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Three essays on North-South trade, growth, and development Chayun, Tantivasadakarn 1994

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THREE ESSAYS ON NORTH-SOUTH TRADE, GROWTH, ANDDEVELOPMENTbyCHAYUN TANTIVASADAKARNB.A., Thammasat University, 1981M.A., Thammasat University, 1985M.A., The University of British Columbia, 1989A THESIS SUBMIITED IN PARTIAL FULFILMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATh STUDIESDepartment of EconomicsWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIADecember 1994© Chayun Tantivasadakarn, 1994In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. it is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)_______________________________Department of EwncnmCSThe University of British ColumbiaVancouver, CanadaDate -Qc j 1?f-DE-6 (2188)ABSTRACTThis thesis focuses on three issues pertaining to growth, development, and trade betweendeveloped and developing countries.The first essay develops an endogenous growth model that incorporates Engel’s law intothe preferences. The model shows that the initial distribution of income is crucial to theoutcome. A closed-economy country where most of its population is poor experiences a low rateof innovation. Income transfers from the rich to the poor can increase the effective laboursupply, thereby enhancing the rate of innovation. Under free trade, only the rich benefit fromtrade. The poor are indifferent unless they already can afford to consume the minimumrequirement of food before trade or the minimum requirement becomes affordable after trade bycheaper 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 labourof the food sector is decreasing. It shows that an increase in population may decrease the growthrate if the initial population is large relative to the productivity of the food sector. Moreover, anincrease in one country’s population may reduce that country’s production share of the world’sinnovation 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 improvingmeasures to both the source and the host countries. When offshore plants are used by parentfirms to compete with domestic firms in the source country, MERs can improve the hostcountry’s welfare by inducing the total sales in the source country to rise, thereby reducing thedistortion generated by imperfect competition. The MERs can simultaneously improve the11welfare of the host country by shifting profits of the foreign firms toward the local firms. If thelocal firms are absent, the host’s welfare may still be improved if sufficient profits from foreignoperations are retained in the host country.111TABLE OF CONTENTSABSTRACT iiTABLE OF CONTENTS ivLIST OF FIGURES viiACKNOWLEDGEMENT viiiI IITRODUCTION 1II NORTH-SOUTH TRADE AI1) THE RICARDIAN GROWTH MODEL 71. Introduction 72. Autarky Model 102.1 Consumer’s intertemporal maximization problem 122.2 Firm’s Problem 162.3 Steady State Equilibrium 212.4 Redistribution of income and growth 273. Free Trade Model 303.1 Trade Patterns 313.2 Consumers 343.3 Trade Equilibrium 364. Redistribution of income under free trade 505. Comparative Steady-state Analyses 545.1 Changes in productivity of the manufacturing sector 545.2 Changes in productivity of the R&D sector 575.3 Changes in productivity of the grain sector 585.4 Changes in labour endowment 656. Conclusion 67Appendix 68ivIll NORTH-SOUTH TRADE AND GROWTH: WITH DIMINISHING MARGINALPRODUCTIVITY 801. Introduction 802. Autarky: 812.1 Country size, population mix, and growth 882.2 Redistribution of income and growth 953. Free Trade 983.1 Consumers 993.2 Trade patterns 993.3 Trade equilibrium with both countries producing R&D 1034. Comparative Steady State Analyses: Trade model 1125. Conclusion 119Appendix 120IV MINIMUM EXPORT REQUIREMENTS: PARETO IMPROVING MEASURES 1261. Introduction 1262. Structure of the Model 1302.1 Minimum-Quantity-Export Requirement (QER) 1312.2 Export-Share Requirement (ESR) 1353. Optimal MERs 1483.1 Optimal quantity-export requirement 1493.2 Optimal export-share requirement 1524. Multiple-duopoly Case 1534.1 Minimum-quantity-export requirements 1534.2 Minimum-export-share requirements 1545. Conclusion 160VAppendix 162REFERENCES 164viLIST OF FIGURESFigure 2.1 Balance of Payments Schedule 40Figure 2.2 Steady State Equilibrium 41Figure 2.3 Effect of the Change in Relative Labour Productivity in ManufacturingGoods 56Figure 2.4 Effect of the Change in the South’s Grain Productivity 63Figure 2.5 Effect of the Change in the North’s Grain Productivity 64Figure 3.1 Balance of Payments Schedule 105Figure 3.2 Patterns of Manufacturing and R&D Production 109Figure 3.3 Steady State Equilibrium 113Figure 4.1 Market Structures and trade flows 132Figure 4.2 Effect of Minimum Export Share Requirements 141Figure 4.3 Effect of Optimal Quantity Export Requirements 151viiACKNOWLEDGEMENTSIt has been my very good fortune to have worked under the supervision of BrianCopeland. I am deeply indebted to him for his guidance, patience and support. I cherish theopportunity I have had to work with him and the example he has set as a teacher and asupervisor.I wish to express my gratitude and thanks to Scott Taylor, my thesis committee, who hasdevoted efforts to a far greater extent than the normal involvement of a committee member. Hisinvaluable insights on endogenous growth models are greatly appreciated. Mukesh Eswaran, theremaining member of my committee, contributed comments and suggestions that brought freshperspectives 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 thesisand valuable comments.My studies at the University of British Columbia have been made possible by ascholarship from the Canadian International Development Agency and by awards of TeachingAssistantships from the Department of Economics. I am grateful to the Faculty of Economicsof Thammasat University for granting me the required study leave.My appreciation also goes to my friend, Alison Gear, for her warm friendship throughoutmy 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 hasstood by me all this time throughout all frustrations and achievements with patience and love.viiiCHAPTER IINTRODUCTIONEconomic development and growth are among the most important goals of allnations especially the less developed countries (LDCs). Economic history has revealedphenomena of a large variation in the growth experiences and long sustenance of growthrates in many countries. These phenomena are believed to be attributed to differenteconomic environments and government policies.Several studies have tried to identify the key factors that sustain and stimulateeconomic 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 thetrade orientation that one country takes. At least two studies confirm this connectionbetween 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 “outwardtrade orientation” outperformed those countries with the “inward trade orientation11’.These findings have prompted theorists to construct models that can explain thelinkage 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 thatis achieved by research and development (R&D) of profit seeking entrepreneurs. Theeconomic environments (including the trade orientation) can influence the incentives ofthe R&D, thereby affecting the growth outcomes.The World Bank reports that during 1973-85 the growth rate of real GDP of thestrongly outward-oriented countries was 7.7 percent per year while it was 2.5 percent forthose of the strongly inward oriented countries. In Syrquin and Chenery (1989), theaverage output growth rate (1952-83) of the countries with the outward trade orientationis 5.22 percent per year versus 4.28 percent for those of the countries with the inwardtrade orientation.1These types of models have provided many important lessons about trade, growthand development especially for the developed countries (DCs). However, there are someimportant characteristics of the LDCs that should be incorporated so that we can betterexplain the situations of the LDCs. There are at least three aspects about the LDCs thatneed special attention.First, the LDCs have serious income distribution problems. With a very skeweddistribution of income, most people in the LDCs are not wealthy enough to demandindustrial products. This insufficient demand may inhibit the ability of the LDCs tosupport R&D necessary for industrialization especially when the economy is closed byprotection. If the problems of income distribution are reduced, the LDCs should havehigher capability to engage in R&D and achieve higher growth.Second, the agricultural sectors of the LDCs are still the major sectors of theireconomies and most of the LDCs’ labour forces concentrate in these sectors. Thus,output of their agricultural sectors tends to suffer from the problem of diminishingmarginal productivity of labour. The problem is more severe for the LDCs with scarceland 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 theproduction pattern of the LDCs, but also because of its implication on the growthperformance. In the country in which land is scarce, an increase in food production toserve the larger population would cause the agricultural sector to be less and lessproductive due to the DMR Hence, it has to draw resources increasingly from othersectors. Consequently, the more the population grows, the fewer resources will beavailable for R&D. This could decrease growth.2Third, the LDCs need to industrialize in order to achieve the desired economicdevelopment and growth. However, the LDCs usually lack both the capital and thetechnology to start their own industrialization. They have to rely on foreign directinvestment (FDI). LDCs often design investment incentive packages which are attractivefor the foreign investors yet still have some mechanisms to control the benefits of FDI.These control mechanisms or Trade Related Investment Measures (TRIMs) areopposed 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 ofTRIMs, particularly minimum export requirements (MERs), may be beneficial for thesource countries for the following reasons. The market structures of the industries thatuse FDI are often highly concentrated. Producers do not need to sell as much as theywould if they were in perfectly competitive industries. As a result, the prices will behigher than the marginal costs which give rise to distortions. The MERs imposed by thehost countries may increase the total sales of the source countries. This increase of salesreduces the gap of prices and marginal costs which, in turn, decreases the distortion inthe source countries; and improves their welfare.This thesis consists of three essays, which deals respectively with each of theissues outlined above. They are presented in Chapter II to W The first two essays areclosely related and deal specifically with growth and development under free tradeenvironments. 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 incomeaffects growth, trade patterns, and welfare. To attain this objective, an endogenousgrowth model is used. Most of the existing endogenous growth models assume that3preferences are homothetic which inhibits their abilities to analyze problems pertainingto 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 ofconsumers: the capitalists and the workers. Workers represent the poor who suffer frommalnutrition 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 thegrain sector is time invariant while the processing technology of the manufacturing sectorcan be improved by R&D. The intensity of R&D determines the speed that theprocessing technology advances which in turn influences the utility growth rate andwelfare. A wealth redistribution from capitalists to workers will allow these workers-turned-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 willno longer have malnutrition problems, so their effective units of labour will rise. Withlarger 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. Thestructure of the model follows the format of the first essay, except that the grain sectoris now subject to DMP. The objective is to determine how the results from the first essaychange with the DMP assumption.An increase in population may increase or decrease R&D and growth. On the onehand, the increase in population adds labour supply to the economy (endowmentexpansion effects). On the other hand, the increase in population also raises the demandfor grain which draws labour resources from the R&D sector because of the diminishingmarginal productivity (diminishing marginal productivity effects). The endowmentexpansion effects increase R&D while the diminishing marginal productivity effects4decrease R&D. An increase in population from an initially low level would generatesmall diminishing marginal productivity effects; thus, R&D would rise. A continuedincrease in population, however, generates increasingly stronger diminishing marginalproductivity effects which will eventually overtake the endowment expansion effects.Therefore, R&D would eventually reduce. A redistribution of wealth from capitalists toworkers, under DMP assumption, also suffers the same phenomenon. Hence, it onlyworks for an initially small population level.In the first two essays, it is assumed that multinational corporations (MNCs) fromDCs 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 establishsubsidiary firms in LDCs and supply the world demand from these firms. The first twoessays also assume that these activities are free from intervention. However, some formsof TRIMS are often applied to FDI. The last essay studies the effects of MinimumExport Requirements (MERs) which are one of most popular TRIMs.The third essay does not deal directly with the growth issues, but concentrates onthe issues related to FDI which are the means for LDCs to attain economic growth. Itfocuses on the strategic interactions between firms in the source and host countries causedby the imposition of MERs. Therefore, the model departs from the endogenous growthframework and adopts the static partial equilibrium framework commonly used in thistype of literature for analyzing trade issues with strategic interactions.The main objective of the last essay is to show that MERs are not always harmfulto the source countries as are normally believed. In fact, they can lead to a Paretoimprovement for both the source and the host countries. The MERs can improve thewelfare of the source country because they help the MNCs to make a commitment to sellto a greater extent than they normally would in the source countries. This raises the total5outputs and reduces the price. The gap of the price over the marginal cost and itseconomic distortion are, therefore, reduced. The MERs can simultaneously improve thewelfare of the host countries by shifting the profits of the MNCs toward the local firmsin the host countries. Even when local firms do not exist, the MERs can still improvewelfare of the host countries if the MERs are tied with other measures such as minimumshare of profits that the MNCs must retain in the host countries.6CHAPTER IINORTH-SOUTH TRADE AND THE RICARDIAN GROWTH MODEL1. IntroductionOne of the recent developments in the endogenous growth model was originated byRomer (1986, 1987). It has been popularized and developed into trade models by Grossman andHelpman (1989, 1990, 199 Ia, b), and Taylor (1993, 1994a, b). Unlike the neoclassical growthmodel developed by Solow (1956) and by Swan (1956), growth in these approaches is generatedby the profit-maximizing behaviour of firms which choose the optimum level of research anddevelopment (R&D) either to develop new varieties of goods (variety approach) or to improvean 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 thefirm, thereby changing the growth rate.These endogenous growth models are very useful in tackling many questions relating tolong-run growth and international trade. But most of these models assume homotheticpreferences. Although the homothetic assumption has helped economists by simplifying thedemand side of the model so that they could concentrate on problems of the supply side, someeconomists have started to express concern about this simplifying assumption. Their concernscome from two sources.First, homothetic preferences deny Engel’s law. When homothetic preferences areassumed, we force the consumption patterns of the rich and the poor to be the same which maybe acceptable for the case of developed countries (the North). This assumption is ratherunrealistic for developing countries (the South) where income distributions are quite skewed. Inaddition, when we consider economic problems pertaining to the South, we might want todistinguish between the impact of some changes on the welfare of the rich and the poor. The7homothetic assumption, nevertheless, does not allow us to do so because anything that affects theconsumption 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. Manyempirical studies in international trade [e.g., Ballance, Fostner, and Murrey (1985), Hunter andMarkusen (1988), Hunter (1991)] have rejected the homothetic preference hypothesis.Consequently, if we are going to use an endogenous growth model to analyze problemspertaining 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 “hierarchicalpreference 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 thehierarchy of needs; i.e., people try to fulfil a minimum need of food before starting to consumemanufactured products.Inspired by these pioneering works, this paper combines the hierarchical preferences ofEswaran 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 featuresof the endogenous growth model but employs the non-homothetic preferences which rectify theproblems 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 andHelpman. However, growth in Taylor’s model is generated by investment in R&D to reduce unitlabour requirements of production. His approach is also very tractable since labour is the onlyinput 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 suitableproperty for North-South trade where factor prices are not often equalized.The paper by E-K explains how patterns of consumer demand which behave according8to Engel’s law can affect real wages and hinder the benefits of industrialization from “tricklingdown” to the poor. Although their approach of incorporating Engel’s law into the preferencesis “stark”, the underlying logic and their results would still hold if the substitution effect betweenfood 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 themodel 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 foodproducts) with a perfectly competitive market structure and time-invariant technology is added.Second, the original functional form of preferences is modified to incorporate grain consumptionand reflect the hierarchical nature based on E-K’s idea. Third, instead of homogeneousconsumers, there are now two classes of people, workers and capitalists. Capitalists, with higherincome 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 onNorth-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 capitalistsare sated with grain.With these modifications, the model is different from its predecessors in the followingways. First, the hierarchical preferences allow us to analyze the effects of a redistribution ofincome on R&D, growth, trade patterns, and welfare. These analyses are not possible under thehomothetic preferences. Second, this functional form does not restrict the consumption units (ofmanufactured 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 firstpriority in the hierarchy of needs, a technological improvement in the agricultural sector createsIn M-S-V, the consumption unit of each manufactured good is either 1 when it isconsumed or 0 when it is not.9static spilover effects in the manufacturing sector. Besides those static effects, this paper cancapture dynamic effects which are not presented in the static framework.Some similarity and differences of the approach used in this paper from other studies’ onredistribution of income should be pointed out. Chou and Talmain (1991) use a similarendogenous 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 intheir 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 inelasticsince consumers in this paper do not consume leisure. Redistribution of income increases thelabour supply and growth because it alleviates malnutrition problems of the poor. Furthermore,Chou and Talmain study only the case of a closed economy while this paper studies both autarkyand free trade cases. Fischer and Sega (1992) employ a trade model with externalities of humancapital to show the negative relationship between inequality and growth. They also conclude thatinequality decreases over time. However, this paper reveals that it persists. The poor are trappedin 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 ofthe model for a closed economy. Section 3 extends the model in section 2 with Ricardiantechnology to a free trade model. The impacts of a redistribution of income and comparativesteady-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 ModelConsider 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 aninterval [0,1]. The grain sector represents a traditional sector with no technological progress10while the manufacturing sector depicts the advanced sector with technological progress. The totalpopulation (L) is fixed consisting of L workers and L capitalists, where L = IL, 0 <1 < 1.Consumers in each group are homogeneous. All consumers share identical hierarchicalpreferences. The consumption pattern derived from these preferences depends on the incomelevel y, where i e {w=worker, c=capitalist}. Consumers will not demand any manufacturedproducts 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. Theywill spend the remaining income on manufactured products only2.It is assumed as in Dasgupta and Ray (1986, 1987) that people who are not sated withgrain suffer from malnutrition and, therefore, have less labour power than those who are sated3.Normalize the unit of labour of any person who is sated with grain to 1 and denote the labourpower of any individual who is not sated with grain as a, where 0 <a < 1. Leisure is assumedto 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 rateof r per period. Since we are interested in the case where income distribution is sufficientlyskewed so that people in different groups demand different consumption shares of grain andmanufactured goods, the following assumptions are made. Income generated from the equitiesand wages allows capitalists to be sated with grain, however, wage income that workers earneddoes 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’sincome: y, = w + rq is greater than the expenditure for i which, in turn, is greater than each2 See justifications of these preferences in E-K, section 4.The theoretical implications of the link between productivity and consumption date backat least to Leibenstien (1957). Also see Rodgers (1975), Mirrlees (1976), Stiglitz (1976), andBliss and Stern (l978a,b) analyses of efficiency wages.11worker’s income: y = ctw, i.e., y, > p> y.Goods are assumed to be produced according to Ricardian technology with labour as theonly input. The grain sector is perfectly competitive and its technology is fixed over time. Firmsin the manufacturing sector have two activities: conducting R&D to discover new technology andthen producing goods using this technology. The leader firm which discovers the newesttechnology of industry z receives an infinite life patent. However, the know-how generatesspillover effects on the public knowledge upon which the subsequent generations of technologieswill be built. Therefore, the overall manufacturing activity exhibits dynamic increasing returnsto scale. With the exclusive right on the best production technology, the leader uses limit pricingto capture the whole market of its industry and earns monopoly profits. The monopoly powercontinues until the next generation of technology is discovered; then the new leader becomes themonopolist. The cost of discovering the next generation of technology is incurred only once andthe up-front cost of R&D is fixed to production activity. Each firm funds its risky R&D byseffing equities to the public. Successful R&D increases labour productivity by reducing the unitlabour requirement which, in turn, reduces prices of manufactured goods and generates utilitygrowth.With the above general idea of the model, the rest of this section describes the formalmodel and provides analyses.2.1 Consumer’s intertemporal maximization problemAll 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) andp(z,t), z E [O,lj respectively. Given these prices and income, a representative consumer i E{w,c) chooses consumption of g(t) and x(z,t) to maximizeSee the proof in footnote 18.12W = fe-Pt 1nudt } (2.1)st. q = y1(t)— e(t). (2.2)where E0 is the expectation taken at time t=O conditional on the current information; p is thesubjective discount rate; and lnu1(t) represents the instantaneous utility at time t. The constraint(2.2) indicates that the rate of change of investment in equities q dq/at is equal to the incomeleftover from consumption expenditure, where y1(t) is the total income and e.