierarchical and workers suffer from malnutrition problems. This section will show that under a free trade situation the redistribution of income may still enhance R&D. However, the welfare results depend on the trade pattern of grain. Proposition 2: When both countries produce grain, a redistribution of income in the South (i) has no effect on the relative wage (o) or the competitive margin (!), (ii) increases the South’s export share of grain (s), but reduces the North’s export share of grain (se), (iii) raises the R&D intensity (1), and the utility growth rate (f3), (iv) improves the welfare of the North’s and the South’s capitalists, but leaves the remaining workers indifferent. Proof: See Appendix 5.1 for part (i) to (iii). The proof for part (iv) can be shown by differentiating W, and W in (3.43) with respect to 1: + = 81 paw* [1-o]L 1 = + iui(n)[l-a]L M nq(n)[1-ci]L > (4.1) pa > (4.2) . 1 p Since the redistribution of income also changes the number of capitalists, we need to calculate the effect on the welfare of individual Southern capitalists and workers. The welfare of each individual in each group is 50 Inj pw pW - q()JF (43) + Iiicc = + fjpF(z,o)c1z (4.4) IflL2g — where m MJLC = [1-aJ+pa/L, p(z,O) is a(zj=O) for z E [O,], and is wa(zj=O) for z [,lj. Differentiating (4.3) and (4.4) with respect to 1 shows that W 8 = — 8! 81 ).pa + Ml = n(n)[ ] 0 _ 1 , (4.5) pa; o (4.6) The individual capitalist will be better off if the dynamic gains, nq(n)[l-aJLJpa, are greater than the static losses, pa/M. With some rearrangement, (4.5) becomes: )4(n)[1_cT]LJnM’ 81 a 2 p — q(n)[1-a]Lc pM F 1 ç nM’ — A A + 1 1 a 2 p - whereü’ , q(n)[1-u]L n[1-Ay][1-a]L +1A n[1—Ay][1—a]L + 1 A n[1—Ay][l—a]L + 1 A = Aq(n)[1-a]L pM a 2 p + + + p — q(n)[1-a]L pa [l—G]Lp 1010 q(n) [lo]L a; pa; J0 [la]L The results in steps three and five are obtained by using t [1—y][1—a]L a; = n[l-a]LJar[l-n]p, and I” = [1- 1 -p/q(z) respectively. The sign is positive since 2 and y are less than one, P and I” are a]LJa positive by condition (2.24) and the constraint given in Appendix 11] 51 The intuition for this proposition is as follows. Part (i) is true because co in this case is determined entirely by the value of 8 on which the change in income redistribution has no impact. Therefore, the relative wage and the competitive margin are unchanged. For part (ii), the redistribution of income increases the population of the South’s capitalists which raises the South’s imports and in turn generates a current account deficit. To maintain the balance of payments, an increase in the South’s net exports is required. When the South is the net exporter of grain, the balance of payments is maintained by an increase in the South’s share of grain exports (s). Recall that s is the fraction of the North’s consumption of grain that is exported from the South. Conversely, when the North is the net exporter of grain, s must fall. For part (iii) I and 13 increase because the redistribution of income adds more capitalists to the economy, thereby raising the demand for manufactured goods and the expected profits of successful R&D. Hence, R&D is stimulated and the growth rate is increased. The welfare of the North is improved by the higher growth rate stimulated by the redistribution of income in the South. The welfare of the South’s capitalists as a group is definitely higher by two factors. The first factor is the increase in consumption of the workerturned-capitalist measured by the first two terms in (4.1). The second factor is the welfare improvement due to the increase in the growth rate depicted by the third term in (4.1). However, the individual extant capitalists suffer static losses owing to the transfer of wealth to the worker while they enjoy the same dynamic gains of a higher growth rate. The static losses and the dynamic gains are depicted, respectively, by pa/M1 and nq(n)[1-alLlpa in (4.5). As in the autarky model, the dynamic gains are larger than the static losses. In other words, each existing capitalist will always be better off. The workers are indifferent because they consume only grain and the price of grain does not change. We can see that the welfare impact of the South’s population when both countries produce grain is quite the same as in autarky. This is because co and are fixed. However, when either country is the sole producer of grain, the redistribution of income will change the equilibrium 52 w and . Consider first the case when the South is the sole producer of grain. In this case, the redistribution of income has a similar effect to an increase in population of the Southern 30 (Lj. It raises the net import of manufacturing goods and generates a deficit on the capitalists Southern current account. This shifts segment AB of the BP() schedule to the right. With a downward sloping A(z) schedule, the relative wage (o) reduces and the competitive margin (!) rises. As o drops, w increases which raises the value of equity income (paw). A higher income means a higher demand for manufactured goods which in turn raises the expected profit of the successful R&D. Thus, the redistribution of income stimulates R&D and increases the utility growth rate. Again, the redistribution of income has no effect on the rest of the South’s workers because they consume only grain and the price of grain does not change. Recall that when the South is the sole producer of grain, the world price of grain in terms of the Southern wage is the same as that of the South’s autarky. Its impact on the welfare of those who are sated with grain is now more complicated by the fact that the relative wage and the competitive margin also change. When the South is the sole producer of grain, the redistribution of income affects the North’s welfare via three channels. First, it increases the Northern wage rate (since o rises and w = 1/co) which raises the equity income of the North and in turn improves the North’s welfare. Second, the higher Northern wage rate increases the prices of goods produced by the North; thus, the North’s welfare is reduced. Third, the redistribution of income increases the number of capitalists who in turn demand more manufactured goods. This stimulates the innovation activities and raises the North’s utility growth rate. The higher growth rate then increases the welfare. Although the effect through the 30 The redistribution of income also decreases the numbers of Southern workers (L,j. But notice that does not appear in both (3.15) and (3.16). Hence, the change in L does not have F any effect on co, 1 and 3. , 53 second channel is negative, Appendix 5.2 shows that the net effect of the first and second channels is positive. Therefore, the overall effects are positive. So the North’s welfare is improved by the South’s redistribution of income. The welfare of the existing Southern capitalists as a group is also affected by the redistribution of income via similar channels. First, it increases the Northern wage rate which raises the equity income of the South (since the South’s capitalists own 2 of the dividends). This in turn improves the welfare of the South’s capitalists. Second, the imported goods from the North are more expensive due to the higher Northern wage; this reduces the welfare of the South’s capitalists. Third, the redistribution of income stimulates the innovation activities and raises the utility growth rate which increases welfare. Unlike the previous case, the net effect of the first and second channels is ambiguous (see Appendix 5.2). Thus, the overall impact of redistribution of income on the welfare of the Southern capitalists is also ambiguous. Finally, the impact of income redistribution in the case where the North is the sole producer of grain is even less conclusive (see Appendix 5.3) since it could shift the BP() schedule in either direction. This can be seen from the right-hand side of (3.36). A redistribution of income affects both the numerator and denominator simultaneously. Its effect on the remaining variables is, therefore, ambiguous. 5. Comparative Steady-state Analyses With the free trade model, we can investigate how the change in some important economic parameters affect the equilibrium relative wage, the trade pattern of each country, and growth. 54 5.1 Changes in productivity of the manufacturing sector Taylor (1993) has shown that a proportionate productivity improvement in all manufactured products in the home country increases the home country ‘s relative wage and the range of manufactured products for which home country has comparative advantage (or the competitive margin). The model here inherits the same result (except when the change in the manufacturing productivity occurs in the region where both countries produce grain, the relative rate and the competitive margin remain constant). What we can learn more from here is how the same productivity change affects both the trade pattern of grain in the South and the South’s workers. To see this, consider a proportionate productivity improvement in all manufactured products in the South which decreases the a(z) schedule and shifts the A(z) upward. productivity change has no effect on the BP() schedule so it stays This the same. From Figure 2.3, if the A(z) shifts upward from A(z)’ to A(z) : 4 (1) the trade pattern of grain changes from the South exporting grain to importing grain; (2) Southern workers turn from being unsated to being sated with grain if the productivity change is large enough to push A(z) intersecting BP() above a/CL. One conclusion to be drawn from the second result is that workers will not gain from trade when the A(z) schedule intersects segments AB and BC of the BP() schedule. This is because workers consume only grain and the grain price (relative to the South’s wage rate) remains the same as in autarky. Moreover, because of the hierarchical nature of preferences, workers will not consume manufactured goods. Thus, these preferences also inhibit Southern workers from absorbing another two sources of gains from trade that Southern capitalists enjoy: first, the gains from an immediate reduction in the prices of manufactured goods for which the North has comparative advantage; second, the gains from future reductions in prices of manufactured goods caused by innovation which is enhanced by free trade. 55 Figure 2.3 Effects of the Change in Relative Labour Productivity in Manufacturing Goods 0) BP(z) E 3 A(z) -y C S 9 : : I 0 3 z 56 1 z 5.2 Changes in productivity of the R&D sector The existing literature has shown that an increase in the value of the inventive step (n) or a decrease in the unit labour requirement for R&D (a;) will stimulate R&D activities. What is less known is how these changes affect the trade flows in the grain sector. The following proposition will show that these changes in the incentive for the Northern R&D stimulate the South’s grain exports. Thus, policies initiated by the North to help its own R&D sector can indirectly help the South’s grain sector. Proposition 3: When both countries produce grain, a drop in the unit labour requirement for R&D (a), or a rise in the inventive step (n) (i) raises the South’s grain exports when the South is the net exporter of grain, (ii) decreases the North’s grain exports when the North is the net exporter of grain. Proof: See details in Appendix 5.1. The proposition can be understood by the following reasons. The reduction in the unit labour requirement of R&D reduces the cost of R&D activities while the increase in the inventive step raises the expected profits of the successful R&D. Hence, both changes stimulate R&D . 31 Since the North is the sole producer of R&D, the increase in R&D activities draws labour from its other sectors, including grain. Thus, while the North’s R&D sector expands, its grain sector shrinks. If the North is the net importer of grain, it needs to import more grain. Therefore, the South’s grain exports must increase. Conversely, if the North is the net exporter of grain, it can export less grain. 31 See also 0-H and Taylor. 57 5.3 Changes in productivity of the grain sector The results of changes in grain productivity depend on which country produces grain in the equilibrium. Thus, there are three cases to consider. First, both countries produce grain; second, the South is the sole producer of grain; and lastly the North is the sole producer of grain. Let us start with the case where both counthes produce grain. The next proposition wifi show that a grain-productivity improvement in the North hinders its own innovation activities. But a grain-productivity improvement in the South or an equiproportionate grain-productivity improvement in both countries stimulates the rate of innovation of the North. Proposition 4: When both countries produce grain, a grain-productivity improvement in the South (1) increases the relative wage (o), but reduces the competitive margin (!), (ii) raises the R&D intensity (I) and the utility growth rate (13). A grain-productivity improvement in the North (iii) decreases (iv) Co, but increases , decreases I and 13. An equiproportionate grain-productivity improvement in both countries (v) (vi) has no effect on o or ; increases I and 13. Proof: See details in Appendix 5.1. Part (i) is true because a grain-productivity improvement in the South (a reduction in increases the value of 8 = ag) alag which is the only determinant of the relative wage (o) for this case. As 0=w/w rises, the relative labour costs of the Southern manufactured goods increase. Thus, the South loses the marginal manufactured product that it can export i.e.; drops. For part (ii), the grain productivity improvement stimulates R&D in two ways. First, it 58 reduces the price of grain and the expenditure for § As the leftover income from grain expenditure rises, the demand for manufactured goods increases. A larger demand for manufactured goods means a larger expected profit for the successful innovation. Hence, the R&D intensity increases. Second, the grain productivity improvement raises w. Thus, the North wage rate (w* = 1/co) is reduced. This in turn lowers the cost of R&D. Both effects reinforce each other, thus, R&D increases. The utility growth rate (f3), therefore, increases since it is positively related to R&D. The grain-productivity improvement in the North (or a drop in a;), on the contrary, decreases 8. Therefore, the relative wage decreases since w=8. As the relative wage drops, the South’s labour cost is cheaper; so the South gains the marginal manufactured products that it can export, or ! rises. The effect of the Northern-grain-productivity improvement on R&D, in part (iii), depends on two effects. First, it reduces the price of grain and the expenditure for § As the leftover income from grain expenditure rises, the demand for manufactured goods and the expected profits for a successful innovation increase. Hence, the R&D intensity increases. Second, the Northerngrain-productivity improvement increases w. This latter effect, however, raises labour costs which discourage R&D. Nonetheless, R&D must decrease by the following reasons. Since the North’s comparative advantage in grain is improved, the North imports less grain when it is the net importer and exports more when it is the net exporter. In both cases, the North’s grain production expands which draws more labour into its grain sector and away from other sectors . 32 With fewer labour resources, R&D activities fall. The equiproportionate productivity improvement of both countries’ grain sectors leaves the absolute advantage in grain of the two countries (0) unchanged. So co and 32 are unaltered Appendix 5.1 provides proof that employment in the Northern grain sector is increased by its own productivity improvement. 59 as stated in part (v). Lastly, the equiproportionate improvement in both countries’ grain sectors reduces the grain price which increases both countries manufacturing expenditures. This increases the expected profits of the successful innovation. Therefore, it stimulates R&D and increases the utility growth rate. The preceding proposition summarizes the results when both countries produce grain. The next two propositions provide the results for the cases where each country is in turn the sole producer of grain. Proposition 5: When the South is the sole producer of grain, a productivity improvement of the South’s grain sector (i) decreases the relative wage (co), but increases the competitive margin (i), (ii) stimulates R&D intensity (1) and the utility growth rate (13). Proof: See details in Appendix 5.2. The result in part (i) can be understood by the following intuition. The grain-productivity improvement (a decrease in ag) generates a deficit on the Southern current account. To see this, consider the balance-of-payments condition in (3.7). The productivity improvement reduces the grain price and the expenditure on § Therefore, the leftover income from grain and demand for manufactured goods increase in both countries. Thus, given the original equilibrium , the South’s net import value of manufactured goods rises. The royalty payments also increase. Altogether, the South has a net outflow of mone? . A rise in 3 which causes an increase in the South’s net exports is, therefore, required to maintain the balance of payments. Graphically, the The import value of z e [!,l] increases by [l-JL; the export value of z e [0,2] and grain rise by [l-z9L; and the royalty payments increase by ntL+L9. The net effect is equal to an outflow of 4l-nhjtL+L9. 60 productivity improvement shifts segment AB of the BP(!) schedule to the right. downward sloping A(!) schedule, the shift causes 0 With a to fall and! to rise. For part (ii), the reduction in 0 increases w which enlarges the value of equity income (pawD. Since equity income is a part of the manufacturing expenditure, the manufacturing expenditures of both the South and the North rise. With a larger world manufacturing expenditure, the expected profits of the successful R&D increase. Therefore, I and 13 are enhanced. Proposition 6: When the North is the sole producer of grain, a productivity improvement in the North’s grain sector (i) increases the relative wage (co), but decreases the competitive margin (ii) raises the R&D intensity (1) and the utility growth rate (2), (13). Proof: See detail proof in Appendix 5.3. When the North is the sole producer of grain, the Northern-grain-productivity improvement (a decrease in a;) reverses the effect on the South’s balance of payments described in Proposition 5. The North’s grain-productivity improvement reduces the grain price and the expenditure on Iwhich increases both countries’ demand for manufactured goods. This in turn increases the South’s net export value of manufactured goods and raises the royalty payments to the North. The cheaper grain price also reduces the value of the South’s grain imports. As a result, the South has a net current account surplus. A drop in 2 which causes a decrease in the South’s net exports is, therefore, required to maintain the balance of payments. The net value of the manufacturing import increases by !WZI payments rise by and the grain import value reduces by a surplus of ![l-n]wtL+L’]. 61 Thus, the [l-2]wL; the royalty w’gEL. The net impact is - Northern-grain-productivity improvement shifts segment CD of the BP(2) schedule to the left. With a downward sloping A(!) schedule, w rises while ! declines as stated in part (i). For part (ii), the Northern-grain-productivity improvement stimulates the innovation and utility growth rate by the following reasons. A reduction in a; releases the labour resource from the grain sector which can be used for R&D. It also lowers w’ which decreases the R&D’s labour cost. Both factors encourage R&D, and hence, they increase the growth rate. Given the results of Proposition 4-6, we can see that the impact of the productivity improvement on the relative wage (o) and the competitive margin () depends on where the A(z) schedule intersects the BP(!) schedule. The productivity improvement of the South’s grain sector shifts segment AB of the BP() schedule to the right and shifts segment BC upward, while leaving segment CD unchanged as shown in Figure 2.4. Consider a small productivity improvement as shown by BP’(!). If the relative productivity of manufactured goods is A’(z), the grain-productivity improvement of the South will decrease the relative wage (o), but will raise the competitive margin (i). However, if the relative productivity of manufactured goods is A (z), the grain-productivity improvement 2 will reverse the previous result. The relative wage will rise while the competitive margin will fall. Now, if the grain-productivity improvement is sufficiently large as shown by BP”(), the A ( 2 z) will no longer intersect segment BC. The relative wage would fall again while the competitive margin would rise again. These changes are depicted by the arrows marked by number 2 in Figure 2.4. This relative wage reversal does not occur for A’(z) as shown by the arrows marked by number 1. On the other hand, the productivity improvement of the North’s grain sector shifts segment CD of the BP(!) schedule to the left and shifts segment BC downward, while leaving segment AB unchanged as shown in Figure 2.5. First, consider a small grain-productivity improvement. If the relative productivity of manufactured goods is A’(z), the grain-productivity 62 Figure 2.4 Effects of the Change in the South’s Grain Productivity C’) 2 A(z) D -r I B e — C A(z) I S S S S A BP(z) BP’(z) BP’(z) z 0 63 Figure 2.5 Effects of the Change in the North’s Grain Productivity U) 2 A(z) BP(z) Az) / BP(z) BP(z) -I, / B e 0’ A z 0 64 improvement of the North will decrease the relative wage, but will raise the competitive margin. The grain-productivity improvement will raise the relat ive wage, but reduce the competitive margin if the A(z) schedule is A (z). However, if the productivity improvement is suffici 2 ently large as shown by BP”(), the A’(z) schedule will no long er intersect segment BC. The changes of the relative wage and the competitive margin could also reverse. The relative wage would first fall and then rise, while the competitive margin wou ld first rise and drop later as depicted by the arrows marked number 1 in Figure 2.5. These results have significant policy implications. A polic y of one country that improves its grain productivity may increase or decrease the range of manufactured goods that one country exports. If it is the sole producer of grain, it will gain the range of manufactured goods it exports. If both countries produces grain in the equilibrium, it will first lose and eventually gain the range of manufactured goods it exports if the grain-prod uctivity improvement is sufficiently large. 