(t) is the totalconsumption expenditure. The instantaneous utility function is assumed to take a form given by3y1(t) pjlnu(t) = (2.3)ma+f ln[x1(z,t)Jd, y1(t) >pj,Each worker has only y(t) = aw(t) as income which, by Satiation Assumption, is lessthan p(t) Thus, the top part of (2.3) is used for the worker. Solving for each worker’s perperiod demand for grain gives: g(t) = ciw(t)Ip(t). It is assumed that workers will not survive ifthey cut back their consumption in order to save. Therefore, workers do not invest in any assetif they are not sated with grain6.The income of each capitalist is y(t) = w(t) + rq(t), where q(t) = Q(t)ILQ and Q(t) is theThe preferences are adapted from E-K’s idea. They are lexicographic since they are notcontinuous 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 usedfor welfare comparison only for the change of income within each income range. Although thefunctional form of the preferences used here is lexicographic, it is needed for solving theconsumer’s optimization problem. A similar functional form which is also lexicographic is usedby M-S-V.6 Bertola (1991), using a similar endogenous growth model, shows that wage earners do notsave.113total 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 aGorman polar form7; thus, it is quasi-homothetic and the Engel’s curves are straight lines.Therefore, aggregation across capitalists is allowed. Furthermore, solving each individualmaximization problem and then aggregating the results up is equivalent to solving themaximization problem of the representative capitalist who has the aggregate income and requiresan aggregate minimum grain consumption of the group.The latter method is used by giving an income of Y(t) = y(t)L to a representativecapitalist who has a minimum grain requirement of G g7. (Note that, throughout the paper,the aggregate variables of the people in group i E {w,c) are denoted by capital letters and theyare 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 intertemporalmaximization problem of the representative capitalist can be solved in two stages. The problemin the second budgeting stage will be solved first, then the result is used for solving the problemin the first budgeting stage. In the second budgeting stage, the representative capitalist choosesper 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 Define this aggregate manufacturing expenditure of thecapitalist as MçQ) [e(t)-p(t).L. Then, the capitalist’s per period demand for grain andmanufactured goods8 is:See Gorman (1961, 1976).The sub-utility function for the manufactured goods is Cobb-Douglas; hence the demandof good z takes the familiar form of a share of total budget divided by its price. Notice that thebudget share for every good z is equal to 1.14G(t) = X(z,t)M(t)zE[O,1], (2.4)p(z,t)respectively, where G Substituting these demands into the bottom part of (2.3) yields:In U(t) = mG + InM(t) - flnp(z,t)dz. (2.5)Then set w(t)=l as a numeraire and rewrite constraint (2.2) as Q— [1+rq(t) ]L - M(t) + p(t)gL= rQ(t) + [1-p(t)g7L- M(t). Now reformulate the first stage problem as the one of choosingM0Q) and Q(t) to maximize the current Hamiltonian: H = 1nU(t) + p(t)Q orH = mG + 1nM(t) — fhw(z,t)dz + IL(t){rQ(t) + [1—p(t)jJL —M(t)J, (2.6)where i(t) is the current value multiplier.From the optimal control theor9, the solution to (2.6) is characterized by the followingnecessary conditions:= M(t)— (t) = 0, (2.7)= pi.(t)— HQ = [p—r](t), (2.8)lim (t)Q(t) = 0, (2.9)t-.Q = rQ(t) ÷ [1 PgGILc— M(t), (2.10)where denotes the derivative of H with respect to k E {M,Q} and u(t)/t is the rate ofchange 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 manufacturingSee Kamien and Schwartz (1981), Part II, Section 2.15expenditure and the transversality condition:= r-p, (2.11)Q(t)= 0, (2.12)M(t)respectively. These two conditions with the intertemporal budget constraint (2.10) govern thedynamics of the economy. The intuition for these conditions is as follows. To smoothmanufacturing 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 thegrowth rate of the marginal utility of manufacturing expenditure () is equal to the opportunitycost of spending’°, (r-p). The intertemporal budget constraint (2.10) then ensures that theincrease in the asset investment does not exceed the income left over from consumptionexpenditure. The transversality condition (2.12) makes sure that the shadow value of assets isequal 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 neededfor clarity.2.2 Firm’s Problem2.2.1 Grain sector: The technology of this sector is time invariant and the marketstructure is perfectly competitive. Thus, every firm in the grain sector earns zero profits andmust 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 returnof r-p.162.2.2 Manufacturing sector:’1 It is possible to improve the technology of this sectorover time. At any moment in time, the newest generation of technology, denoted by j, definesthe state of the art of z production process. With generation j technology employed in industryz 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 [1,0], (2.13)where a(z) is a pure labour requirement component and is time invariant; 4(j) represents atechnology component.Potential competitors race to discover the next generation of technology in every industryby exploiting the existing know-how accumulated in the previous generation of technology. Ifa technological breakthrough has been made for industry z, its state of the art jumps by onegeneration. This breakthrough is represented by a reduction in 4 which evolves according to12:4(j) = [1-n](j—1), 1 > n 0. (2.14)where n is the inventive step’3. In other words, labour productivity in the manufacturing sectoris rising over time. The new technology of each industry z is assumed, for simplicity, to generateknow-how spilover only on the subsequent innovation of its own industry. An exclusiveinfinite-life patent is granted to the inventor who succeeds first in discovering the next generationof 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 theoriginal Taylor model they are industry specific.The interpretation of technological improvement used here is interchangeable with the oneused in Grossman and Helpman (1991a) in which the innovation purpose is to improve productquality instead of cost cutting. Thus, there are many characteristics shared by both models. Inthis paper, these facts will be used in reference to some of the proofs that have already been donein their paper.17Denote the firm which owns the newest generation of technology of industry z as theleader 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 followersets a price equal to its unit cost while the leader charges a price minutely below its competitor’sprice.This solution can be understood by the following reasons. The follower would not seta price higher than its unit cost, a(z)4(j-1), since the leader who has the lowest unit cost canalways undercut the price. Nor would the follower charge a price lower than its unit cost sinceit would incur losses. Thus, the optimal response for the follower is to set the price equal toa(z)(j-l) and earn zero profits. ‘With this price, the leader also would have no incentive to seta price higher than a(z)4(j-l) since its demand and profit would be zero, nor the leader wouldhave any incentive to charge a price discretely below a(z)c(j-l). This is because themanufactured demand is unit elastic and the total revenue is always constant, but the leaderincurs higher total cost.As a result, the leader uses limit pricing to capture the entire market. This limit pricingis 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 differencebetween 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 theaggregate demand X(z) = MJp(j,z):18U(j,z) 1t(J,z)M na(z)4(j—1)M= nM, z e[O,1]. (2.17)p(j,z) a(z)(/-1)Note that these profits are the same for every industry z and are independent of j and willhenceforth be denoted by just Innovation sector: As in Grossman and Helpman (1991a, henceforth G-H), theexisting leaders do not conduct R&D to acquire the technological lead for more than onegeneration’4. To show this, consider a leader firm which succeeds in discovering two inventivesteps over its nearest competitor. It would have a unit cost: a(z)(j+l) = a(z)4(j-l) [1-n]2 andwould 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 conducting 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 thanthe incremental reward of discovering the technology j. Hence, only non-leader firms undertakeR&D to discover the technology j+l since the incremental reward accrued to them is higher thanthat of the leader firm.Potential innovators that are non-leaders can target any product z to discover the nextgeneration of technology. Since profits, as shown in (2.17), are independent of z and theexpected duration of leadership in all z’s is assumed to be equal, all industries are targeted at thesame aggregate degree.A potential innovator, contemplating the discovery of the next generation of technologyin industry z, recognizes that if the innovation succeeds, it will capture the whole market ofindustry z and start to earn a flow of profits associated with industry leadership of z. These profitflows will be reflected in the value of equity 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.19Denote the stock market value of an industry-leading firm as V. The innovators devote anaggregate 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 isassumed to follow Poisson distribution with an average success rate of Idt. The innovatorsfinance the up-front cost of innovation by issuing equities that pay nothing if the R&D effortsfail but pay dividends if the efforts succeed. The market is perfectly competitive; hence, freeentry will guarantee that the stock market value of each firm must equal the expected cost ofmarket 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&Defforts 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 nextgeneration of technology is discovered. Hence, the expected rate of returns on equity stocks,ignoring terms of order (dt)2, is [H + V- 1V]dt/V. The rate of returns is uncertain but the riskis assumed to be statistically independent. Therefore, stock market arbitraging will reduce thegap between the expected rate of returns from R&D and the risk free rate of returns (r) until theyare equal’5,orr{n+r.’—vi] (2.18)VBy setting w = 1, V = a, and V= 0. Using these and H = nM, equation (2.18) becomesr (2.19)a,Substituting (2.19) in (2.11), the differential equation for M becomes15 See the discussion on this point in Grossman and Helpman (1991a, page 48) and in Taylor(1993a, footnote 7).20= (2.20)a1This 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 supplyof labour is N = aL + L6. Employment in the manufacturing sector is a(z)4(j)X =a(z)(j)MJp(zj) = [l-n]M16. Employment in the grain sector is ag[aLw/p+g7c] = cth--aL.Lastly, employment in the innovation sector is a1!. Equating the labour supply to totalemployment and rearranging gives:[1—a1]L = [1 —n]M + a/. (2.21)2.3 Steady State EquilibriumThe differential equation (2.20) and the resource constraint (2.21) are two equations inM 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 wifibe identical if preferences are homothetic and 1-n = iD. where . is the common step of qualityladders in their model.The solution to (2.20) and (2.21) also immediately jumps to the steady state as in 0-Hfor 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 keepsincreasing, 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) = oo. This event wouldviolate the transversality condition (2.12).16 This is because p(zj) = a(z)(f-i) and 4(J) = [1-n]Ø(j-1).21To solve for the steady state equilibrium, multiply both sides of (2.20) by a1 and set= 0 for steady state, then solve for a. Substituting the result in (2.21) and rearranging yields:M’ = [1 — a + pa1, (2.22)1A =—p= —-[[1-a]L+pa,]-p, (2.23)a, a,where a 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,[w-a1L, and the profit income, pa17.The steady state R&D intensity in (2.23) may take zero or positive value. The necessaryand sufficient conditions that ensure positive 1A are.1 > a, and L > ! pa, (2.24)n [1-a]The first condition is obtained by rearranging (2.23) to get JA = 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 acorner solution of 1A = 0. Thus 1 > a is the necessary condition’8. To get the second conditionin (2.24), set IA> 0, then rearrange for L using the fact that 1-a is positive.Suppose we interpret that F’ > 0 means the economy is successful taking off toindustrialization and fails when F’ = 0. Then, (2.24) tells us that a closed economy needs severalfactors to succeed in “taking off.” First, it needs a sufficiently productive food sector (low a8)to provide inexpensive food so that people are sated with the minimum need of food and start17 The last term is profit income since kI = 0 implies that r=p and the present value of theequity stocks is V = a1.18 It is necessary to ensure that the capitalists are sated with grain while the workers are noti.e., y, > p1> y. Recall that p = a8, so p= a. By defmition y = M/L+p hence, y, = [1-a]+pa1/L+ = 1+pa,/L. Since 1 > a by (2.24), y, > a = pg. To ensure that pj> y, it is assumedthat a> cx because y,,, = cx.22consuming 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 largeL implies that there are enough people holding equities or the distribution of wealth issufficiently even’9. Third, it needs sufficient labour productivity in innovation (small a,) andfourth, a large inventive step (n) so that there is enough incentive for R&D. Lastly, it requiresa sufficiently low rate of time preferences (p) so that the opportunity cost of capital is low sincer=p.In the case where R&D intensity is positive, the prices of manufacturing goods will bereduced over time. This reduction in prices increases the amount of manufactured products thatthe capitalists consume, thereby raising their utilities. This growth rate of utility can becalculated as follows.Substitute X(z,t) = MJp(zj) and p(zj) = a(z)4(O)[l-n] into the bottom part of (2.3) toderivelnU(t) = luG + InM - flna(z)4(O)dz- E{In[1 -nf }, (2.25)where E, is the expectation at time t conditional on current information. Let Pr(j,t) be theprobability that process technology of a given product will improvej step in a time interval t andeach industry follows the same Poisson process with a mean of arrival equal to tI. Then, theutility growth rate of the capitalist can be calculated once the expected value of the technologicalimprovement has been determined. Summing over all possible probabilities off, we have19 These first and second factors are the same as in M-S-V. The differences are that, in thispaper, once the growth process has started, it can be sustained forever instead of a once offphenomenon.23E{ In[1—nI } = Prq,t) in[1—n] = tI In[1—n]. (2.26)Substitute (2.26) into (2.25) to getlnU(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 utilitypA= q(n)IA= q(n)—- [1—01 L — [1—n] p (2.28)a1where q(n) -ln{1-n] > 0. The last equality is obtained by substituting the value of aggregateinnovation intensity from (2.23).The growth rate in this paper shares many common characteristics to those of itspredecessor endogenous-growth models. From (2.28), the growth rate is faster the larger theinventive step (larger n), the greater the labour productivity in innovation (smaller a1), and themore patient the consumers (smaller p). Nonetheless, some results that are not present in thepredecessor endogenous-growth models are worth noting.Before moving on to those results, it is helpful to calculate the welfare representations ofthe worker and the capitalist. Use (2.27) and the fact that lnU(t) = ctLw/ag in (2.1) and integratethe right hand sides to get— I Ap W = mG + InM- fIn[a(z)(O)]dz + (2.29)PT’w = lnaL - 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’ welfare24exhibits no growth. This is true for two reasons. First, by the hierarchical preferences, workersdo not substitute grain for manufacturing goods when their prices are reduced by the newtechnologies. Workers, who are not yet sated with grain, consume only grain whose price isfixed2° by the technology (p=ag). Second, the division of labour among sectors and the realwage of workers remain unchanged though the prices of manufacturing goods keep declining byR&D. These result from the assumption that the demand for manufacturing goods has unitaryprice elasticity. A reduction in price will be matched by the same proportional increase indemand. Therefore, technological progress of the manufacturing sector does not draw morelabour away from the grain sector. The demand for grain is also constant since the capitalistsare already sated with grain. Thus, the amount of labour employed in the grain sector stays thesame and so does the real wage in terms of grain. In summary, technological progress of themanufacturing sector improves the welfare of the capitalist, but the benefit does not “trickledown” to the worker when the worker is too poor21. Furthermore, the change in the values ofn, a1 and p have no effect on the utility of the worker.Second, an improvement in grain productivity (a reduce in ag) will enhance innovationin the manufacturing sector. This is because an improvement in grain productivity will reducethe price of grain. The capitalists who are already sated with grain will demand the same amountof grain but will pay less. Consequently, more expenditure can be spent on manufactured goodssince [l-a]L is larger. As demand for manufactured goods increases, R&D and the growth rateof the capitalist’s utility are higher.20 Even when the price of grain can vary, workers remain indifferent. See details inChapter ifi.21 This result may be interpreted as a dynamic version of Proposition 2 in Eswaran andKotwal (1993). As also mentioned by them, if preferences are not exacting hierarchically in thereal world, the benefits filtered down to workers would, nonetheless be modest as long as themagnitude of substitutability between the two groups of goods were sufficiently low.25Note that a rise in grain productivity strictly improves the welfare of all consumers in theclosed economy. Workers are directly better off by the cheaper price of grain while capitalistsare better off by a once-off increase in consumption of manufactured goods. These two channelsof welfare improvement are shown in E-K. Moreover, the welfare of the capitalists, in thispaper, 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 inpopulation mix will not change the rate of innovation. This paper, however, will show that whenpreferences are hierarchical and workers are not sated with grain, an increase in the number ofcapitalists will increase the rate of innovation.As the condition in (2.24) has shown, an economy needs a sufficiently large L to havea positive R&D intensity. Suppose, we compare two economies which are identical in everyway, except that one has LG lower than the second condition in (2.24) and the other economy hasthe required L. Clearly, the latter economy enjoys a positive growth while the former has nogrowth.For the economy which already has parameters that satisfy the conditions in (2.24), anincrease 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> 0. (1.30)a1By (2.24), when I’ is positive, [1-a] is also positive; thus, the sign of (2.30) is positive and thecountry which has a higher 4, grows faster.Since different mixes of population can affect the growth rate, the immediate policyimplication is whether the redistribution of income that changed the population mix alsoincreased growth rate. The analysis in the next section provides the answer.262.4 Redistribution of income and growthOne of the widely known properties of the homothetic preferences is that a redistributionof income does not affect the aggregate consumption expenditure. Thus, an income redistributioncannot affect the R&D intensity or the utility-growth rate of the endogenous growth models withthe homothetic preferences since these variables depend on the aggregate expenditure. However,the hierarchical preferences used here allow a redistribution of income to change the aggregatemanufacturing expenditure. Therefore, the R&D intensity and the utility-growth rate would beaffected by the redistribution.Note that here the redistribution of income means that a fraction of equity assets ofcapitalists are transferred to workers such that they have sufficient income to consume jand gaintheir labour force from cc to one, due to better nutrition, and therefore become capitalists. Ineffect, this type of redistribution of income is equivalent to an increase in the ratio of capitalists-to-total-population.To get the impact of income redistribution on the growth rate, substitute L0 in (2.28) with1L. Then, differentiating (2.28) with respect to 1 fixing L and rearranging yields= nq(n) {[1-a] -[a—c]}L > 0. (1.31)a1The terms in the first square bracket of the (2.31) represent the impact of the increase in thelabour force of the worker-turn-capitalist from a to 1 due to a better nutrition. The terms in thesecond square bracket capture the effect of the increase in labour demanded in the grain sectorto satisfy the higher demand for grain of the worker-turn-capitalist. The former effect stimulatesR&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 theresult here. If the model only incorporate the hierarchical preferences, the redistribution of27income would have reduced the growth rate since the workers must spend a part of thetransferred income on grain so that they are sated before they start consuming manufacturedgoods. This can be seen by assuming that the labour force of the worker-turn-capitalist stay thesame 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 wouldhave caused the sign of (1.31) to be negative instead. The most striking result probably is thateven with the effect of the hierarchical preferences working against the increase in labourproductivity, 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 logicalquestion 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 capitalistconsumes i and x(z) = {[1-aJ+pa/L}/p(z) and enjoys the same growth rate as that of thecapitalist’s group, while each worker consumes only g=alag. The welfare of each person in eachgroup can be written similar to (2.29) as1 Ap w 1n + 111m - f1iazi0Idz + (2.29a)0PW = IIIct - lflL2g•Now differentiating W and W,. in (2.29) and w, and w. in (2.29a) give the impacts on thewelfare:= —1< o, (2.32)8! p[l-!]= o, (2.33)a!288W 1 1 fl17(fl’p— = — ÷ — ÷ ‘‘ ‘ [1-alL > 0, (2.34)81 1 M pa18w pa= -____+‘[1—alL (2.35)81 Ml pa,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 satedwith grain and the price of grain is unchanged (p = ag). The worker-turned-capitalist now enjoysthe benefits of innovation in manufactured goods and the existing capitalists gain a higher growthrate (as shown in (2.34)). Each original capitalist can be better off if the static losses, pa/Mi,are smaller than the dynamic gains, nq(n){l-aJL/a1as shown in (2.35). The static losses measurea once-off reduction in the income of the existing capitalists used by income redistribution. Thedynamic gains measure the increase in the growth rate of utility stimulated by a greater level ofaggregate consumption from the worker-turn-capitalist. With some rearranging, (2.35) becomesnM- p2a,81 a, q(n)[1-o]LInM p2a,-p+pa, q(n)[l-a]LI+pa l n1-a1L+ ‘ 0, where = ‘1’. Il. .1 (2.36)[ [1—aJL pMand is the second-best optimal level of R&D intensity. The value of l is obtained bymaximizing 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 andare non-negative; thus, the sign of (2.36) is also non-negative. In other words, the existinga1 qQi)29capitalist will always be better off by a redistribution of income. The following propositionrecaps the result.Proposition 1: In a closed economy, a redistribution of income from capitalists to workerssuch that they become capitalists(i) raises the rate of innovation,(ii) increases the welfare of the existing capitalist while the remaining workers areindifferent.3. Free Trade ModelThe preceding section has answered some questions pertaining to industrialization,redistribution of income, growth, and welfare for the closed economy. Although they areimportant, the answers will not be complete without considering the case of an open economysince 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 developedcountry (North) and a developing country (South). It is found that a redistribution of incomefrom Southern capitalists to its workers increases the growth rate as in autarky, however, itsimpacts on the consumer welfare depend on the trade patterns of grain. The gains from tradewill not filter down to the Southern workers unless the South imports all of its grain from theNorth. Furthermore, the workers will remain un-sated with grain and experience no utilitygrowth unless the imported grain is sufficiently inexpensive. The productivity improvement inthe grain sector stimulates R&D and growth in all cases, unless both countries produce grain andthe North is the net exporter of grain. The change in population mix may improve the South’sbalance of trade, and affect the growth rate.Consider a world economy consisting of two countries: North and South. The North30represents the developed countries while the South represents the developing countries. Denotethe South variables as before and the North variables by the superscript “*“• Consumers in bothcountries have identical preferences, but the population sizes are not necessarily the same. Asnormally observed, the income distribution is quite skewed in developing countries, but it is moreevenly distributed in developed countries; thus it is assumed that the South’s population consistsof capitalists and workers while all the Northern population is capitalist. Again, it is assumedthat, before trade, Southern workers are not sated with grain, but all capitalists are.3.1 Trade PatternsEach country is efficient in producing certain kinds of products depending on the relativelabour productivity of the products and the equilibrium relative wage. Define the equilibriumrelative wage rate between the North and the South as Co w/w and retain the normalizationw=l. If Co is treated as given for the time being, the trade patterns (with no trade barriers andtransportation costs) can be determined as follows.3.1.1 Grain sector: Defme the relative grain productivity of the two countries as 0ar/ag and for simplicity let 0 = 1 (a = ar). In other words, no one has an absolute advantagein the grain production22. Then three possible trade outcomes can occur. If o <0, the Southhas a lower production cost of grain (wag < wa) and it will export grain. Conversely, if co>0, the North will export grain. Finally, if o = 0 both countries may import or export grain sincethey are equally efficient.Assuming that either of them has absolute advantage in grain production does not changethe conclusions made in this paper, as long as ‘y < 0 <a7cc.313.1.2 Manufacturing sector: The trade pattern for this sector can be determined similarlyto the case of grain. At time t=0, let each country have its own pure unit labour requirementschedule, a(z), and its own patents on the technologies 4(j), for z E [0,1]. The generation oftechnology j for each industry may be different between countries, however, there is only oneset of most advanced technology (j) for the whole world. It is assumed that the South own aportion 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 technologydomestically or become “multinational corporations” and apply the technology abroad. Thisassumption implies that cp(j) is the same for both countries and a relative labour productivity inmanufactured goods can be defined as:A(z) a*(z)4(j,t=0) a*(z) z e [0,1]. (3.1)a(z)(j,t=0) a(z)Following the static Ricardian model by Dornbusch, Fischer and Samuelson (1977), z is indexedin the order of declining comparative advantage of the South. Therefore, A(z) is continuous anddecreasing in z. For a given relative wage rate, the South will export any manufactured productz 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 forwhich the labour costs are cheaper or wlw* a(z)/a(z). Hence, by the continuity of A(z) theremust exist the competitive margin () such that the North-South relative wage equates A(!):A(f). (3.2)a()If o is known, can be solved from (3.2) and world production of manufactured goods wifi bedivided into two sets. The South has a comparative advantage in z E [0,] and the North has acomparative advantage in z E [2,1].323.1.3 Innovation sector: The North is assumed to have an absolute advantage inconducting R&D. Specifically, I assume23 that a = ya1, where 0 <y < 1, i.e., the North’s unitlabour requirement for R&D is strictly smaller than the South’s. By similar reasoning used inthe case of grain, there are three possible trade outcomes depending on the values of co andThe North is the sole producer of R&D when (0 > , all R&D is undertaken by the South when0) <y and both countries conduct R&D when co =Since it is rare for developing countries to undertake all innovation activities, y will beassumed to be sufficiently small such that for all values of 0) considered in the model, Wa1 > wa1and 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 someof the next generation of their technologies domestically to serve world demand for products forwhich they have comparative advantage. For products for which the South has comparativeadvantage, the Northern firms become multinational corporations and license or “trade thetechnology with their Southern subsidiaries in return for royalty payments. This is because it ismore profitable to implement the most advanced technology (j) in the country which has thelowest 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, theprofit margin will be given byp(zj)-a(zj) = na(z)4(j-l) as derived in (2.16). Thus, the aggregateprofit for this choice will be H(zj) = na(z)Ø(j-1)WMIp(z,j) = nWM. Alternatively, if the nextgeneration 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 choiceThis 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 simplifythe balance of payments schedule that will be derived later.33will be IT(zj) = { 1 - wA(z)[l-n] }WM. Taking the difference between these two alternativesshows that H(zJ) - lT(zj = [wa(z)-a(z)] [1-njWM/a(z). It is positive since wa(z) > a(z) for ze [0,2]. Therefore, it is more profitable to apply the most advanced technology in the South forindustry z E [0,2].For products z E [2,1], if the next generation of technology is applied in the North, theprofit 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, theprofit margin will be p(zj)-a(zj) = wa(z)(j-1)-a(z)4(j-1)[1-nj = wa(zj){ 1-[1-n]O)/A(z)}. Theaggregate profit for this choice will be H(zj)= { 1 - [1-n]wIA(z) }WM. Taking the differencebetween these two alternatives shows that H*(zj) - H(zj) = [a(z)-wa(z)][1-n]WM/[wa(z)j. Itis positive since a(z) > w*a*(z) for z E [2,1]. Hence, it is more profitable to apply the mostadvanced technology in the North for industry z E [2,1].The Northern firms fund their R&D by issuing equity claims which must provide thesame rate of returns as the risk free portfolio of equities. From equation (2.19) of the autarkymodel, we know that r = H/V - I = nMJwa, - I, where M represents the market size for theclosed economy. By the same analogy, we haven[McfM*]—1* =____— 1*.Wa1 Wa1Notice that the term nWM is the aggregate profit, where WM M, + M is the worldmanufacturing expenditure consisting of both countries’ expenditure since each z is sold in bothcountries.3.2 ConsumersOn the demand side, let us start with the determination of who will be sated with grainafter trade. The proof below will show that if capitalists are sated with grain in autarky, they34also will be sated with grain after trade. Southern workers who are not sated with grain inautarky, 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 are satedwith grain in autarky, w4 > wAaj or 1 > agg. Multiply both sides of this last inequality with w’to get WF> waj. But p” wFag when the South exports grain. Hence, the Southern wage isalways greater than the expense for Iwhenever it exports grain. If the South, however, importsgrain, the import price of grain must be cheaper than wag. Thus, Southern capitalists also mustbe able to buy Iwith their post-trade wage income. Therefore, capitalists are always sated withgrain after trade.Note that if Southern workers are not sated with grain in autarky, wAaj> ctwA. This canbe rearranged to read: agict = a/ct> 1. The inequality implies that a/ct> 9 since 9 = 1. Then,if w a/ct, w must be greater than 0 and the South must import grain atp = wa. But w a/ctimplies that ctw wai = p i.e., the wage income of Southern workers is sufficient toconsume br they are sated with grain. Conversely, when (3 <w < a/ct, the South still importsgrain but workers are not sated. Lastly, if the South exports grain (o < 9), pF pA = ag.Therefore, workers will remain unsated after trade since ct <Given these facts, only capitalists will demand for X(z) when 0) < a/cr., but all consumerswill demand for X(z) if o> a/ct. Hence, the South’s consumer-optimization condition when itsworkers are not sated with grain after trade remains the same as in the autarky model. For theNorth, all consumers are capitalists; thus they are always sated with grain by the argument givenabove. So the North’s consumer-optimization condition is similar to that of the Southerncapitalist. Therefore, in place of equation (2.11), we have the following differential equations:35iç = r—p, = (3.4)If, however, the South’s worker is sated with grain after trade (when o a/ce), the term Iv willbe replaced by M where M M + M and WM will become M + M.3.3 Trade EquilibriumWith the information given in the previous sections, we are ready to describe the tradeequilibrium 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 > 0)); and Southern workers are unsated with grain(since 0) < a/CL).With this trade and consumption patterns in mind, the labour market clearing conditionscan be written as:N = l1—n]WM ÷ aL÷a[L÷L], (3.5)L* [1—][1—n]WM + (3.6)w*where N = aL+L. The left hand side of each condition is the labour supply. The first term onthe right hand side of each condition is the labour demanded by each country’s manufacturingsector. 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 Southproduces z E [0,2] for the world market represented by WM = M-i-M. The corresponding termfor the North is calculated similarly by the fact that the North produces z€ [2,1]. The termsccL+a[L+L] measure the employment in the South’s grain sector since the South is the soleproducer of grain. Similarly, aP measures the labour demanded in the North’s R&D sector36because the North conducts all R&D.To close the model, we must ensure that the balance of payments holds. This requiresthatJJ* +aL-[l-z9M = fn[M÷M*] _Apaw*. (3.7)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 theSouthern import value of manufactured goods. Terms on the right hand side of (3.7) depict theSouth’s service account which measures a net outflow of service payments abroad. The termzn[M+M] represents royalty payments of subsidiaries in the South to their Northern parent firmsand paw quantifies Southern shares of the world profit income.Recall from (3.4) that ?v = r-p and lvi’ =-p. Then applying the assumption ofperfect-international-capital mobility, we have r = r. Therefore, r’ can be substituted from (3.3)into (3.4) to obtain:flWM_JF_, (3.8)C* *w a1nWM_JF, (3.9)wMultiply both sides of (3.8) and (3.9) with w*a and add them up to get:wa[1’f +1 3 102= nWM — w*a[IF+p],Now summing (3.5) and (3.6) yields the world resource constraint: L+w’L’-a[L-i-L’] = [l-n]WM+ war. The differential equation (3.10) and this world resource constraint characterize thesteady 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 similar37reasons given in the autarky modeP. The solution of the steady-state equilibrium is obtainedby setting [A+M9= 0.To solve for the solution, using r = r in (3.4) yields fv =Af. Since [k-i-M]= 0, r rp. Next solving the world resource constraint for waF and substituting it into (3.10) yieldsw*a,*[1If +*1112= {wM — + pa;]— L + (3. )Then setting [l’4÷M} = 0 for the steady state gives the world manufacturing expenditure:WM = w*[L* + pa1] + L — a[L+L*]. (3.12)Now rearrange (3.7) to obtain: M = aL + pw* + {1-n]WM and substitute [1-n]WM =[1-ajL-aL from (3.5) to getM= [1—a]L + Xpaw. (3.13)Deducting M from WM in (3.12) then givesM*F = [w _a]L* + [1_AJpaw*. (3.14)Both manufacturing expenditures of the North’s consumers and the South’s capitalists consist ofincome 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 obtain1F = {Lc_o[Lc+L*]+w*[L*+pa;]}—p. (3.15)w a1To show this, replace the terms M with M+M, ?i with A-fM, and equation (2.21) withthe 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 steady-state rate of returns. Recall that Southern capitalists are assumed to own of the world’s mostadvanced technology and Northern consumers own the remaining [1-j share.38Finally, solve for WM from (3.5), then substitute the result in (3.12) and rearrange for l/wto gef:1 = z11—n L + pa; (3.16)l-z[1-n] L-a[L÷L]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 thecombinations of 0 and that maintain the balance of payments. This equation describes segmentAB of the BP(2) schedule corresponding to 2 E [z1,J in Figure 2.1. The values of z1 and z2 aregiven in Appendix 2.Note that the value A. plays no role in (3.16); i.e., the BP(2) schedule is independent ofthe distribution of asset ownership across countries. This is because all owners of theinternational assets have identical quasi-homothetic preferences. As a result, a change in thedistribution of assets among them at the steady state leaves the world expenditure unchanged, andthe world equilibrium unaltered.Appendix 3 shows that this segment of the BP(!) has a positive slope which can beunderstood 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 ofpayments, 0) must increase so that net imports would rise and reduce the initial surplus in theSouth’s current account. Therefore, the BP(!) schedule slopes upward.Combining 0 = BP(2), 2 E [z1,2] with = A(!) determines the steady state equilibriumof and w, and starts the motion of the dynamic evolution of the world economy as shown inFigure 2.2. The A(z) schedule gradually rotates around the steady-state equilibrium as shown inFor a positive value of o in (2.16), it is assumed that L > a[L-i-L9.39Figure 2.1Balance of Payments ScheduleCt)BP(z)(Tnx):Eaa. :DB S C97....I z0 zs40Figure 2.2Steady State Equilibrium0)A(z;t>O) BP(z)Ct)A(z;t=O)A(z;t>O)z0—z41the figure because the next generation of technology for z E [O,] is applied only in the Southand technology for z E [!,1] is applied only in the North. As the A() schedule rotates,nonetheless, the North-South relative wage, the geographic specialization pattern of worldproduction, and R&D are left undisturbed. The balance of payments is also maintained inequilibrium. Then successful innovations improve the technologies in the manufacturing sectorand propel growth. The dynamic evolution of the world economy of the cases presented belowalso follows the same characteristic just described so it will not be repeated for the followingcases.3.3.2 co = 0: The parameters in this case indicate that both countries diversify their fmalgood production (grain and manufactured goods) and they are equally efficient at grain. TheSouth’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 = w = 1since 0 = 1. Tn place of the differential equations (3.8) and (3.9), we have= nWM— 1F— P, (3.17)a,= nWM- 1F—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. Itwill be shown below that BC is flat i.e., when co = 0, the balance of payments can be maintainedby a set of E [z2,3]. Appendix 2 shows that the end points are given by z2 = {L0 -a[L÷L] }/‘y,and z3 = {aL + L}/w, where N’ = [1-n] {[1-a][L+L]+pa). Since ciL+L > L-a[L,-i-L], z3>These characteristics of the steady state are first given in Taylor (1993), page 225.42z2 and the set [z2,3] is not empty.Three trade outcomes may result depending on where the A(z) schedule intersects thissegment of BP() schedule. If the intersection point is exactly at point 5, trade in grain is zeroor both countries are self sufficient in grain by producing the exact amount of grain needed fordomestic consumption. If the intersection is in the range between B and S, the South will be thenet exporter of grain. Conversely, if the intersection is in the range between S and C, the Southwill be the net importer of grain. The following sub-sections provide the solution for each caserespectively.3.3.2.(a) Self sufficiency in grain: Note that all capitalists are sated with grain while theSouth’s workers remain unsated. Hence the corresponding resource constraints when bothcountries are self sufficient in grain are:N= z3[1 -n] WM + aL + aLe, (320)L*= O[1—zJ[1—n]WM + + ar*P.where z denotes the competitive margin that causes both countries to be self sufficient in grainas 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. yieldsa[?vfE ÷ME*] 321__________= WM-[1-o][L + L*] - pa.Again, the steady-state solution requires that [?v-i-M] = 0. Set the left hand side of (3.21) equalto zero for the steady state and solve to obtainWM = [1— a][L ÷L*] + pa1. (3.22)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 as43M= [1—a]L ÷ M*F = [1.a]L* ÷ [1—]pa. (3.23)Substituting WM from (3.22) into I” = nWMIa-p as in section 3.3.1. yields1F= —{[1_a][L÷L*]}— [1—n]p. (3.24)a1Finally, the solution of z can be calculated by equating WM = {[l-a]L}/{[l-n]z,}, from theSouth’s resource constraint, to the right hand side of (3.22) and rearranging:z[1k,where ‘P = [1_n]{[1_a]{L÷L*]+ pa}. (3.25)3.3.2.(b) The South is the net exporter of grain: This case corresponds to the solutionwhen A(z) intersects BP(!) between B and S in Figure 2.1. The South’s workers remain unsatedwith grain while all capitalists are sated. Both countries produce grain, but the North importsa fraction s of its grain consumption from the South. This fraction wifi be later called theSouth’s export share of grain. The resource constraints for this case are:N [1 —ii] WM + ccL + a[L +sL *1, (326)L*= O[1—f][1—n]WM ÷ [1_s]a*L* ÷ a,IF.Setting 0 = 1, a a, and combining the two resource constraints with (3.19) as before yield thesolution of WM which is exactly the same as shown in (3.22). For a given schedule A(z), 2 isdetermined entirely by A(2) = o = 1; i.e., 2 =A1(o=1). Thus, the solution for s can be explicitlyexpressed as[1—a]L — z —S =____________= , E [;,z8]. (3.27)GL* Z-Z2The first expression is obtained by equating WM= { [1 -aJL - saLe }/{ [1-n)!), from the South’sresource constraint, to the right hand side of (3.22) and solving for s. The second expression isobtained by using the definition z in (3.25) and the fact that z, - z2 = aL7’{’. The numerator of44s 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 ofsegment 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 iszero. If they intersect at B, !=z2 and s=l; the North imports all of its grain from the South. Anyintersection point between B and S gives s E (0,1).Now we are ready to explain why the BP() schedule for co = e is fiat. The balance-of-payments condition for this case is M*- [1-JM + saLe = nWM - pa. Start from point B andincrease . We can see that a current-account surplus generated by an increase in ! can becompletely offset by a reduction in s without adjusting co to maintain the balance of payment asneeded in section 3.3.1. This process of adjustment continues until s—() where the economyarrives at point S in the figure.Using the balance-of-payments condition given above with (3.26) and (3.22) also yieldsthe same solutions of M and M as given in (3.23). The solution for the R&D intensity (?) isalso 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 solutionwhen A(z) intersects BP(!) between S and C in Figure 2.1. Recall that all capitalists are satedwith 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 resourceconstraints for this case can be written as:N = zll —n]WM + [1 _s*][aLw + aLe], (3 28)V = O[1 -][1 —n]WM + ÷ s*[OaL ÷ a*L] +Again, setting a = a’, 9 = 1, and combining the two resource constraints with (3.19) yields theexact solution of WM given in (3.22). Hence, its solution of R&D intensity (P) is also the sameas shown in (3.24). Moreover, the solutions for M and M can be calculated as in section453.3.2.(a) by using the balance-of-payments condition (given below), (3.28) and (3.22). They areagain the same as given in (3.23).To get the expression for s, equating WM = {N - [ls*][c,Lw+aLc]}/{[1nJ!}, from theSouth’s resource constraint, to the right hand side of (3.22) yields*— [1—o]L—z -s =_____________= , z e [z,z3] (3.29)aL+oL z3-;where the second equation is obtained by using the definition z, and the fact that z3 - 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=z3 and s=1; the Southimports all of its grain from the North. Any intersection point between S and C gives? E (0,1).The balance-of-payments condition for this case is = 2nWM-&pa.The BP(2) schedule for the range between S and C is also flat by the similar reason given insection 3.3.2.(b). The balance of payments can be maintained without adjusting o by an increasein s when 2 increases beyond z,. The process of increase in 2 without an upward pressure on 0)continues until s=1 and 2 = z3. Then a further increase in 2 will eventually cause a surplus inthe South’s current account and cause the BP(2) schedule to slope upward again (see nextsection).3.3.3 okx> w> 0: The BP(!) schedule corresponding to this case is given by segmentCD in Figure 2.1 and the boundary of this case is marked by 2 E [z3,4] (see Appendix 2). Theparameters for this case indicate that the North exports grain and the Southern workers are notsated with grain after trade. The North also exports R&D since 0 > y by assumption. Thus, therate 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:46N = z11—n]T4M, (3.30)L* [l_z1[1_n]WM÷1CLy+a[L+L*]+a*JF (3.31)w* w*The balance-of-payments condition for this case also must reflect the fact that the North exportsgrain. It can be written asf*_[1_Z9Mc_[OLw÷W*GLc] = n[M+M*] _Apaw*. (3.32)Combining differential equation (3.10) with the new labour market clearing conditions asbefore and setting [Iv÷MJ = 0 givesWM = w*{L* ÷ pa, - L7[Lc±L*]j + L. (3.33)The derivation of the remaining solution is analogous to that in section 3.3.1., so it willbe 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). Subtractingthe 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 [1_W*a]Lc + )ptZ1W, (334)M*F = w*{[1_a]L* += ‘ {[L + w*[L* — — [1—n]p, (3.35)wV + pa; — aL+L*] (336= zll-nlN - z11-n]LThe right hand side of (3.36) represents the BP(2) schedule for this case. It is depicted bysegment CD in Figure 2.1. Appendix 3 shows that the slope of this segment of BP() is positive.47Combining (3.36) with 0 = A(), then gives the equilibrium o and , for E [z3,4].3.3.4 o > a/a: The BP(2) schedule corresponding to this case is depicted by segment DEin Figure 2.1. The boundary of this case is marked by ! E [z4,1]29. The trade pattern in thiscase is the same as in section 3.3.3. However, the Southern workers are sated with grain andeach of them now has one unit of effective labour productivity. The labour market clearingconditions become:L = I1—n]WM, (3.37)L* [1 —fJ[1—n]WM + a[L ÷L*] + aIF. (3.38)The balance-of-payments condition for this case must also reflect the fact that the South’sworkers are sated with grain. It can be written asfM _[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. Thesolution is given as followsMF’ [1_w*a]L + )pa;w, (3.40)M*F = w*[[1_o]L*÷ [1—.]pai],1F = ‘ {L + w*[L* — a[L+L*]]}— [1—nIp, (3.41)w— 41 -ii] + pa; — oL ÷L*] (3.42)1-41-n] Lwhere the right hand side of (3.42) depicts the last segment of the BP() schedule. The slope of29 Appendix 2 provides the value of z4 and shows that the endpoint of segment CD and thebeginning point of segment DE are the same.48segment DE is also positive (see Appendix 3) and is steeper than the slope of segment CD (seeAppendix 4). The schedule reaches its maximum value co(max) at = 1 with the Southspecializing in all manufactured production and the North specializing in R&D and grain (thevalue of co(max) is given in Appendix 2).Given the solution of R&D intensity in each case, the utility growth rate can be calculatedas in the autarky model. Substituting the appropriate aggregate R&D intensity in f3F = q()JFgives the utility growth rate of the consumers who are sated with grain. Under free trade, theirutility 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) scheduleintersects the last segment of the BP(2) schedule. However, if the A(z) schedule intersects othersegments of the BP() schedule, Southern workers are not sated with grain, and will thereforeexperience no utility growth as in the autarky case.The welfare of consumers can also be calculated similarly to the autarky case. They canbe written asp W = InjL + frJF - ‘lnp Fcz,O) + q(ii)1FpW = 1ncL - Inp, (3.43)p W = lnjL* + - flnpF(zo)o,z+ q(1j)JFwhere pF(zO) is a(zj=O) 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 toinvestigate the effects of the redistribution of income and other exogenous factors.494. Redistribution of income under free tradeIn the autarky model, we have seen that a redistribution of income from capitalists tosome workers enhances R&D and improves the welfare of capitalists when preferences arehierarchical and workers suffer from malnutrition problems. This section will show that undera free trade situation the redistribution of income may still enhance R&D. However, the welfareresults 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 shareof 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 theremaining workers indifferent.Proof: See Appendix 5.1 for part (i) to (iii). The proof for part (iv) can be shown bydifferentiating W, and W in (3.43) with respect to 1:=+ [1-o]L + iui(n)[l-a]L> (4.1)81 1 M papaw*= nq(n)[1-ci]L> . (4.2)p1Since the redistribution of income also changes the number of capitalists, we need to calculatethe effect on the welfare of individual Southern capitalists and workers. The welfare of eachindividual in each group is50pw Inj+-fjpF(z,o)c1z + q()JF (43)pW = Iiicc—IflL2g (4.4)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 that8W = — ).pa + n(n)[1_0], (4.5)8! Ml pa;= o (4.6)81The individual capitalist will be better off if the dynamic gains, nq(n)[l-aJLJpa, are greater thanthe static losses, pa/M. With some rearrangement, (4.5) becomes:)4(n)[1_cT]LJnM’ — p2a81 pM q(n)[1-a]Lcç1F nM’— 1A + 1A - p2a, whereü’= Aq(n)[1-a]Lq(n)[1-u]L pMn[1-Ay][1-a]L A p2a+1 + p —________q(n)[1-a]Ln[1—Ay][1—a]L+ 1A + pa [l—G]Lp1010[lo]L a; q(n)n[1—Ay][l—a]L + 1A + pa; J0 [1—y][1—a]L[la]L a;The results in steps three and five are obtained by using t = n[l-a]LJar[l-n]p, and I” = [1-a]LJa1 -p/q(z) respectively. The sign is positive since 2 and y are less than one, P and I” arepositive by condition (2.24) and the constraint given in Appendix 11]51The intuition for this proposition is as follows. Part (i) is true because co in this case isdetermined entirely by the value of 8 on which the change in income redistribution has noimpact. 