5.4 Changes in labour endowment In the standard Ricardain trade model with the homothe tic preferences, if a country’s labour endowment increases, the export levels of goods for which it has comparative advantage will increase. However, when preferences are hierarchical and workers are not sated with grain, this may not always be true. The next proposition will show that though an increase in the labour force of the South’s capitalist increases the South’s grain exports, an increase in the labour force of the South’s worker may not always generate the same effect. 65 Proposition 7: When both counthes produce grain, an increase in popula tion of the South’s capitalists (La) (i) raises the South’s grain-export share (s) when the South is the net export er of grain, (ii) decreases the North’s grain-export share (s*) when the North is the net exporter of grain. An increase in population of the South’s workers (Lw) (iii) has no effect on s when the South is the net exporter of grain, (iv) decreases s’ when the North is the net exporter of grain. Proof: See details in Appendix 5.1. The intuition for part (i) is as follows. An increase in L generates a higher demand for manufactured products. Using the balance of payment condition given in section 3.3.2.(b), the increase in L raises the South’s value of manufacturing imports and the royalty payments repatriated to the North. These cause a current account deficie . 5 When the South is the net exporter of grain, an increase in the South’s export s is required to offset the deficit. This is obtained by an increase in the South’s export share of grain (s). Recall that s is the fraction of the North’s grain consumption that is export ed from the South. When the North is the net exporter of grain as stated in part (ii), the increas e in L raises the value of the South’s grain imports in addition to the increases in the South’s value of manufactured imports and the royalty payments mentioned in previous case. Therefore, the South also has a current account deficit. A reduction in the North’s export share (s*) which reduces the South’s imports is needed to compensate for the deficit. Unlike the case of L, the increase of L does not have any impact on the current account when the South is the net exporter of grain for two reasons. First, the net imports of “ The South’s value of manufacturing imports increases by !n[1-a], while the royalty payments raises by [1-][1-a]. Thus, the South has a current account deficit of [1-a]{1-[1-n]}. 66 manufactured goods are unchanged sinc e workers are not yet sated with grain (because o <a/a). Second, a rise in L does not increase the excess supply of grain since the labour force added by the workers, cxL, is totally absorbed by the equal increase in the level of dem and for grain, ag[cLLw/ag]. As the current account stays in bala nce, there is no need for s to change as in the case when L rises. However, when the South is the net imp orter of grain, the South’s current accoun t will be affected. This is because the increas e in L raises the South’s import valu e of grain (it increases by sea). Consequently, the South has a current account deficit whi ch requires a decrease in grain imports to maintain the balance of payments. Thus, s must fall. 6. Conclusion The main purpose of this paper is to build an endogenous growth model whi ch incorporates Engel’s law so that it can answer the questions involving North-S outh trade, redistribution of income, and growth. To accomplish this, the paper combines the hierarchical preferences with the dynamic Ricardian trad e model. The model shows that the initial distribu tion of endowment and income is crucial to the outcome. A closed-economy country whe re most of the population is poor experie nces a low (or even no) rate of innovation. A redistribu tion of income enlarges the aggregate con sumption and labour force, thereby enhancing the rate of manufacturing innovation and the welfare of the rich. When free trade is established, only the rich benefit from trade. The poor are indiffe rent unless they are sated with grain before trade or become sated after trade by cheaper imp orts of food. Again, the initial distribution of endowm ent and income influences the trade patt ern outcomes. A redistribution of income in a free trade environment also increases the growth rate. Its effect on welfare depends on the trade pattern s of grain. 67 Appendix 1. Derivation for The second best optimal level of R&D intensity is obtained by maximizing the capitalist’s welfare (2.29) subject to the resource constraint (2.21): Max pW s.t. = friG. [1 —a1L = + 1nM [1—n] M Solve the constraint to get M fIn[wa(z)4(O)]dz - + + q(n)! (A.1) a ! 1 . { [1-ajL,-a,I }I[1-nj. Substituting this result in the objective = function, problem (A.l) becomes an unconstraint maximization problem. Solvin g this problem 36 yields = [1-a]L - 1 a q(n) 0. (A.2) To ensure that the right hand side of (A.2) is positive, it is assumed that 1 > 1 ][p /{q(n)[1-a]. a Note that if i° is positive, JA is also positive since 1/q(n) > > a and 4 [1-nj/n. 2. Derivation for the end points of each segment of the BF() schedule: Each segment of the BP() schedule is marked by z 1 to z . To solve for z 4 , setting the left 1 hand side of (3.16) equal to y and rearranging for ! yields: = L — a[L+L9 (A.3) [1n] {L÷L*Iy ÷paj_a[Lc+L*]} Conversely, equating the left hand side of (3.16) to 0=1 and rearranging for 36 yields: Note that the value of (A.2) will be the same as in equation (15) of Grossman and Helpman (1991) if a=O, L=L, and n = 1/A., where A. is the quality step in their paper. 68 LC - a[LC +L*] [1_n][[1_cy][Lc+L*] (A.4) + pa,]] , follow the procedure as above. Setting the left hand 4 3 and z To solve for the end points z side of (3.36) equal to 0=1 gives aLw 3 z +LC [l_n][[1_u][L÷L*] (A.5) + ] 1 pa Equating (3.36) to a/cc and using the fact that cc increases to one and workers are sated with grain and N = 4 z = L when co=a/cc yields aL/ca (A.6) . [1 _n][[1 _o]L* + pa, ÷ [1 _oz]Lo/ccJ * To prove that the end point of segment CD and the starting point of segment DE of the BP(2) schedule are the same, setting the left hand side of (3.42) equal to a/cc and solving for 2 . 4 gives the same value as z Finally, substituting =l in (3.42) gives the maximum value of the BP(!) schedule: G)(max) = 1-n L * + pa; — a [L + L ] (A.7) — n L 3. Derivation of the slopes of the BP() schedule Differentiating the appropriate equation in the text with respect to 2 gives the slope of the corresponding BP(!) schedule as follows aBP(z) BP(f) [1-n] f[1—n][1—[1—n]] E [z 1 ,z ] 2 69 (A.8) aBP(z) BP(z)N 4N-[l-n]Lj = 3BP(z) BP(z) [1-f[1-n]J > 0, > (A.9) , f[z (A.1O) ,1j 4. Proof that the slope of segment DE is higher than segment DE’s: Denote segments CD and DE of the BP() schedule by BPcD() and BPD) respectively, and denote their slope by BPDE(z ) 4 [1 —z 4 z [1 —nJ] 4 Note that BP(z ) 4 ‘. Using (A.9) and (A.lO), if BPD’B(z ) 4 > ), we must have 4 BP(z BPcD(z,)L {L—z z [ 4 1 —n]L] = ) 4 BPDE(z (A.11) and N = L at 0 = a/(x. Rearrange the above inequality give: z [l4 nIL> z [l-n]L, which is always true. 4 5. Comparative steady state analyses 5.1 Both countries produce grain: (a) Redistribution of income: To get the impacts of the changes specified in part (i) of Proposition 2, note that 0 = 8 and = (o=O). Hence, the change in 1 has no effect on them. 1 A For part (ii) differentiating (3.27) and (3.29) in the text with respect to 1 yields: [1—a]L{1 —[1—n]} > GL* OL* -[1 -a]L}[a -alL 1 -[1 -a]L} [aL+aL]{fW {‘ = = ai - ai — (A.12) [aL÷L] 2 2 + [a_a]Lz11_n]{[1_aJL*+pa} a[1—o]{1—[1—n]}L — < 0 2 [aL+aL] where 1 ‘P = [1-n][1-a]L. The proof for part (iii) is obtained by differentiating (3.24) and 70 13F = q(n)r with respect to 1: F 81 = --[l-a]L 0, > = ‘‘[l-a]L > 0. (A.13) (b) Changes in n and a;: To get the impact of the change specified in Proposition 3, differentiating (3.25), (3.27), and (3.29) in the text with respect to n yields: - = 0, > - aL fl (A.14) < = where 0, ‘f’ aL÷L - { [1 —a] [L + L*] + pa; }. Next, perform the differentiation with respect to a on the same set of equations to get -[l-n]p OL* OL* aa * = ZT aJ* xL+L < o (A.15) = Z—ri_i L’ P xL÷L > 0, where ‘ 1 a [1—n] p. (c) Changes in grain productivity: For the effect of the changes in grain productivity in Proposition 4, let us define two shift parameters: a for the South and a for the North. Then redefme the unit labour requirement of the South’s grain sector as aag and that of the North as a*a. A decrease in a (resp. a) evaluated at one, would represent a productivity improvement of the South’s (resp. North’s) grain sector, while a reduction in both a and a at the same rate would depict an equiproportionate improvement. (c.1) Changes in the South’s grain productivity: The result in Proposition 4 (i) is obtained by differentiating Co on A(!) - Oa7a = = Oa/a with respect to a, and applying Implicit Function Theorem 0. Their derivatives are given by 71 = = 2 a -1 0, < (A.16) A’ A’ Note that all derivatives are evaluated at a=a=9=1. With the new definition of the unit labour requirement, differentiating (3.27), (3.29), and (3.24) with respect to a yields: OL+Ta+T + [1-o]L-VF = [1_n][[1_a*JL*÷pa_aLc} aL * ‘F/A’ - < oL* [aLw+aLc][V+To+aLcj = [aLp 0, — [zT—[1—a]L1aL (A.17) L] 2 } [cL+aL] ‘F/A’ 1 aL [aL÷L][1 -zil —ii]] + aLI1 -n]{ [1 _o]L* +pa = + - > 81 — = - Since = —I[1-a]L ÷LCj C *1 1 a = [ccL+oL] 2 nL —S < 0. * 1 a - q(n)I, f3/aa is also negative. (c.2) Changes in the North’s grain productivity: Similarly, applying the same procedure for a yields the results for Proposition 4 part (iii) and (iv): = - 0 = 1 > 0, (A.18) =i=_<o A’ A’ 72 - = [1_n]{L* + pa;] — oL* — [1_n]{L* pa] + — ¶1/A’ = —f- = eEL ÷ aL —-{[1_aJL aL*} = a; >0, (A.19) 0 0. > The sign of the last derivative is positive since it is assumed that L (3.16) will be negative since f3 = > a{L+L9, otherwise (0 in q(n)I, 3/aa is also positive. Next we have to show that the labour employed in the North’s grain sector is increased by its productivity improvement (a reduction in a). Thus, there are less labour resources available for the R&D sector which in turn causes I to fall. From (3.26), the labour employed in the North’s grain sector when the North is the net importer of grain is L = [1s]aL* sja*ag7i Differentiating this with respect to a then evaluating the result at a=1, ag = [1- and a=a yield aL* __!. = = = 1 e3s o*L*1 —s——— 1 [1—o]L—fT ( oLd’ * aL1— aL* 4 — = (A.20) } * — — } + ¶1/A’ — — = oL* ¶1_[1_njL*+pa] + ¶1/A’ [1—01k + J L + oIL + L + [1 —nj{ [1 —a][L+L 9 + pa; L pa; a[L÷L*]} + z1l_n]{L_a[L÷L*J} + ¶1/A’ {L {1 z11—n]}{L a[L ÷L*]} ÷ ‘f/A’ < 0. — = 1P/Ac_z1l_n][L*+pa;] + — — — The sign is negative because 1-[1-n] > 0, L-c[L+L9 > 0, and A’ <0. Now when the North is the net exporter of grain, from (3.28), the labour employed in the North’s grain sector is L = &L*+s*[OctL+GL]. evaluating the result at d=l and 8 a = a yield 73 Differentiating this with respect to a and g aa* = + I [aL÷oL] s* + — I * = aL = GL* * I ‘F—[1—a]L +[L+aL] ,+oL 1 ( cgL [1—a]L 4 z11_n][L*÷pa]_V/A - } + - (A.21) aL+oL ‘f’fA’ < 0. + Notice that the last line is the exactly the same as the result in the third line of (A.20); hence, its sign is negative. Both (A.20) and (A.21) make clear that the labour used in the North’s grain sector is increased by the North’s grain productivity improvement (a reduction in a*). (c.3) Equiproportionate changes in grain productivity: Then, performing similar differentiations with respect to both a and change of a and a by on the same set of equations used for aL+V1’ + [1-alL part (i) and (ii) and evaluating a=a*=l give: -‘ = pa;] = - L [aL+aLJ[fl.+aLj _[1_fl]O[Lc+L*] <0 aL* = [z.V-[l-a]L]aL - [aLw +aL] 2 C [cLL÷aL]aL = — [1 —nJ a[[ccL ÷L][L ÷L*] [4xL > > ai 8aa* = - Denote an equiproportionate --a[L+LJ a; ÷ paL1 (A.22) c7L] 2 L[cL+L] + [l_n]{[aLw4Lc][Lc+L*] +LpaA} < 0. To prove that the sign of as/aaa is negative, assume the contrary to the assertion that it is positive. Then ! must be greater than value of! E LJ{ [1-n] [L+L+pa] }. Since z is the highest possible ,zj, z must satisfy this condition as well; i.e., 2 [z 74 [1-ci]L L [1_n]{L+L*+paj*} [1_nJ{[1_a][Lc+L*]+pafl 1 [1—o][L÷L ]+[1—a]pa This implies that -> must be any other € > (A.23) [1—a][L÷L ]÷pa,. 0, a contradiction. Thus, z, must be smaller than LJ{ [1-nj [L-i-L+paj } as ,zj which is smaller than z. Therefore, as/aaa’ 2 [z < 0. For the sign of as*Iiaa, it is easy to show that the condition given in (A.22) is consistent with E ,z 3 [z ] . (d) Changes in labour endowment: The results in Proposition 7 part (i) to (iii) are obtained by differentiating (3.27) and (3.29) with respect to as 4: {1-f[1-n]J[1-aJ OL* — aL [aLW÷aLC]{9fL—[1—a]} — [aL o{fV-[1—a]L) (A.24) aL] 2 {1—f[1—n]}[1—a]aL ÷ a[1—nJ{[1—a]L*÷pa,4} - + < where = [1-n][1-a] > [ccL 0. + 2 oL] Similarly, the results in Proposition 7 part (iv) and (v) are obtained by differentiating the same set of equations with respect to L to derive: = - 0 3L cz[iV-[1-a]L] = - < 0. (A.25) ccL ÷ L [ccL ÷ L] 2 5.2 South is the sole producer of grain: The appropriate equations for the comparative steady state analysis are the BP(z) schedule for be rearranged to read: 75 ,z and A(z) 1 [z j e 2 = o. The two equations can [1 —(1 —n]][L—a [L÷L *]} —[1 —n]w *[L * ÷pa] 1/w* 0 A(z) 0 (A.26) - This is a system of two equations in two unknowns w and 1 -A’(f)k(zC = + [1-n] WM . Its Jacobian determinant is (A.27) o. > [w*]2 [1-n]. Note that from the South’s labour market clearing condition WM where k() +L]/k(). Substituting this into P 6 [L V - p and using w = 1/o from (3.16), yields: (A.28) = 1 -[1 -n] where C nWM/aw L fL*+pa,* j F 1 = = k - a, 1 4c[] a — pa. This equation will be used for the following comparative steady state + analyses. (a) Change in ag: Differentiating (A.26) with respect to ag and using Cramer’s rule, yields: = [1 _ f)]A I(z[L’L*]j &Sg aag = 0 -[1 _k(z)][L+L*]j [w*1Z 1 D ‘g = -jLC + )pa-— <0, n[ at [1 -W)] a 2 g =jL* + [L*+[1_A]pa]_ < 1 n]C ‘ aZ <0, (A.29) g 0, The effects on MED, ME*, and I are obtained by using (3.3), (3.14) and (A.28). (b) Change in L, and 1: Differentiating (A.26) with respect to L and using Cramer’s rule, yields: 76 = 8L 0 -[1-k()]A’(Z[ 1-oj> 8 1 D ‘ =[1-aJ 8L 8M* + [1-k(2][1-o] 81* pa-—>0, 1 n[1-n]C = =[L + [1_A]paj]_.—_ 8L (A.30) _> 8L 8L >0 a 8L 2 [1 -k(z] >0, For the case of the change in 1, just replace L with IL and use the same procedure. The signs of the results for the change in 1 are the same as the change in L, so they will not be repeated. For the effect of the redistribution of income on the welfare, differentiating the appropriate welfare equations in (3.43) yields: 8W = 81 1 ow p = 81 air +!+ = APa;_[1_j M M <0, [1 [L*÷ 1 [l_).]pa,] , ,* p81> 0, — p 8 1 M* = < 81 w zM + aL 4 w*M* 81 * (A.31) - [1_zlOw* w* 0! + 81 p 8! + p81 o > 5.3 North is the sole producer of grain: The appropriate system of equations to be used for proving Proposition 6 is the BP(z) schedule for ! e ] 4 , 3 [z z and A(z) Co. Rearrange these two equations to get: aL+[1 -k(]L k(Z)w *{Ls + pa -a [L +L 9] =0 0 - The determinant of the Jacobian matrix for this system of equations is 77 (A.32) 2 -A’(f)k(zDC = ÷ [1-n] WM > [w*]2 0• (A.33) Note that r can be rewritten as L _L*+pa,_a[L+L*]÷_ —p W a, = where C 2 = = L , —C ÷ 2 ----- —p, W a, (A.34) L+paa[L+L*1. (a) Change in a;: Differentiate (A.32) with respect a; and use Cramer’s rule, to get: - 0 _k(Fjk()w*[L +L*]i> 2 D — = -w 81* — —— - ‘ k(f)[L+L*]j [w*] 2 D — ãw*> 8M* [?. pa; a *LC] —<0, aag L 8w* [Lc+L*]i+ C < 0, [w*]2 ; + - = -w *gL * > + o M*aw*> <0, — — (A.35) W & 4 Zg — The effects on M, M, and I are obtained by using (3.29), (3.30), and (A.34). (b) Change in L: Differentiating (A.32) with respect to L and using Cramer’s rule, yields: [1_k(Z)]+k(z)w*a >0 _! >0 2 D [w*] D 2 ‘8L 8M ôw* 8M* M*8w* =[1_w*a] + [?bpa-aL ]—>0, =———-->0 , C 8L w* ai* L ii [1_w*o] <0 [w*]z 0L aL w > a; _[[1_k(.f)]+k(!)w*a]A/(f (A.36) - For the case of the change in L, just replace L with IL and L with [1-ilL. Then use the same procedure. The signs of the results for the change in L are the same as the change in L, so they 78 will not be repeated. (c) Change in 1: Replace L with IL and L with [1-[JL in (A.32), then differentiating (A.32) with respect to I and using Cramer’s rule, yields: = [[a_1]+k()[1_w*aJ]k() 81 2 D 8! 0 _[c_1] _k([1_w*a]< [w*] D 2 =[1-wa] + [Apa-aL]—<0, [1-w’o] l - 1 - 4 <0 2 [w] 8M (A.37) >0, The signs are as shown if and only if k(2’)[1-w)> 1-c’. This condition can be rearranged to read z’> [1-ct]/{[1-n][1-waj}. Notice that there are endogenous variables which appear in both sides of this condition. Thus, the signs of all derivatives are ambiguous. 79 CHAPTER III NORTH-SOUTH TRADE AND GROWTH: WITH DIMINISHING MARGINAL PRODUCTIVITY 1. Introduction The development of models with endogenous technological change have provided economic tools for answering many important questions pertaining to industrialization and economic growth. However, several endogenous growth models’ imply that high population economies grow faster. This implication might not be suitable for developing countries which often face problems related to fast-growing populations. This result of high population leading to high growth stems from the non-rival property of technology and constant returns to scale assumption. As pointed out by Romer (1990), the cost of discovering new technology is independent of the number of people who use it since it is incurred only once. With the constant returns to scale assumption, the share of resources used by the research and development (R&D) sector remains constant as the population grows. Thus, a larger population enhances technological progress. This result, however, does not seem to fit well with the case of less developed countries which often have high density populations. This paper provides reconciliation by presenting an endogenous growth model which shows that a large population can lead to either an increase or decrease in technological progress when the agricultural sector operates under diminishing marginal labour productivity. The agricultural sectors of the developing countries are still the major sectors of their economies and most of their labour forces are concentrated in these sectors. Thus, outputs of their agricultural sector tend to suffer from the problem of a diminishing marginal product of labour. The problem is more severe for the countries with scarce land and rapid population growth. See Grossman and Helpman (1990), and Aghion and Howitt (1992). 80 The model presented here is an extension of the model in Chapter II. It is an endogenous growth model with three sectors: manufacturing, R&D, and grain. It is assumed that outputs of manufactured goods and R&D are produced by labour only with Ricardian produc tion functions. The major change in this assumption from the model in Chapter II is that the produc tion function of grain is subjected to a diminishing marginal product of labour. In this model, an increase in population will alter the share of resources used in the R&D and grain sectors. An increase in population from an initially small level (relative to the fixed factor of the grain sector) will enlarge the resources devoted to R&D; hence, techno logy will grow faster. Nevertheless, a continued increase in population will eventually draw resources away from the R&D sector since the grain sector is less and less productive. Hence, R&D will fall and technological progress will decrease. The organization of the rest of the chapter is as follows. After this introduction, Sectio n 2 lays down the model for autarky. The structure of the model in this chapter remain s the same as in the previous chapter, with the exception of the grain sector. Therefore, the structu re of the model that overlaps with Chapter II is described only briefly. Section 3 extend s the autarky model to a trade model between two countries. Comparative steady state analys es for the free trade model are provided in Section 4 and Section 5 provides the conclusion. 