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 theSouth’s imports and in turn generates a current account deficit. To maintain the balance ofpayments, an increase in the South’s net exports is required. When the South is the net exporterof grain, the balance of payments is maintained by an increase in the South’s share of grainexports (s). Recall that s is the fraction of the North’s consumption of grain that is exportedfrom 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 capitaliststo the economy, thereby raising the demand for manufactured goods and the expected profits ofsuccessful 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 theredistribution of income in the South. The welfare of the South’s capitalists as a group isdefinitely higher by two factors. The first factor is the increase in consumption of the worker-turned-capitalist measured by the first two terms in (4.1). The second factor is the welfareimprovement 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 workerwhile they enjoy the same dynamic gains of a higher growth rate. The static losses and thedynamic gains are depicted, respectively, by pa/M1 and nq(n)[1-alLlpa in (4.5). As in theautarky model, the dynamic gains are larger than the static losses. In other words, each existingcapitalist will always be better off. The workers are indifferent because they consume only grainand the price of grain does not change.We can see that the welfare impact of the South’s population when both countries producegrain is quite the same as in autarky. This is because co and are fixed. However, when eithercountry is the sole producer of grain, the redistribution of income will change the equilibrium52w and .Consider first the case when the South is the sole producer of grain. In this case, theredistribution of income has a similar effect to an increase in population of the Southerncapitalists30 (Lj. It raises the net import of manufacturing goods and generates a deficit on theSouthern current account. This shifts segment AB of the BP() schedule to the right. With adownward 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 higherincome means a higher demand for manufactured goods which in turn raises the expected profitof the successful R&D. Thus, the redistribution of income stimulates R&D and increases theutility growth rate.Again, the redistribution of income has no effect on the rest of the South’s workersbecause they consume only grain and the price of grain does not change. Recall that when theSouth is the sole producer of grain, the world price of grain in terms of the Southern wage is thesame as that of the South’s autarky.Its impact on the welfare of those who are sated with grain is now more complicated bythe fact that the relative wage and the competitive margin also change. When the South is thesole 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 equityincome of the North and in turn improves the North’s welfare. Second, the higher Northern wagerate 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 moremanufactured goods. This stimulates the innovation activities and raises the North’s utilitygrowth rate. The higher growth rate then increases the welfare. Although the effect through the30 The redistribution of income also decreases the numbers of Southern workers (L,j. Butnotice that does not appear in both (3.15) and (3.16). Hence, the change in L does not haveany effect on co, , 1F and 3.53second channel is negative, Appendix 5.2 shows that the net effect of the first and secondchannels is positive. Therefore, the overall effects are positive. So the North’s welfare isimproved by the South’s redistribution of income.The welfare of the existing Southern capitalists as a group is also affected by theredistribution of income via similar channels. First, it increases the Northern wage rate whichraises the equity income of the South (since the South’s capitalists own 2 of the dividends). Thisin turn improves the welfare of the South’s capitalists. Second, the imported goods from theNorth are more expensive due to the higher Northern wage; this reduces the welfare of theSouth’s capitalists. Third, the redistribution of income stimulates the innovation activities andraises the utility growth rate which increases welfare. Unlike the previous case, the net effectof the first and second channels is ambiguous (see Appendix 5.2). Thus, the overall impact ofredistribution 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 soleproducer 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). Aredistribution of income affects both the numerator and denominator simultaneously. Its effecton the remaining variables is, therefore, ambiguous.5. Comparative Steady-state AnalysesWith the free trade model, we can investigate how the change in some importanteconomic parameters affect the equilibrium relative wage, the trade pattern of each country, andgrowth.545.1 Changes in productivity of the manufacturing sectorTaylor (1993) has shown that a proportionate productivity improvement in allmanufactured products in the home country increases the home country ‘s relative wage and therange of manufactured products for which home country has comparative advantage (or thecompetitive margin). The model here inherits the same result (except when the change in themanufacturing productivity occurs in the region where both countries produce grain, the relativerate and the competitive margin remain constant). What we can learn more from here is howthe same productivity change affects both the trade pattern of grain in the South and the South’sworkers.To see this, consider a proportionate productivity improvement in all manufacturedproducts in the South which decreases the a(z) schedule and shifts the A(z) upward. Thisproductivity change has no effect on the BP() schedule so it stays 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 productivitychange 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 fromtrade when the A(z) schedule intersects segments AB and BC of the BP() schedule. This isbecause 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 Southernworkers 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 theNorth has comparative advantage; second, the gains from future reductions in prices ofmanufactured goods caused by innovation which is enhanced by free trade.55Figure 2.3Effects of the Change in Relative Labour Productivity in Manufacturing Goods0) BP(z)EA(z)3S C9 :-y :I z0 z3 1565.2 Changes in productivity of the R&D sectorThe 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. Whatis less known is how these changes affect the trade flows in the grain sector. The followingproposition will show that these changes in the incentive for the Northern R&D stimulate theSouth’s grain exports. Thus, policies initiated by the North to help its own R&D sector canindirectly help the South’s grain sector.Proposition 3: When both countries produce grain, a drop in the unit labour requirement forR&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 unitlabour requirement of R&D reduces the cost of R&D activities while the increase in the inventivestep raises the expected profits of the successful R&D. Hence, both changes stimulate R&D31.Since the North is the sole producer of R&D, the increase in R&D activities draws labour fromits other sectors, including grain. Thus, while the North’s R&D sector expands, its grain sectorshrinks. If the North is the net importer of grain, it needs to import more grain. Therefore, theSouth’s grain exports must increase. Conversely, if the North is the net exporter of grain, it canexport less grain.31 See also 0-H and Taylor.575.3 Changes in productivity of the grain sectorThe results of changes in grain productivity depend on which country produces grain inthe 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 wifishow 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-productivityimprovement in both countries stimulates the rate of innovation of the North.Proposition 4: When both countries produce grain, a grain-productivity improvement in theSouth(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 Co, but increases ,(iv) decreases I and 13.An equiproportionate grain-productivity improvement in both countries(v) has no effect on o or ;(vi) 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 ag)increases the value of 8 = alag which is the only determinant of the relative wage (o) for thiscase. 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, it58reduces the price of grain and the expenditure for § As the leftover income from grainexpenditure rises, the demand for manufactured goods increases. A larger demand formanufactured goods means a larger expected profit for the successful innovation. Hence, theR&D intensity increases. Second, the grain productivity improvement raises w. Thus, the Northwage rate (w* = 1/co) is reduced. This in turn lowers the cost of R&D. Both effects reinforceeach other, thus, R&D increases. The utility growth rate (f3), therefore, increases since it ispositively 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, theSouth’s labour cost is cheaper; so the South gains the marginal manufactured products that it canexport, or ! rises.The effect of the Northern-grain-productivity improvement on R&D, in part (iii), dependson two effects. First, it reduces the price of grain and the expenditure for § As the leftoverincome from grain expenditure rises, the demand for manufactured goods and the expected profitsfor a successful innovation increase. Hence, the R&D intensity increases. Second, the Northern-grain-productivity improvement increases w. This latter effect, however, raises labour costswhich discourage R&D. Nonetheless, R&D must decrease by the following reasons. Since theNorth’s comparative advantage in grain is improved, the North imports less grain when it is thenet importer and exports more when it is the net exporter. In both cases, the North’s grainproduction expands which draws more labour into its grain sector and away from other sectors32.With fewer labour resources, R&D activities fall.The equiproportionate productivity improvement of both countries’ grain sectors leavesthe absolute advantage in grain of the two countries (0) unchanged. So co and are unaltered32 Appendix 5.1 provides proof that employment in the Northern grain sector is increased byits own productivity improvement.59as stated in part (v).Lastly, the equiproportionate improvement in both countries’ grain sectors reduces thegrain price which increases both countries manufacturing expenditures. This increases theexpected profits of the successful innovation. Therefore, it stimulates R&D and increases theutility growth rate.The preceding proposition summarizes the results when both countries produce grain. Thenext two propositions provide the results for the cases where each country is in turn the soleproducer of grain.Proposition 5: When the South is the sole producer of grain, a productivity improvement of theSouth’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-productivityimprovement (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 thegrain price and the expenditure on § Therefore, the leftover income from grain and demand formanufactured goods increase in both countries. Thus, given the original equilibrium , theSouth’s net import value of manufactured goods rises. The royalty payments also increase.Altogether, the South has a net outflow of mone?3. A rise in which causes an increase in theSouth’s net exports is, therefore, required to maintain the balance of payments. Graphically, theThe import value of z e [!,l] increases by [l-JL; the export value of z e [0,2] and grainrise by [l-z9L; and the royalty payments increase by ntL+L9. The net effect is equal to anoutflow of 4l-nhjtL+L9.60productivity improvement shifts segment AB of the BP(!) schedule to the right. With adownward sloping A(!) schedule, the shift causes 0 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 manufacturingexpenditures of both the South and the North rise. With a larger world manufacturingexpenditure, the expected profits of the successful R&D increase. Therefore, I and 13 areenhanced.Proposition 6: When the North is the sole producer of grain, a productivity improvement in theNorth’s grain sector(i) increases the relative wage (co), but decreases the competitive margin (2),(ii) raises the R&D intensity (1) and the utility growth rate (13).Proof: See detail proof in Appendix 5.3.When the North is the sole producer of grain, the Northern-grain-productivityimprovement (a decrease in a;) reverses the effect on the South’s balance of payments describedin Proposition 5. The North’s grain-productivity improvement reduces the grain price and theexpenditure on Iwhich increases both countries’ demand for manufactured goods. This in turnincreases the South’s net export value of manufactured goods and raises the royalty payments tothe North. The cheaper grain price also reduces the value of the South’s grain imports. As aresult, the South has a net current account surplus. A drop in 2 which causes a decrease in theSouth’s net exports is, therefore, required to maintain the balance of payments. Thus, theThe net value of the manufacturing import increases by !WZI- [l-2]wL; the royaltypayments rise by and the grain import value reduces by w’gEL. The net impact isa surplus of ![l-n]wtL+L’].61Northern-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 andutility growth rate by the following reasons. A reduction in a; releases the labour resource fromthe grain sector which can be used for R&D. It also lowers w’ which decreases the R&D’slabour 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 productivityimprovement 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 asshown in Figure 2.4. Consider a small productivity improvement as shown by BP’(!). If therelative productivity of manufactured goods is A’(z), the grain-productivity improvement of theSouth will decrease the relative wage (o), but will raise the competitive margin (i). However,if the relative productivity of manufactured goods is A2(z), the grain-productivity improvementwill reverse the previous result. The relative wage will rise while the competitive margin willfall. Now, if the grain-productivity improvement is sufficiently large as shown by BP”(), theA2(z) will no longer intersect segment BC. The relative wage would fall again while thecompetitive margin would rise again. These changes are depicted by the arrows marked bynumber 2 in Figure 2.4. This relative wage reversal does not occur for A’(z) as shown by thearrows marked by number 1.On the other hand, the productivity improvement of the North’s grain sector shiftssegment CD of the BP(!) schedule to the left and shifts segment BC downward, while leavingsegment AB unchanged as shown in Figure 2.5. First, consider a small grain-productivityimprovement. If the relative productivity of manufactured goods is A’(z), the grain-productivity62Figure 2.4Effects of the Change in the South’s Grain ProductivityC’)Dez02A(z)A(z)B-r —I CISSSABP(z) BP’(z)SBP’(z)63Figure 2.5Effects of the Change in the North’s Grain ProductivityU)BP(z)e0’z02A(z)Az)BP(z)BP(z) /-I,/BA64improvement of the North will decrease the relative wage, but will raise the competitive margin.The grain-productivity improvement will raise the relative wage, but reduce the competitivemargin if the A(z) schedule is A2(z). However, if the productivity improvement is sufficientlylarge as shown by BP”(), the A’(z) schedule will no longer intersect segment BC. The changesof the relative wage and the competitive margin could also reverse. The relative wage wouldfirst fall and then rise, while the competitive margin would first rise and drop later as depictedby the arrows marked number 1 in Figure 2.5.These results have significant policy implications. A policy of one country that improvesits grain productivity may increase or decrease the range of manufactured goods that one countryexports. If it is the sole producer of grain, it will gain the range of manufactured goods itexports. If both countries produces grain in the equilibrium, it will first lose and eventually gainthe range of manufactured goods it exports if the grain-productivity improvement is sufficientlylarge.5.4 Changes in labour endowmentIn the standard Ricardain trade model with the homothetic preferences, if a country’slabour endowment increases, the export levels of goods for which it has comparative advantagewill 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 thelabour force of the South’s capitalist increases the South’s grain exports, an increase in the labourforce of the South’s worker may not always generate the same effect.65Proposition 7: When both counthes produce grain, an increase in population of the South’scapitalists (La)(i) raises the South’s grain-export share (s) when the South is the net exporter of grain,(ii) decreases the North’s grain-export share (s*) when the North is the net exporter ofgrain.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 formanufactured products. Using the balance of payment condition given in section 3.3.2.(b), theincrease in L raises the South’s value of manufacturing imports and the royalty paymentsrepatriated to the North. These cause a current account deficie5.When the South is the net exporter of grain, an increase in the South’s exports is requiredto 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 exported from the South.When the North is the net exporter of grain as stated in part (ii), the increase in L raisesthe value of the South’s grain imports in addition to the increases in the South’s value ofmanufactured imports and the royalty payments mentioned in previous case. Therefore, the Southalso has a current account deficit. A reduction in the North’s export share (s*) which reduces theSouth’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 accountwhen 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 royaltypayments raises by [1-][1-a]. Thus, the South has a current account deficit of [1-a]{1-[1-n]}.66manufactured goods are unchanged since 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 bythe workers, cxL, is totally absorbed by the equal increase in the level of demand for grain,ag[cLLw/ag]. As the current account stays in balance, there is no need for s to change as in thecase when L rises.However, when the South is the net importer of grain, the South’s current account willbe affected. This is because the increase in L raises the South’s import value of grain (itincreases by sea). Consequently, the South has a current account deficit which requires adecrease in grain imports to maintain the balance of payments. Thus, s must fall.6. ConclusionThe main purpose of this paper is to build an endogenous growth model whichincorporates Engel’s law so that it can answer the questions involving North-South trade,redistribution of income, and growth. To accomplish this, the paper combines the hierarchicalpreferences with the dynamic Ricardian trade model.The model shows that the initial distribution of endowment and income is crucial to theoutcome. A closed-economy country where most of the population is poor experiences a low (oreven no) rate of innovation. A redistribution of income enlarges the aggregate consumption andlabour 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 indifferent unlessthey are sated with grain before trade or become sated after trade by cheaper imports of food.Again, the initial distribution of endowment and income influences the trade pattern outcomes.A redistribution of income in a free trade environment also increases the growth rate. Its effecton welfare depends on the trade patterns of grain.67Appendix1. Derivation forThe second best optimal level of R&D intensity is obtained by maximizing the capitalist’swelfare (2.29) subject to the resource constraint (2.21):Max pW = friG. + 1nM - fIn[wa(z)4(O)]dz + q(n)! (A.1)s.t. [1—a1L = [1—n] M + a1!.Solve the constraint to get M = { [1-ajL,-a,I }I[1-nj. Substituting this result in the objectivefunction, problem (A.l) becomes an unconstraint maximization problem. Solving this problemyields36=[1-a]L-0. (A.2)a1 q(n)To ensure that the right hand side of (A.2) is positive, it is assumed that 1 > a and 4> [pa1]/{q(n)[1-a]. Note that if i° is positive, JA is also positive since 1/q(n) > [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 z1 to z4. To solve for z1, setting the lefthand 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 yields:36 Note that the value of (A.2) will be the same as in equation (15) of Grossman andHelpman (1991) if a=O, L=L, and n = 1/A., where A. is the quality step in their paper.68L - a[L +L*]C C (A.4)[1_n][[1_cy][Lc+L*] + pa,]]To solve for the end points z3 and z4, follow the procedure as above. Setting the left handside of (3.36) equal to 0=1 givesaL +Lz3 w C (A.5)[l_n][[1_u][L÷L*] + pa1]Equating (3.36) to a/cc and using the fact that cc increases to one and workers are sated withgrain and N = L when co=a/cc yieldsaL/caz4=*. (A.6)[1 _n][[1 _o]L* + pa, ÷ [1 _oz]Lo/ccJTo prove that the end point of segment CD and the starting point of segment DE of theBP(2) schedule are the same, setting the left hand side of (3.42) equal to a/cc and solving for 2gives the same value as z4.Finally, substituting =l in (3.42) gives the maximum value of the BP(!) schedule:1-n L * + pa; — a [L + L ] (A.7)G)(max) = —___________________n L3. Derivation of the slopes of the BP() scheduleDifferentiating the appropriate equation in the text with respect to 2 gives the slope of thecorresponding BP(!) schedule as followsaBP(z) BP(f) [1-n]E [z ,z2] (A.8)f[1—n][1—[1—n]] 169aBP(z) = BP(z)N> , (A.9)4N-[l-n]Lj3BP(z) BP(z)> 0, f[z ,1j (A.1O)[1-f[1-n]J4. 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 ‘. Using (A.9) and (A.lO), if BPD’B(z4)> BP(z4), we must haveBPDE(z4) BPcD(z,)L (A.11)z4[1 —z4[1 —nJ] z4{L—z[1—n]L]Note that BP(z4)= BPDE(z4) and N = L at 0 = a/(x. Rearrange the above inequality give: z4[l-nIL>z4[l-n]L, which is always true.5. Comparative steady state analyses5.1 Both countries produce grain:(a) Redistribution of income: To get the impacts of the changes specified in part (i) ofProposition 2, note that 0 = 8 and =A1(o=O). Hence, the change in 1 has no effect on them.For part (ii) differentiating (3.27) and (3.29) in the text with respect to 1 yields:== [1—a]L{1 —[1—n]}>ai GL* OL*[aL+aL]{fW1-[1 -a]L}- {‘ -[1 -a]L}[a -alLai [aL÷L]2 (A.12)—— a[1—o]{1—[1—n]}L2+ [a_a]Lz11_n]{[1_aJL*+pa}< 0[aL+aL]2where ‘P1 = [1-n][1-a]L.The proof for part (iii) is obtained by differentiating (3.24) and 13F = q(n)r with respect to 1:7081F= --[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,fl aL (A.14)= aL÷L< 0, where ‘f’- { [1 —a] [L + L*] + pa; }.Next, perform the differentiation with respect to a on the same set of equations to get_____-[l-n]p< oaaOL* OL*(A.15)* ZT * —ri_i= aJ= Z L’ P > 0, where ‘ [1—n] p.xL+L xL÷L a1(c) Changes in grain productivity: For the effect of the changes in grain productivityin Proposition 4, let us define two shift parameters: a for the South and a for the North. Thenredefme the unit labour requirement of the South’s grain sector as aag and that of the North asa*a. A decrease in a (resp. a) evaluated at one, would represent a productivity improvementof the South’s (resp. North’s) grain sector, while a reduction in both a and a at the same ratewould depict an equiproportionate improvement.(c.1) Changes in the South’s grain productivity: The result in Proposition 4 (i) isobtained by differentiating Co = Oa/a with respect to a, and applying Implicit Function Theoremon A(!) - Oa7a = 0. Their derivatives are given by71== -1 < 0,a2 (A.16)A’ A’Note that all derivatives are evaluated at a=a=9=1. With the new definition of the unit labourrequirement, 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’-< 0,oL*= [aLw+aLc][V+To+aLcj — [zT—[1—a]L1aL (A.17)[aLp + L]2= aL [aL÷L][1 -zil —ii]] + aLI1 -n]{ [1 _o]L* +pa1}- [cL+aL] ‘F/A’>[ccL+oL]281 nL— =- —I[1-a]L ÷L = - —S < 0.*1 C Cj *a1 a1Since = q(n)I, f3/aa is also negative.(c.2) Changes in the North’s grain productivity: Similarly, applying the same procedurefor a yields the results for Proposition 4 part (iii) and (iv):= 0 = 1 > 0,(A.18)- =i=_<oA’ A’72- [1_n]{L* + pa;]=— >0,oL*=— [1_n]{L* + pa]—¶1/A’0 (A.19)eEL ÷ aL—f-= —-{[1_aJL aL*} = > 0.a;The sign of the last derivative is positive since it is assumed that L > a{L+L9, otherwise (0 in(3.16) will be negative since f3 = q(n)I, 3/aa is also positive.Next we have to show that the labour employed in the North’s grain sector is increasedby its productivity improvement (a reduction in a). Thus, there are less labour resourcesavailable for the R&D sector which in turn causes I to fall. From (3.26), the labour employedin the North’s grain sector when the North is the net importer of grain is L = [1s]aL* = [1-sja*ag7i Differentiating this with respect to a then evaluating the result at a=1, ag and a=ayieldaL* 1 e3s__!. = o*L*1—s———* 1 [1—o]L—fT 1P/Ac_z1l_n][L*+pa;]= aL1— +( oLd’ oL* (A.20)= aL*—[1—01k+ 4 ¶1_[1_njL*+pa] } + ¶1/A’=— L + oIL + L J + [1 —nj{ [1 —a][L+L 9 + pa; — L * — pa; } + ¶1/A’=— {L — a[L÷L*]} + z1l_n]{L_a[L÷L*J} + ¶1/A’=— {1— z11—n]}{L— a[L ÷L*]} ÷ ‘f/A’ < 0.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 theNorth’s grain sector is L = &L*+s*[OctL+GL]. Differentiating this with respect to a andevaluating the result at d=l and a8=a yield73Ig=+ [aL÷oL] s* + —aa* I* * I ‘F—[1—a]L z11_n][L*÷pa]_V/A (A.21)= aL +[L+aL] -____________( cgL1,+o aL+oL= GL*- [1—a]L+ 4 } + ‘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 grainsector is increased by the North’s grain productivity improvement (a reduction in a*).(c.3) Equiproportionate changes in grain productivity: Denote an equiproportionatechange of a and a by Then, performing similar differentiations with respect to both a andon the same set of equations used for part (i) and (ii) and evaluating a=a*=l give:aL+V1’ + [1-alL -‘_____________________= _[1_fl]O[Lc+L*]pa;]- L= <0aL*= [aL+aLJ[fl.+aLj - [z.V-[l-a]L]aL[aL +aL]2w C (A.22)= [cLL÷aL]aL — [1 —nJ a[[ccL ÷L][L ÷L*] ÷ paL1[4xL + c7L]2>L[cL+L]> [l_n]{[aLw4Lc][Lc+L*] +LpaA}ai =---a[L+LJ < 0.8aa* a;To prove that the sign of as/aaa is negative, assume the contrary to the assertion that itis positive. Then ! must be greater than LJ{ [1-n] [L+L+pa] }. Since z is the highest possiblevalue of! E [z2,zj, z must satisfy this condition as well; i.e.,74[1-ci]L L[1_nJ{[1_a][Lc+L*]+pafl [1_n]{L+L*+paj*} (A.23)[1—o][L÷L ]+[1—a]pa > [1—a][L÷L ]÷pa,.This implies that -> 0, a contradiction. Thus, z, must be smaller than LJ{ [1-nj [L-i-L+paj } asmust be any other € [z2,zj which is smaller than z. Therefore, as/aaa’ < 0. For the sign ofas*Iiaa, it is easy to show that the condition given in (A.22) is consistent with E [z3,].(d) Changes in labour endowment: The results in Proposition 7 part (i) to (iii) areobtained by differentiating (3.27) and (3.29) with respect to 4:as {1-f[1-n]J[1-aJOL*— [aLW÷aLC]{9fL—[1—a]}— o{fV-[1—a]L)aL- [aL + aL]2 (A.24){1—f[1—n]}[1—a]aL ÷ a[1—nJ{[1—a]L*÷pa,4}<[ccL + oL]2where = [1-n][1-a] > 0.Similarly, the results in Proposition 7 part (iv) and (v) are obtained by differentiating the sameset of equations with respect to L to derive:= 0 - cz[iV-[1-a]L] = -_______< 0. (A.25)3L [ccL ÷ L]2 ccL ÷ L5.2 South is the sole producer of grain: The appropriate equations for the comparativesteady state analysis are the BP(z) schedule for e [z1,2j and A(z) = o. The two equations canbe rearranged to read:75[1 —(1—n]][L—a [L÷L *]} —[1 —n]w *[L * ÷pa] 0 (A.26)A(z) - 1/w* 0This is a system of two equations in two unknowns w and . Its Jacobian determinant is= -A’(f)k(zC1 + [1-n] WM > o. (A.27)[w*]2where k() [1-n]. Note that from the South’s labour market clearing condition WM = L[L6+L]/k(). Substituting this into P = nWM/aw-p and using w = 1/o from (3.16), yields:1F jfL*+pa,*-=_____—(A.28)1 -[1 -n] k a, 1 4c[] awhere C V + pa. This equation will be used for the following comparative steady stateanalyses.(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 = -[1 _k(z)][L+L*]j0&Sg‘g D1[w*1Z ‘= -jL + )pa-— <0, at n[ n]C1 aZ <0, (A.29)aag C g [1 -W)]2a g=jL* + [L*+[1_A]pa]_ < 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’srule, yields:76____=-[1-k()]A’(Z[1-oj>0 8 [1-k(2][1-o] >08L D1 ‘=[1-aJ + pa-—>0, 81* = n[1-n]C_> (A.30)8L 8L [1 -k(z]2a 8L8M*=[L + [1_A]paj]_.