2. Autarky: The economy consists of two sectors: grain and a continuum of manufactured produc ts. Their respective quantities, at time t, are denoted by g(t) and x(z,t), z E [0,1]; and their respective prices are p(t) and p(z,t). The total population is fixed and denoted by L. It consists of L workers and L capitalists, where L = IL, 0 <1 < 1. All consumers have identic al hierarchical 81 2 prefere nces defined by t Inu,(t)dt, fe = In 1 g ( t), where 1 lnu ( t) y(t) pj 1 Inj the subscript i (2.1) E +f (2.2) ln[x,(z,t)]dz, 1 (y t)>pj, {w=worker, c=capitalist}; p is the subjective discount rate; 1 lnu ( t) represents the instantaneous utility 3 at time t, and 1 y ( t) is income. In other words, consumers will not demand any manufactured goods unless their incomes are sufficient to consume the minimum need of grain (i). Once their incomes are sufficient for j they will devote the remaining income to consume manufactured goods. Each capitalist who is sated with grain is endowed with one unit of labour force and equity stocks. Each worker who is not sated with grain and suffers from malnutrition is endow ed with only a unit of labour force, where 0 <a < 1. Labour is supplied inelastically. Denote the wage rate per unit of labour force as w and set it to one as a numeraire. Then each worker’s income y = a, where a <pjby assumption. Thus, the top part of (2.2) is used for the worker. The optimal consumption of workers is given by: G(t) = ciLIp(t). It is assumed that workers do not invest in any assets if they are not sated with grain. Each capitalist’s income y, is assumed to be greater than pg. So, the bottom part of (2.2) is applicable to the capitalist. The optimal consumption and expenditure of the capital ist are 2 A detailed justification of this assumption can be found in Eswaran and Kotwa l (1993), Section 4. As in Murphy, Shliefer, and Vishny (1989), the preferences used here are lexicog raphic. However, they are needed for solving the consumer’s optimization problem. 82 given by : G(t) 4 MQ) = = = G, X(z,t) M(t)/p(z,t), and [dM(t)/dtJ/M r-p [y(t)-p(t)g7L. is the aggregate-manufacturing expenditure of the capitalist. where The last condition states that the aggregate manufacturing expenditure must increase at the same rate as the net rate of returns. On the supply side, all productions in the manufacturing sector have constant marginal productivity of labour while the grain sector has a declining marginal productivity of labour. The unit labour requirement of manufactured product z, with technology of generation j, is defined by a(z,j) = a(z)Ø(j), where 0(j) = [1-n]Ø(j-l), and n is the inventive step between generations. The industhal leader who owns the most advanced technology of z limits pricing its competitors out of the market and earns a profit of H(z) = nM, for all z. The technology of the manufacturing sector can be improved over time. To discover the next generation of technology, firms have to incur up-front expenses on R&D equal to waj, where a 1 is the labour requirement per unit of R&D intensity, I. Inventor firms fund their expenses by issuing equity stocks which have the market value denoted by V = wa,. All risk is assumed to be independent; hence, their equity stocks pay an expected rate of return equal to the risk free rate of return (r). It can be shown that the rate of returns on equities is: r Substituting r into A = 1 a = = nMJa 1 I. r-p yields: —i—p. (2.3) This is the condition that ensures consumer and capital market equilibrium. Unlike the manufacturing sector, the technology of the grain sector is time invariant. Its production function is given by: GS = B[Lg1½, where Lg is the amount of labour employed in the grain sector, and B is its productivity index reflecting technology and the underlining fixed factor ‘ See details derivation for the consumers’ optimal consumption in Chapter II. 83 . Solving the first-ordered condition of the problem Fig land ) such as 5 L = IIg 2w = Max PB[Lg]WLg, yields (2.4) pB--w 2w 2w 4w The capitalist is assumed to own the profits from grain. Setting w=l, the market clearing condition for the grain sector is: B p 2 2 (2.5) + p where the left hand side is the supply of grain B[Lg]½. The first and second terms on the right hand side are the grain demand of workers and capitalists respectively. The condition can be p 2 rearranged as a quadratic form: B - 2ILp - 2aL 0. Hence, using the familiar formula for = 6 solving the root of the quadratic equation gives the price of grain + IZ 2 {[jL] +2ULwB 2 2 B where E jL ÷ 8 (2.6) 2 B - +2aLB } and the superscript “A” denotes the autarky solution. ] {[ 2 , it must be true that a <pj: 7 To ensure that workers are not sated with grain as assumed Substituting pA from (2.6) and rearranging this inequality gives B < [2LIa]½ B. This B is the highest level of grain productivity that keeps the grain price high enough such that workers This diminishing return assumption is equivalent to assuming that grain production uses two inputs: labour as a mobile factor and another specific fixed factor such as land. Since labour is paid according to its value of marginal product, the profit rate generated from the grain sector is the rate of return on this specific fixed factor. 6 The solution of pA with negative ö is not feasible since ö §L, and pA will be negative. The condition for capitalists to be sated with grain will be given below. 84 . 8 remain unsated with grain With the solution of pA from (2.6), the amount of labour employed in the grain sector and its profit are LA (2.7) . g 2B g j 2B j The model is closed by a labour-market-clearing condition which can be stated as: N where N = [1—n]M = cth--L = + L (2.8) , ÷ 1 a ! [a[l-11+1]L is the labour supply. The terms on the right hand side represent the labour employed by the manufacturing, grain, and R&D sectors respectively. The differential equation (2.3) and the resource constraint (2.8) determine the steady state . The steady state solution to these equations is obtained by setting 9 solution of the economy [I+p]. Next, solving (2.8) for a,! and 1 a M=O in (2.3) and rearranging the result to get nM substituting the result in the previous equation yields the solution for M as shown below. M = N - L + 1 pa N - { gIf 6 j2 + (2.9) pa With some arranging, the solution of M can be expressed alternatively as follows The value of B can also be solved by substituting pA condition in (2.5) and solving for B. ‘ ‘ aL/I into the grain market clearing The economy is immediately converged to the steady state. If not, either the profit maximization or the lransversality condition will be violated (see details in Chapter II). 85 M = [aLw+Lc_L+paj]_pAjL+pAjLc = [1 _pAjJL + 1 {[aL ÷PAILI —L} ÷ p = [1 pAj]L + AB[LA] -Lf [1 p’j]L + ll = + + (2.10) 1 pa ,. 1 pa The result in step three is obtained by employing the market clearing condition: ciL+pAgL, = PAB[LAI½. Using the definition of F1 gives the result in the last step. With the solution for M, the capitalists’ income can be written as — PAjL = (2.11) . 1 L ÷ ll’ ÷ pa In other words, the capitalists’ income consists of wage income (Lj, profit income from grain (H), and income from equitie&° (pa ), while the capitalists’ manufacturing expenditure is equal 1 to the leftover income from grain. Notice that H is the extra term resulting from the diminishing marginal productivity assumption. If grain production were Ricardian as assumed in Chapter II, fl would be zero. To obtain the solution for R&D intensity, rearrange (2.3) to read JA = 1 nMja - p and use (2.9) to get - [i-nip, = - [i-nip, (2.12) There are three restrictions needed so that the solutions given above are consistent with the assumptions that have been made. First, for the manufacturing sector to progress, the R&D intensity must be positive. This requires that N-14-K> 0, where K = . Solving this 1 {[l-n]/n}pa condition for B yields = j.l/ Setting M,=O in M= r-p gives r=p. Moreover, the equity value V is equal to a,; hence, pa, is the equity income. 86 B ]1/2 jL[ 4N-K xL ÷2L -K (2.13) Second, the labour employed in the grain sector (L) must be less than the labour supply (N), otherwise production of other sectors would be zero. obtained by set K in (2.13) to zero which yields B The required restriction can be [21LJP9/[cIL+2L] B. That is, the actual value of B must be at least as high as fl. This condition is satisfied if (2.13) holds since B, > .. Third, we need to ensure that capitalists are sated with grain while workers are not. It will be shown that this can be satisfied if the actual level of grain productivity, B, lies between LB]. Note that capitalists will be sated with grain if and only if the manufacturing expenditure is positive because they will consume manufactured goods only when = j is attained. From M N-L+pa,, the manufacturing expenditure will be positive if N-L is positive. requirement B B causes N Since the L, it also guarantees that the manufacturing expenditure is positive. Thus, if the grain productivity is sufficiently large, capitalists will be sated with grain. However, the grain productivity cannot be too large otherwise the price of grain will be so low that workers will be sated with grain. As discussed earlier, it is required that B B = 1[2L/a]. Hence, the restriction that causes capitalists to be sated with grain while keeping the workers unsated is: B E [,B]. Equation (2.12) and condition (2.13) have the following interpretation. From (2.12), it is clear that if B B, then N L and I’ will be negative. Thus, for the R&D intensity to be positive, it is necessary for the productivity of grain to be higher than B so that capitalists are sated with grain and start consuming manufactured goods. For the R&D intensity to be positive at all, the grain productivity must exceed B, so that the profits generated from the capitalists’ consumption are high enough to support viable R&D. A large inventive step (large n), efficient labour in R&D (low a,), and willingness to sacrifice for the future (low p) also help improve the 87 viability of R&D activity. With the steady-state R&D intensity given in (2.12), the utility growth rates of the capitalist can be calculated by” 13A = q()JA, where q(n) = - ln[l-nJ. Substituting R&D intensity into this formula gives pA - 1 a 2BJJ (2.14) [1-n]q(n)p. As in Chapter II, technical progress of the manufacturing sector improves only the welfare of capitalists, but the benefit does not “trickle down” to workers because they consume only grain and the real wage in terms of grain is unchanged. The real wage is unaltered due to the following reasons. First, capitalists are all sated with grain, while workers who are not sated with grain do not substitute manufacturing goods for grain by the hierarchical nature of preferences. Hence, there is no increase in demand for grain by either type of consumer. So the price and real wage remain the same. Second, though the unit labour requirement of manufacturing goods keeps declining by R&D, the division of labour among sectors remains unchanged since the demand for manufactured goods has unitary price elasticity. Thus, the amount of labour employed in the grain sector stays the same as does the real wage. Therefore, workers are . 2 indifferent’ 2.1 Country size, population mix, and growth Grossman and Helpman (1991a) have shown that, unlike most endogenous growth models, larger economies do not necessarily grow faster. Only larger endowments of factors that are used See Chapter II for detail derivation. 12 This result may be interpreted as a dynamic version of Proposition 2 in Eswaran and Kotwal (1993). As also mentioned by them, if preferences are not exacting hierarchically in the real world, the benefits filtered down to workers would, nonetheless, be modest as long as the magnitude of substitutability between the two groups of goods are sufficiently low. 88 most intensively in R&D activities ensure faster growth. This essay, however, will show that a larger level of labour force (the factor that is used most intensively in R&D activities in this model) may slow down growth when preferences are hierarchical and the marginal product of labour of the grain sector is decreasing. This possibility is demonstrated in the following simplified example and summarized by Propositions 1 and 2 below. Example: For simplicity, let assume that L—O which implies that N = §L, L = , and 2 [g7/B] JA = j{L-[gEL/B] 1 [n/a } 2 - = L = L. Moreover, [1-nip. Suppose the initial level of labour —½[B/gI The conesponding R&D intensity is 1 L . force is given by 2 = —_r — 1 gj 4a (2.15) [l—n]p. —¾[B/g] Then, the R&D intensity for this case is L . Now let the labour force increases to 2 A ‘2 = 3nB1 2 1 jj 16a — [1—nip. Clearly, the R&D intensity declines since I > I. As the utility growth rate is q()JA, it also decreases. Hence, a larger level of labour force can slow down the growth rate. Proposition 1: In a closed economy, an increase in the worker population always increases the utility growth rate, while an increase in the capitalist population may increase or decrease the growth rate. The sufficient condition for the growth rate to increase is L Proof: < . 2 ½[B/g] Differentiating the utility growth rate in (2.14) with respect to L holding L, constant yields 89 nq(n) 1 a = aL } + J 2 (2.17) > Thus, an increase in L always increases the growth rate. The sign is positive since ö Now differentiating the utility growth rate in (2.14) with respect to L holding L constant gives = 8L nq(n)J 1 1 a (2.18) . nq(n) 1 a — The sign of (2.18) depends on the value of A { [jlL]÷ 2c41-l]LB 2 }i [L+]/& Since B, 1 2 [2aL] jL, = 0 (2.19) 1=1 we have 1,1=0 - (2.20) = jL+jL gL = 2, 1 = 1 In other words, A e [1,2] for I e [0,1]. Using the above information gives 90 j[2aLj2BaL 2B 2 2B B 2 2g[2gL] , 2 2Lf1 (2.21) LBi 2 2B i = Hence, the value of (2.18) becomes E 0L - 1 a ( - B 2 , J ‘‘i -i.., BJJ 1 a , for 1 e [0,1]. (2.22) To show that an increase in L can reduce the growth rate, use the case of 1=1 as an example. This corresponds to the case given by the second term in (2.22). The sign of (2.22) for this case will be negative if L > . 2 ½[B1g] The derivation for the sufficient condition that ensures a higher growth rate with larger L proceeds as follows. First, it will be shown that (2.22) is monotonically decreasing in 1. So, the value of (2.22) at 1=1 is the minimum. Second, the condition that ensures a positive value of the minimum of (2.22) is derived. This condition will be the required sufficient condition since it guarantees that even the lowest possible value of (2.22) is positive. (a) To show that (2.22) is monotonically decreasing in 1, taking derivatives of (2.14) with respect to L and then I yields: 91 aZpA - aLgal as — = aLgal +8]128gL 2 2[B8] ÷ I jL[jL+8]I C 3 8 2 2B > 0, - -czB [jL] L 2 C C [8 -jLj Si — ] 2 [gL] as [gL C +5]2_ ai — 25[jLC ÷8] gL+— 3l 2( 2[B8] j[jLC = (2.23) o < I c’-Lg where nq(n) 8L 1 a aLal + — > jL, and JjL_÷8 C ] a ± 2 B L i since 8 C 2 SB - a pj - 2 rijLB a > 0. 2 B Because (2.22) is decreasing in 1, its minimum must be at the point where I is at the maximum; i.e., when I = 1. This means that the second boundary value of (2.22) is the minimum. The minimum value of (2.22) will be positive if 1 that L < - 2 is positive which requires 2L[j/B] . This is the sufficient condition given in the proposition. 0 2 ½[B/g} An increase in the population of the capitalist (La) may increase or decrease the growth rate because of the following reasons. Using equation (2.12), it is clear that the R&D intensity depends on the value of N L. On the one hand, an increase in L enlarges the labour supply - which tends to increase R&D and the growth rate (endowment-expansion effects). On the other hand, a higher Lr also generates a higher demand for grain. consume i since Recall that capitalists always they are sated with grain. This higher demand for grain increases the grain price and raises the labour needed in the grain sector (L) which reduces the labour available for the R&D sector. This in turn reduces the growth rate (diminishing marginal productivity effects). The net result depends on whether the endowment-expansion or diminishing marginal productivity effects are stronger. For a small initial level of L, the demand for grain is small and its corresponding 92 equilibrium price is low. An increase in the capitalists’ population from this initial level will add the labour supply to the economy (endowment-expansion effects) more than pushing up the labour demanded for grain (diminishing marginal productivity effects). Therefore, R&D and the growth rate will increase. However, a continued increase in the capitalists’ population will put more and more pressure on the fixed factor of production in the grain sector (B). Consecutively, more and more labour will be needed in the grain sector and less and less labour will be available for other The increase in population in this case will generate larger diminishing marginal sectors. productivity effects than endowment-expansion effects. Therefore, R&D and the growth rate are reduced. The increase in population of workers (Lw), however, always increases the growth rate by the following intuition. diminishing effects. The rise in L also generates similar endowment-expansion and Nevertheless, workers demand for grain is not fixed (at j as the capitalists’s) since workers are not yet sated with grain. Recall that their demand is given by G = ciL,Jp. The increase in grain price created by the additional worker will proportionately reduce the demand for grain of all workers. Therefore, the increase in labour used in the grain sector will be smaller than the case of the rise in L and the diminishing effects will be smaller. Proposition 2: In a closed economy, an increase in total population (fixing the ratio of capitalists to total population) may increase or decrease growth. Further, if all consumers are capitalists, an increase in population will increase growth if and only if L < . 2 ½[B/g1 Proof: Differentiating (2.14) with respect to L (using the fact that L=1L, and L=[l-[JL) yields 93 = 8L = = _÷ 1 nq(n)[ 1 a nq(n) a[1 -11+1 1 a nq(n) N L 1 a - aL - [iL + 81L LA - g 6 = (2.24) ‘(){N L 1 a - ALA}. g The sign of (2.24) depends on the value of I and its effects on other parameters. We already know that A E [1,2] for I e [0,1] from (2.20). The corresponding values of other parameters for respective values of 1 ft glL+]/2B] 2 E [0,1] are: N = [a[l-I]+1] L € [aL,LJ; ö e {[2aL]B, §Z]; and L = e {aL/2, [g_LfB2]. Using this information in (2.24), it becomes 8L E nqn)a 1 2a nq(n) i —2L BjJ 1 a (2.25) Hence, when most consumers are workers or I approaches zero, the increase in total population always increases the utility growth rate. 2 On the other hand, when most consumers are capitalists or I approaches one, 1-2L[7B] will be positive if L if L < < . Therefore, (2.25) will be positive 3 , and negative if otherwise’ 2 ½[B/g1 , and vice versa if L 2 ½[B/g] > . Thus, an increase of L from an initially small 2 ½[B/g1 value will increase the utility growth rate. However, a consecutive increase of L will eventually reduce the growth rate. El An increase in population, holding the same value of 1, may increase or decrease the ; that is why the increase of 2 Notice that the value of L 1 given in the example is ½BI) 1 L intensity. population from to L 2 decreases the R&D “ 94 growth rate because of similar reasons to those given in the previous proposition. An increase in population generates both endowment-expansion effects and diminishing marginal productivity effects. The net result depends on which effects are stronger. A continued increase in population may reduce the growth rate because it may divert resources from the (dynamic) increasing returns to scale industry (the manufacturing and R&D sectors) to the diminishing returns to scale industry (the grain sector). productivity falls. Thus, the average This argument is similar to the explanation used in Graham (1923), and Helpman and Krugman (1990) to describe the possibility of loss from free trade. However, the source of the diversion of resources in this model is the hierarchical preferences, not free trade. 2.2 Redistribution of income and growth The previous analyses have shown that an increase in the population of workers always increases the growth rate. This result seems to suggest that skewness in income distribution promotes growth. However, the increase in population of capitalists can also increase the growth rate if the initial population is small. The immediate policy implication is whether a redistribution of income that changes the population mix can increase growth rate. The analysis in the next section provides the answer. Note that the redistribution of income means a transfer of equity stocks and income from capitalists to some workers so that they become capitalists. Thus, it is equivalent to an increase in the ratio of capitalists to total population (1). Proposition 3: In a closed economy, a redistribution of income from capitalists to workers such that they are sated with grain will increase the utility growth rate of the capitalist if L Proof: Differentiate (2.14) with respect to I holding L constant to get 95 < - = 81 ‘‘[1-cE]L 1 a = - L gL C ÷5 5 2 2B nq(n)Lf 1 a a, - = 81 j [1-aJL 1 a = - nqQz)L 1 a a, - - - [ ‘‘1f[1-a]L 1 a - jL+5 2 2B jL÷ 81 L-aB {Sj+i ] 2 _ _ 4 [[iL + 2 2B - (2.26) ] 2 aB A gL + 5 2 2 B To show that (2.26) can be increase or decrease, let 1 approach one which causes A the terms in the curly bracket become 1 and negative if L > - = . Thus, (2.26) will be positive if L 2 2L[7B] 2. Then, < 2 ½[B/g7 . 2 ½[BI] The sufficient condition which guarantees that the redistribution of income will increase the growth rate can be derived similarly to the sufficient condition in Proposition 1. First, it will be shown that (2.26) is decreasing in I and it has the minimum value at the point where I = 1. Second, the condition that ensures a positive value of the minimum of (2.26) is derived to give the required sufficient condition since it guarantees that even the lowest possible value of (2.26) is positive. (a) To show that (2.26) is monotonically decreasing in I, note that PA 2 8 - 812 nq(n) 1 a (2.27) 012 Differentiate L with respect to I to get a14 = ÷8 jL ÷8 ] - 8! 