—_ >0,8L 8LFor the case of the change in 1, just replace L with IL and use the same procedure. The signsof 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 appropriatewelfare equations in (3.43) yields:8W= +!+ APa;_[1_j < 0,81 1 M M w 81 p81>owp = — <0,81 [1 (A.31)air = [L*÷ [l_).]pa,],,* - [1_zlOw* +p81 M* 81 w* 0! p81= zM4 + aL * +> ow*M* 81 p 8!5.3 North is the sole producer of grain: The appropriate system of equations to be usedfor proving Proposition 6 is the BP(z) schedule for ! e [z3,4] and A(z) Co. Rearrange these twoequations to get:aL+[1 -k(]L - k(Z)w *{Ls + pa -a [L +L 9] 0 (A.32)=0The determinant of the Jacobian matrix for this system of equations is77= -A’(f)k(zDC2 ÷ [1-n] WM > 0• (A.33)[w*]2Note that r can be rewritten asL,L= _L*+pa,_a[L+L*]÷_—p = —C2÷----- —p, (A.34)a, W a, Wwhere C2 = L+paa[L+L*1.(a) Change in a;: Differentiate (A.32) with respect a; and use Cramer’s rule, to get:____- _k(Fjk()w*[L+L*]i>0- k(f)[L+L*]j> o— D2 ‘ — D2[w*]ãw*> 8M* M*aw*>= -w + [?. pa; - a *LC] —<0, = -w *gL * + —— <0, (A.35)aag W4&Zg81* L 8w*——— [Lc+L*]i+ C — < 0,[w*]2 ;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(.f)]+k(!)w*a]A/(f>0 _![1_k(Z)]+k(z)w*a>0D2 ‘8L D2[w*]8M ôw* 8M* M*8w*=[1_w*a] + [?bpa-aL ]—>0, =———-->0, (A.36)C 8L w *ai* ii [1_w*o] - L<0aL a; w [w*]z 0L >For the case of the change in L, just replace L with IL and L with [1-ilL. Then use the sameprocedure. The signs of the results for the change in L are the same as the change in L, so they78will 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()<081 D2_[c_1]_k([1_w*a]<08! D2[w*](A.37)=[1-wa] + [Apa-aL]—<0, 8M[1-w’o]- 1- >0,l 4 [w]2The signs are as shown if and only if k(2’)[1-w)> 1-c’. This condition can be rearranged toread z’> [1-ct]/{[1-n][1-waj}. Notice that there are endogenous variables which appear in bothsides of this condition. Thus, the signs of all derivatives are ambiguous.79CHAPTER IIINORTH-SOUTH TRADE AND GROWTH: WITH DIMINISHING MARGINALPRODUCTIVITY1. IntroductionThe development of models with endogenous technological change have providedeconomic tools for answering many important questions pertaining to industrialization andeconomic growth. However, several endogenous growth models’ imply that high populationeconomies grow faster. This implication might not be suitable for developing countries whichoften face problems related to fast-growing populations.This result of high population leading to high growth stems from the non-rival propertyof technology and constant returns to scale assumption. As pointed out by Romer (1990), thecost of discovering new technology is independent of the number of people who use it since itis incurred only once. With the constant returns to scale assumption, the share of resources usedby 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 fitwell with the case of less developed countries which often have high density populations. Thispaper provides reconciliation by presenting an endogenous growth model which shows that alarge population can lead to either an increase or decrease in technological progress when theagricultural sector operates under diminishing marginal labour productivity.The agricultural sectors of the developing countries are still the major sectors of theireconomies and most of their labour forces are concentrated in these sectors. Thus, outputs oftheir agricultural sector tend to suffer from the problem of a diminishing marginal product oflabour. 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).80The model presented here is an extension of the model in Chapter II. It is an endogenousgrowth model with three sectors: manufacturing, R&D, and grain. It is assumed that outputs ofmanufactured goods and R&D are produced by labour only with Ricardian production functions.The major change in this assumption from the model in Chapter II is that the production functionof 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&Dand grain sectors. An increase in population from an initially small level (relative to the fixedfactor of the grain sector) will enlarge the resources devoted to R&D; hence, technology willgrow faster. Nevertheless, a continued increase in population will eventually draw resourcesaway from the R&D sector since the grain sector is less and less productive. Hence, R&D willfall and technological progress will decrease.The organization of the rest of the chapter is as follows. After this introduction, Section 2lays down the model for autarky. The structure of the model in this chapter remains the sameas in the previous chapter, with the exception of the grain sector. Therefore, the structure of themodel that overlaps with Chapter II is described only briefly. Section 3 extends the autarkymodel to a trade model between two countries. Comparative steady state analyses for the freetrade 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 products.Their respective quantities, at time t, are denoted by g(t) and x(z,t), z E [0,1]; and their respectiveprices are p(t) and p(z,t). The total population is fixed and denoted by L. It consists of Lworkers and L capitalists, where L = IL, 0 <1 < 1. All consumers have identical hierarchical81preferences2defined by= f et Inu,(t)dt, (2.1)In g1(t), y(t) pjwhere lnu1(t) 1 (2.2)Inj +f ln[x,(z,t)]dz,y1(t)>pj,the subscript i E {w=worker, c=capitalist}; p is the subjective discount rate; lnu1(t) represents theinstantaneous utility3 at time t, and y1(t) is income. In other words, consumers will not demandany manufactured goods unless their incomes are sufficient to consume the minimum need ofgrain (i). Once their incomes are sufficient for j they will devote the remaining income toconsume manufactured goods.Each capitalist who is sated with grain is endowed with one unit of labour force andequity stocks. Each worker who is not sated with grain and suffers from malnutrition is endowedwith 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. Theneach worker’s income y = a, where a <pjby assumption. Thus, the top part of (2.2) is usedfor the worker. The optimal consumption of workers is given by: G(t) = ciLIp(t). It is assumedthat 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 capitalist are2 A detailed justification of this assumption can be found in Eswaran and Kotwal (1993),Section 4.As in Murphy, Shliefer, and Vishny (1989), the preferences used here are lexicographic.However, they are needed for solving the consumer’s optimization problem.82given by4: G(t) = = G, X(z,t) M(t)/p(z,t), and [dM(t)/dtJ/M r-p whereMQ) = [y(t)-p(t)g7L. is the aggregate-manufacturing expenditure of the capitalist. The lastcondition states that the aggregate manufacturing expenditure must increase at the same rate asthe net rate of returns.On the supply side, all productions in the manufacturing sector have constant marginalproductivity 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 betweengenerations. The industhal leader who owns the most advanced technology of z limits pricingits 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 thenext generation of technology, firms have to incur up-front expenses on R&D equal to waj,where a1 is the labour requirement per unit of R&D intensity, I. Inventor firms fund theirexpenses by issuing equity stocks which have the market value denoted by V = wa,. All risk isassumed to be independent; hence, their equity stocks pay an expected rate of return equal to therisk free rate of return (r). It can be shown that the rate of returns on equities is: r = nMJa1-I.Substituting r into A = r-p yields:=—i—p. (2.3)a1This is the condition that ensures consumer and capital market equilibrium.Unlike the manufacturing sector, the technology of the grain sector is time invariant. Itsproduction function is given by: GS = B[Lg1½, where Lg is the amount of labour employed in thegrain 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.83such as land5). Solving the first-ordered condition of the problem Fig = Max PB[Lg]WLg, yieldsL=II pB--w (2.4)2w g 2w 2w 4wThe capitalist is assumed to own the profits from grain. Setting w=l, the market clearingcondition for the grain sector is:B2p___+(2.5)2 pwhere the left hand side is the supply of grain B[Lg]½. The first and second terms on the righthand side are the grain demand of workers and capitalists respectively. The condition can berearranged as a quadratic form: B2p - 2ILp - 2aL = 0. Hence, using the familiar formula forsolving the root of the quadratic equation gives the price of grain6+ {[jL]2+2ULwBIZ jL ÷ 8 (2.6)B2 - B2where E { [ ]2+2aLB } and the superscript “A” denotes the autarky solution.To ensure that workers are not sated with grain as assumed7,it must be true that a <pj:Substituting pA from (2.6) and rearranging this inequality gives B < [2LIa]½ B. This B is thehighest level of grain productivity that keeps the grain price high enough such that workersThis diminishing return assumption is equivalent to assuming that grain production usestwo inputs: labour as a mobile factor and another specific fixed factor such as land. Since labouris paid according to its value of marginal product, the profit rate generated from the grain sectoris 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.84remain unsated with grain8.With the solution of pA from (2.6), the amount of labour employed in the grain sector andits profit areLA_____._____(2.7)g 2B j g 2B jThe model is closed by a labour-market-clearing condition which can be stated as:N= [1—n]M + L ÷ a1!, (2.8)where N = cth--L = [a[l-11+1]L is the labour supply. The terms on the right hand side representthe 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 statesolution of the economy9. The steady state solution to these equations is obtained by settingM=O in (2.3) and rearranging the result to get nM a1[I+p]. Next, solving (2.8) for a,! andsubstituting the result in the previous equation yields the solution for M as shown below.M = N - L + pa1 N- { gIf 6 j2 + pa (2.9)With some arranging, the solution of M can be expressed alternatively as follows‘ The value of B can also be solved by substituting pA aL/I into the grain market clearingcondition in (2.5) and solving for B.‘ The economy is immediately converged to the steady state. If not, either the profitmaximization or the lransversality condition will be violated (see details in Chapter II).85M = [aLw+Lc_L+paj]_pAjL+pAjLc= [1 _pAjJL + {[aL ÷PAILI —L} ÷ p1 (2.10)= [1 pAj]L + AB[LA] -Lf + pa1= [1 p’j]L + ll + pa1,.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= L ÷ ll’ ÷ pa1. (2.11)In other words, the capitalists’ income consists of wage income (Lj, profit income from grain(H), and income from equitie&° (pa1), while the capitalists’ manufacturing expenditure is equalto the leftover income from grain. Notice that H is the extra term resulting from thediminishing marginal productivity assumption. If grain production were Ricardian as assumedin Chapter II, fl would be zero.To obtain the solution for R&D intensity, rearrange (2.3) to read JA = nMja1-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 withthe assumptions that have been made. First, for the manufacturing sector to progress, the R&Dintensity must be positive. This requires that N-14-K> 0, where K = {[l-n]/n}pa1. Solving thiscondition for B yieldsSetting M,=O in M= r-p gives r=p. Moreover, the equity value V is equal to a,; hence, pa,=j.l/ is the equity income.86B jL[ 4N-K]1/2(2.13)xL ÷2L -KSecond, the labour employed in the grain sector (L) must be less than the labour supply(N), otherwise production of other sectors would be zero. The required restriction can beobtained by set K in (2.13) to zero which yields B [21LJP9/[cIL+2L] B. That is, the actualvalue 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. Itwill be shown that this can be satisfied if the actual level of grain productivity, B, lies betweenLB].Note that capitalists will be sated with grain if and only if the manufacturing expenditureis 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. Since therequirement B B causes N L, it also guarantees that the manufacturing expenditure ispositive. 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 beso 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 theworkers unsated is: B E [,B].Equation (2.12) and condition (2.13) have the following interpretation. From (2.12), itis clear that if B B, then N L and I’ will be negative. Thus, for the R&D intensity to bepositive, it is necessary for the productivity of grain to be higher than B so that capitalists aresated with grain and start consuming manufactured goods. For the R&D intensity to be positiveat 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), efficientlabour in R&D (low a,), and willingness to sacrifice for the future (low p) also help improve the87viability of R&D activity.With the steady-state R&D intensity given in (2.12), the utility growth rates of thecapitalist can be calculated by” 13A = q()JA, where q(n) = - ln[l-nJ. Substituting R&D intensityinto this formula givespA- [1-n]q(n)p. (2.14)a1 2BJJAs in Chapter II, technical progress of the manufacturing sector improves only the welfareof capitalists, but the benefit does not “trickle down” to workers because they consume only grainand the real wage in terms of grain is unchanged. The real wage is unaltered due to thefollowing reasons. First, capitalists are all sated with grain, while workers who are not sated withgrain 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 andreal wage remain the same. Second, though the unit labour requirement of manufacturing goodskeeps declining by R&D, the division of labour among sectors remains unchanged since thedemand for manufactured goods has unitary price elasticity. Thus, the amount of labouremployed in the grain sector stays the same as does the real wage. Therefore, workers areindifferent’2.2.1 Country size, population mix, and growthGrossman 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 usedSee Chapter II for detail derivation.12 This result may be interpreted as a dynamic version of Proposition 2 in Eswaran andKotwal (1993). As also mentioned by them, if preferences are not exacting hierarchically in thereal world, the benefits filtered down to workers would, nonetheless, be modest as long as themagnitude of substitutability between the two groups of goods are sufficiently low.88most intensively in R&D activities ensure faster growth. This essay, however, will show that alarger level of labour force (the factor that is used most intensively in R&D activities in thismodel) may slow down growth when preferences are hierarchical and the marginal product oflabour of the grain sector is decreasing. This possibility is demonstrated in the followingsimplified example and summarized by Propositions 1 and 2 below.Example: For simplicity, let assume that L—O which implies that N = L = L. Moreover,= §L, L = [g7/B]2, and JA = [n/a1j{L-[gEL/B]2}- [1-nip. Suppose the initial level of labourforce is given byL1—½[B/gI2. The conesponding R&D intensity is=—_r — [l—n]p. (2.15)4a1 gjNow let the labour force increases toL2—¾[B/g]. Then, the R&D intensity for this case isA 3nB12‘2 = — [1—nip.16a jjClearly, the R&D intensity declines since I > I. As the utility growth rate is q()JA, it alsodecreases. 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 theutility growth rate, while an increase in the capitalist population may increase or decrease thegrowth rate. The sufficient condition for the growth rate to increase is L < ½[B/g]2.Proof: Differentiating the utility growth rate in (2.14) with respect to L holding L,constant yields89= nq(n) +aL a1 2 J (2.17)} >The sign is positive since ö Thus, an increase in L always increases the growth rate.Now differentiating the utility growth rate in (2.14) with respect to L holding L constantgives= nq(n)J18L a1. (2.18)nq(n)1 —aThe sign of (2.18) depends on the value of A [L+]/& Since{ [jlL]÷ 2c41-l]LB }i [2aL]B, 1 = 0 (2.19)jL, 1=1we have- 1,1=0=(2.20)jL+jL= 2, 1 = 1gLIn other words, A e [1,2] for I e [0,1]. Using the above information gives90j[2aLj2BaL___2B B 2 (2.21)2B 2g[2gL] 2Lf1, i =2B LBiHence, the value of (2.18) becomesE - - , ‘‘i -i.., , for 1 e [0,1]. (2.22)0L a1 ( B 2 J a1 BJJTo show that an increase in L can reduce the growth rate, use the case of 1=1 as anexample. 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 > ½[B1g]2.The derivation for the sufficient condition that ensures a higher growth rate with largerL 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 valueof the minimum of (2.22) is derived. This condition will be the required sufficient conditionsince 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) withrespect to L and then I yields:91aZpA- nq(n) 8L< o (2.23)aLgal a1 aLalIc’-L — as — aswhere g = 25[jL ÷8] gL+— - [gL +5]2_aLgal 2[B8] ( C 3l C aij[jL +8]1 [jL]2-czBLC 28gL ÷ [8-jLj C C2[B8] I SijL[jL+8]I-____= C— [gL]2] + SB2 C— a ± rijLB22B83 i L B2JjL_÷8> 0, since 8 > jL, and ] C - a pj - a > 0.B2Because (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 - 2L[j/B] is positive which requiresthat L < ½[B/g}2. This is the sufficient condition given in the proposition. 0An increase in the population of the capitalist (La) may increase or decrease the growthrate because of the following reasons. Using equation (2.12), it is clear that the R&D intensitydepends on the value of N - L. On the one hand, an increase in L enlarges the labour supplywhich tends to increase R&D and the growth rate (endowment-expansion effects). On the otherhand, a higher Lr also generates a higher demand for grain. Recall that capitalists alwaysconsume i since they are sated with grain. This higher demand for grain increases the grainprice and raises the labour needed in the grain sector (L) which reduces the labour available forthe 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 marginalproductivity effects are stronger.For a small initial level of L, the demand for grain is small and its corresponding92equilibrium price is low. An increase in the capitalists’ population from this initial level will addthe labour supply to the economy (endowment-expansion effects) more than pushing up thelabour demanded for grain (diminishing marginal productivity effects). Therefore, R&D and thegrowth rate will increase.However, a continued increase in the capitalists’ population will put more and morepressure on the fixed factor of production in the grain sector (B). Consecutively, more and morelabour will be needed in the grain sector and less and less labour will be available for othersectors. The increase in population in this case will generate larger diminishing marginalproductivity effects than endowment-expansion effects. Therefore, R&D and the growth rate arereduced.The increase in population of workers (Lw), however, always increases the growth rate bythe following intuition. The rise in L also generates similar endowment-expansion anddiminishing effects. Nevertheless, workers demand for grain is not fixed (at j as thecapitalists’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 reducethe demand for grain of all workers. Therefore, the increase in labour used in the grain sectorwill 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 capitaliststo 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 < ½[B/g12.Proof: Differentiating (2.14) with respect to L (using the fact that L=1L, and L=[l-[JL)yields93= nq(n)[1_÷ -8L a1 aL= nq(n)a[1-11+1- [iL + 81L (2.24)a1= nq(n) N -_____LA= ‘(){N - ALA}.a1L 6 g a1L gThe sign of (2.24) depends on the value of I and its effects on other parameters. We alreadyknow that A E [1,2] for I e [0,1] from (2.20). The corresponding values of other parameters forrespective values of 1 E [0,1] are: N = [a[l-I]+1] L € [aL,LJ; ö e {[2aL]B, §Z]; and L =ft glL+]/2B] 2 e {aL/2, [g_LfB2].Using this information in (2.24), it becomesEnqn)a nq(n) i —2L (2.25)8L 2a1 a1 BjJHence, when most consumers are workers or I approaches zero, the increase in totalpopulation always increases the utility growth rate.On the other hand, when most consumers are capitalists or I approaches one, 1-2L[7B]will be positive if L < ½[B/g12, and negative if otherwise’3. Therefore, (2.25) will be positiveif L < ½[B/g]2, and vice versa if L > ½[B/g12. Thus, an increase of L from an initially smallvalue will increase the utility growth rate. However, a consecutive increase of L will eventuallyreduce the growth rate. ElAn increase in population, holding the same value of 1, may increase or decrease the“ Notice that the value of L1 given in the example is ½BI)2; that is why the increase ofpopulation from L1 to L2 decreases the R&D intensity.94growth rate because of similar reasons to those given in the previous proposition. An increasein population generates both endowment-expansion effects and diminishing marginal productivityeffects. The net result depends on which effects are stronger.A continued increase in population may reduce the growth rate because it may divertresources from the (dynamic) increasing returns to scale industry (the manufacturing and R&Dsectors) to the diminishing returns to scale industry (the grain sector). Thus, the averageproductivity falls. This argument is similar to the explanation used in Graham (1923), andHelpman and Krugman (1990) to describe the possibility of loss from free trade. However, thesource of the diversion of resources in this model is the hierarchical preferences, not free trade.2.2 Redistribution of income and growthThe previous analyses have shown that an increase in the population of workers alwaysincreases the growth rate. This result seems to suggest that skewness in income distributionpromotes growth. However, the increase in population of capitalists can also increase the growthrate if the initial population is small. The immediate policy implication is whether aredistribution of income that changes the population mix can increase growth rate. The analysisin the next section provides the answer. Note that the redistribution of income means a transferof 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 suchthat 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 get95-= ‘‘[1-cE]L - = ‘‘1f[1-a]L - jL+5 jL÷81 a1 81 j a1 2B 81___gL ÷5[1-aJL- L C {Sj+i2L-aB]a1 2B5 (2.26)= nq(n)Lf1- a- _4[[iL + - aB2]a, 2B= nqQz)L1- a- A gL + 5a, [ 2 B2To show that (2.26) can be increase or decrease, let 1 approach one which causes A = 2. Then,the terms in the curly bracket become 1 - 2L[7B]. Thus, (2.26) will be positive if L < ½[B/g72and negative if L > ½[BI]2.The sufficient condition which guarantees that the redistribution of income will increasethe growth rate can be derived similarly to the sufficient condition in Proposition 1. First, it willbe 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 givethe 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 that82PA- nq(n)____(2.27)812 a1 012Differentiate L with respect to I to geta14 = ÷8 jL ÷8 ]- ajL +8 1i? - (2.28)8! 28 2Bf 2[ B2f96i’- ÷ -tIL + (2.29)812 2 ( B2 f j 81 2B I. Ol J[j2L-aB]Lwhere— =___________= --{8jL+[j2L_aB2]L}= -{[jL+8] - aB2}J21 1L+8l_ 1 —=—8[ B2 j J 8ii —— 881 [j2L-ccB]L—= —8gL-gL—. = —8L-Lor 821 calJ 821 c= {82- [jLJ2 ÷ cB2L} > 0, since 8 > jL.D38Lg 1- 8A AjLThus,812= pg]--+ 281IOA AjL1 -= —— + [pg-aJ > 0.21.81 8 JHence, (2.27) is negative and (2.26) is monotonically decreasing in 1. Its minimum must be atthe point where I is at the maximum; i.e., I = 1. Evaluating (2.26) at I = 1 yields:= nq(n)L1- a - 2LI1l -81 , a1 ( 2 {Bj J (2.30)nq(n)L1- 2L > 0 if L < -a1 ( BjJ 2gThis is the sufficient condition given in the proposition. ElThe intuition for this proposition is as follows. The redistribution of income turnsworkers to capitalists which creates two impacts on the growth rate. First, it raises the labourforce of the worker-turned-capitalist from a to 1 since none of them suffer any longer frommalnutrition problems. This effect on the growth rate is represented by the terms nq(n)L[ 1-al/a97in (2.26). Second, the redistribution of income increases the demand for grain of each worker-turn-capitalists which raises the expenditure on grain. The aggregate manufacturing expenditureis, therefore, decreased since it is the leftover income from j With lower aggregatemanufacturing 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 initialpopulation is small, the former effect dominates the latter effects and the redistribution of incomeincreases the utility growth rate.3. Free TradeThis section extends the autarky model to a trade model between two countries. Itconsiders a trade situation between a developing country and a developed country where thedeveloping country imports most of its R&D needs. The objective of this section is to find outwhat determines the level of the developing country’s dependency on imported R&D. As it isshown in the autarky model, an increase in population may decrease the R&D intensity if theinitial population is large. It stands to reason that in a free trade economy, an increase inpopulation of a country that causes an increase in the world population (to be too large) couldreduce the world’s R&D intensity. The same increase in population may also decrease thecountry’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 developingcountry called South. Southern variables are denoted as in autarky while Northern variables aredenoted by superscript983.1 ConsumersThe North ‘s population is L which can differ from L. With the decreasing marginalproduct of labour in the grain sector, the model becomes complicated very quickly. Thus, tokeep the model tractable, it is assumed that all consumers are capitalists and are sated with grainboth before and after trade.Northern consumers share the same preferences defined in Section 2. Thus, the optimalgrowth rates of manufacturing expenditure are governed by= r—p. icr =-(3.1)3.2 Trade patternsTo depict the real situation as closely as possible, the developed North is assumed to bemore efficient in R&D activities. The South, on the other hand, is more efficient in grainproductions. Here, the South represents a particular type of developing country that has attaineda certain degree of industrialization. Although its main export is grain, the South is capable ofexporting some manufactured goods for which some of the production technologies are locallyconducted, but most are ‘imported” from the North’4.Let Co wIw be the equilibrium relative wage. Then, assume that the North has anabsolute advantage in R&D activities; i.e., a = ‘ya,, where 0 <y < 1. With this fixed value ofy, three trade outcomes are possible. If Co >,the North is the sole producer of R&D.Conversely, if o <y, or Wa1 <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 bothcountries 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 ofmultinational corporations setting subsidiaries and applying Northern technology in the South.99As 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 < ‘ isignored because it is unlikely that the South would be the sole producer of R&D. The casewhere to y is chosen over the case where to > y for three reasons. First, when to=y, there isa possibility that some Southern firms would be indigenous instead of being Northern subsidiariesas when to > y. Second, the relative wage of the South is always strictly less than that of theNorth since to=y and ‘y < 1. These two characteristics seem to fit the actual observation of theNorth and the South. Third, changes in most exogenous parameters do not alter the relative wageor the competitive margin when to = Hence, we can concentrate only on the direct effects ofthese factors. The case where the North is the sole producer of R&D (when to > y) can also beused, but the relative wage in that case will be altered by the changes in the exogenousparameters. The change in the relative wage would obscure the direct effects and unnecessarilycomplicate the analyses.With the equilibrium relative wage to fixing at ‘y the trade pattern of the manufacturedgoods is determined as follows. Each country has its own unit-labour-requirement schedulea(z)Ø(j,t=0). The set of the world’s most advanced technology (J) is unique and the South isassumed to own a fraction ?. of this set of technology while the North owns the remainingfraction l-?. Firms can apply the most advanced technology anywhere in the world. Thus, therelative labour productivity of manufacturing sectors can be defined asA(z) = a*(z) z e [0,1]. (3.2)a(z)Then the borderline product that both countries produce at the same labour cost or thecompetitive margin (2) is given by 2 = A’(y). The South specializes in industries z e [0,2] whilethe North specializes in industries z e [2,1].The case where to y is described in the Appendix 1.100For the grain sector, the Northern production function is given by C[L], where C is theproductivity index of the Northern grain sector. The Southern production function is the sameas is given in autarky. To simplify the calculation, it is assumed that ‘yC2 = B2. Normalizing w= I and solving the profit maximization problem of each country gives:L* = ycp12 y2. (3.3)g 2] g 2 j 2The grain market clearing condition when everyone is sated with grain is given by[L÷L*J [B2 + yC2]. (3.4)Solving this equation yields the equilibrium price of grain:F 2j[L + L9 = ILB2+yC B2where, L’ L+L* is the world population. Hence, the employment of the grain sector in eachcountry isLF B ILW 12 ILWf (3.6)B2+yCj 2B ]L*F,,,yCjLK12 = iLj (37)B2÷yCj 2B jTo 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 large16; i.e.,‘‘ As in the autarky, these conditions also ensure that all consumers are sated with grain sincethey cause the manufacturing expenditure of each country to be positive.1011 !rW -—,wB > , and C > 1 2L (3.8)L 2 L* 2The value of the right hand side of each inequality is analogous to B in the autarky model. Thetrade pattern of grain is determined as follows. Define net grain export functions of the Southand the North asG = B[L:]2 - jL, G = C[L] - IL*. (3.9)Then assume thatTJ21Ty < A(0) < “, (3.10)C2/L *where A(0) = a*(0)/a(0) is the relative labour productivity of zO. The first inequality ensuresthat the South produces some z in the equilibrium. This is because the A(z) schedule isdownward sloping and 0i y; their intersection must be at the point where! > 0.The second inequality assumes that the South’s relative grain productivity (adjusted bypopulation) is strictly greater than the relative labour productivity of the manufactured good forwhich the South has the highest comparative advantage (z=0). It ensures that the South remainsthe net exporter of grain as long as the South exports some manufactured products in theequilibrium. To show this use the inequality ‘y < [B2IL}/[CIL*j. Then, multiply both sides of theinequality by C2L and add both sides of the result by B2L to get: 2BL<B2Lw. Then, multiplyingboth sides of this last inequality by §7[2B21 yields: jL <jV’/2. Notice that the right hand sideisB2[L1½. Rearranging this givesB2[LYA- = G> 0. Thus, condition (3.10) implies that thenet grain exports of the South are positive; i.e., the South exports grain as claim. Note that sinceB2 is assumed to be equal to the conditionB2/L]/[C] > ‘y implies that L* must be biggerthan L.With the specified trade patterns, the following section describes the trade equilibrium.1023.3 Trade equilibrium with both countries producing R&DWhen o = y, both countries are equally efficient in R&D and the world’s R&D: 1FI + 1. The rates of return on equities for both countries are the same and can be written as rnWM/a, - 1F, where WM = M+M” is the world aggregate manufactured expenditure.Assuming perfect international capital mobility, this implies that r r’. Use theexpression of r in (3.1), to get M= nWM/a1 - jF-p, and M = nWM/a1 --p. Then multiplyingeach equation with a1 and adding the results yield the differential equation that governs the worldmanufacturing expenditure:a_______= nWM—a1[P+p1. (.2Like Chapter II, the trade equilibrium is determined by the intersection of the A(z)schedule and the balance of payments schedule, BP(2)17. The BP(2) schedule corresponding tothis 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 [z1,2J’8.Three trade outcomes may result depending on where the A(z) schedule intersects thissegment of the BP(2) schedule. If the intersection is between the range of S and C, the Northwill be the net exporter of R&D. Conversely, if the intersection is between the range of B and5, the South will be the net exporter of R&D. If the intersection point is exactly at point S. tradein R&D is zero. Both countries produce the exact amount of R&D needed for their domesticuses. The following sub-sections provides the solution for each case. The solution for the casewhere 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 Detailedconstructions of the BP(2) schedule with corresponding equilibria for the cases where (I) y areprovided in Appendix 1.Appendix 2 shows that z3 > z2; therefore, the set [z2,z,] is not empty.103The solution for the case where both countries are self sufficient follows immediately since it isa special case of the first one. The solution for the case where the South is the net exporter ofR&D is provided lastly for completeness.3.3.1 North is the net exporter of R&DThis case corresponds to the solution when A(z) intersects BP(2) between S and C inFigure 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 fractions of its needs for R&D from the North. This fraction s measures how much the South dependson the North’s R&D; henceforth it will be called the South’s dependency on imported R&D. Theresource constraints for this case are:L = [1-n]WM ÷ + (3.12)= y[1—][1—n]WM + 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 manufacturingproductions of each country. The other two terms measure the labour needed for grain and R&Drespectively. Adding labour market clearing conditions yields a world resource constraintL* F L 314L + — = [l—n]WM + [Lg + a1IF.Y YThe differential equations (3.11) and the world resource constraint (3.14) characterize the steadystate equilibrium similarly to (2.3) and (2.8) in the autarky model. The steady state equilibriumhas its solution at M+M = 0.To obtain the solution, solve at from the combined resource constraints to get: at = LL-f-[L-L;]fl-[ l-nIWM. Then, substituting the result into (3.11) with M-i-Pv! setting to zero yields:104Figure 3.1Balance of Payments Schedule(I)BP(z)DB S ClwoZ1 z3 z2z105F[L* — L*F]WM = [LLg]± g ÷paY (3.15)L*= L + + pa — —y 2BThe result in the second step is obtained by using (3.6) and (3.7). Substituting this solution ofWM in (3.11) then gives the R&D intensity:fl1 F{L*_L*F]l1F =— [L— Lg] + g r — [1—n]p,Y (3.16)I 2= -L+L_!-[1-nJp.y 2 B JTo solve for s, substitute af = nWM-pa1from (3.11) into the South’s resource constraintand rearrange to get:z1WM — pa1] - [L— L:]z[nWM - pa,]JL+L_jLw2]-L+ILW2 (3.17)= [ y 2 B J 2B+L* 1[iLw]2]- [1n]pai}Given the South’s dependency on imported R&D, it is possible to solve for the boundary valuesof 2 that support this case. For the lower bound, we know that if s = 0, the South is selfsufficient in R&D. Hence, imposing s = 019 in (3.17) and solving for 2 gives the 2 that causesthe South to be self sufficient in R&D. This 2 is denoted by z. and will be called the R&D self-sufficiency margin. It can be written as:For s to be non-negative and less than one, it is required that !/[l-!] ‘y{[L-L]/[L-L92[l-n.]/{ l-2[l-n]}, where! = A’(’y) and the values of L and L are given by (3.6) and (3.7).106= L - L - {jL’/2Bj2. (3.18)- pa1 L + L*/y - ![ILW,B]For the upper bound, s = 1 or the South imports all its R&D. Thus, setting s = 1 in (3.17)yields which causes the South to rely totally on the North’s R&D. It is denoted by z2 and canbe written as:= L-L L - [jL”f2BJ2. (3.19)[1-nJWM [1_n]{L+L*/y_![iLwlBr}The intermediate values between 0 and 1 of s, therefore, represent the case where the North isthe net exporter of R&D.To complete the picture on R&D, it is also interesting to know how much the South’sR&D is relative to the world production. For this purpose, define z1 [l-s]! as the fraction ofworld R&D produced in the South20. Using this definition in (3.12) and rearranging terms gives[L—LF]— [1—n]WM (3.20)InWM-pa1By definition, it is smaller than or equal to 2 since s e [0,1]. Note that imposing 2 = z, in (3.20)and rearranging terms yields z, = [L-L]/[WM-pa1which is z as given in (3.19). Thus, z, is thespecial z1 that equals to 2.Finally, the solution for each country’s manufacturing expenditure can be solved by usingWM given in (3.15) and the balance-of-payments condition. The balance-of-payments conditionfor this case can be written as:20 This is the same as :‘ in Taylor (1 994a).107fJVI*F- [l-z9M’ + pG - s nWM ÷ A[1-z9pa’/y - [1-A]pa, = 0 (3.21)The meaning of the condition is as follows. The first terms, 2M*F - [1]MF, are the value of thenet Southern exports of manufactured goods since the South’s export demand is M*/p(z), for ze {0,] and its import demand is M/p(z), for z E [,l]. The second term, PFG is the Southerngrain export value. These first and second terms represent the South’s trade account. Any deficitin this account must be compensated by a surplus in the service account depicted by the last threeterms. Since the South has to import a fraction s! of R&D from the North, it has to pay royaltyof sWM. Now, recall that the South owns of the world equity stocks which have a marketvalue of V = a1 = 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 theSouthern dividend that is paid to the North’s shareholders. This balance-of-paymentscondition can be simplified further asIWM - M” ÷ + [z1-z9nWM + [)—z1]pa = 0 (3.22)The first two terms are obtained by using the fact that - MF. The lastterm is obtained by using a/y = a1. The interpretation of the condition is quite the same. TheSouth’s manufacturing firms must pay a net of [2-z,]nWM as royalty payments for using thetechnology imported from the North because z. is smaller than ! (see Figure 3.2). It also receivesa net dividend of [-]pa, from the North.108Figure 3.2Patterns of Manufacturing and R&D Production--- South’s R&D----.I North’s R&D -II I I II1 1I South’s Production North’sProductionCondition (3.22) can be used for the calculation of each country’s manufacturingexpenditure as follows. M is obtained by substituting a,P = nWM - pa, from (3.11) into theSouth’s resource constraint (3.12) to get [z,-2]nWM = L - L - WM + z1pa,; then use this in (3.22)to get Mi’. Deducting MF from WM and using G = -G then gives M*F. They can be written asMF= L - LgF + PFG+APa (3.23)= L_pFaL÷{pFB[L:]z_L:}÷pai = [1p”jjL÷ll’+)pa[L* — L*FIM*F=g± pFG*+[1_)1pa(3.24)[1_F1 ]J*+ll*F+[1_)]PaThe interpretation for the world and each country’s manufacturing expenditures is much the sameas that of autarky. The manufacturing expenditure consists of leftover-wage income from grain,grain profits, and income from equities.1093.3.2 South is the net exporter of R&D21This case corresponds to the solution when A(z) intersects BP(z) between B and S inFigure 3.1. It is a mirror case of the previous one. Both countries produce R&D, but the Northimports a fraction s, of its R&D needs from the South. Therefore, the resource constraints forthis case are:L = zll—n]WM + L + adz+sj[1_zl}IF, (3.25)L*= y[1—][1—n]WM + L ÷ aj*[1_s,][l_f]IF. (3.26)As in the previous case, solving a,I’ from the combined resource constraints and substituting theresult in (3.11) yields the same world manufacturing expenditure given in (3.15). Thus, the R&Dintensity is also the same as (3.16).To solve for s1, substitute a1I’’ = nWM-pa1from (3.11) into the South’s resource constraintgiven in (3.25) and rearrange to get:= L - - [WM-pa1][1—][nWM - pa1]L--+ L*- [jL W]2 (3.27)2Bj 1 y D J[1_zl{n[L + i__[L)ij - [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. Forthe 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 s1 = 1 yields thelower bound:21 The case is rare in the real world, but it is given here for completeness.110L-L-[nWM-pa1] = [1_n][L_L+ pa1] - n[L*_L]fy (3.28)1 [1—n]WM [1—n]{L-L÷ pa1 + [L*_L;FJJY}This is the 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+s1[l-] as the fraction of world R&D produced in the South. Then, using this definitionin (3.25) and rearranging terms gives the same z1 as given in (3.20).With this definition of z1, the balance-of-payments condition can be written as:— [1_]MF + PFG +s1[1—f]nWM + [).-zpa1J = 0 (3.29)or fWM - MF + pFG + [z,—f] nWM + [?.-z1pa1 = 0Notice that this condition is exactly the same as (3.22) which is the balance-of-paymentscondition when the North is the net exporter of R&D. Therefore, its solution for M and M*F arealso the same as in section 3.3.1.Having the trade equilibria for all cases where o= y, we are now ready to explain whysegment BC of the BP(2) schedule is flat. Start from point B where 2=z1 in Figure 3.1 andincrease 2. We can see that a current-account surplus generated by an increase in 2 can becompletely offset by a reduction in the South’s R&D exports (a reduction in s1 or z,). Theadjustment in the South’s exports to maintain the balance of payments does not require anincrease in w as is needed when one country is the sole producer of R&D. This process ofadjustment continues until s1=0 and z,=z where the economy arrives at point S in Figure 3.1 andboth countries are self sufficient in R&D. A further increase in 2 now requires the South toimport R&D (s increases while z1 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. Any furtherincrease in 2 would require an increase in tO to maintain the balance of payments which wouldcause the BP(2) schedule to slope upward as shown by segment CD in Figure 3.1.111In Summary, segment BC of the BP(!) schedule is flat. From point B to S, the Southgradually reduces its R&D export until the net export is zero. Then, from point S to C, itgradually 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 Figure3.3. The intersection point of this segment of the BP(!) schedule and the A(!) yields the samerelative wage, the world and individual countries’ manufacturing expenditures, and the R&Dintensity.This completes the detailed construction of the trade model. Now we are ready for thecomparative steady state analyses.4. Comparative Steady State Analyses: Trade modelThe objective of this section is to find out how the change in important economicparameters 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 growthrate and the welfare of consumers. The other two variables are not directly important to welfaresince the utility growth rate and the welfare of each country depend on the world’s R&Dintensity, not on its share of world’s R&D or the level of R&D imports. However, these aresignificant in terms of non-welfare objectives. The Southern government may consider its shareof world R&D and dependency on imported R&D as indicators for its success in industrializationand economic independence.As mentioned earlier, the analyses will concentrate only on the case where both countriesconduct some R&D activities (when Ci)=y) and the South has to rely on some of its R&D needsfrom the North. The impacts of two parameters, population and grain productivity, are analyzed112Figure 3.3Steady State EquilibriumU)A(z;t>O)BP(z)A(z;t=O)A(z;t>O)_____________I0— 1z113here. First of all, let us determine the impact of the economic variables on the relative wage andthe 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 ofgrain 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) sinceco depends entirely on the ratio of a/a,=‘y As to is constant, the relative costs of productionof all manufactured goods are the same. Thus, the borderline manufactured product (2) thatdivides the set of manufacturing exports of each country is also unchanged.The first economic variable that this section will investigate is population. Similar to theresult in Proposition 2 of the autarky model, it will be shown that under a free trade economyan increase in population may increase or decrease the world’s R&D intensity depending on theinitial 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’ < [B/g)2. Similarly, a small increase in the North’s population (L) raisesthe world’s R&D intensity if and only if L’s’ < [BIg2/.Proof: Differentiating (3.16) with respect to L and then L* yields:=- 1 - L’’ 12 1’ > if L’ < (4.1)BjJ < > ii=- LW..L12J> if L’ < - 12 c. (4.2)a,y BjJ < > yjj114The reasons why an increase in population22 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 theworld population, the demand for grain is small and its price is low. Because the world’sproductivity of grain, represented by B2 + ‘C2 = 2B, is still large compared to Lw, an increase inthe world population from this initial level will add more labour supply (endowment-expansioneffects) to the economy than push up the labour demanded for grain (diminishing marginalproductivity effects). As a result, more resources are available to produce manufactured goodsand 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 labourneeded for grain production will drastically increase since the grain’s marginal product of labouris decreasing. An increase in population in this case will generate larger diminishing marginalproductivity effects than endowment-expansion effects. As a result, fewer resources are availablefor 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&Dintensity depending on the size of the initial world population. An important question is how thepopulation change would effect the South’s share of the world’s R&D production and its degreeof dependency on imported R&D. Can an increase in the Southern population induce the Southto depend more on imported R&D?The simplest way to show this is to assume that the world economy is exactly at the pointwhere 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 impactof this change, differentiate z [given in (3.18)1 with respect to L to get22 A population increase in this model can be interpreted as an proportionate increase in allresources other than the fixed factor used in the grain sector.115= {Pa]1 +[LLF]lL;]}/[JPa8L g y8LSince 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- 1 aL;F8L y 3L> 0 if Lw < 212gj (4.4)gL LH’ j2Bj 2B=< 0 if Lw > 21 2 BjJ 4 B] gThe sign in the second step is obtained by substituting the value of 3L/L = ½L’[7B]2and usingthe fact that L > L from (3.8). The sign of the final step is obtained since the assumption thatB2 = ‘y’C2 implies that L > L. Thus, the increase in the South’s population will increase z for asmall world population and vice versa for a large population. Because z, z for this case, itfollows that the R&D production share of the South (z1) will also decrease for a large population.The reduction of z, also means that point S on the BP(2) schedule is moved to the left. Sinceis fixed by Lemma 1 and point S moves to the left, the South is transformed from the selfsufficiency situation to an importing R&D situation. In other words, the South’s dependencyon imported R&D increases.The effects of the increase in the Southern population for the general case where theSouth imports some R&D can be calculated by differentiating z1 [given in (3.20)] with respectto L to get116a/F{ 1 _zii_ni’M } - fl[L_L_[1_flJWM]8”8LF[ajIF]2ãLg WM1— { z[1—n] i-z,n ] 8LThe derivation in the second step is obtained by dividing both the numerator and denominatorin step one by at and using the definition of z1. Since the term 2[1-nJ+z,n is positive, the signof (4.5) is determined byi_!=i_!.—12>O ifL”’<2l2,2 B] < > gj (4.6)1-L”l>O ifL’<2•8L B]< > gThus, the sufficient condition which ensures that (4.5) is positive is when L’ has values in theset ([B1g]2,2[B/}.For the impact of the increase in population on the South’s dependency in imported R&D(s), recall that by definition s = [!-z1]/!. It is clear that the sign of the change in s is theopposite of the sign of the change in z, since 2 is fixed by Lemma 1. Therefore, the degree ofthe South’s dependency on imported R&D will fall if Lw {[B/g]2,2[ 1 1). The followingproposition summarize the results.Proposition 5: A small increase in the South’s population (L) may increase or decrease theSouth’s share of the world’s R&D production (z1) and the South’s dependency on imported R&D(s). A sufficient condition which ensures that z1 will increase and s will decrease is LV e{[B/2,2[B/g }.117The proposition can be understood by the following reasons. The increase in the South’spopulation raises the world price of grain. Consequently, the labour needed by the grain sectorsof both countries rises. For the North, this increase in the grain sector’s employment meansfewer 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 theincrease in its own population. When the initial population is sufficiently small (Lw < 2[BI])more resources will be added into the South’s economy which can be used by the South’s R&Dsector. Therefore, the South’s share of the world’s R&D increases. As its share of the world’sR&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 grainsector on its own R&D. It turns out that this productivity improvement will increase the South’sdependency on imported R&D since the South is induced to export more grain and reduce itsown R&D production.Proposition 6: A small increase in the South’s grain productivity (B) decreases the South’sshare of the world’s R&D production (z1), 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 theSouth in grain. Thus, the South increases its grain productions for exports while the Northreduces its grain outputs. As the North reduces its grain outputs, labour moves out of the grainsector toward other sectors, including the R&D sector. Hence, the North’s R&D rises. For theSouth, the productivity improvement increases its grain productions. Consequently, labour movesinto the South’s grain sector and less labour is left for R&D. Therefore, the South’s R&Dshrinks while the North’s R&D expands. It follows that the South’s share of the world’s R&D118falls. Since the South still exports the same range of manufactured goods (i.e., is constant), thereduction in its share of the world’s R&D means that the South must depend more on importedR&D.5. ConclusionThe result of this essay can be summarized as follows. In a closed economy, it is foundthat the increase in total population, population of capitalists, and redistribution of income mayincrease or decrease R&D and growth. They will increase R&D and growth only when the initialpopulation is sufficiently small. A continued increase in the total population will eventuallyreduce R&D activities.Under a free trade environment, an increase in the Southern population may also increaseor decrease the world’s R&D. It will raise the world’s R&D if and only if the initial worldpopulation is small. It will also raise the South’s share of world’s R&D and reduce itsdependency on imported R&D if the world population is sufficiently small. An increase in theSouthern grain productivity, however, will reduce the South’s share of world’s R&D productionand increase its dependency on imported R&D.119Appendix1. Derivation of the trade equilibrium for the case where wWhen 0) y, the equilibrium price of grain is determined by2gL”where D = B2+oC. (A.1)Substituting this equilibrium price ii Lg = [Bp/2]2 and L = [coCp/212 yields the respectiveemployment 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 Northconducts all R&D for the world. Hence, I = 0 and 1F = J’ > 0.The rate of returns on equities here is given by r = nWM/w’a - 1F• Since r = r* byperfect international capital mobility, using this r* in (3.1) yields M = nWM/w*a - JF-p, andM* = nWM/w*a - JF-p. Then multiplying each equation with wa and adding the results yieldsthe equation that maintains M+M* = 0 which can be written asnWM = w*a[I÷p]. (A.2)The labour-market-clearing conditions for both countries when only the North conducts R&D areL = f[1 -n] WM + L, (A.3)L* = [1 f] [in] WM + L*F ÷ aIF. (A.4)gCombining (A.3) and (A.4), then solving for aT and substituting the result into (A.2) yields120(A.5)WM = [L-L] + w*[L*F_L;÷ pa;].Using this in (A.2) then give the solution for the R&D intensity1F = { [LL8F] + w*[L*_L;F] } — [1—n]p. (A.6)wThen solve (A.3) for WM and equate the result to (A.5) to getFcD(,z_) = [L- L] - [L-L] + - L;F + pa;] = o. (A.7)zil -ii]Upon substituting the values of L and LF, this equation implicitly defines the segment CD ofthe w = BP(2) schedule shown in Figure 3.1. It describes the combination of o and 2 thatmaintains the balance of payments.Applying Implicit Function Theorem on Fc)(co,2) = 0, yields=- aFCDIaI> o (A.8)ÔFCD LLgwhere - >0,az [1—n]z28FCD 1 -[1 -n]- 1+ L* - L;F + pa <[1-n] )2 &.3LF 2LFC2 ãL*F 2L*FB2=— g, <,g = gDHence, segment CD of the BP(!) schedule is upward sloping. The boundaries of this segmentof the BP(2) schedule are marked by (co=y,!