28 jL +8 a 2[ f 2 2B 96 i1? f 2 B (2.28) - i’ 812 where 2 ( f 2 B 81 j -tIL 2 I. 2B ÷ - (2.29) + Ol J L-aB 2 [j ] L = — --{8jL+[j2L_aB2]L} = -{[jL+8] = 1 J21 1L+8l_ - } 2 aB — =— 8[ 2 B ii 881 —8gL-gL—. calJ 821 = {82 — — or 812 8A 1- pg]-- = + 1IOA 21.81 = —— —8L-Lc 821 = 2 ÷ 2 [jLJ cB L } - 3 D 8Lg 8 J = — Thus, j > 0, since 8 > jL. AjL 28 AjL1 [pg-aJ 8 J - + L-ccB 2 [j ] L 0. > Hence, (2.27) is negative and (2.26) is monotonically decreasing in 1. Its minimum must be at the point where I is at the maximum; i.e., I = 81 , nq(n)L 1 1 ( a nq(n)L 1 1 ( a - - a 2L - 2 BjJ = 1. Evaluating (2.26) at I 2 2LI1l {Bj > 0 = 1 yields: - J if L (2.30) < - 2g This is the sufficient condition given in the proposition. El The intuition for this proposition is as follows. The redistribution of income turns workers to capitalists which creates two impacts on the growth rate. First, it raises the labour force of the worker-turned-capitalist from a to 1 since none of them suffer any longer from malnutrition problems. This effect on the growth rate is represented by the terms nq(n)L[ 1-al/a 1 97 in (2.26). Second, the redistribution of income increases the demand for grain of each workerturn-capitalists which raises the expenditure on grain. The aggregate manufacturing expenditure is, therefore, decreased since it is the leftover income from j With lower aggregate manufacturing expenditure, the incentive for R&D declines and the utility growth rate reduces. This effect on the growth rate is captured by the second terms in the curly bracket of (2.26) which can be written as nq(n)L[pAgxJA/2 in (2.26). These two effects work against one another, so the net effect may result in an increase or decrease in the utility growth rate. When the initial population is small, the former effect dominates the latter effects and the redistribution of income increases the utility growth rate. 3. Free Trade This section extends the autarky model to a trade model between two countries. It considers a trade situation between a developing country and a developed country where the developing country imports most of its R&D needs. The objective of this section is to find out what determines the level of the developing country’s dependency on imported R&D. As it is shown in the autarky model, an increase in population may decrease the R&D intensity if the initial population is large. It stands to reason that in a free trade economy, an increase in population of a country that causes an increase in the world population (to be too large) could reduce the world’s R&D intensity. The same increase in population may also decrease the country’s share of the world’s R&D and force it to rely more on foreign R&D. The world economy consists of a developed country called North and a developing country called South. Southern variables are denoted as in autarky while Northern variables are denoted by superscript 98 3.1 Consumers The North ‘s population is L which can differ from L. With the decreasing marginal product of labour in the grain sector, the model becomes complicated very quickly. Thus, to keep the model tractable, it is assumed that all consumers are capitalists and are sated with grain both before and after trade. Northern consumers share the same preferences defined in Section 2. Thus, the optimal growth rates of manufacturing expenditure are governed by = r — p. icr (3.1) = - 3.2 Trade patterns To depict the real situation as closely as possible, the developed North is assumed to be more efficient in R&D activities. The South, on the other hand, is more efficient in grain productions. Here, the South represents a particular type of developing country that has attained a certain degree of industrialization. Although its main export is grain, the South is capable of exporting some manufactured goods for which some of the production technologies are locally conducted, but most are ‘imported” from the North’ . 4 Let Co wIw be the equilibrium relative wage. Then, assume that the North has an absolute advantage in R&D activities; i.e., a y, three trade outcomes are possible. = If Co > ‘ya,, where 0 <y < 1. With this fixed value of , the North is the sole producer of R&D. Conversely, if o <y, or Wa 1 <wa, then the South is the only country conducting R&D. Lastly, if o = y, both counthes are equally efficient. For this case, R&D activities are conducted by both countries although one country may be the net exporter of R&D. ‘ The term “R&D imports” is used loosely here to represent the whole process of multinational corporations setting subsidiaries and applying Northern technology in the South. 99 As described above, the case where both countries conduct some R&D are of interest, thus, this paper will concentrate only on the case where to = . The case where to < ‘ is ignored because it is unlikely that the South would be the sole producer of R&D. The case where to y is chosen over the case where to > y for three reasons. First, when to = y, there is a possibility that some Southern firms would be indigenous instead of being Northern subsidiaries as when y. Second, the relative wage of the South is always strictly less than that of the to > North since to = y and ‘y < 1. These two characteristics seem to fit the actual observation of the North and the South. Third, changes in most exogenous parameters do not alter the relative wage or the competitive margin when to = Hence, we can concentrate only on the direct effects of these factors. The case where the North is the sole producer of R&D (when to > y) can also be used, but the relative wage in that case will be altered by the changes in the exogenous parameters. The change in the relative wage would obscure the direct effects and unnecessarily complicate the analyses. With the equilibrium relative wage goods is determined as follows. to fixing at ‘y the trade pattern of the manufactured Each country has its own unit-labour-requirement schedule a(z)Ø(j,t=0). The set of the world’s most advanced technology (J) is unique and the South is assumed to own a fraction ?. of this set of technology while the North owns the remaining fraction l-?. Firms can apply the most advanced technology anywhere in the world. Thus, the relative labour productivity of manufacturing sectors can be defined as A(z) = a*(z) (3.2) z e [0,1]. a(z) Then the borderline product that both countries produce at the same labour cost or the competitive margin (2) is given by 2 = A’(y). The South specializes in industries z e [0,2] while the North specializes in industries z e [2,1]. The case where to y is described in the Appendix 1. 100 For the grain sector, the Northern production function is given by C[L], where C is the productivity index of the Northern grain sector. The Southern production function is the same as is given in autarky. To simplify the calculation, it is assumed that ‘yC 2 = = . Normalizing w 2 B I and solving the profit maximization problem of each country gives: L* g ycp12 2 j = g 2] y . 2 2 (3.3) The grain market clearing condition when everyone is sated with grain is given by [L÷L*J 2 [B + yC2]. (3.4) Solving this equation yields the equilibrium price of grain: F 2j[L + L9 = +yC 2 B where, L’ IL 2 B L+L* is the world population. Hence, the employment of the grain sector in each country is B ILW LF 12 ILWf 2B +yC 2 B j L*F ,,, yCjLK12 ÷yC B j 2 = (3.6) ] iLj 2B j (37) To ensure that the labour employed by the grain sectors do not exhaust all the labour supplies, it is assumed that the grain productivity of each country is sufficiently large ; i.e., 16 As in the autarky, these conditions also ensure that all consumers are sated with grain since they cause the manufacturing expenditure of each country to be positive. ‘‘ 101 1 B > !rW L 2 and , C > -—,w 2L 1 L* (3.8) 2 The value of the right hand side of each inequality is analogous to B in the autarky model. The trade pattern of grain is determined as follows. Define net grain export functions of the South and the North as G = B[L:]2 - jL, G C[L] = - (3.9) IL*. Then assume that y where A(0) < A(0) < 1T 2 TJ (3.10) “, C / 2 L* = a*(0)/a(0) is the relative labour productivity of zO. The first inequality ensures that the South produces some z in the equilibrium. downward sloping and 0i This is because the A(z) schedule is y; their intersection must be at the point where! > 0. The second inequality assumes that the South’s relative grain productivity (adjusted by population) is strictly greater than the relative labour productivity of the manufactured good for which the South has the highest comparative advantage (z=0). It ensures that the South remains the net exporter of grain as long as the South exports some manufactured products in the IL}/[CIL*j. Then, multiply both sides of the 2 equilibrium. To show this use the inequality ‘y < [B <B L w. Then, multiplying inequality by C L and add both sides of the result by B 2 L to get: 2B 2 L2 2 both sides of this last inequality by §7[2B 1 yields: jL <jV’/2. Notice that the right hand side 2 [B L1½. Rearranging this gives B [LYA 2 is 2 - = G> 0. Thus, condition (3.10) implies that the net grain exports of the South are positive; i.e., the South exports grain as claim. Note that since 2 is assumed to be equal to B the condition 2 /L]/[C B / L] > ‘y implies that L* must be bigger than L. With the specified trade patterns, the following section describes the trade equilibrium. 102 3.3 Trade equilibrium with both countries producing R&D When o I + = y, both countries are equally efficient in R&D and the world’s R&D: F 1 1. The rates of return on equities for both countries are the same and can be written as r nWM/a, - F, 1 where WM = M+M” is the world aggregate manufactured expenditure. Assuming perfect international capital mobility, this implies that r 1 expression of r in (3.1), to get M= nWM/a - jF - p, and M = 1 nWM/a - r’. Use the p. Then multiplying 1 and adding the results yield the differential equation that governs the world each equation with a manufacturing expenditure: a = 2 (. P+p1. nWM—a [ 1 Like Chapter II, the trade equilibrium is determined by the intersection of the A(z) . The BP(2) schedule corresponding to 17 schedule and the balance of payments schedule, BP(2) this case is given by segment BC in Figure 3.1. It will be shown below that BC is flat; i.e., when w = y, the balance of payments can be maintained by a set of 2 E ’ z 8 , 1 [z J 2 . Three trade outcomes may result depending on where the A(z) schedule intersects this segment of the BP(2) schedule. If the intersection is between the range of S and C, the North will be the net exporter of R&D. Conversely, if the intersection is between the range of B and 5, the South will be the net exporter of R&D. If the intersection point is exactly at point S. trade in R&D is zero. Both countries produce the exact amount of R&D needed for their domestic uses. The following sub-sections provides the solution for each case. The solution for the case where the North is the net exporter of R&D is derived first because it is the most likely case. ‘ This section will provide only the construction of BP(!) when w = ‘y Detailed constructions of the BP(2) schedule with corresponding equilibria for the cases where (I) y are provided in Appendix 1. 3 Appendix 2 shows that z > z,] is not empty. ,[z ; therefore, the set 2 2 z 103 The solution for the case where both countries are self sufficient follows immediately since it is a special case of the first one. The solution for the case where the South is the net exporter of R&D is provided lastly for completeness. 3.3.1 North is the net exporter of R&D This case corresponds to the solution when A(z) intersects BP(2) between S and C in Figure 3.1. The South requires 2 of the world’s R&D for its own manufacturing sector z e [0,2] while the North needs [1-!] of the world’s R&D for its production. The South imports a fraction s of its needs for R&D from the North. This fraction s measures how much the South depends on the North’s R&D; henceforth it will be called the South’s dependency on imported R&D. The resource constraints for this case are: L [1-n]WM ÷ = y[1—][1—n]WM = (3.12) + + LF ÷ a{[1_zl ÷s*f}IF (3.13) The first term on the right hand side of each equation is the labour needed for manufacturing productions of each country. The other two terms measure the labour needed for grain and R&D respectively. Adding labour market clearing conditions yields a world resource constraint L L* + — = [l—n]WM Y + F [Lg L + IF. 1 a 314 Y The differential equations (3.11) and the world resource constraint (3.14) characterize the steady state equilibrium similarly to (2.3) and (2.8) in the autarky model. The steady state equilibrium has its solution at M+M = 0. To obtain the solution, solve at from the combined resource constraints to get: at = L L-f-[L-L;]fl-[ l-nIWM. Then, substituting the result into (3.11) with M-i-Pv! setting to zero yields: 104 Figure 3.1 Balance of Payments Schedule (I) BP(z) D S B Cl wo z 3 z 1 Z 105 2 z [L* F WM = L*F] — g [LLg]± ÷pa Y = L L* + + y pa — (3.15) — 2B The result in the second step is obtained by using (3.6) and (3.7). Substituting this solution of WM in (3.11) then gives the R&D intensity: F 1 = 1 fl — F [L — + Lg] {L*_L*F]l g r Y [1—n]p, (3.16) I = — 2 -L+L_! 2 y -[1-nJp. J B To solve for s, substitute af = 1 from (3.11) into the South’s resource constraint nWM-pa and rearrange to get: ] 1 z1WM pa — z[nWM - - [L — L:] pa,] jLw2] = JL+L_ [ y 2 + L* B -L+ J 2 ILW (3.17) 2B 1[iLw]2] - [1n]pai} Given the South’s dependency on imported R&D, it is possible to solve for the boundary values of 2 that support this case. For the lower bound, we know that if s sufficient in R&D. Hence, imposing s = 019 margin. 0, the South is self in (3.17) and solving for 2 gives the 2 that causes the South to be self sufficient in R&D. This 2 is denoted by sufficiency = z. and will be called the R&D self- It can be written as: For s to be non-negative and less than one, it is required that !/[l-!] ‘y{[L-L]/[L-L9 l-2[l-n]}, where! = A’(’y) and the values of L and L are given by (3.6) and (3.7). 2[l-n.]/{ 106 = L - (3.18) - - For the upper bound, s yields 2 {jL’/2Bj L 2 ![ILW,B] L*/y 1 pa L + . - 1 or the South imports all its R&D. Thus, setting s = = 1 in (3.17) 2 and can which causes the South to rely totally on the North’s R&D. It is denoted by z be written as: = L - L L 2 [jL”f2BJ [1_n]{L+L*/y _![iLwlBr} (3.19) - [1-nJWM . The intermediate values between 0 and 1 of s, therefore, represent the case where the North is the net exporter of R&D. To complete the picture on R&D, it is also interesting to know how much the South’s 1 R&D is relative to the world production. For this purpose, define z [l-s]! as the fraction of . Using this definition in (3.12) and rearranging terms gives 20 world R&D produced in the South [L—LF] I — [1—n]WM (3.20) 1 nWM-pa By definition, it is smaller than or equal to 2 since s e [0,1]. Note that imposing 2 and rearranging terms yields z, = = z, in (3.20) ] which is z as given in (3.19). Thus, z, is the 1 [L-L]/[WM-pa 1 that equals to 2. special z Finally, the solution for each country’s manufacturing expenditure can be solved by using WM given in (3.15) and the balance-of-payments condition. The balance-of-payments condition for this case can be written as: 20 This is the same as :‘ in Taylor (1 994a). 107 fJVI*F - [l-z9M’ + pG s nWM ÷ A[1-z9pa’/y - - The meaning of the condition is as follows. The first terms, [1-A]pa, 2M*F - = [1]MF, (3.21) 0 are the value of the net Southern exports of manufactured goods since the South’s export demand is M*/p(z), for z e {0,] and its import demand is M/p(z), for z E [,l]. The second term, PFG is the Southern grain export value. These first and second terms represent the South’s trade account. Any deficit in this account must be compensated by a surplus in the service account depicted by the last three terms. Since the South has to import a fraction s! of R&D from the North, it has to pay royalty of sWM. Now, recall that the South owns value of V = 1 a = of the world equity stocks which have a market a/y and earn a rate of returns r = = p. The term ?[ l-2]pa/’y is, therefore, the Northern dividend paid to the South’s shareholders. The remaining term, [1-1pa , is the 1 Southern dividend that is paid to the North’s shareholders. This balance-of-payments condition can be simplified further as IWM - M” ÷ + -z9nWM 1 [z + ]pa [)—z 1 The first two terms are obtained by using the fact that term is obtained by using a/y = = (3.22) 0 - MF. The last . The interpretation of the condition is quite the same. The 1 a South’s manufacturing firms must pay a net of [2-z,]nWM as royalty payments for using the technology imported from the North because z. is smaller than ! (see Figure 3.2). It also receives a net dividend of [-]pa, from the North. 108 Figure 3.2 Patterns of Manufacturing and R&D Production --- North’s R&D South’s R&D----.I I I - I I 1 1 North’s Production South’s Production I Condition (3.22) can be used for the calculation of each country’s manufacturing expenditure as follows. M is obtained by substituting a,P South’s resource constraint (3.12) to get [z,-2]nWM = L L - to get Mi’. Deducting MF from WM and using G MF LgF L = L_pFaL÷{pFB[L:]z_L:}÷pai [L* M*F + nWM - pa, from (3.11) into the WM + z pa,; then use this in (3.22) 1 -G then gives M*F. They can be written as PFG+APa = - = - = (3.23) — L*FI g ± = [1p”jjL÷ll’+)pa pFG*+[1_)1pa (3.24) = [1 1 _F ]J*+ll*F+[1_)]Pa The interpretation for the world and each country’s manufacturing expenditures is much the same as that of autarky. The manufacturing expenditure consists of leftover-wage income from grain, grain profits, and income from equities. 109 21 3.3.2 South is the net exporter of R&D This case corresponds to the solution when A(z) intersects BP(z) between B and S in Figure 3.1. It is a mirror case of the previous one. Both countries produce R&D, but the North imports a fraction s, of its R&D needs from the South. Therefore, the resource constraints for this case are: L = L* = zll—n]WM + L y[1—][1—n]WM As in the previous case, solving + adz+sj[1_zl}IF, (3.25) + L ÷ aj*[1_s,][l_f]IF. (3.26) a,I’ from the combined resource constraints and substituting the result in (3.11) yields the same world manufacturing expenditure given in (3.15). Thus, the R&D intensity is also the same as (3.16). I’’ 1 To solve for s , substitute a 1 = 1 from (3.11) into the South’s resource constraint nWM-pa given in (3.25) and rearrange to get: = L - - ] 1 [WM-pa [1—][nWM ] 1 pa - - + L L* - - 1 2Bj [1_zl{n[L + y [jL W]2 D J i__[L)ij - (3.27) [1_nlPai} where the second expression is obtained by substituting L and WM. With (3.27), the boundary values of the of 2 that support this case can be calculated. For the upper bound, imposing s, = 0 and solving for 2 yields the same value of z as given in (3.18) which confirms that the South is self sufficient in R&D at! = z. While setting s 1 lower bound: 21 The case is rare in the real world, but it is given here for completeness. 110 = 1 yields the ] 1 L-L-[nWM-pa 1 This is the [1_n][L_L+ pa ] 1 = [1—n]WM 1 [1—n]{L-L÷ pa - + n[L*_L]fy (3.28) [L*_L;FJJY} that corresponds to the case where the South is the sole producer of R&D. The South’s share of world R&D can be solved similarly to the previous case. Define [l-] as the fraction of world R&D produced in the South. Then, using this definition 1 +s 1 as given in (3.20). in (3.25) and rearranging terms gives the same z With this definition of — or fWM - [1_]MF MF + + pFG , 1 z the balance-of-payments condition can be written as: PFG + J 1 [s 1 1—f]nWM + [).-zpa 1 = 0 1 pa [z,—f] nWM + [?.-z + = 0 (3.29) Notice that this condition is exactly the same as (3.22) which is the balance-of-payments condition when the North is the net exporter of R&D. Therefore, its solution for M and M*F are also the same as in section 3.3.1. Having the trade equilibria for all cases where o = y, we are now ready to explain why 1 in Figure 3.1 and segment BC of the BP(2) schedule is flat. Start from point B where 2=z increase 2. We can see that a current-account surplus generated by an increase in 2 can be 1 or z,). The completely offset by a reduction in the South’s R&D exports (a reduction in s adjustment in the South’s exports to maintain the balance of payments does not require an increase in w as is needed when one country is the sole producer of R&D. This process of adjustment continues until s =0 and 1 z,=z where the economy arrives at point S in Figure 3.1 and both countries are self sufficient in R&D. A further increase in 2 now requires the South to import R&D (s increases while z 1 decreases further). The adjustment can continue until s=l and !=z,. At this point the South ceases its domestic R&D and imports all R&D. increase in 2 would require an increase in tO Any further to maintain the balance of payments which would cause the BP(2) schedule to slope upward as shown by segment CD in Figure 3.1. 111 In Summary, segment BC of the BP(!) schedule is flat. From point B to S, the South gradually reduces its R&D export until the net export is zero. Then, from point S to C, it gradually increases its imports until all of its needed R&D is imported from the North. Combining this Co = BP() y with Co = A() gives the steady state solution: co = y and = A’(y). This then starts the motion of the dynamic evolution of the world economy as shown in Figure 3.3. The intersection point of this segment of the BP(!) schedule and the A(!) yields the same relative wage, the world and individual countries’ manufacturing expenditures, and the R&D intensity. This completes the detailed construction of the trade model. Now we are ready for the comparative steady state analyses. 4. Comparative Steady State Analyses: Trade model The objective of this section is to find out how the change in important economic parameters can affect the world R&D intensity, the South’s share of the world’s R&D production, and the South’s dependency on imported R&D. The level of world’s R&D is definitely important since it determines the utility growth rate and the welfare of consumers. The other two variables are not directly important to welfare since the utility growth rate and the welfare of each country depend on the world’s R&D intensity, not on its share of world’s R&D or the level of R&D imports. However, these are significant in terms of non-welfare objectives. The Southern government may consider its share of world R&D and dependency on imported R&D as indicators for its success in industrialization and economic independence. As mentioned earlier, the analyses will concentrate only on the case where both countries conduct some R&D activities (when Ci) = y) and the South has to rely on some of its R&D needs from the North. The impacts of two parameters, population and grain productivity, are analyzed 112 Figure 3.3 Steady State Equilibrium U) A(z;t>O) BP(z) A(z;t=O) A(z;t>O) I 0 — z 113 1 here. First of all, let us determine the impact of the economic variables on the relativ e wage and the competitive margin. This can be summarized by the following lemma. Lemma 1: When both countries conduct R&D, a small change in population or productivity of grain leaves the relative wage rate (co) and the competitive margin (2) unchanged. Small changes of these parameters do not have any effect on the relative wage (co) since co depends entirely on the ratio of a/a, = ‘y As is constant, the relative costs of production to of all manufactured goods are the same. Thus, the borderline manufactured product (2) that divides the set of manufacturing exports of each country is also unchanged. The first economic variable that this section will investigate is population. Similar to the result in Proposition 2 of the autarky model, it will be shown that under a free trade econom y an increase in population may increase or decrease the world’s R&D intensity depending on the initial world population relative to the grain productivity. Proposition 4: A small increase in the South’s population (L) raises the world’s R&D intensity (JF) if and only if L’ < . Similarly, a small increase in the North’s population (L) raises 2 [B/g) the world’s R&D intensity if and only if L’s’ < [BIg / 2 . Proof: Differentiating (3.16) with respect to L and then L* yields: = - 1 = - - a,y L’’ 12 1’ BjJ LW..L12J BjJ > < > < if L’ > if L’ 114 (4.1) < < > ii - 12 c. yjj (4.2) The reasons why an increase in popula 22 tion may reduce or raise world R&D intensity (JF) are similar to those of the autarky model. An increase in L has two effects: endowment- expansion effects and diminishing marginal productivity effects. For a small initial level of the world population, the demand for grain is small and its price is low. productivity of grain, represented by B 2 + 2 ‘C = Because the world’s , is still large compared to Lw, an increase in 2 2B the world population from this initial level will add more labour supply (endowment-expansion effects) to the economy than push up the labour demanded for grain (diminishing marginal productivity effects). As a result, more resources are available to produce manufactured goods and R&D. Consequently, R&D increases. A continued increase in the population level, however, will put more pressure on the fixed factors. Eventually, the price of grain and labour needed for grain production will drastically increase since the grain’s marginal product of labour is decreasing. An increase in population in this case will generate larger diminishing marginal productivity effects than endowment-expansion effects. As a result, fewer resources are available for manufactured goods and R&D activities, so R&D declines. Now we know that an increase in population may increase or decrease the world’s R&D intensity depending on the size of the initial world population. An important question is how the population change would effect the South’s share of the world’s R&D production and its degree of dependency on imported R&D. Can an increase in the Southern population induce the South to depend more on imported R&D? The simplest way to show this is to assume that the world economy is exactly at the point where both countries are self sufficient in R&D; i.e., the A(z) schedule intersects the BP(2) schedule exactly at point S. Then, let the population of the South increase. To derive the impact of this change, differentiate z [given in (3.18)1 with respect to L to get 22 A population increase in this model can be interpreted as an proportionate increase in all resources other than the fixed factor used in the grain sector. 115 = 8L {Pa]1 +[LLF]lL;]}/[JPa g y8L Since the denominator of (4.3) is positive, the sign of (4.3) depends on the sign of the numerator. Substituting the value of WM, L, LF, and their derivatives in the numerator of (4.3) yield - 8L - 8L > 1 aL;F y 3L 0 if Lw < 212 gj (4.4) gL LH’ j 2Bj 2B = 1 2 BjJ 4 < B] 0 if Lw > 2 g The sign in the second step is obtained by substituting the value of 3L/L the fact that L 2 B = > = 2 and using ½L’[7B] L from (3.8). The sign of the final step is obtained since the assumption that 2 implies that L ‘y’C > L. Thus, the increase in the South’s population will increase z for a small world population and vice versa for a large population. Because z, z for this case, it follows that the R&D production share of the South (z ) will also decrease for a large population. 1 The reduction of z, also means that point S on the BP(2) schedule is moved to the left. Since is fixed by Lemma 1 and point S moves to the left, the South is transformed from the self sufficiency situation to an importing R&D situation. In other words, the South’s dependency on imported R&D increases. The effects of the increase in the Southern population for the general case where the South imports some R&D can be calculated by differentiating z 1 [given in (3.20)] with respect to L to get 116 a/F{ _zii_ni’M 1 8L } - ” 8 fl[L_L_[1_flJWM] 2 [ajIF] F 1 ãLg — { z[1—n] i-z,n ] WM 8L The derivation in the second step is obtained by dividing both the numerator and denominator in step one by at and using the definition of z . Since the term 2[1-nJ+z,n is positive, the sign 1 of (4.5) is determined by i_!=i_!.—12>O 2 B] < , 2 ifL”’<2l > gj (4.6) 2• 8L 1-L”l > 2 O B]< ifL’< > g Thus, the sufficient condition which ensures that (4.5) is positive is when L’ has values in the ,2[B/g] 2 ([B1g] set } . For the impact of the increase in population on the South’s dependency in imported R&D (s), recall that by definition s = [!-z ] 1 /!. It is clear that the sign of the change in s is the opposite of the sign of the change in z, since 2 is fixed by Lemma 1. Therefore, the degree of the South’s dependency on imported R&D will fall if Lw ,2[B1g1 2 {[B/g] ) . The following proposition summarize the results. Proposition 5: A small increase in the South’s population (L) may increase or decrease the South’s share of the world’s R&D production (z ) and the South’s dependency on imported R&D 1 (s). A sufficient condition which ensures that z 1 will increase and s will decrease is LV e ,2[B/g }. [B/ {2 117 The proposition can be understood by the following reasons. The increase in the South’s population raises the world price of grain. Consequently, the labour needed by the grain sectors of both countries rises. For the North, this increase in the grain sector’s employment means fewer labour resources are available for its R&D sector, so the North’s production of R&D falls. The rise in labour needed in the South’s grain sector, on the other hand, is counteracted by the increase in its own population. When the initial population is sufficiently small (Lw < ) 2 2[BI] more resources will be added into the South’s economy which can be used by the South’s R&D sector. Therefore, the South’s share of the world’s R&D increases. As its share of the world’s R&D rises, the South’s dependency on imported R&D (s) falls. Next, let us consider the impact of the productivity improvement of the Southern grain sector on its own R&D. It turns out that this productivity improvement will increase the South’s dependency on imported R&D since the South is induced to export more grain and reduce its own R&D production. Proposition 6: A small increase in the South’s grain productivity (B) decreases the South’s share of the world’s R&D production 1 (z ) , and raises the South’s dependency on imported R&D (s). Proof: See Appendix 3. The South’s grain-productivity improvement raises the comparative advantage of the South in grain. Thus, the South increases its grain productions for exports while the North reduces its grain outputs. As the North reduces its grain outputs, labour moves out of the grain sector toward other sectors, including the R&D sector. Hence, the North’s R&D rises. For the South, the productivity improvement increases its grain productions. Consequently, labour moves into the South’s grain sector and less labour is left for R&D. Therefore, the South’s R&D shrinks while the North’s R&D expands. It follows that the South’s share of the world’s R&D 118 falls. Since the South still exports the same range of manufactured goods (i.e., is constant), the reduction in its share of the world’s R&D means that the South must depend more on imported R&D. 5. Conclusion The result of this essay can be summarized as follows. In a closed economy, it is found that the increase in total population, population of capitalists, and redistribution of income may increase or decrease R&D and growth. They will increase R&D and growth only when the initial population is sufficiently small. A continued increase in the total population will eventually reduce R&D activities. Under a free trade environment, an increase in the Southern population may also increase or decrease the world’s R&D. It will raise the world’s R&D if and only if the initial world population is small. It will also raise the South’s share of world’s R&D and reduce its dependency on imported R&D if the world population is sufficiently small. An increase in the Southern grain productivity, however, will reduce the South’s share of world’s R&D production and increase its dependency on imported R&D. 119 Appendix 1. Derivation of the trade equilibrium for the case where w When y, the equilibrium price of grain is determined by 0) 2gL” where D = Substituting this equilibrium price ii (A.1) +oC B . 2 Lg = 2 and L [Bp/2] = 2 yields the respective [coCp/21 employment in the grain sector of each country. 1.1 The North is the Sole Producer of R&D: When 0) > y, the North’s labour cost of R&D is cheaper than the South’s, so the North conducts all R&D for the world. Hence, I = 0 and F = 1 J’ The rate of returns on equities here is given by r > 0. = nWM/w’a perfect international capital mobility, using this r* in (3.1) yields M M* = nWM/w*a - JF - = F• 1 Since r nWM/w*a - JF - = r* by p, and p. Then multiplying each equation with wa and adding the results yields the equation that maintains M+M* nWM = - = 0 which can be written as (A.2) w*a[I÷p]. The labour-market-clearing conditions for both countries when only the North conducts R&D are L L* f[1 -n] WM = = + (A.3) L, [1 f] [in] WM + L*F ÷ g aIF. (A.4) Combining (A.3) and (A.4), then solving for aT and substituting the result into (A.2) yields 120 WM = [L - L] (A.5) w*[L*F_L;÷ pa;]. + Using this in (A.2) then give the solution for the R&D intensity = F 1 F] 8 { [LL w + } w*[L*_L;F] — [1—n]p. (A.6) Then solve (A.3) for WM and equate the result to (A.5) to get FcD(,z_) [L = [L-L] - - L] + - L;F + pa;] o. = zil -ii] Upon substituting the values of L and LF, (A.7) this equation implicitly defines the segment CD of the w = BP(2) schedule shown in Figure 3.1. It describes the combination of o and 2 that maintains the balance of payments. Applying Implicit Function Theorem on Fc)(co,2) = 0, yields - = o > LLg ÔFCD where aFCDIaI >0, - az (A.8) 2 [1—n]z 8FCD 1 -[1 -n] — g D & ãL*F 2LFC2 = + )2 [1-n] .3LF 1 - , g <, = L* - L;F + pa < 2L*FB2 g Hence, segment CD of the BP(!) schedule is upward sloping. The boundaries of this segment of the BP(2) schedule are marked by (co=y,!=z ) and (O=Oa=l). Since z 2 2 must locate at the point where o = y, z-, is given by (3.19) in the text. The value of Omax is implicitly defined by (A.8) with 2 set to 1. Combining this schedule with Co using w = A(2) gives the steady state solution for Co and 2. Then 1/Co in (A. 1), (A.5), and (A.6) yield the solution to 121 pF, WM, and JF for this case. 1.2 The South is the Sole Producer of R&D: When co <y, the South’s labour cost of R&D is cheaper than the North’s, so the South conducts all R&D for the world. Thus, P I> 0 while I = = 0. The rate of returns on equities of the South can be written as: r perfect international capital mobility, this implies that r to get M 1 nWM/a = - P p, and M* - = 1 nWM/a P - - = = nWM/a[ - 1 F • Assuming r. Use this expression of r in (3.1), p. Then multiplying each equation with a and adding the results up yield the equation that maintains M+M’ = 0 as given in (A.2). As the South is the sole producer of R&D, the corresponding labour-market-clearing conditions for both countries are L [l -nJ WM = + L [1-][1-n]WM w (A.9) ÷ a I’, 1 + L*F (A.1O) * Adding both labour market clearing conditions yields the world resource constraint L + w*L* = [1—n]WM ÷ [L’÷W*L;F] + (A.11) a/’’. To find the equilibrium solution, solve the world resource constraint to get a 1 + w[L* - Lv’] WM - = = L - L [l-nIWM. Then, substituting the result into (A.2) yields L - L’ ÷ W*[L*_L;F] + (A.12) pa . 1 . Using (A. 12) in (A.2) then give the R&D intensity jF = !{ a. 1 [LLgi + w*[L*_L;F] } [1—nip. — (A.13) For the relative wage, solve (A.9) for WM and equate the result to (A. 12) to get [L F - Lgl + w*[L*_L; Fj Upon substituting the values of L and LF, - * w[L—L] g + 1 pa = 0. A14 this equation implicitly defines the segment AB of 122 the 0 = BP() schedule shown in Figure 3.1. It describes the combination of o and that maintain balance of payments. Applying Implicit Function Theorem on 2E’A812 ur !uZ 2 - = where FAB(Wz) = 0, shows that o, > (A.15) aF/&) w*[L*_L* ] 17 aF g - < = 0z 0, 2 [1—n][1—f] = - aø _L + t3L; 1 -[1 -n][1 C*) g - = > g 0, 2L*fB2 2LFC2 ãLF ÷ [L* _L*Fl [1-n][1-j , g = <0, >• D In other words, segment AB of the BP() schedule is upward sloping. The boundaries of this segment of the BP() schedule are marked by ((o=o,!=0) and . (oy,!=z ) 1 The value of o is implicitly defined by (A. 15) with 1 is given by (3.28) in the text. point z Continuous increasing function in downward sloping o = . . The other end 23 set to zero Hence, segment AB of the o Combining the o = BP(2) schedule is a BP(!) schedule with the continuous A(2) schedule gives the steady state solution for 0 and . the motion of the dynamic evolution of the world economy. Then using w (A. 12) and (A. 13) yield the solution to pF, WM and 2. Proof that z 2 > JF This then starts = l/o in (A.l), respectively. : 1 z 2 2 given in (3.28) and (3.19) have the same denominator. Hence, if z Notice that z 1 and z > , it is required that the numerator of (3.19) must be greater than (3.28) or 1 z 23 It is assumed that o,,, is non-negative. 123 y[L-L] y [L - > LF] - _LgF]+ ] 1 y[l-n][L-L+ pa y [L L] - > - [L* _L*’] g > yn[L - - fl[L*_L] F] 8 L + 1 y [1-n] pa n[L * L;F] - - 1 y[1—n]pa (A.16) + [L* _L*F] g > [1—nip Y + 4 -Lj [L g —[1-nIp >0. Y But the left hand side of the last condition is F 1 > , 2 z > F 1 which is positive by assumption. Thus, when . 1 z 3. Proof for Proposition 6: Differentiating (3.15) with respect to B yields: = aB - aB t yBD = i yB [YL:+2L;l’]B2 where B 2 = - — [yC2]LgF } 2[[yC]} YBD[Df Note that the formulae of L and 2 yC [B ] ÷ 4B 2 D yD B = LF (A.17) = B[] 2 > o. used for the differentiation are not evaluated at the point 2 since only the change in the grain productivity of the South is considered. Then, yC differentiating (3.20) with respect to B and using the fact that al 124 = 1 give: nWM-pa a,i’{ _! -zll-n]” - I (A.18) 2 [a/F] < IF 1 a 0. The terms in the second square bracket of the last line are z, which is positive. Using this fact 2 with (A. 17), we can conclude that (A. 18) will be negative if yC 2 automatically satisfied since ‘yC = . 2 B This condition is 2 by assumption. Lastly, differentiating s with respect to B B yields Z 8 1 - > (A.19) 0 125 CHAPTER IV MINIMUM EXPORT REQUIREMENTS: PARETO IMPROVING MEASURES 1. Introduction It is commonly observed that countries which receive foreign direct investments (FDIs) often impose some form of trade-related investment measures (TRIMs) on foreign investors. The US Benchmark Surveys in 1977 and 1982 found, respectively, that 29 and 28 per cent of US affiliates in less developed countries (LDCs) were subject to one or more TRIMs. In Guisinger and Associates (1985) the figure was as high as 51 per cent (38 out of 74 projects). All three studies plus that of the OECD (1987) found that one of the most frequently used TRIMs was minimum export requirements (MERs). In the view of the host countries, TRIMs are tools which enable them to control the economic benefits generated by foreign investment. Nevertheless, the source country (from which the investments come) views TRIMs as non-tariff barriers that distort investment and trade flows, and thereby reduce their welfare. These two different views have generated a confrontation between the developed countries (DCs) and the LDCs. The main purpose of this paper is to show that this confrontation need not necessarily arise. Some TRIMs, particularly MERs, can be Pareto improving measures to both the host and the source countries’. Before attempting to demonstrate this claim, we review the existing literature. The literature on MERs can be classified into two groups according to market-structure assumptions. Models in the first group assume a perfectly competitive market structure for the host-country. The papers in this group are, for instance, Herander and Thomas (1986), and Rodrik (1987). Herander and Thomas show that MERs may worsen the balance of trade unless they are accompanied by import barriers such as tariffs on final goods. Rodrik (1987), unlike Herander For other trade policies as Pareto improving measures see Anis and Ross (1992). 126 and Thomas, employs a general equilibrium framework. He demonstrates that MERs can raise home welfare by reducing the output of the over-produced sectors and reducing foreign capital . 2 payments Models in the second group assume duopolistic competition between a foreign subsidiary and a domestic firm in the host-country. The first paper is by Davidson, Matusz, and Kreinin (1985). They argue that MERs reduce the welfare of the world, the source country, and the host country. However, the result on the welfare of the host country contradicts the finding by Rodrik in his duopolistic interaction model. Rodrik concludes that MERs can improve the host-country’s welfare by reducing sales of the foreign firms and shifting profits toward domestic firms. These contrasting results stem from the fact that Davidson et al. assumes that the marginal costs of the local firm are higher than those of the subsidiary while Rodrik assumes that they are the same. Most of the literature on MERs has concentrated on the consequences on the host country’s welfare. It provides us with better understanding of how MERs affect the host country’s economy and is important in its own right. However, it remains deficient in the following aspects. First, there has been very little attention given to the effect of MERs on the welfare of the source country, except from the literature in the second group. Both studies in this group assume that the unit cost of production of the host country is higher than that of the source country. Hence, there is no incentive for the subsidiary firm to export unless the MER is enforced. They then conclude that MERs reduce the welfare of the source country since the source country is forced to absorb a higher cost. However, we cannot apply this logic to a case 2 Chao and Yu (1990), also using a general equilibrium framework with urban unemployment, show that MERs may improve welfare if the home country consistently adopts the second-best optimal quota policy. 