=z2)and (O=Oa=l). Since z2 must locate at thepoint 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 = A(2) gives the steady state solution for Co and 2. Thenusing w 1/Co in (A. 1), (A.5), and (A.6) yield the solution to pF, WM, and JF for this case.1211.2 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 Southconducts 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 = nWM/a[ - 1F• Assumingperfect international capital mobility, this implies that r = r. Use this expression of r in (3.1),to get M = nWM/a1 - P-p, and M* = nWM/a1 - P-p. Then multiplying each equation with aand 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-clearingconditions for both countries areL = [l -nJ WM + L ÷ a1I’, (A.9)[1-][1-n]WM + L*F (A.1O)*wAdding both labour market clearing conditions yields the world resource constraintL + w*L* = [1—n]WM ÷ [L’÷W*L;F] + a/’’. (A.11)To find the equilibrium solution, solve the world resource constraint to get a1 = L - L+ w[L*- Lv’]- [l-nIWM. Then, substituting the result into (A.2) yieldsWM = L-L’ ÷ W*[L*_L;F] + pa1.. (A.12)Using (A. 12) in (A.2) then give the R&D intensityjF= !{ [LLgi + w*[L*_L;F] } — [1—nip. (A.13)a1.For the relative wage, solve (A.9) for WM and equate the result to (A. 12) to get*F F w[L—L] A14[L- Lgl + w*[L*_L; j - g + pa1 = 0.Upon substituting the values of L and LF, this equation implicitly defines the segment AB of122the 0 = BP() schedule shown in Figure 3.1. It describes the combination of o and thatmaintain balance of payments.Applying Implicit Function Theorem on FAB(Wz) = 0, shows that2 2E’A812=- ur !uZ> o, (A.15)aF/&)aF w*[L*_L*17]where = - g < 0,0z [1—n][1—f]2____= - + _L 1 -[1 -n][1 t3L; ÷ [L* _L*Fl > 0,aø C*) [1-n][1-j gãLF 2LFC2 2L*fB2=- g, <0, = g >•DIn 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,!=z1). The value of o is implicitly defined by (A. 15) with set to zero23. The other endpoint z1 is given by (3.28) in the text. Hence, segment AB of the o = BP(2) schedule is aContinuous increasing function in . Combining the o BP(!) schedule with the continuousdownward sloping o = A(2) schedule gives the steady state solution for 0 and . This then startsthe motion of the dynamic evolution of the world economy. Then using w = l/o in (A.l),(A. 12) and (A. 13) yield the solution to pF, WM and JF respectively.2. Proof that z2 > z1:Notice that z1 and z2 given in (3.28) and (3.19) have the same denominator. Hence, if z2> z1, it is required that the numerator of (3.19) must be greater than (3.28) or23 It is assumed that o,,, is non-negative.123y[L-L] > y[l-n][L-L+ pa1] - fl[L*_L]y [L - LF]-y [L-L] > - yn[L -L8F] + y [1-n] pa1 - n[L * - L;F][L* _L*’]_LgF]+ g > y[1—n]pa(A.16)[L* _L*F]+ g> [1—nipY[L4 -Lj+ g—[1-nIp >0.YBut the left hand side of the last condition is 1F which is positive by assumption. Thus, when1F > , z2 > z1.3. Proof for Proposition 6:Differentiating (3.15) with respect to B yields:___= -- i___=[B2- yC2] ÷ 4BaB aB yB B D yDyBDt[YL:+2L;l’]B2 — [yC2]LgF } (A.17)= YBD[Df 2[[yC]} = 2B[] > o.Note that the formulae of L and LF used for the differentiation are not evaluated at the pointwhere B2 = yC2 since only the change in the grain productivity of the South is considered. Then,differentiating (3.20) with respect to B and using the fact that al = nWM-pa1 give:124a,i’{ _!-zll-n]”I-___[a/F]2 (A.18)< 0.The terms in the second square bracket of the last line are z, which is positive. Using this factwith (A. 17), we can conclude that (A. 18) will be negative if yC2 B2. This condition isautomatically satisfied since ‘yC2 = B2 by assumption. Lastly, differentiating s with respect to Byields-18Z> 0 (A.19)a1IF125CHAPTER IVMINIMUM EXPORT REQUIREMENTS: PARETO IMPROVING MEASURES1. IntroductionIt is commonly observed that countries which receive foreign direct investments (FDIs)often impose some form of trade-related investment measures (TRIMs) on foreign investors. TheUS Benchmark Surveys in 1977 and 1982 found, respectively, that 29 and 28 per cent of USaffiliates in less developed countries (LDCs) were subject to one or more TRIMs. In Guisingerand Associates (1985) the figure was as high as 51 per cent (38 out of 74 projects). All threestudies plus that of the OECD (1987) found that one of the most frequently used TRIMs wasminimum export requirements (MERs).In the view of the host countries, TRIMs are tools which enable them to control theeconomic benefits generated by foreign investment. Nevertheless, the source country (fromwhich the investments come) views TRIMs as non-tariff barriers that distort investment and tradeflows, and thereby reduce their welfare. These two different views have generated aconfrontation between the developed countries (DCs) and the LDCs. The main purpose of thispaper is to show that this confrontation need not necessarily arise. Some TRIMs, particularlyMERs, can be Pareto improving measures to both the host and the source countries’.Before attempting to demonstrate this claim, we review the existing literature. Theliterature 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 areaccompanied by import barriers such as tariffs on final goods. Rodrik (1987), unlike HeranderFor other trade policies as Pareto improving measures see Anis and Ross (1992).126and Thomas, employs a general equilibrium framework. He demonstrates that MERs can raisehome welfare by reducing the output of the over-produced sectors and reducing foreign capitalpayments2.Models in the second group assume duopolistic competition between a foreign subsidiaryand 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 hostcountry. However, the result on the welfare of the host country contradicts the finding by Rodrikin his duopolistic interaction model. Rodrik concludes that MERs can improve the host-country’swelfare by reducing sales of the foreign firms and shifting profits toward domestic firms. Thesecontrasting results stem from the fact that Davidson et al. assumes that the marginal costs of thelocal 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 hostcountry’s welfare. It provides us with better understanding of how MERs affect the hostcountry’s economy and is important in its own right. However, it remains deficient in thefollowing aspects.First, there has been very little attention given to the effect of MERs on the welfare ofthe source country, except from the literature in the second group. Both studies in this groupassume that the unit cost of production of the host country is higher than that of the sourcecountry. Hence, there is no incentive for the subsidiary firm to export unless the MER isenforced. They then conclude that MERs reduce the welfare of the source country since thesource country is forced to absorb a higher cost. However, we cannot apply this logic to a case2 Chao and Yu (1990), also using a general equilibrium framework with urbanunemployment, show that MERs may improve welfare if the home country consistently adoptsthe second-best optimal quota policy.127where FDIs are the result of the search for the lower costs of production3. Exports from the hostcountries would already exist without the intervention although the export level may not be ashigh as the host countries would wish. The host countries may have an incentive to use MERsto further boost their exports. Would MERs always, then, improve the welfare of the sourcecountries?Second, strategic interactions of firms in the source country have been overlooked4. Theimposition of MERs affects profits of the foreign investors which in turn have repercussions onthe marginal profits of their rivals in the source country. These strategic interactions couldentirely change the welfare implications of MERs.Third, the changes in profits from the operation of foreign firms in the host countries dueto MERs have not been taken into account in the welfare calculation. For instance, bothDavidson et. al and Rodrik assign zero weight to the entire earnings from the operation of theforeign firms. It seems strange that the host country requires foreign firms to increase theirexports (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 amaximum ratio of profit allowed to be repatriated, etc.Lastly, all of the existing literature treats MERs as given. In light of the fact that MERsare often applied to industries that operate in imperfectly competitive environments, thegovernment of the host country should be able to use MERs to manipulate the outcomes insteadFor instance, the major reason for the US surge of investment for semiconductorproduction in East Asia during the I 970s is to utilize the huge pools of cheap and unemployedlabour, 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 thehost country is totally absorbed by an equal reduction in domestic production levels in the sourcecountry. Thus, the sales of the parent firm in the source country are independent of MERs. Inthis paper, however, all productions come from the host country; hence, the sales in the sourcecountry depend on the level of the MER.128of acting passively.This paper has incorporated the following remedies to these shortcomings. To capturethe strategic interaction of firms in the source country, I assume a duopolistic market structurein 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 thecase of relatively advanced-technology industries in which the MNC provides the technology andthe host LDC provides cheap labour. The industries that the model might be applied to are, e.g.,automobiles, semiconductors6.In such industries, oligopolistic structures for the source countryshould 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 LDCssince they often lack the necessary technology and capital to start their own indigenous firms (thevery reason LDCs use the investment incentives in the first place). Moreover, to compete forforeign direct investment, the LDCs’ governments usually guarantee a certain degree of monopolypower 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 tocapture the benefit from allowing foreign firms to operate in the host countries. This is one ofthe sources of welfare generated by MERs other than the consumer surplus derived fromdomestic consumption. In the existing literature, consumer surplus and profits of domestic firmsare added to get a welfare measure of the host country. MERs, then, benefit the host country byshifting profits from foreign firms toward domestic firms7. When the South-indigenous firm isThe 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 theindustries that had the highest incidents of TRIMs.See Brander and Spencer (1985) for the case of subsidies as tools for profit-shifting.129absent, 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 forthe host to retain benefits of the MER. This maximum ratio is chosen because it does not changethe 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, theywould 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 andKemperer (1985). However, constant returns to scale are assumed for all production to rule outjoint economies or joint diseconomies analyzed in their paper, so that we can concentrate onlyon the effect of MERs. In Bulow et al., the two markets are related because changes in outputsin one market affect the joint marginal cost. The optimum choices of outputs of the two marketsare, therefore, linked. In this paper, the optimum choices of outputs of the two markets wouldhave been independent (by the constant marginal cost assumption) if there were no MERs. Thelinkage 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 themodel and analyzes the effect of both quantity and shared export requirements. The analyses inthese two sections assume that the levels of MERs are exogenously given. In Section 3, thisassumption is relaxed so we can analyze the impacts of MERs when the host country employedthe optimal MER as a tool to achieve the second-best welfare. Section 4 relaxes the monopolymarket 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 ModelConsider a two-country world economy consisting of a source country called North and130a host country called South. There are two firms in the economy: a local Northern firm8, anda multinational corporation (the MNC) consisting of a parent firm located in the North and itssubsidiary firm located in the South. The market structure in the North is a Cournot duopolywhile the market structure in the South is monopoly (see Figure 4.1). The monopoly power ofthe MNC for the South’s domestic sales is granted by the government. In return, the Southrequires the MNC to export either a minimum fixed quantity of output or a minimum share ofits 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 domesticallywhile all productions of the MNC are manufactured by its plant in the South. The unit costs andmarginal costs of the MNC and the North’s firm are assumed to be constant9 and are denotedby c and c, respectively.For the sake of exposition, the following sub-section provides a simple example in whichthe South requires the MNC to export a fixed quantity instead of a normal export sharerequirement.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 firstand 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 inverseThroughout this chapter, the word “local Northern firm” will be used interchangeably withthe word “North’s firm”.The results presented in this paper will also hold when the cost functions take the form asC(x+z) with C > 0 and C’ 0, and C(y) with C” > 0 and C” 0. See details in footnote 11.131Figure 4.1Market Structures and trade flowsdemand curve p = p(Q), where Q = x + y and p’(Q) <0. Both p(Q) and q(z) are assumed to belinear. For simplicity, it is assumed for the moment that the MNC can repatriate all the profitsback to its parent firm; i.e., v = 1.In a quantity Coumot game, the MNC takes y as given and maximizes its joint profitssubject to a constraint x X; i.e.,Max {p(x+y)x + zq(z) — c[x+zJ x X),x.z(2.1)where X is the minimum-quantity-export requirement. Assuming that the QER constraint isbinding and let ? be the Lagrange multiplier, we have x = X, p(Q) + xp’(q) - c + , andq(z) + zq’(z) - c = 0 as the first-order conditions. Clearly, the solution for x and z are132independent. On the other hand, the local Northern firm solvesMax { p(x÷y)y — c”y }, (2.2)yThe first-order condition for this problem is: p(Q) + yp’(Q) - c’ = 0. It implicitly defines thereaction function of the North’s firm: y = R(x). Substituting x = X into this reaction functiongives 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; it is the maximum value of theMNC’s profits; and it denotes the maximum value of the local Northern firm’s profits. To getthe impacts of QER on the North’s welfare, we need to calculate the impact of QER on the salelevels, total consumptions, and profits. Applying implicit function theorem onp(y+X) + yp’(y+X)- c’ = 0 and differentiating,it, and it with respect to X yield the followingresults< 0, (2.4)2p’ 2= 1- -> 0, (2.5)=xp’y -- > 0, (2.6)= yr.’ < 0. (2.7)Note that (2.6) is true only at the point where the QER constraint just binds. With the aboveresults, differentiate (2.3) with respect to X to get133W =- + + =- P-[Q÷X-2y] = - -{2X-y]. (2.8)The sign of (2.8) will be positive if and only if X > y/2. In other words, the welfare of the Northwill be improved by a small QER if the sales of the MNC in the North are greater than a halfof 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 = 0). Furthermore, by the first-order condition of problem (2.2), -yp’=p - c. Substituting these two conditions into the righthand side of (2.8) givesW .[2[p—c] — [p_cJ] = .[p—c ÷ c5 —c] > 0, if CS c. (2.8a)The condition in (2.8a) is true since p - c = -Xp’ > 0 when the QER constraint just binds. Inother words, the welfare of the North will be improved by a small QER if the MNC’s unit costis lower than that of the local Northern firm.The QER improves the Northern welfare by the following reasons. First, the QERreduces the duopoly distortion in the North. This distortion exists since both firms produce atthe 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 reductionthen helps to curtail the distortion. Second, when the unit cost of the local Northern firm isstrictly higher than that of the MNC (i.e., c > c), the QER reallocates production from theinefficient 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 isindependent of QER. Therefore, in this special case the QER can improve the welfare of theNorth and has no effect on the South’s welfare; i.e., the use of QER can be potentially Paretoimproving.Allowing the value of v strictly < 1 does not change the conclusion on the welfare of the134North but causes the South’s welfare to improve. When v < 1, all of the above results are thesame except (2.6) and (2.8a). Equation (2.6) now becomes it, = -vXp72 > 0, while equation(2.8a) now becomes W = ½{ v[p-c] + c’.-c ) > 0, if c* c. Thus, when a fraction of the MNC’sprofits must be retained in the South, the QER also improves the Northern welfare if the MNC’sunit cost is lower than that of the local Northern firm. The retained profits then improve theSouthern welfare. Therefore, the use of QER can lead to a Pareto improvement in this case aswell.2.2 Export-Share Requirement (ESR)In the real world, most of the MERs are not QER, but they are often defined as aminimum export share to total production. This section will show that the results obtained in theabove example still hold.Recall that x also denotes the exports from the South. Hence, it must satisfy the ESRconstraint: x x[z + x], where o is the minimum export-share requirement and z+x is the South’stotal 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 ESRconstraint. Its maximization problem can be written asMax {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 functionof this problem are:135p(Q) + xp’(Q) — c + .‘.y = 0, (2.10)q(z) ÷ zq’(z) — c — = 0, (2.11)yx- z 0, (2.12)where 2 is the Lagrange multiplier. These three first-order conditions determine the levels of xand z that maximize the profits defined in (2.9). The solution depends on whether the ESRconstraint 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) becomep(Q) + xp’(Q) — c = (2.13)q(z) ÷ zq’(z) — c = 0 (2.14)Consequently, the solutions for x and z are independent of each other and the MNC can solveits profit maximization problem as if these two markets are separated.(2) Restrictive ESR: If the ESR is binding, > 0 and (2.12) holds with equality; i.e.,z = r. Rearranging (2.11) for , we have= q(z) + zq’(z) — c > 0. (2.15)As a result, q(z) + zq’(z) > c or the marginal revenue of z is greater than its marginal cost. Inother words, when the ESR constraint is binding, the South’s output for domestic sales is alwaysunder-produced relative to the output in the case when the ESR is non-restrictive.Substitute z with r in (2.15) to get in terms of x. Then substituting the result in (2.10),the first-order conditions are reduced top() + 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 weightedsum of the marginal revenue of both markets equals the weighted sum of the marginal cost The136weights 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 aimplies a maximum y, denoted by , which is defined by the ratio of where and are thesolutions to (2.13) and (2.14) respectively.To rule out the case of non-restrictive ESR, it is assumed, henceforth, that a is setsufficiently large such that ‘y . With this assumption, the constraint (2.12) always holds withequality. So we can substitute z with x in the objective function in (2.9) and solve as a non-constrained maximization problem. Denote this maximum profit value of the integrated firm byH. 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 } = 0, (2.18)= v { 2p’(Q)÷xp”(Q) +2[2q’()÷yxq”()] } < 0, (2.19)where the first and second subscripts denote, respectively, the first and second partial derivativeswith respect to x. For the local Northern firm, the maximum value of profits is defined as= Max {p(x-t-y)y - c4y }, (2.20)yand its first and second-order conditions are=p(Q) ÷ yp”(Q) — c = 0, (2.21)= 2p’(Q) + yp”(Q) < 0. (2.22)The two first-order conditions (2.18) and (2.21) implicitly define the reaction functions of theparent firm and the local Northern firm, R(y) and Rx), respectively. Together, they determine137the 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 totalrevenue and total cost of the MNC. The level of v only influences the distribution of profitsbetween the MNC and the South’°.For asymptotic stability and uniqueness of the equilibrium, I assume thatH-= { p’[3p’÷Qp11] + } = viz > 0, (2.23)where = v[p’÷xp”], 1t) = Ii y2[2q”÷yxq’’] < 0,h p’[3p”÷Q”p”] + I.7c > 0.Note that terms in parentheses are omitted for brevity. The term p is the slope of the South’smarginal revenue. It is negative since the second-order condition for (2.9): 2q’ + zq” < 0. Giventhat p is negative, it is sufficient to assume” that 2p’+xp < 0 to ensure the negativeness of thesecond-order condition in (2.19). It is also sufficient to assume that 3p’+Qjf < 0 to ensure theuniqueness 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 MNCand the local Northern firm when its rival sales increase. The signs of these two terms can beeither positive or negative depending on the curvature of the demand curves.If the North demand curve is linear or concave; i.e., p” 0, then, whatever the outputlevels, ir,, <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 holdeven when demand is slightly convex. That is, when p> 0 and x (respectively y) is sufficientlysmall such that <0 (4,, <0), the sales of the North’s firm (the MNC) are still strategicThe neutrality of v will prove useful when we analyze the effect of MERs on the welfareof the South.If the MNC were to sell its product only in the North market, this assumption would berequired to satisfy the second-order condition of its corresponding maximization problem.138substitutes. 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 ESRThis section provides analyses of the effects of a small increase in the ESR compared tothe non-intervention situation. These can be done by performing standard comparative staticanalyses of the change in a., then evaluating them at the point where the ESR constraint is justbinding; i.e., at y =(1) Effects on outputs in the North: Totally differentiating (2.15) and (2.18) withrespect to a., we get the following comparative static results:=____> o (2.24)aa2h—‘p (2.25)a2h’where p q + ‘r q’ - c + pxfl. Since i <0 by the second-order condition and h > 0 by thestability condition (2.23), the sign of (2.24) is the opposite of the sign of .From (2.13), we know that ? = q + ‘ q’ - c which is positive when the ESR constraintis binding or zero when the constraint is not binding. Hence, at y = , = 0 and 0 = <0.Thus, the sign of p evaluated at is negativ&2. Therefore, x > 0; i.e., a small ESR increasesthe sales of the MNC in the North.The effect of the ESR on the sales of the local Northern firm is determined by the signof (2.25) which, in turn, depends on both 0 and whether the MNC’s outputs are strategicsubstitutes (i, <0) or strategic complements (4, > 0). Again, evaluating (2.25) at y = , causes12 For a more general cost function; e.g., C = C(x+z), 0 becomes ?