127 . Exports from the host 3 where FDIs are the result of the search for the lower costs of production countries would already exist without the intervention although the export level may not be as high as the host countries would wish. The host countries may have an incentive to use MERs to further boost their exports. Would MERs always, then, improve the welfare of the source countries? . The 4 Second, strategic interactions of firms in the source country have been overlooked imposition of MERs affects profits of the foreign investors which in turn have repercussions on the marginal profits of their rivals in the source country. These strategic interactions could entirely change the welfare implications of MERs. Third, the changes in profits from the operation of foreign firms in the host countries due to MERs have not been taken into account in the welfare calculation. For instance, both Davidson et. al and Rodrik assign zero weight to the entire earnings from the operation of the foreign firms. It seems strange that the host country requires foreign firms to increase their exports (e.g., to earn more foreign exchange), yet derives no benefit from such action. In reality, the host country should be able to retain some of these profits, e.g., by using taxes, setting a maximum ratio of profit allowed to be repatriated, etc. Lastly, all of the existing literature treats MERs as given. In light of the fact that MERs are often applied to industries that operate in imperfectly competitive environments, the government of the host country should be able to use MERs to manipulate the outcomes instead For instance, the major reason for the US surge of investment for semiconductor production in East Asia during the I 970s is to utilize the huge pools of cheap and unemployed labour, Rada (1982). Davidson et al. (1985) assumes a monopolist for the source country. In Rodrik (1987), the market structure in the source country is irrelevant since an increase in export levels from the host country is totally absorbed by an equal reduction in domestic production levels in the source country. Thus, the sales of the parent firm in the source country are independent of MERs. In this paper, however, all productions come from the host country; hence, the sales in the source country depend on the level of the MER. 128 of acting passively. This paper has incorporated the following remedies to these shortcomings. To capture the strategic interaction of firms in the source country, I assume a duopolistic market structure in the source country where one of the duopolists makes FDI to set a plant in the host country. The market structure for the host country is monopoly. The model is intended to capture the case of relatively advanced-technology industries in which the MNC provides the technology and the host LDC provides cheap labour. The industries that the model might be applied to are, e.g., . In such industries, oligopolistic structures for the source country 6 automobiles, semiconductors should be better representatives than competitive or monopoly structures. For the host countries, a monopolistic structure is assumed to render simplicity and seems realistic enough for LDCs since they often lack the necessary technology and capital to start their own indigenous firms (the very reason LDCs use the investment incentives in the first place). Moreover, to compete for foreign direct investment, the LDCs’ governments usually guarantee a certain degree of monopoly power to foreign firms (e.g., by putting tariffs or import quotas on substitutable import products, promising no competition by the state firms, etc.). A maximum ratio of profit repatriation to the parent firm is introduced to the model to capture the benefit from allowing foreign firms to operate in the host countries. This is one of the sources of welfare generated by MERs other than the consumer surplus derived from domestic consumption. In the existing literature, consumer surplus and profits of domestic firms are added to get a welfare measure of the host country. MERs, then, benefit the host country by shifting profits from foreign firms toward domestic firms . When the South-indigenous firm is 7 The model structure is closest to the models by Davidson et al. (1985) and Rodrik (1987), although, in their models, duopolistic market structure is assumed for the host market. 6 According to the 1977 US Benchmark Survey, these two industries are among the industries that had the highest incidents of TRIMs. See Brander and Spencer (1985) for the case of subsidies as tools for profit-shifting. 129 absent, using MERs would be pointless if the South could not retain any benefit from doing so. An enforcement of the maximum ratio of profit allowed to be repatriated is one of the ways for the host to retain benefits of the MER. This maximum ratio is chosen because it does not change the solution to the profit maximization of the firm; i.e., it is neutral to the behaviour of the firm. Other forms of intervention are, of course, possible (e.g., income or sale taxes), however, they would alter the behaviour of the firm and unnecessarily complicate the model. The structure of the model in this paper is similar to that of Bulow, Geanakopolos and Kemperer (1985). However, constant returns to scale are assumed for all production to rule out joint economies or joint diseconomies analyzed in their paper, so that we can concentrate only on the effect of MERs. In Bulow et al., the two markets are related because changes in outputs in one market affect the joint marginal cost. The optimum choices of outputs of the two markets are, therefore, linked. In this paper, the optimum choices of outputs of the two markets would have been independent (by the constant marginal cost assumption) if there were no MERs. The linkage between the two markets is through the joint marginal revenue created by the MERs. The rest of the analysis proceeds as follows. Section 2 provides a formal structure of the model and analyzes the effect of both quantity and shared export requirements. The analyses in these two sections assume that the levels of MERs are exogenously given. In Section 3, this assumption is relaxed so we can analyze the impacts of MERs when the host country employed the optimal MER as a tool to achieve the second-best welfare. Section 4 relaxes the monopoly market structure assumed in Section 2 by adding another local firm to the host country. Finally, Section 5 summarizes the results and discusses some possible extensions. 2. Structure of the Model Consider a two-country world economy consisting of a source country called North and 130 a host country called South. There are two firms in the economy: a local Northern firm , and 8 a multinational corporation (the MNC) consisting of a parent firm located in the North and its subsidiary firm located in the South. The market structure in the North is a Cournot duopoly while the market structure in the South is monopoly (see Figure 4.1). The monopoly power of the MNC for the South’s domestic sales is granted by the government. In return, the South requires the MNC to export either a minimum fixed quantity of output or a minimum share of its total output, and to repatriate no more than a share v of its profits back to its parent firm. Denote the sales of the parent firm, the local Northern firm, and the subsidiary as x, y, and z, respectively. The local Northern firm manufactures and sells all of its products domestically while all productions of the MNC are manufactured by its plant in the South. The unit costs and 9 and are denoted marginal costs of the MNC and the North’s firm are assumed to be constant by c and c, respectively. For the sake of exposition, the following sub-section provides a simple example in which the South requires the MNC to export a fixed quantity instead of a normal export share requirement. 2.1 Minimum-Quantity-Export Requirement (QER) The price q of the output sold in the South is given by the inverse-demand curve q = q(z), where q’(z) <0. Note that variables with primes and double primes denote their respective first and second derivatives; and variables with subscripts denote their partial derivatives. The price of the final product sold in the North is p which is given by the North inverse Throughout this chapter, the word “local Northern firm” will be used interchangeably with the word “North’s firm”. The results presented in this paper will also hold when the cost functions take the form as C(x+z) with C > 0 and C’ 0, and C(y) with C” > 0 and C” 0. See details in footnote 11. 131 Figure 4.1 Market Structures and trade flows demand curve p = p(Q), where Q = x + y and p’(Q) <0. Both p(Q) and q(z) are assumed to be linear. For simplicity, it is assumed for the moment that the MNC can repatriate all the profits back to its parent firm; i.e., v = 1. In a quantity Coumot game, the MNC takes y as given and maximizes its joint profits X; i.e., subject to a constraint x {p(x+y)x Max + zq(z) — c[x+zJ X), x (2.1) x.z where X is the minimum-quantity-export requirement. Assuming that the QER constraint is binding and let ? be the Lagrange multiplier, we have x q(z) + zq’(z) - c = 0 as the first-order conditions. 132 = X, p(Q) + xp’(q) - c + , and Clearly, the solution for x and z are independent. On the other hand, the local Northern firm solves { p(x÷y)y Max y — }, c”y (2.2) The first-order condition for this problem is: p(Q) reaction function of the North’s firm: y = + yp’(Q) - c’ R(x). Substituting x = = 0. It implicitly defines the X into this reaction function gives the equilibrium value of y. Define the welfare function of the North as = f p(i)& - p(Q)Q (2.3) + + where the first two terms denote the North’s consumer surplus; MNC’s profits; and it it is the maximum value of the denotes the maximum value of the local Northern firm’s profits. To get the impacts of QER on the North’s welfare, we need to calculate the impact of QER on the sale levels, p(y+X) total + consumptions, yp’(y+X) - c’ = and Applying profits. 0 and differentiating , it, and it implicit function theorem on with respect to X yield the following results 2 2p’ = 1 - < 0, (2.4) > 0, (2.5) > 0, (2.6) - = xp’y = yr.’ < -- (2.7) 0. Note that (2.6) is true only at the point where the QER constraint just binds. With the above results, differentiate (2.3) with respect to X to get 133 W = - + - + = P-[Q÷X-2y] The sign of (2.8) will be positive if and only if X > = - (2.8) -{2X-y]. y/2. In other words, the welfare of the North will be improved by a small QER if the sales of the MNC in the North are greater than a half of the local Northern firm’s sales. However, note that by the first-order condition of problem (2.1), -Xp’ p - c when the QER constraint just binds (since 2 order condition of problem (2.2), -yp’ = p = 0). Furthermore, by the first- c. Substituting these two conditions into the right - hand side of (2.8) gives W .[2[p—c] — [p_cJ] The condition in (2.8a) is true since p = - c .[p—c ÷ c 5 —c] = -Xp’ > > 0, if CS c. (2.8a) 0 when the QER constraint just binds. In other words, the welfare of the North will be improved by a small QER if the MNC’s unit cost is lower than that of the local Northern firm. The QER improves the Northern welfare by the following reasons. First, the QER reduces the duopoly distortion in the North. This distortion exists since both firms produce at the points where the price is strictly greater than each of their marginal costs: p > c and p > c. By (2.5) the QER increases the total sales; and, hence, lowers the price. This price reduction then helps to curtail the distortion. Second, when the unit cost of the local Northern firm is strictly higher than that of the MNC (i.e., c > c), the QER reallocates production from the inefficient producer (the North’s firm) to the efficient firm (the MNC). For the South, since z does not depend on QER and v 1, the welfare of the South is independent of QER. Therefore, in this special case the QER can improve the welfare of the North and has no effect on the South’s welfare; i.e., the use of QER can be potentially Pareto improving. Allowing the value of v strictly < 1 does not change the conclusion on the welfare of the 134 North but causes the South’s welfare to improve. When v < same except (2.6) and (2.8a). Equation (2.6) now becomes (2.8a) now becomes W = ½{ v[p-c] + c’.-c ) > 0, if c* 1, all of the above results are the it, = -vXp72 > 0, while equation c. Thus, when a fraction of the MNC’s profits must be retained in the South, the QER also improves the Northern welfare if the MNC’s unit cost is lower than that of the local Northern firm. The retained profits then improve the Southern welfare. Therefore, the use of QER can lead to a Pareto improvement in this case as well. 2.2 Export-Share Requirement (ESR) In the real world, most of the MERs are not QER, but they are often defined as a minimum export share to total production. This section will show that the results obtained in the above example still hold. Recall that x also denotes the exports from the South. Hence, it must satisfy the ESR constraint: x x[z + x], where o is the minimum export-share requirement and z+x is the South’s total outputs. Rearranging this, we have z [l-c]x/c = yz, where y [l-cc]/cx and y = -l/& <0. For a given level of y, the MNC tries to maximize its joint profits subject to the ESR constraint. Its maximization problem can be written as Max {px+y)x+zqz—cx+zj yx z}. (2.9) Assuming an interior solution for x and z, the first-order conditions for the Lagrangian function of this problem are: 135 p(Q) xp’(Q) + q(z) ÷ zq’(z) yx - — — c c + .‘.y (2.11) 0, = — (2.10) 0, = (2.12) 0, z where 2 is the Lagrange multiplier. These three first-order conditions determine the levels of x and z that maximize the profits defined in (2.9). The solution depends on whether the ESR constraint is restrictive or not. (1) Non-restrictive ESR: If the minimum export requirement is not binding, = 0, and (2.12) holds with strict inequality. It follows that (2.10) and (2.11) become p(Q) + xp’(Q) q(z) ÷ zq’(z) — — c c (2.13) = (2.14) 0 = Consequently, the solutions for x and z are independent of each other and the MNC can solve its profit maximization problem as if these two markets are separated. (2) Restrictive ESR: If the ESR is binding, z = r. Rearranging (2.11) for = q(z) As a result, q(z) + + zq’(z) zq’(z) > — , c > 0 and (2.12) holds with equality; i.e., we have > (2.15) 0. c or the marginal revenue of z is greater than its marginal cost. In other words, when the ESR constraint is binding, the South’s output for domestic sales is always under-produced relative to the output in the case when the ESR is non-restrictive. in terms of x. Then substituting the result in (2.10), Substitute z with r in (2.15) to get the first-order conditions are reduced to p() + xp”() + y{q( ÷ yxq’Oj = [1+y]c. (2.16) Thus, for a given y, the MNC allocates its outputs between the two markets until the weighted sum of the marginal revenue of both markets equals the weighted sum of the marginal cost The 136 weights of one and ‘y are put on the North and the South markets respectively. We can see from the above two cases that if a is too small, the ESR will be redundant. Thus, there is a minimum a such that the ESR constraint is just binding. This minimum a implies a maximum y, denoted by , which is defined by the ratio of where and are the solutions to (2.13) and (2.14) respectively. To rule out the case of non-restrictive ESR, it is assumed, henceforth, that a is set sufficiently large such that ‘y . With this assumption, the constraint (2.12) always holds with equality. So we can substitute z with x in the objective function in (2.9) and solve as a nonconstrained maximization problem. Denote this maximum profit value of the integrated firm by H. A fraction of v belongs to the MNC and the rest 1-v belongs to the South. Define the maximum value of profits accrued to the MNC as ‘it Max = { v[ p(Q)x ÷ q(yx)yx - [1+y]cx 11 (2.17) The first and the second-order conditions for (2.17) are = = v{p(Q)÷xp’(Q)÷y[q()÷yxq)]—[1+yJc { 2p’(Q)÷xp”(Q) v + [2q’()÷yxq”()] 2 y } = } < 0, (2.18) 0, (2.19) where the first and second subscripts denote, respectively, the first and second partial derivatives with respect to x. For the local Northern firm, the maximum value of profits is defined as = Max {p(x-t-y)y - y 4 c y }, (2.20) and its first and second-order conditions are = = p(Q) ÷ 2p’(Q) yp”(Q) — + yp”(Q) c < = (2.21) 0, (2.22) 0. The two first-order conditions (2.18) and (2.21) implicitly define the reaction functions of the parent firm and the local Northern firm, R(y) and Rx), respectively. Together, they determine 137 the Nash-Cournot equilibrium outputs in the North market: x = x(c), y = y(x). Notice that the equilibrium outputs do not depend on v since it neutrally affects the total revenue and total cost of the MNC. The level of v only influences the distribution of profits between the MNC and the South’°. For asymptotic stability and uniqueness of the equilibrium, I assume that H ] 11 { p’[3p’÷Qp = - where = h v[p’÷xp”], Ii 1t) = p’[3p”÷Q”p”] Note that terms in parentheses + I.7c are > + } [2q”÷yxq’’] 2 y viz = < > (2.23) 0, 0, 0. omitted for brevity. The term p is the slope of the South’s marginal revenue. It is negative since the second-order condition for (2.9): 2q’ + zq” < 0. Given that p is negative, it is sufficient to assume” that 2p’+xp < 0 to ensure the negativeness of the second-order condition in (2.19). It is also sufficient to assume that 3p’+Qjf < 0 to ensure the uniqueness and stability condition in (2.23) since p is positive. The terms iç and 4,, are, respectively, the changes of the marginal revenues of the MNC and the local Northern firm when its rival sales increase. The signs of these two terms can be either positive or negative depending on the curvature of the demand curves. If the North demand curve is linear or concave; i.e., p” levels, ir,, 0, then, whatever the output <0 and ri,,,, <0. In the terminology of Bulow, Geanakopolos and Kemperer (1985), both firms’ outputs are strategic substitutes for each other. This strategic substitute case will hold even when demand is slightly convex. That is, when p> 0 and x (respectively y) is sufficiently small such that <0 (4,, <0), the sales of the North’s firm (the MNC) are still strategic The neutrality of v will prove useful when we analyze the effect of MERs on the welfare of the South. If the MNC were to sell its product only in the North market, this assumption would be required to satisfy the second-order condition of its corresponding maximization problem. 138 substitutes. On the other hand, if p’> 0 and x (respectively y) is sufficiently large such that > 0 (i > 0), the sales of the North’s firm (the MNC) are strategic complements. 2.2.1 Effects of a change in the degree of ESR This section provides analyses of the effects of a small increase in the ESR compared to the non-intervention situation. These can be done by performing standard comparative static analyses of the change in a., then evaluating them at the point where the ESR constraint is just binding; i.e., at y = (1) Effects on outputs in the North: Totally differentiating (2.15) and (2.18) with respect to a., we get the following comparative static results: = h 2 a — (2.24) o > a ‘p (2.25) a2h’ where p q + ‘r q’ - c + pxfl. Since i <0 by the second-order condition and h stability condition (2.23), the sign of (2.24) is the opposite of the sign of From (2.13), we know that ? = q + ‘ q’ - p evaluated at 0 by the . c which is positive when the ESR constraint is binding or zero when the constraint is not binding. Hence, at y = Thus, the sign of > . Therefore, x 2 is negativ& > , = 0 and 0 <0. = 0; i.e., a small ESR increases the sales of the MNC in the North. The effect of the ESR on the sales of the local Northern firm is determined by the sign 0 and whether the MNC’s outputs are <0) or strategic complements (4, > 0). Again, evaluating (2.25) at y of (2.25) which, in turn, depends on both substitutes (i, = strategic , causes For a more general cost function; e.g., C = C(x+z), 0 becomes ?+px/y-xC, where p is redefined as y[2q’+vq-C. Then, 0 evaluated at will be negative if C 0. 12 139 ( = pxl < 0. If the MNC’s outputs are strategic substitutes, However, if outputs are strategic complements, y > 4 are negative, then < 0. 0. The following propositions recap the results on the outputs in the North. Proposition 1 A small minimum-export-share requirement will increase the MNC’s sales. It will decrease the sales of the local Northern firm if the MNC’s sales are strategic substitutes, and vice versa if the MNC’s sales are strategic complements. ’ means a small increase t Note that the term “a small minimum-export-share requirement of the minimum-export-share requirement from the point where the ESR constraint just binds. This small ESR can change the sales as stated in the proposition by the following reasons. An increase in the minimum ESR (ce) implies that the ratio of the sales in the South over the sales in the North (-y’) must decrease. Thus, given the initial level of sales in the North, the increase in ESR decreases the MNC’s sales in the South. With a downward-sloping marginal-revenue curve, the decrease in the Southern sales then increases the MNC’s marginal revenue. This in turn signals the MNC to sell more in the South market. In order to do that the MNC must also increase its sales in the North to maintain the minimum export requirement. As shown in Figure 4.2, the increase in ESR shifts the reaction function of the MNC to the right and its sales in the North expand. The result of the sales of the local Northern firm follows from the first result. A small ESR raises the MNC’s sales in the North. If the MNC’s sales are strategic substitutes, the North firm’s best response is to reduce its sales. But if the MNC’s sales are strategic complements, a small ESR will increase the local Northern firm’s sales. Once we know the effect of ESR on the sales of each firm in the North, the next question is what happens to the total consumption in the North. The following proposition provides the answer. 140 Figure 4.2 Effects of Minimum Export Share Requirements y Rx) x Proposition 2 A small minimum-export-share requirement will raise the total consumption in the North. Proof: Combine (2.24) and (2.25) to get Qci czh (2.26) [yx1 Again, evaluate p at y = causes p h 2 a = <0. Since h > 0 and p’ <0, an increase in cx will increase Q.fl It is obvious that total sales will rise when the MNC’s outputs are strategic complements since, by Proposition 1, both sales increase. The results are less obvious when the MNC’s outputs are strategic substitutes because the sales of the two firms move in opposite directions. 141 However, the change in ESR has a first-order effect on the output of the MNC while it has a second-order effect on the output of the North’s firm. Therefore, the change of the MNC’s output always outbalances the change of the Northern firm’s output. So the total consumption in the North will change in the same direction of the change in the MNC’s sales in the North. Consequently, the North’s total consumption increases. (2) Effects on profits: Now let us analyze the effects of ESR on the profits of the two rivals. Totally differentiating (2.17) and (2.20) with respect to cx and using the Envelope Theorem, we have: - [q + yxq’ - cJ}. it: 6 it = ypxx. The term in the squared bracket on the right hand side of (2.27) is equal to ./& which becomes zero when it is evaluated at y p’ <0. For it, = . Thus the sign of ç is the opposite of the sign of y since its sign is the opposite of the sign of x. By applying Proposition 1, we have the following Corollaries. Corollary 1.1 A small minimum-export-share requirement will decrease the local Northern firm’s profits. Corollary 1.2 A small minimum-export-share requirement will increase the MNC’s profits if the MNC’s outputs are strategic substitutes, and vice versa if the MNC’s sales are strategic complements. The intuition for both corollaries is quite straight forward. We know that a larger rival output means a smaller residual demand for any firm, and vice versa for a smaller rival output. Thus, the maximized profits of each firm are inversely related to the output of its rival. Since 142 the MNC’s output is increased by the ESR, the Northern firm’s profits decline. Likewise, the conditions that cause an increase (decrease) in the Northern firm’s output will reduce (raise) the MNC’s profits. These two corollaries show that MERs need not always benefit the MNC, as suggested in Greenaway (1991). In fact, the MNC can be hurt by the ESR when we take the strategic interactions into account. As Proposition 2 shows that the ESR increases the total Northern consumption. The consumer surplus of the Northern consumers is increased. Could the ESR then lead to an improvement in the North’s welfare? This is the topic discussed in the following sub-section. (3) Effects on welfare of the North: Let us define welfare of the North by the sum of the North consumer surplus and the profits accrued to the North as = f p(di - Qp(Q) (2.29) + + Differentiate (2.29) with respect to cx to get * = / * —pQQ÷it+t. 23O Substituting the results from (2.27) and (2.28) into (2.30) and evaluating = jiK { 1 [2p’+yp”]y = K { 1 [y-vx][p’+yp” -xjY} - v[p’+yp”]x - [x+y]p’ 0 at y = , yield } (2.31) = where K 1 = - xp 7 jct h <0. The terms outside of the curly bracket are positive since 2 also that -xp’ is positive. Hence, when (2.31) positive is vx > y. However, if 4, ji <0. Note 4 <0, the sufficient condition that makes the sign of > 0, it is sufficient to have vx <y for the sign of (2.31) 143 to be positive. Note that even when the MNC is forced to leave all of its profits in the South or v = 0, the welfare of the North still can be improved when 4. > 0. If the Northern demand curve is linear, (2.31) can be simplified further. Note that the first-order condition (2.18) implies that -xp’ = p - c + ‘y[q+zq’-c]. Since point where the ESR constraint just binds, we have -p’ condition (2.21) implies that yp’ = -[p = p - c. = q+zq-c 0 at the Moreover, the first-order ce]. Using these two conditions and p” - = = 0, (2.31) becomes W1. = = {v[p—c] 1 K The condition is true since p - = [l+v]xp’} — c + — = c} IJ.Ki{_[p_c*] > 0, + if c t [1÷v][p—c]} 2.31a) c. -xp> 0 when the ESR constraint just binds. Notice that the condition for the welfare improvement of the North does not depend on the value of v. Moreover, this sufficient condition for welfare improvement is the same condition as that in the case of QER given by (2.8a) in section 2.1. Proposition 3 A small minimum-export-share requirement will increase the welfare of the North if (a) the sales of the MNC are large (vx > y) and they are strategic substitutes, or (b) the sales of the MNC are small (vx <y) and they are strategic complements. Moreover, when the Northern demand is linear, the welfare of the North will be improved if the unit cost of the MNC is lower than or equal to that of the local Northern firm (c The proposition can be understood as follows. c*). On the consumer side, a small ESR increases the total sales in the North by the result in Proposition 2. With the larger sales, the price is lower. As a result, the duopoly distortion caused by the overcharged pricing above the marginal costs is improved. This reduction in distortion is depicted by an increase in the North’s consumer surplus. On the producer side, Corollary 1.1 and 1.2 indicate that a small ESR reduces 144 profits of the local Northern firm, but profits of the MNC (repatriated from its subsidiary) may increase or decrease. When the MNC’s outputs are strategic substitutes, by Corollary 1.2, profits of the MNC increase. If the MNC’s sales are also sufficiently large, the net profits of the two firms will increase. Thus, the welfare of the North will increase. Profits of the MNC, however, decrease when the MNC’s outputs are strategic complements. For the welfare to improve, an initially large sale-volume of the local Northern firm is needed so that the sum of the profits does not reduce to the point of overtaking the increase in the consumer surplus. When the North demand is linear, the ESR improves the distortion on the demand side as before. On the supply side, the MNC’s sales are strategic substitutes since the demand is linear. By Proposition 1, the sales of the MNC expand while the sales of the local Northern firm shrink. Thus, the welfare of the North can be improved when c c because production is reallocated to a more efficient source. The above proposition implies that in the presence of imperfect competition, MERs are not always bad for the source country since they may induce firms in the North to increase sales closer to the level under perfect competition and reallocate production to a more efficient source. Notice also that national interest in the North may conflict with that of the local Northern firm. This is because, by Corollary 1.1, the local Northern firm is always worse off by the ESR. However, the North’s government would prefer the South’s ESR policy when the condition in Proposition 3 holds. This can further complicate the political-economic problems of the TRIMs negotiations. It is claimed earlier that MERs may not lead to a North-South conflict. The analysis thus far has shown that MERs can improve the welfare of the North. Hence, it is left to be shown that they can simultaneously improve the South’s welfare. (4) Effects on welfare in the South: To determine the impacts of MERs on welfare of the South, first we have to determine the impacts of ESR on the consumption level of the South. 145 As we know, the sales in the South when the ESR is restrictive are always less than the maximized profit sales when the ESR is not restrictive because, from (2.15), X.> 0. However, for concreteness, differentiating z=”p, with respect to ct and evaluated at x yx — = z 2 - 2 = - = x = -— yields h 2 - [3p’ h] h 2 a h 2 ct + Qp”] < 0. (2.32) The last equality is obtained by using the definition of h from (2.23). Recall that 3p’+Qp” < 0 for uniqueness and stability; hence, the sign of zc, is negative. Next, we have to determine the profits accruing to the South. The profits accruing to the MNC are it = vU!, where U! is the total profits of joint operation between the MNC and the South. Hence, the profits accruing to the South are [1 -viii Given this, the welfare of the South can be defined by the summation of consumer surplus, S(z), and profits accrued to the South as W = S(z) ÷ [1 -vi II, Differentiate (2.33) with respect to Wa = — where S(z) X = f q(i)di - zq(z). (2.33) to get (2.34) zq”z ÷ [1v]lla. The first term on the right hand side of (2.34) is the change in the South’s consumer surplus while the second term is the change in its profits. Since z negative because -zq > < 0 by (2.32), the first term is always 0. The sign of the second term, nonetheless, can be either positive or negative. From Corollary 1.2, when the MNC’s outputs are strategic complements, a small ESR reduces the MNC’s profits. That is, the second term on the right hand side of (2.32) is also negative. Thus, for these cases, a small ESR decreases the welfare of the South. 146 However, when the MNC’s outputs are strategic substitutes, a small ESR increases the MNC’s profits. Consequently, the sign of the second term is positive while the sign of the first term is negative; hence, the net effect can be either positive or negative. Nevertheless, a small ESR may increase the welfare of the South if v is sufficiently small, since we know that the size of v has no effect on the profit maximized level of outputs. Moreover, Z( and Fl are also independent of the size of v. Therefore, if v is smaller, [l-vJfl will be larger while -zq’z , stay 0 the same. Eventually, for a sufficiently small level of v, the profit gain may outweigh the consumer surplus loss and W > 0. The condition that causes the welfare improvement in the South depends on the curvatures of demands in both countries. To demonstrate this, take the case where the Northern demand is linear as an example. In this situation, (2.34) becomes’ 3 Wa where 2 K = K - +Eqfz] 2 { [lV][ xzq I — } Ij2 > 0 if v < E, q,z -l Eq!,z + 2 (2.35) II > , E, q,z Since v is positive, the elasticity of q’ with respect to z, e qçi’ must be greater than one. This in turn requires q’ to be negative. In other words, the Southern demand must be concave and v must be sufficiently small for the South’s welfare to improve. A concave demand curve means that the price increase in the South due to the imposition of the ESR tends to be modest. As a result, the consumer surplus loss is also small. Hence, if the South can retain a large profit share (a small v), then its welfare can be improved. The following proposition summarizes the effects of the MER on the welfare of the South. Appendix I provides the intermediate derivation for (2.35). 147 Proposition 4 A small minimum-export-share requirement with a sufficiently large profit share accruing to the South may increase the welfare of the South if the MNC’s outputs are strategic substitutes. The proposition can be understood as follows. A small ESR imposed by the South can help the MNC to credibly commit to sell in the North more than it would without the ESR (see details in section 3). By doing so, the MNC gains market share at the expense of the local Northern firm and achieves higher profits. As the pie of profits increases, the South gains a larger slice of the benefit. Furthermore, knowing that the MNC benefits from this ESR, the South’s government may be able to negotiate for even a larger share. If sufficient gains are retained in the South, they can counteract or even outweigh the loss of consumer surplus incurred by the ESR. As a result, the South also can gain from a small ESR. Since both countries can be better off by a small ESR, the last thing left to be shown is that they can be better off simultaneously. Again, take the linear Northern demand as example. Recall that the condition for the Northern welfare improvement when its demand is linear is that the unit cost of the MNC is smaller than the unit cost of the North’s firm [see (2.31a)J. This condition for the Northern welfare improvement is independent of both the value of v and the curvature of the Southern demand that are required for the Southern welfare improvement shown in (2.35). Therefore, in this situation a small ESR can be a Pareto improving measure; i.e., both countries can be gained by a small ESR’ . 4 3. Optimal MERs The previous section has shown that a small MER can increase the welfare of the South by shifting the reaction function of the MNC so that its overall profits increase. Since the Appendix I provides some sufficient conditions under specific situations that ensure both Proposition 3 and 4 to hold simultaneously. 148 welfare of the South depends partly on the MNC’s profits, the South’s welfare improves. What, then, will be the effect of a larger increase of the MER and can the South’s government use the MER to maximize the welfare of the South? The following analysis will demonstrate that when the MER is chosen optimally, it can help the MNC to credibly commit to sell more in the North than it otherwise would. To prove this claim, the analysis is separated into two parts. First, I analyze the optimal MER when the requirement is defined by the QER, then the ESR is analyzed. The sequence of moves in this case is as follows: (1) the South government chooses the MER; (2) both firms observe the MER and then choose their quantities x and y simultaneously. 3.1 Optimal quantity-export requirement As before, X denotes the level of export set by QER. We solve the problem by backward induction. First, the North’s firm solves its maximization problem given X. This yields the reaction function y = R(X). For the MNC, it solves the maximization problem Max {p(x,y)x + q(z)z — [x+z]c X x x,z } (3.1) which gives the reaction function x = Max{ X, R(y) (3.2) }. Since the South government can anticipate that both firms will respond to X optimally according to their reaction functions, the South’s objective function is Max S(z) x ± [1—v] ll(x=X,y=R*(X)), (3.3) Notice that S(z) is not a function of X since z is independent of the export requirement level. Also note that, for the time being, it is assumed that the South does not try to choose v to maximize (3.3). Later, v will be chosen simultaneously with X. 149 In this special case the South’s indifference curves can be represented by the iso-profit curves of the MNC . Lastly, 15 as an example, the case where the MNC’s sales are strategic substitutes is used Since we know from Corollary 1.2 that the MNC’s profits will increase. The first-order condition of (3.3) is [1—v][llxX) + ll(x=X,RX)] = 0, (3.4) — = ll(x=X) Solving (3.4) gives the optimal value of X. Note that R is the slope of the Northern firm’s reaction function and - HTI is the slope of the MNC’s iso-profit curve. Therefore, the optimal X (when v is fixed) locates at the point where the MNC’s iso-profit line tangents to the Northern firm’s reaction curve. We can see that this solution is the Stackelberg equilibrium. The case is shown in Figure 4.3. Note that, the reaction functions are drawn as straight lines for simplicity. The Northern firm’s reaction function is not affected by the QER, but the MNC’s reaction function becomes the kinked line ASBD. The solution point is denoted by S (as opposed to Nash-Cournot equilibrium denoted by point C). In other words, the MER set in this way allows the MNC to achieve higher profits by credibly committing to sell in the North more than it would without the MER . As the pie of profit increases, the South gains a larger slice of the benefit. 16 Now let the South government choose X and v simultaneously. Here, a new variable M is introduced. It represents the minimum profits that the South’s government must allow the MNCs to take. It is used for two reasons. First, the market for FDI is very competitive. To get FDI at all, the South’s government must ensure that the MNCs get a deal at least as good as those offered by other LDCs. Second, we need a constraint to put a bound on the solution of So we have to maximize the South’s welfare subject to the constraint: vFl = V. M. Hence, The welfare function W is just an affine transformation of H since S(z) is independent of X and [l-v] > 0. ‘ See Brander and Spencer (1983) for the case of R&D as strategic commitment. 150 Figure 4.3 Effects of Optimal Quantity Export Requirements y A R(y) C S R*(x) 0 X X 151 D v = MILl and [l-v]fl Max S(z) x ÷ = H - M. Substitute this into the South’s objective function to get (X)) 4 ll(x=X,y=R - M. (3.5) Differentiating (3.5) with respect to X also gives the same condition as given in (3.4). 3.2 Optimal export-share requirements Now we come back to the case of MER defined by a as a share of total outputs produced in the South. Again the minimum profit constraint is applied here so that v = filM. The South’s objective function now becomes Max S(z(a)) + ll(x(a),y=R*(x(a)) - M. (3.6) Differentiate (3.6) with respect to a to get the first-order condition and reanange to get — = — SZ II,, llyXa Now we get another extra term > 0. (3.7) . - SzJfI,x. The term is negative since Sz < 0, Ll <0, and x This extra term causes the slopes of the South’s indifference curves to be steeper. Therefore, the tangency point in this case must locate on the R(x) curve to the left of point S in Figure 4.3. It must also locate to the right of point N if the ESR constraint binds. It should be noted that although a small increase in the MER can be Pareto-improving, a large increase in the MER which maximizes the South’s welfare is likely to decrease the North’s welfare. This is because the South would try to choose both the MER and the profits share so that as many of the profits as possible are shifted to the South. Thus, the aggregate profits of the North are likely to be reduced drastically so that they will overwhelm the welfare improvement coming from the reduction in duopoly distortion. 152 4. MultipIe-duopoly Case The result in section 2 has shown that a small MER may result in a potential-Pareto improvement. It is now interesting to ask whether this result will hold when there is a local Southern firm which competes locally with the subsidiary of the MNC. The following analysis will make clear that the results pertaining to the North are virtually unchanged. For the South, the chance of welfare improvement rises when ESRs are used. Having another local Southern firm provides an additional channel for the ESR to improve the Southern welfare by shifting profits from the MNC to the local Southern firm. Thus, even if the MNC is allowed to take all the profits generated in the South, it is still possible to get Pareto improvement with the MER. 4.1 Minimum-quantity-export requirements As there are now two firms competing in the South, the maximized value of the MNC’s profits becomes: Max = x,z { v [p(Q)x + q(Z)z — [x+z]c ] x X } (4.1) where Z denotes the total sales in the South’s market. Solving this problem we have: x q(Z) + zq’(Z) - c = = X, and 0. Clearly, the two markets here are independent. Thus, we can perform the comparative statics of the QER only on the reaction functions of the firms in the North. Recall that the reaction function of the local Northern firm is implicitly defined by its first-order condition (2.18). Applying implicit function theorem on (2.21) and evaluated at x differentiating , t, iu, = X, then and W with respect to X gives the following results * P’ + YP” 2p +yp = - - o 153 if (4.2) = 1 = + 2p ÷yp { Xp”y,] (4.5) o, < = (4.4) 0, 0 iff 2p ÷yp // { [y — vX]n - Xp” (4.6) j We can see that all the results pertaining to the North as stated in section 2.1 hold. Again, if v 1, the welfare of the South is unaltered; if v < 1, the Southern welfare will be improved. 4.2 Minimum-export-share requirements Let us move on to the case of the MER defined as a minimum export share cc. The profit maximization problems of the local Northern firm and of the MNC are the same as in section 2.2, except that the argument of the inverse-demand of the South now becomes q = q(r+w), . The corresponding first and second-order 7 where w is the sale level of local Southern firm’ conditions are, therefore, similar to equations (2.18), (2.19), (2.21), (2.22). As in section 2.2, the two markets are linked by the ESR; hence, we cannot ignore the effects of ESR on the domestic market as in 4.1. Let Cd be the unit cost of the local Southern firm and define the maximized value of the local Southern firm as ip = max { [q(y x +w) — Cd] W }. (4.7) Its corresponding first and second-order conditions are To keep things tractable, the local-southern firm is assumed to serve only its domestic market. 154 wq” = q = 2q’ ÷ wq” + Cd - < (4.8) 0, = (4.9) 0. The first-order conditions (4.8), (2.18), (2.21) implicitly define the reaction functions of the local Southern firm, the MNC, and the local Northern firm respectively. Together, they determine the Nash-Cournot equilibrium outputs: w=w(o), x=x(ct), and y=y(c). Total differentiate these three equations to get “ww’ ‘ 0 Vwx’ dw 2 xlrdafya dx ‘ o, (4.10) 2 vcpdcqc = dy 0 For asymptotic stability of the equilibrium, I assume that the two markets are stable both separately and jointly; i.e., ° (4.11) 0, > = - H J > = (4.12) 0, - = < — (4.13) 0. Note that the determinant H is the same as in section 2.2. Performing the comparative static procedure and evaluating the results at y = 7 as in section 2.2 yield the following results: * x >0 = J 2 a 0 = if 0, - 155 (4.15) / —--{it;-;] = (4.16) 0, > -— aJ 1* VXGPlcyx / vxp a 7C > * . o if = (417 0, > - I * a a = where a - * Y°P / 418 <0, J 2 a Qp’Q > 0 if = [v44ç + it + t. 0 and 7t - = -f;{ vx x7tIJ j/y [y-vx]it a < > - xp” } (4.19) y, 0. The proof for the positive sign of a is provided in Appendix 2. Thus, the results in Propositions 1-3 and Corollary 1.1 and 1.2 all hold as before. In other words, a small ESR increases the MNC’s sales in the North, may increase or decrease sales of the local Northern firm, increases total consumption in the North, decreases profits of the local Northern firm, may increase or decrease profits of the MNC, and finally may improve the welfare of the North. All intuition and explanations given in section 2.2 are applied here as well. Therefore, there is no change in results pertaining to the North when we add another firm in the South. Using the same procedure as the case for the North yields the following comparative static results for the South: Za = YXa = __- a { ait - { x4fi - xJ }/a2j - .