+px/y-xC, where p isredefined as y[2q’+vq-C. Then, 0 evaluated at will be negative if C 0.139( = pxl < 0. If the MNC’s outputs are strategic substitutes, 4 are negative, then < 0.However, if outputs are strategic complements, y > 0. The following propositions recap theresults on the outputs in the North.Proposition 1 A small minimum-export-share requirement will increase the MNC’s sales. Itwill decrease the sales of the local Northern firm if the MNC’s sales are strategic substitutes, andvice versa if the MNC’s sales are strategic complements.Note that the term “a small minimum-export-share requirementt’means a small increaseof 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. Anincrease in the minimum ESR (ce) implies that the ratio of the sales in the South over the salesin the North (-y’) must decrease. Thus, given the initial level of sales in the North, the increasein ESR decreases the MNC’s sales in the South. With a downward-sloping marginal-revenuecurve, the decrease in the Southern sales then increases the MNC’s marginal revenue. This inturn signals the MNC to sell more in the South market. In order to do that the MNC must alsoincrease its sales in the North to maintain the minimum export requirement. As shown in Figure4.2, the increase in ESR shifts the reaction function of the MNC to the right and its sales in theNorth expand.The result of the sales of the local Northern firm follows from the first result. A smallESR raises the MNC’s sales in the North. If the MNC’s sales are strategic substitutes, the Northfirm’s best response is to reduce its sales. But if the MNC’s sales are strategic complements, asmall 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 questionis what happens to the total consumption in the North. The following proposition provides theanswer.140Figure 4.2Effects of Minimum Export Share RequirementsyRx)xProposition 2 A small minimum-export-share requirement will raise the total consumption inthe North.Proof: Combine (2.24) and (2.25) to getQci [yx1czh a2h(2.26)Again, evaluate p at y = causes p = <0. Since h > 0 and p’ <0, an increase in cx willincrease Q.flIt is obvious that total sales will rise when the MNC’s outputs are strategic complementssince, by Proposition 1, both sales increase. The results are less obvious when the MNC’soutputs are strategic substitutes because the sales of the two firms move in opposite directions.141However, the change in ESR has a first-order effect on the output of the MNC while it has asecond-order effect on the output of the North’s firm. Therefore, the change of the MNC’soutput always outbalances the change of the Northern firm’s output. So the total consumptionin 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 tworivals. Totally differentiating (2.17) and (2.20) with respect to cx and using the EnvelopeTheorem, we have:it:- [q + yxq’ - cJ}.it6= ypxx.The term in the squared bracket on the right hand side of (2.27) is equal to ./& which becomeszero when it is evaluated at y = . Thus the sign of ç is the opposite of the sign of y sincep’ <0. For it, its sign is the opposite of the sign of x. By applying Proposition 1, we havethe following Corollaries.Corollary 1.1 A small minimum-export-share requirement will decrease the local Northernfirm’s profits.Corollary 1.2 A small minimum-export-share requirement will increase the MNC’s profits ifthe MNC’s outputs are strategic substitutes, and vice versa if the MNC’s sales are strategiccomplements.The intuition for both corollaries is quite straight forward. We know that a larger rivaloutput 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. Since142the MNC’s output is increased by the ESR, the Northern firm’s profits decline. Likewise, theconditions that cause an increase (decrease) in the Northern firm’s output will reduce (raise) theMNC’s profits.These two corollaries show that MERs need not always benefit the MNC, as suggestedin Greenaway (1991). In fact, the MNC can be hurt by the ESR when we take the strategicinteractions into account.As Proposition 2 shows that the ESR increases the total Northern consumption. Theconsumer surplus of the Northern consumers is increased. Could the ESR then lead to animprovement 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 ofthe 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* / * 23O= —pQQ÷it+t.Substituting the results from (2.27) and (2.28) into (2.30) and evaluating 0 at y = , yield= jiK1{[2p’+yp”]y- v[p’+yp”]x- [x+y]p’ }= K{[y-vx][p’+yp” -xjY}(2.31)=-where K1 = xp 7 jct2h <0. The terms outside of the curly bracket are positive since ji <0. Notealso that -xp’ is positive. Hence, when 4 <0, the sufficient condition that makes the sign of(2.31) positive is vx > y. However, if 4, > 0, it is sufficient to have vx <y for the sign of (2.31)143to be positive. Note that even when the MNC is forced to leave all of its profits in the Southor 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 thefirst-order condition (2.18) implies that -xp’=p - c + ‘y[q+zq’-c]. Since = q+zq-c = 0 at thepoint where the ESR constraint just binds, we have -p’=p - c. Moreover, the first-ordercondition (2.21) implies that yp’ = -[p - ce]. Using these two conditions and p” = 0, (2.31)becomesW1. = — [l+v]xp’} = IJ.Ki{_[p_c*] + [1÷v][p—c]} 2.31a)= K1{v[p—c] +— c} > 0, if ct c.The condition is true since p - c = -xp> 0 when the ESR constraint just binds. Notice that thecondition 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 thecase of QER given by (2.8a) in section 2.1.Proposition 3 A small minimum-export-share requirement will increase the welfare of the Northif (a) the sales of the MNC are large (vx > y) and they are strategic substitutes, or (b) the salesof the MNC are small (vx <y) and they are strategic complements. Moreover, when theNorthern demand is linear, the welfare of the North will be improved if the unit cost of the MNCis lower than or equal to that of the local Northern firm (c c*).The proposition can be understood as follows. On the consumer side, a small ESRincreases the total sales in the North by the result in Proposition 2. With the larger sales, theprice is lower. As a result, the duopoly distortion caused by the overcharged pricing above themarginal costs is improved. This reduction in distortion is depicted by an increase in the North’sconsumer surplus. On the producer side, Corollary 1.1 and 1.2 indicate that a small ESR reduces144profits of the local Northern firm, but profits of the MNC (repatriated from its subsidiary) mayincrease or decrease. When the MNC’s outputs are strategic substitutes, by Corollary 1.2, profitsof the MNC increase. If the MNC’s sales are also sufficiently large, the net profits of the twofirms 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, aninitially large sale-volume of the local Northern firm is needed so that the sum of the profits doesnot 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 sideas before. On the supply side, the MNC’s sales are strategic substitutes since the demand islinear. By Proposition 1, the sales of the MNC expand while the sales of the local Northern firmshrink. Thus, the welfare of the North can be improved when c c because production isreallocated to a more efficient source.The above proposition implies that in the presence of imperfect competition, MERs arenot always bad for the source country since they may induce firms in the North to increase salescloser 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 Northernfirm. 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 inProposition 3 holds. This can further complicate the political-economic problems of the TRIMsnegotiations.It is claimed earlier that MERs may not lead to a North-South conflict. The analysis thusfar has shown that MERs can improve the welfare of the North. Hence, it is left to be shownthat they can simultaneously improve the South’s welfare.(4) Effects on welfare in the South: To determine the impacts of MERs on welfare ofthe South, first we have to determine the impacts of ESR on the consumption level of the South.145As we know, the sales in the South when the ESR is restrictive are always less than themaximized 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 yields— x xz= yx -— =___-2 2 2=- h]= h-[3p’ + Qp”] < 0. (2.32)a2h ct2hThe last equality is obtained by using the definition of h from (2.23). Recall that 3p’+Qp” < 0for 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 theMNC 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 bedefined by the summation of consumer surplus, S(z), and profits accrued to the South asW = S(z) ÷ [1 -vi II, where S(z)= f q(i)di - zq(z). (2.33)Differentiate (2.33) with respect to X to getWa = — zq”z ÷ [1v]lla. (2.34)The first term on the right hand side of (2.34) is the change in the South’s consumer surpluswhile the second term is the change in its profits. Since z < 0 by (2.32), the first term is alwaysnegative because -zq > 0. The sign of the second term, nonetheless, can be either positive ornegative.From Corollary 1.2, when the MNC’s outputs are strategic complements, a small ESRreduces the MNC’s profits. That is, the second term on the right hand side of (2.32) is alsonegative. Thus, for these cases, a small ESR decreases the welfare of the South.146However, when the MNC’s outputs are strategic substitutes, a small ESR increases theMNC’s profits. Consequently, the sign of the second term is positive while the sign of the firstterm is negative; hence, the net effect can be either positive or negative. Nevertheless, a smallESR may increase the welfare of the South if v is sufficiently small, since we know that the sizeof v has no effect on the profit maximized level of outputs. Moreover, Z( and Fl are alsoindependent of the size of v. Therefore, if v is smaller, [l-vJfl will be larger while -zq’z0, staythe same. Eventually, for a sufficiently small level of v, the profit gain may outweigh theconsumer surplus loss and W > 0. The condition that causes the welfare improvement in theSouth 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’3E, -lWa = K { [lV][2+Eqfz] — } > 0 if v < q,zEq!,z + 2 (2.35)I Ij2 IIwhere K2 - xzq > , E,q,zSince v is positive, the elasticity of q’ with respect to z, e qçi’ must be greater than one. This inturn requires q’ to be negative. In other words, the Southern demand must be concave and vmust be sufficiently small for the South’s welfare to improve. A concave demand curve meansthat the price increase in the South due to the imposition of the ESR tends to be modest. As aresult, 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).147Proposition 4 A small minimum-export-share requirement with a sufficiently large profit shareaccruing to the South may increase the welfare of the South if the MNC’s outputs are strategicsubstitutes.The proposition can be understood as follows. A small ESR imposed by the South canhelp the MNC to credibly commit to sell in the North more than it would without the ESR (seedetails in section 3). By doing so, the MNC gains market share at the expense of the localNorthern firm and achieves higher profits. As the pie of profits increases, the South gains alarger slice of the benefit. Furthermore, knowing that the MNC benefits from this ESR, theSouth’s government may be able to negotiate for even a larger share. If sufficient gains areretained in the South, they can counteract or even outweigh the loss of consumer surplus incurredby 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 isthat 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 thatthe unit cost of the MNC is smaller than the unit cost of the North’s firm [see (2.31a)J. Thiscondition for the Northern welfare improvement is independent of both the value of v and thecurvature of the Southern demand that are required for the Southern welfare improvement shownin (2.35). Therefore, in this situation a small ESR can be a Pareto improving measure; i.e., bothcountries can be gained by a small ESR’4.3. Optimal MERsThe previous section has shown that a small MER can increase the welfare of the Southby shifting the reaction function of the MNC so that its overall profits increase. Since theAppendix I provides some sufficient conditions under specific situations that ensure bothProposition 3 and 4 to hold simultaneously.148welfare 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 theMER to maximize the welfare of the South? The following analysis will demonstrate that whenthe MER is chosen optimally, it can help the MNC to credibly commit to sell more in the Norththan it otherwise would.To prove this claim, the analysis is separated into two parts. First, I analyze the optimalMER 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 theMER; (2) both firms observe the MER and then choose their quantities x and y simultaneously.3.1 Optimal quantity-export requirementAs before, X denotes the level of export set by QER. We solve the problem by backwardinduction. First, the North’s firm solves its maximization problem given X. This yields thereaction function y = R(X). For the MNC, it solves the maximization problemMax {p(x,y)x + q(z)z — [x+z]c x X } (3.1)x,zwhich gives the reaction functionx = Max{ X, R(y) }. (3.2)Since the South government can anticipate that both firms will respond to X optimally accordingto their reaction functions, the South’s objective function isMax S(z) ± [1—v] ll(x=X,y=R*(X)), (3.3)xNotice that S(z) is not a function of X since z is independent of the export requirementlevel. Also note that, for the time being, it is assumed that the South does not try to choose vto maximize (3.3). Later, v will be chosen simultaneously with X. In this special case the149South’s indifference curves can be represented by the iso-profit curves of the MNC15. Lastly,as an example, the case where the MNC’s sales are strategic substitutes is used Since we knowfrom 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’sreaction function and - HTI is the slope of the MNC’s iso-profit curve. Therefore, the optimalX (when v is fixed) locates at the point where the MNC’s iso-profit line tangents to the Northernfirm’s reaction curve. We can see that this solution is the Stackelberg equilibrium. The case isshown 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 reactionfunction becomes the kinked line ASBD. The solution point is denoted by S (as opposed toNash-Cournot equilibrium denoted by point C). In other words, the MER set in this way allowsthe MNC to achieve higher profits by credibly committing to sell in the North more than it wouldwithout the MER16. As the pie of profit increases, the South gains a larger slice of the benefit.Now let the South government choose X and v simultaneously. Here, a new variable Mis introduced. It represents the minimum profits that the South’s government must allow theMNCs to take. It is used for two reasons. First, the market for FDI is very competitive. To getFDI at all, the South’s government must ensure that the MNCs get a deal at least as good asthose offered by other LDCs. Second, we need a constraint to put a bound on the solution of V.So we have to maximize the South’s welfare subject to the constraint: vFl = M. Hence,The welfare function W is just an affine transformation of H since S(z) is independent ofX and [l-v] > 0.‘ See Brander and Spencer (1983) for the case of R&D as strategic commitment.150Figure 4.3Effects of Optimal Quantity Export RequirementsyA0 XR(y)CSR*(x)X D151v = MILl and [l-v]fl = H - M. Substitute this into the South’s objective function to getMax S(z) ÷ ll(x=X,y=R4(X)) - M. (3.5)xDifferentiating (3.5) with respect to X also gives the same condition as given in (3.4).3.2 Optimal export-share requirementsNow we come back to the case of MER defined by a as a share of total outputs producedin the South. Again the minimum profit constraint is applied here so that v = filM. The South’sobjective function now becomesMax 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 (3.7)II,, llyXaNow we get another extra term- SzJfI,x. The term is negative since Sz < 0, Ll <0, and x> 0. 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 inFigure 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 theNorth’s welfare. This is because the South would try to choose both the MER and the profitsshare so that as many of the profits as possible are shifted to the South. Thus, the aggregateprofits of the North are likely to be reduced drastically so that they will overwhelm the welfareimprovement coming from the reduction in duopoly distortion.1524. MultipIe-duopoly CaseThe result in section 2 has shown that a small MER may result in a potential-Paretoimprovement. It is now interesting to ask whether this result will hold when there is a localSouthern firm which competes locally with the subsidiary of the MNC. The following analysiswill 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 Southernfirm provides an additional channel for the ESR to improve the Southern welfare by shiftingprofits from the MNC to the local Southern firm. Thus, even if the MNC is allowed to take allthe profits generated in the South, it is still possible to get Pareto improvement with the MER.4.1 Minimum-quantity-export requirementsAs there are now two firms competing in the South, the maximized value of the MNC’sprofits becomes:= Max { v [p(Q)x + q(Z)z — [x+z]c ] x X } (4.1)x,zwhere Z denotes the total sales in the South’s market. Solving this problem we have: x = X, andq(Z) + zq’(Z)- c = 0. Clearly, the two markets here are independent. Thus, we can perform thecomparative statics of the QER only on the reaction functions of the firms in the North. Recallthat the reaction function of the local Northern firm is implicitly defined by its first-ordercondition (2.18). Applying implicit function theorem on (2.21) and evaluated at x = X, thendifferentiating,t, iu, and W with respect to X gives the following results*P’ + YP” = - - o if (4.2)2p +yp153= 1+=________2p ÷yp{ Xp”y,] 0 iff 0, (4.4)=< o, (4.5)// { [y — vX]n - Xp” j (4.6)2p ÷ypWe can see that all the results pertaining to the North as stated in section 2.1 hold. Again, if v1, the welfare of the South is unaltered; if v < 1, the Southern welfare will be improved.4.2 Minimum-export-share requirementsLet us move on to the case of the MER defined as a minimum export share cc. The profitmaximization problems of the local Northern firm and of the MNC are the same as in section2.2, except that the argument of the inverse-demand of the South now becomes q = q(r+w),where w is the sale level of local Southern firm’7. The corresponding first and second-orderconditions are, therefore, similar to equations (2.18), (2.19), (2.21), (2.22). As in section 2.2, thetwo markets are linked by the ESR; hence, we cannot ignore the effects of ESR on the domesticmarket as in 4.1. Let Cd be the unit cost of the local Southern firm and define the maximizedvalue of the local Southern firm asip = max { [q(y x +w) — Cd] W }. (4.7)Its corresponding first and second-order conditions areTo keep things tractable, the local-southern firm is assumed to serve only its domesticmarket.154= q + wq”- Cd = 0, (4.8)= 2q’ ÷ wq” < 0. (4.9)The first-order conditions (4.8), (2.18), (2.21) implicitly define the reaction functions of the localSouthern firm, the MNC, and the local Northern firm respectively. Together, they determine theNash-Cournot equilibrium outputs: w=w(o), x=x(ct), and y=y(c).Total differentiate these three equations to get“ww’ Vwx’ 0 dw xlrdafya2(4.10)‘‘ dx= vcpdcqc2o, dy 0For asymptotic stability of the equilibrium, I assume that the two markets are stable bothseparately and jointly; i.e.,° =-> 0, (4.11)H= -> 0, (4.12)J =—< 0. (4.13)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 insection 2.2 yield the following results:*x = >0a2J=-____0 if 0, (4.15)155/—--{it;-;] = -— > 0, (4.16)aJ1*/ VXGPlcyx > . * (4177C vxp a =-o if>0,I ** / Y°P 418<0,a aa2J=- Qp’Q + it + t.= -f;{ [y-vx]it - xp” }a (4.19)> 0 if 7t 0 and vx<y,where a = [v44ç- x7tIJ j/y > 0.The proof for the positive sign of a is provided in Appendix 2. Thus, the results in Propositions1-3 and Corollary 1.1 and 1.2 all hold as before. In other words, a small ESR increases theMNC’s sales in the North, may increase or decrease sales of the local Northern firm, increasestotal consumption in the North, decreases profits of the local Northern firm, may increase ordecrease profits of the MNC, and finally may improve the welfare of the North. All intuitionand explanations given in section 2.2 are applied here as well. Therefore, there is no change inresults 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 staticresults for the South:Za = YXa - { ait - xJ }/a2j=__-{ - - .‘ }a (4.20)x4fi *=___aJvxiji= - p”[3p’ + Qp’] < 0.The third line is obtained by using the definition of J from (4.13) and the last line is obtained156by using the definition of H given in (2.23). The sign of (4.20) is negative because Ps,,, < 0 bythe 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 withthe result in the case where the MNC is the monopolist. The MNC reduces its sales in the Southto export more and satisfy the ESR constraint.The sign for the change in the local Southern firm is given bywa=[H - vp.4 j = VX4Iwxf[3/÷QffJ > 0. (4.21)ya2J ya2JThe sign of w depends on whether the MNC’s sales are strategic substitutes or strategiccomplements. However, it seems reasonable enough to assume that sales of the local Southernfirms 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’soutputs are strategic substitutes for the local Southern firm. Therefore, sales of the localSouthern firm increase.As sales of the local Southern firm increase, its profits rise. This can be shown bydifferentiating (4.7) with respect to ct and applying Envelope Theorem:vxq”wiJ= wq’; p”[3p’+Qp”] > 0. (4.22)2jThus a small ESR also serves as a mechanism that shifts the rent from the MNC to the localfirm.For the impact on total consumption in the South, Z, combining (4.21) and (4.22), give:Za = wa + Za—____< 0. (4.23)a2.!The final form of equation (4.23) is obtained by using ‘+‘, from (4.9) and = y[q’+wq”] andrearranging terms. Equation (4.23) tells us that a small ESR reduces total consumption in the157South 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 theMNC’s reaction function in the Northern market to the right it shifts the MNC’s reaction functionin the Southern market to the left. As a result, sales of the MNC decline. Sales of the localfirm, then, increase since the MNC’s sales are strategic substitutes for the local firm. Totalconsumption must decline since the reduction in the sales of the MNC has the first-ordermagnitude while the rise in the sales of the local firm has the second-order magnitude.Finally, define welfare of the South asW = S(Z) ÷ [1—v]ll ÷ (424)This is similar to the one defined in section 2, except that the consumer surplus now depends onthe total sales of both firms and the profits of the local firm are added. Differentiate the welfareof the South with respect to c to getW = - Zq’Z + [1—v]ll + 7. (4.25)Like section 2, the first term is the reduction in the South’s consumer surplus while the secondterm is the change in the MNC’s profits retained by the South. Again given that the MNC’ssales are strategic substitutes, the Southern welfare could improve if the value of v is sufficientlysmall.The extra welfare effect that turns up when a local Southern firm is added to the modelis depicted by the third term. This positive P is an increase in the profits of the local Southernfirm. 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 that158the possibility of welfare improvement of the South relies on the South’s ability to capture theMNC’s profits. In reality, most MNCs often manage to avoid this profit capturing (i.e., by usingtransfer 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 welfareimprovement of the South would be much higher. In fact, even when the MNC can keep all theprofits 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 getW=K3{ [w-’-z]q’ — = K3{ [w+z]q’ — w[2q’÷w] }- K3{ [z-w]q - (w) q (4.26)I If 2 1 11 1where K = vxq P L .-‘P p . >cz2JNow 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 haveWa = K3{ c-c—(w)2q”} (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 Southernwelfare if and only if the local Southern firm has a lower unit cost than that of the MNC (orc > c)’8. A cost advantage of the local Southern firm ensures that the profits shifted from theMNC are large enough to overtake the consumer-surplus losses. However, a small ESR will notaffect the welfare of the South if both the local Southern firm and the MNC’s subsidiary havethe same unit cost (or c = Cd).Second, when the South demand is not linear and c = c, a small ESR will improve theIS This is the exact condition for welfare improvement given in Davidson et al. (1985).159South’s welfare if and only if the South demand is concave (or q” < 0). This condition ensuresa welfare improvement because a concave demand curve associates with a smaller consumer-surplus 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)becomesw, = -P-{yp’-2xp’}u2Ji (4.28)= —-{[p—cJ ÷c —c}a2J> 0 if c c.The second step is obtained by using yp’ {pc*], and -xp’ = [p-c] when the ESR constraint justbinds. Thus, a small ESR can be Pareto improvement when the North’s demand is linear, theSouth’s demand is linear or concave, and c c c.5. ConclusionThe main point of this paper is to show that minimum-export requirements (MERs) canbe Pareto improvement measures. The paper employs a two-country model where one countryis the source of foreign direct investments (FDIs) and the other country is the host. The FDIsare conducted by a multinational corporation (the MNC) for which the parent firm is located inthe source country. The parent firm has to compete with another local firm for its domesticmarket. The subsidiary firm may be a monopolist or may compete with another local firm. Thehost country requires the MNC to export a minimum quantity or a minimum share of its totalproductions. It is found that under this situation the impact of MERs on the North depends uponthe strategic interactions between the rival firms in the source country. The MER imposed onthe MNC can help the MNC to gain a strategic advantage with respect to its rivals by being160considered as a credible commitment by the MNC to sell more than it otherwise would. TheMNC will gain the strategic advantage when its sales in the source country are substitutes. Thestrategic advantage will shift toward the local firm in the source country, however, if the MNC’ssales are strategic complements. A MER policy can improve the welfare of the source countrysince it increases the total consumption of the source country, thereby reducing the duopolydistortion. It can also improve the host-country’s welfare by shifting profits from the MNC tothe local firm in the source country. When the local firm does not exist, the host-country’swelfare can still be improved if a sufficient amount of the MNC’s profits is retained in the hostcountry.Some extensions are possible. First, the duopolistic market structure can be extended tothe case of oligopoly. As long as the size of the MNC’s sales is still large, most of the resultsobtained here should hold. Second, it is possible to modify the model to capture a three-countrycase in which the MNC locates in the East and exports to compete with the local firm in theWest. Again, MERs can be viewed as tools to help the MNC to credibly commit its sales higherthan it normally would. In such a case, it is possible that the East and South may gain fromMERs at the expense of the West.161Appendix1. Sufficient conditions for W> 0 and Pareto improvementSubstitute the value of x0, from (2.24) into it in (2.27), then use the result with the valueof z. from (2.32), and the definition of p in (2.34) to getWa-•-{ zq”[3p”÷Qp11]— [1—v]x[2q”÷zq”]r }a h (1.1)—[1—vj[2q’÷zq1j[p”+ypJ — qE’[3p1’+QpU] }.a2h(a) Linear Northern demand: When the North’s demand is linear or = 0, (Al)becomesWa = — [1—v][2q’+zq’jY — 3p”q’ }cch=— xzq[p’] [1 —v][2 + - 3a2h q’K { [1V][2+Eqf,z] — 3 } (A.2)E, -1> 0 if v < q,zEqIz ÷2I 112 IIwhere K2 - xzq ‘ > 0, EqI,zah qSince v is positive, the elasticity of q’ with respect to z, E q’.z must be greater than one. This inturn requires that q” must be negative. In other words, the Southern demand must be concaveand v must be sufficiently small for the South’s welfare to be improved. Note that theseconditions do not conflict with the condition (2.31 a) that ensures welfare improvement of theNorth.(b) Linear Southern demand: When the South’s demand is linear or q = 0, then (Al)becomes162=— XP’Z{ 2[1—v]q’p”÷yp”]— q”[3p”+Qp”J }(1.3)— { 2[1—v][p’+yp’’] — [3p’+Oji”] }.ahNotice that the term outside the curly bracket is negative and recall that 3p’+Qp is negative [toensure 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 restrictionis needed. Recall from Proposition 3 that when the MNC’s sales are strategic substitutes (i.e.,it <0), it is required that the MNC’s sales must be greater than those of the North’s firm (i.e.,x > y). 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