‘ } (4.20) * = aJ vxiji = - p”[3p’ + Qp’] < 0. The third line is obtained by using the definition of J from (4.13) and the last line is obtained 156 by using the definition of H given in (2.23). The sign of (4.20) is negative because Ps,,, < 0 by the second-order condition (4.9), [3p’+Qp’9 and J are negative by the stability conditions (1.23) and (4.13). Thus, a small ESR reduces sales of the MNC in the South. This is consistent with the result in the case where the MNC is the monopolist. The MNC reduces its sales in the South to export more and satisfy the ESR constraint. The sign for the change in the local Southern firm is given by = wa [H - j vp.4 J 2 ya = /÷QffJ 3 VX4Iwxf[ > 0. (4.21) J 2 ya The sign of w depends on whether the MNC’s sales are strategic substitutes or strategic complements. However, it seems reasonable enough to assume that sales of the local Southern firms are small relative to sales of the MNC. Thus even if q” is positive, it is unlikely that ‘P,, will be positive. Henceforth, the sign of W,, wifi be assumed as negative; i.e., the MNC’s outputs are strategic substitutes for the local Southern firm. Therefore, sales of the local Southern firm increase. As sales of the local Southern firm increase, its profits rise. This can be shown by differentiating (4.7) with respect to ct and applying Envelope Theorem: = wq’; vxq”wiJ p”[3p’+Qp”] 0. > (4.22) j 2 Thus a small ESR also serves as a mechanism that shifts the rent from the MNC to the local firm. For the impact on total consumption in the South, Z, combining (4.21) and (4.22), give: Za = wa — + Za < 0. (4.23) .! 2 a The final form of equation (4.23) is obtained by using ‘+‘, from (4.9) and = y[q’+wq”] and rearranging terms. Equation (4.23) tells us that a small ESR reduces total consumption in the 157 South regardless of whether the MNC’s sales are strategic substitutes or complements. Proposition 5 A small ESR will increase sales and profits of the South’s domestic firm, decrease the MNC’s sales in the South, and decrease total consumption in the South. The intuition is quite similar to the case of the North. While a small ESR shifts the MNC’s reaction function in the Northern market to the right it shifts the MNC’s reaction function in the Southern market to the left. As a result, sales of the MNC decline. Sales of the local firm, then, increase since the MNC’s sales are strategic substitutes for the local firm. Total consumption must decline since the reduction in the sales of the MNC has the first-order magnitude while the rise in the sales of the local firm has the second-order magnitude. Finally, define welfare of the South as W = (424) S(Z) ÷ [1—v]ll ÷ This is similar to the one defined in section 2, except that the consumer surplus now depends on the total sales of both firms and the profits of the local firm are added. Differentiate the welfare of the South with respect to c to get W = - Zq’Z + [1—v]ll + (4.25) 7. Like section 2, the first term is the reduction in the South’s consumer surplus while the second term is the change in the MNC’s profits retained by the South. Again given that the MNC’s sales are strategic substitutes, the Southern welfare could improve if the value of v is sufficiently small. The extra welfare effect that turns up when a local Southern firm is added to the model is depicted by the third term. This positive P is an increase in the profits of the local Southern firm. It represents the second channel through which the ESR can improve the South’s welfare. This second channel has a very important policy implication. Recall from section 2.2 that 158 the possibility of welfare improvement of the South relies on the South’s ability to capture the MNC’s profits. In reality, most MNCs often manage to avoid this profit capturing (i.e., by using transfer pricing). In such cases, the South’s welfare may not improve or may even worsen. Therefore, if the MNC’s profits can be shifted to the local-Southern firm, the chance for welfare improvement of the South would be much higher. In fact, even when the MNC can keep all the profits generated from the South, a small ESR can still be a Pareto improvement measure. To demonstrate the role of this second channel, set v = 1 so that the second term of (4.25) becomes zero. Then use (4.22) and (4.23) in (4.25) to get W = - where K = { [w-’-z]q’ 3 K { [z-w]q 3 K vxq I If P L 2.-‘P 1 = — - { [w+z]q’ 3 K — (w) q p 11 w[2q’÷w] } (4.26) 1 . > J 2 cz Now recall that the first-order condition of the MNC’s maximization problem implies that zq’ - [q-cJ when the ESR constraint just binds. Moreover, wq - = q-c by the first-order condition (4.8). Substituting these two facts in (4.26), we have Wa = { c-c—(w) 3 K q” 2 (4.27) } Two conclusions can be drawn from this equation. First, when the South demand is linear (or q” 0), a small ESR will improve the Southern welfare if and only if the local Southern firm has a lower unit cost than that of the MNC (or c > . A cost advantage of the local Southern firm ensures that the profits shifted from the 8 c)’ MNC are large enough to overtake the consumer-surplus losses. However, a small ESR will not affect the welfare of the South if both the local Southern firm and the MNC’s subsidiary have the same unit cost (or c = Cd). Second, when the South demand is not linear and c IS = c, a small ESR will improve the This is the exact condition for welfare improvement given in Davidson et al. (1985). 159 South’s welfare if and only if the South demand is concave (or q” < 0). This condition ensures a welfare improvement because a concave demand curve associates with a smaller consumersurplus loss. To show that the welfare of the two countries can be improved simultaneously with v 1, take the case of linear Northern demand as an example. When v = 1 and p’ = = 0, (4.19) becomes w, = -P-{yp’-2xp’} J 2 u (4.28) i = > —-{[p—cJ ÷c —c} J 2 a c. 0 if c The second step is obtained by using yp’ {pc*], and -xp’ = [p-c] when the ESR constraint just binds. Thus, a small ESR can be Pareto improvement when the North’s demand is linear, the South’s demand is linear or concave, and c c c. 5. Conclusion The main point of this paper is to show that minimum-export requirements (MERs) can be Pareto improvement measures. The paper employs a two-country model where one country is the source of foreign direct investments (FDIs) and the other country is the host. The FDIs are conducted by a multinational corporation (the MNC) for which the parent firm is located in the source country. The parent firm has to compete with another local firm for its domestic market. The subsidiary firm may be a monopolist or may compete with another local firm. The host country requires the MNC to export a minimum quantity or a minimum share of its total productions. It is found that under this situation the impact of MERs on the North depends upon the strategic interactions between the rival firms in the source country. The MER imposed on the MNC can help the MNC to gain a strategic advantage with respect to its rivals by being 160 considered as a credible commitment by the MNC to sell more than it otherwise would. The MNC will gain the strategic advantage when its sales in the source country are substitutes. The strategic advantage will shift toward the local firm in the source country, however, if the MNC’s sales are strategic complements. A MER policy can improve the welfare of the source country since it increases the total consumption of the source country, thereby reducing the duopoly distortion. It can also improve the host-country’s welfare by shifting profits from the MNC to the local firm in the source country. When the local firm does not exist, the host-country’s welfare can still be improved if a sufficient amount of the MNC’s profits is retained in the host country. Some extensions are possible. First, the duopolistic market structure can be extended to the case of oligopoly. As long as the size of the MNC’s sales is still large, most of the results obtained here should hold. Second, it is possible to modify the model to capture a three-country case in which the MNC locates in the East and exports to compete with the local firm in the West. Again, MERs can be viewed as tools to help the MNC to credibly commit its sales higher than it normally would. In such a case, it is possible that the East and South may gain from MERs at the expense of the West. 161 Appendix 1. Sufficient conditions for W> 0 and Pareto improvement Substitute the value of x , from (2.24) into 0 it in (2.27), then use the result with the value of z. from (2.32), and the definition of p in (2.34) to get [1—v]x[2q”÷zq”]r } ] 11 zq”[3p”÷Qp -•-{ a h qE’[3p1’+QpU] j[p”+ypJ 11 — a2 h [1—vj[2q’÷zq }. Wa — (1.1) — (a) Linear Northern demand: When the North’s demand is linear or = 0, (Al) becomes Wa — — = = [1—v][2q’+zq’jY cch xzq[p’] [1 —v][2 + h 2 a K > where 2 K { 0 if v - q’ [1V][2+Eqf,z] -1 E, q,z I ah —3} (A.2) < EqIz xzq — 3p”q’ } -3 112 ‘ > ÷2 II 0, EqI,z q Since v is positive, the elasticity of q’ with respect to z, E q’.z must be greater than one. This in turn requires that q” must be negative. In other words, the Southern demand must be concave and v must be sufficiently small for the South’s welfare to be improved. Note that these conditions do not conflict with the condition (2.31 a) that ensures welfare improvement of the North. (b) Linear Southern demand: When the South’s demand is linear or q becomes 162 = 0, then (Al) = — XP’Z{ 2[1—v]q’p”÷yp”] — } q”[3p”+Qp”J (1.3) — ah { 2[1—v][p’+yp’’] — [3p’+Oji”] }. Notice that the term outside the curly bracket is negative and recall that 3p’+Qp is negative [to ensure the stability condition (2.23)]. Thus, a negative value of it. = p’+yp is required, otherwise the terms in the curly bracket would be positive and the South’s welfare would fall. W will be positive if v {[y-x]p-p’}/2[p-i-yp]. < To ensure that the welfare of both countries improves simultaneously, a further restriction is needed. Recall from Proposition 3 that when the MNC’s sales are strategic substitutes (i.e., it x > <0), it is required that the MNC’s sales must be greater than those of the North’s firm (i.e., y). Therefore, y-x is negative and p’ must also be restricted to be positive so that the right hand side of the above condition is positive. This in turn requires that (p ‘1 < [x-yjp. In other words, the North’s demand curve must be convex. Note that if both demand curves are linear, the welfare of the South can only decline since the terms in the curly bracket of (A.l) will become [1-v]2pq - 3pq’ = -[l+2v]pq’ <0. 2. Proof for the sign of a Rearranging a given in the text, then using the fact that ; and evaluating the result at “y a = = [vy1P vx[ - = , vy[q’+zq”], ‘f = q’+wq, yields the following Xtrw1lfWx ]Iy [q”+zq”]ijr JIY vx[ [2q”+zq”]{2q”÷wq”] [q’-’-zq”][q +wq”] vx{q’[3q’÷Zq”] > 0. (1.4) — — = = I The sign of the last equality is determined by the sign of 3q+zq’ which is assumed to be negative to ensure that the determinant of coefficients of dw and dx or 163 e is positive. REFERENCES Anis, Aslam H. and Thomas W. Ross. “Imperfect competition and Pareto improving strategic trade policy,” Journal of International Economic, 33 (1992): 363-371. Balasubramanyam, V.N. “Putting TRIMs To Good Use,” World Development, 19 (1991): 12151224. Ballance, Robert, Helm Fostner, and Tracy Murrey. “On Measuring Comparative Advantage: A note on Bowen’s indices,” Weltwirtschaftliches Archiv, 121 (1985): 346-354. Bertola, Giuseppe. “Factor Shares and Savings in Endogenous Growth,” Princeton University, (August 5, 1991). Brander, James A., and Barbara J. Spencer. “Export subsidies and international market share rivalry,” Journal of International Economics, 18, (1985): 85-100. “Strategic Commitment with R&D: The Symmetric Case,” Bell Journal of Economics, Spring (1983): 225-35. Bliss Christopher and Nicolas Stern. “Productivity, wages and Nutrition: Part I: The theory,” Journal of Development Economics, 5 (1978a): 33 1-362. “Productivity, wages and Nutrition: Part II: Some Observations,” Journal of Development Economics, 5 (1978b): 363-398. Bulow, Jeremy I., John D. Geanakoplos, and Paul D. Kiemperer. “Multimarket Oligopoly: Strategic Substitutes and Complements,” Journal of Political Economy, 93 (1985): 488511. Cho, C.C., and E.S. Yu. “Export-Share Requirements and Unemployment: The Case of Quota,” Southern Economic Journal, 56 (1990): 743-51. Chou, Chien-fu and Gabriel Talmain. “R&D, Endogenous Growth, Wealth Distribution, and Labour Supply,” State University of New York at Albany, (October 14, 1991). Dasgupta, Partha, and Debraj Ray. “Inequality as a determinant of Malnutrition and unemployment: Theory,” The Economic Journal, 96 (1986): 1011-1034. “Inequality as a determinant of Malnutrition and unemployment: Policy,” The Economic Journal, 97 (1987): 177-188. Davidson, C., Si. Matusz, and M.E. Kreinin. “Analysis of Performance Standards for Direct Foreign Investments,” Canadian Journal of Economics, XVIII (1985): 876-90. Dornbusch, R., S. Fischer, and P.A. Samuelson. “Comparative Advantage, Trade and Payments in a Ricardian Model with a Continuum of Goods,” American Economic Review, LXVII (1977): 823-39. 164 Eswaran, Mukesh, and Ashok Kotwal. The Theory of Real Wage Growth in LDCs,” Journal of Development Economics, 42 (1993): 243-269. “ Fischer, Ronald D. and Pablo Serra. “Growth, Trade and the Distribution of Human Capital,” University of Virginia and Universidad de Chile (1992). Gorman, W. M. “On a Class of Preference Fields,” Metroeconomica, 13 (1961): 53-6. “Tricks with utility Functions,” Essay in Theory and Measurement of Consumer Behaviour. Ed. M. Artis and R. Nobay. Cambridge: Cambridge University Press, 1976. Graham, Frank D. “Some Aspects of Protection Further Considered,” Quarterly Journal of Economics, 37 (1923): 199-227. Greenaway, D. “Why are We Negotiating on TRIMs?.” Global Protectionism. Ed. D Greenaway. London: MacMillan Academic and Professional, 1991. Grossman, G.M. and E. Helpman. “Product Development and International Trade,” Journal of Political Economy, 97 (1989): 126 1-83. “Comparative Advantage and Long-Run Growth,” The American Economic Review, 80 (1990): 796-815. “Quality Ladders in Theory of Growth,” The Review of Economic Studies, LVIII (1991a): 43-61. “Quality Ladders and Product Cycles,” The Quarterly Journal ofEconomics, (1991b): 557586. Guisinger, S. and Associates. Investment Incentives and Peiformances Requirements. New York: Praeger, 1985. Helpman, Elhanan, and Paul R. Krugman. Market Structure and Foreign Trade: Increasing returns, Impeifect Competition, and the International economy. Cambridge: MIT Press, 1990. Herander, M. and C.R. Thomas. “Export Performance and Export-Import Linkage Requirements,” Quarterly Journal of Economics, CI (1986): 59 1-607. Hunter, Linda. “The Contribution of Nonhomothetic Preferences to Trade,” Journal of International Economics, 30 (1990): 345-358. Hunter, Linda and James R. Markusen. “Per Capita Income as a Basis for Trade,” Empirical Methods for International Trade. Ed. Robert Feensta. MIT Press: Cambridge, 1988. Kaniien, Morton, and Nancy L. Schwartz. Dynamic Optimization: The calculus of variations and optimal control in economics and management. Amsterdam: North-Holland, 1981. 165 Liebenstine, H. Economic backwardness and economic growth, New York: Wiley, 1957. Mirrlees, J. A. “A pure theory of under-developed economies,” in L. Reynolds, ed., Agriculture in development theory, New Haven, CT: Yale University Press). Murphy, Kevin M., Andrei Shliefer, and Robert Vishny. “Income Distribution, Market Size, and Industrialization,” Quarterly Journal of Economics, (1989): 537-564. OECD. Trade Related Investment Measures: an Overview of Characteristic, Incidence and Effects. Trade Committee TC/WP(87) 78, 1st rev., 1987. Rada, J. The Structure and Behaviour of the Semiconductor Industry. Geneva: United Nations Centre on Transnational Corporations, 1982. Rodgers, G. B. “Nutritionally based wage determination in the low income labour market”, Oxford Economic Papers, 27, (1975): 61-81. Rodrik, D. “The Economics of Export-performance Requirements,” Quarterly Journal of Economics, 102 (1987): 633-50. Romer, P. M. “Endogenous Technological Change,” Journal of Political Economy, 98 (1990): S71-S 102. Stiglitz, J. E. “The efficiency wage hypothesis, surplus labour and the distribution of income in L.D.C.’s,” Oxford Economic Papers, 28, (1976): 185-207. Syrquin, Moshe, and Hollis Chenery. “Three Decades of Industrialization,” World Bank Economic Review, 3 (1989): 145-181. Solow, R. M. “A contribution to the theory of economic growth,” Quarterly Journal of Economics, 70 (1956): 65-94. Swan, T. W. “Economic growth and capital accumulation,” Economic Record, 32 (1956): 334-61. Taylor, M. Scott. “Quality Ladders and Ricardian Trade,” Journal of International Economics, 34 (1993): 225-243. “TRIPS Trade and Growth,” International Economic Review, 35 (l994a): 361-181. “Once off Losses and the Dynamic Gains from Trade,” Review of Economic Studies, 61 (1994b): 589-601. World Bank, World Development Report, Washington, 1987. 166
- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- UBC Theses and Dissertations /
- Three essays on North-South trade, growth, and development
Open Collections
UBC Theses and Dissertations
Featured Collection
UBC Theses and Dissertations
Three essays on North-South trade, growth, and development Chayun, Tantivasadakarn 1994
pdf
Page Metadata
Item Metadata
Title | Three essays on North-South trade, growth, and development |
Creator |
Chayun, Tantivasadakarn |
Date Issued | 1994 |
Description | This thesis focuses on three issues pertaining to growth, development, and trade between developed and developing countries. The first essay develops an endogenous growth model that incorporates Engel’s law into the preferences. The model shows that the initial distribution of income is crucial to the outcome. A closed-economy country where most of its population is poor experiences a low rate of innovation. Income transfers from the rich to the poor can increase the effective labour supply, thereby enhancing the rate of innovation. Under free trade, only the rich benefit from trade. The poor are indifferent unless they already can afford to consume the minimum requirement of food before trade or the minimum requirement becomes affordable after trade by cheaper imported food. The initial distribution of income influences the trade patterns. Moreover, income redistribution in a free trade environment also increases the growth rate. The second essay extends the first one by assuming that the marginal product of labour of the food sector is decreasing. It shows that an increase in population may decrease the growth rate if the initial population is large relative to the productivity of the food sector. Moreover, an increase in one country’s population may reduce that country’s production share of the world’s innovation and increase its dependency on imported technology. The last essay analyzes the welfare impact of minimum-export requirements (MERs) imposed on foreign direct investments. This essay shows that MERs can be Pareto improving measures to both the source and the host countries. When offshore plants are used by parent firms to compete with domestic firms in the source country, MERs can improve the host country’s welfare by inducing the total sales in the source country to rise, thereby reducing the distortion generated by imperfect competition. The MERs can simultaneously improve the welfare of the host country by shifting profits of the foreign firms toward the local firms. If the local firms are absent, the host’s welfare may still be improved if sufficient profits from foreign operations are retained in the host country. |
Extent | 3666243 bytes |
Subject |
International economic relations Developing countries -- Foreign economic relations |
Genre |
Thesis/Dissertation |
Type |
Text |
File Format | application/pdf |
Language | eng |
Date Available | 2009-06-11 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0088919 |
URI | http://hdl.handle.net/2429/8978 |
Degree |
Doctor of Philosophy - PhD |
Program |
Economics |
Affiliation |
Arts, Faculty of Vancouver School of Economics |
Degree Grantor | University of British Columbia |
Graduation Date | 1995-11 |
Campus |
UBCV |
Scholarly Level | Graduate |
Aggregated Source Repository | DSpace |
Download
- Media
- 831-ubc_1995-983558.pdf [ 3.5MB ]
- Metadata
- JSON: 831-1.0088919.json
- JSON-LD: 831-1.0088919-ld.json
- RDF/XML (Pretty): 831-1.0088919-rdf.xml
- RDF/JSON: 831-1.0088919-rdf.json
- Turtle: 831-1.0088919-turtle.txt
- N-Triples: 831-1.0088919-rdf-ntriples.txt
- Original Record: 831-1.0088919-source.json
- Full Text
- 831-1.0088919-fulltext.txt
- Citation
- 831-1.0088919.ris
Full Text
Cite
Citation Scheme:
Usage Statistics
Share
Embed
Customize your widget with the following options, then copy and paste the code below into the HTML
of your page to embed this item in your website.
<div id="ubcOpenCollectionsWidgetDisplay">
<script id="ubcOpenCollectionsWidget"
src="{[{embed.src}]}"
data-item="{[{embed.item}]}"
data-collection="{[{embed.collection}]}"
data-metadata="{[{embed.showMetadata}]}"
data-width="{[{embed.width}]}"
async >
</script>
</div>
Our image viewer uses the IIIF 2.0 standard.
To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0088919/manifest