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International trade policy, oligopoly and learning-by-doing (with applications to the international aircraft… Fok, Andy K. 1992

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International Trade Policy, Oligopoly andLearning-by-Doing (with Applications to theInternational Aircraft Industry)byANDY KA-PO FOKB.Sc., Simon Fraser University, 1987M.A., The University of British Columbia, 1990A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THEREQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE(BUSINESS ADMINISTRATION)inTHE FACULTY OF GRADUATE STUDIES(THE FACULTY OF COMMERCE AND BUSINESSADMINISTRATION)We accept this thesis as conforming to the required standardTHE UNIVERSITY OF BRITISH COLUMBIAOCTOBER, 1991© Andy Ka-Po Fok, 1991In 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 Commerce and Business Administration The University of British ColumbiaVancouver, CanadaNovember 10, 1991DateDE-6 (2/88)11AbstractDespite the non-cooperative outcome predicted by the model of Prisoner Dilemma, throughoutthe history of international trade, mutual conflicts leading to an equilibrium which has the lowestjoint payoffs is not so frequently observed. Trade barriers have indeed been gradually removedsince the end of World War II. The objective of this thesis is to investigate various policyimplications for international trade under duopoly with learning effects and to examine underwhat assumptions of strategy adopted by the rival will result in trade disputes. Interestingly, theadoption of a "tit-for-tat" strategy can be claimed by a government to achieve free trade. In thispaper, four major results are obtained. All theoretical results involve a duopolistic industry inwhich two firms, belonging to two different countries, attempt to export a homogeneous goodto a third market. Assuming a Cournot game for competition at the firm level, and a "tit-for-tat"strategy adopted by the rival, the first result indicate that the presence of learning effects rendercooperation (removal of subsidies) between governments difficult to achieve. The second resultshows that in a dynamic economy with infinite horizons in which a government only plans fortwo periods, a policy of unconditional free trade cannot provide sufficient penalties because thegains from going down the learning curve through production subsidies outweighs the lossesfrom retaliation. The third objective of this study is to evaluate the validity of infant industryargument under duopoly. Fourth, I examine the civil aircraft manufacturing industry which hasa very close market structure discussed in this paper using two different approaches: a generaldescriptive case study of the industry and an empirical evaluation of its performance in the pasttwenty years.iiiTable of ContentAbstract ^  iiTable of Contents ^  iiiList of Tables  ivList of Graph  vAcknowledgement  viAbstract ^  iiIntroduction  1Other Related Literature ^  7The Structure of the Game  9The Nature of a Trade Agreement ^  10The Modelling of Learning Effects  12The Model ^  13First Stage: Free Trade vs. Optimal Subsidy ^  15Second Stage: Free Trade vs. the Cournot Nash Equilibrium ^ 22Unconditional Free Trade without Learning Effects  28Second Stage: Free Trade vs. the Cournot Nash Equilibriumwith Learning Effects ^  29Implications ^  37Unconditional Free Trade with Learning Effects ^  38Summary of Results  40The Infant Industry Argument ^  43Case Study: Civil Aircraft Manufacturing ^  57Empirical Evidence ^  64Test for Heteroscedasticity and Autocorrelation ^  66Test for the Decline of the Civil Aircraft Industry  68Concluding Remarks ^  75Appendix ^  78Bibliography  94ivList of TablesTable 1, Payoffs in a Static Model ^  39Table 2, Payoffs Relative to Free Trade  40Table 3, Whether Free Trade is a Solutionwith Weak Learning Effects ^  41Table 4, Whether Free Trade is a Solutionwith Strong Learning Effects  41Table 5, Estimated Coefficients of RelativeWeight in the Aircraft Industry ^  65Table 6, Important Statistics of RelativeWeight in the Aircraft Industry  65Table 7, Estimated Coefficients of US MarketShare ^  71Table 8, Important Statistics of US Market Share ^  71VList of GraphsGraph 1: Total Seats, US ^  80Graph 2: Total Seats, Airbus  81Graph 3: Total Seats, US & Airbus ^  82Graph 4: 737, Number of Aircraft  83Graph 5: Airbus 300/310, Number of Aircraft ^  84Graph 6: Market Share of US, Number of Aircraft  85Graph 7: Wages Differnece ^  86Graph 8: Wages Ratio  87Graph 9: Returns to Employee ^  88Graph 10: Returns on Equity  89Graph 11: Returns to Seat ^  90Graph 12: Manufacturing Ratio, Aircraft and Auto ^  91Graph 13: Manufacturing Ratio, Aircraft & Computers  92Graph 14: Productivity Comparision ^  93viAcknowledgementI would like to thank Professors James Brander, Keith Head, and Ilan Vertinsky as membersof my thesis committee. Professor Brander has provided me with invaluable assistance tonot only the completion of this paper, but also the development of my critical thinking. Iwould also like to thank Professors Keith Head, Tae Oum and Ilan Vertinksy for theirhelpful suggestions. I, of course, bear all responsibility for errors.1Introduction"Should we support free trade with the U.S.?" was a question that appeared mostfrequently during the last election in Canada. Similar questions will perhaps be asked againwhen North America is facing more and more pressure from the European Community incertain subsidized industries. The purpose of this paper is to give an explanation for tradedisputes under different circumstances. These circumstances include (1) the strategy that onegovernment believes the other adopts and (2) the presence of learning effects in aduopolistic industry. Another purpose of this paper is to examine whether or not subsidiesare justified in an infant industry with strong learning effects and to use the internationalaircraft industry as an example to explore what has happened to the aircraft industry whichhas a similar market structure discussed in this paper.The investigation of the impacts of learning effects upon imperfect competition and tradepolicies is the first focus of this paper. Brander and Spencer (1985) offer a possibleexplanation for exports subsidies based on market structure. Krugman (1984) uses ageneralized version of the model developed by Spence (1981) to show that there is asimilarity between dynamic and static economies of scale; both studies result in a tendencyfor a government to adopt strategic trade policy. To the best of my knowledge, this paperis the first one which attempts to explore how the introduction of learning effects andmarket structure will affect the behaviour of a government in deciding on whether it shouldsubsidize its industries. My results show that market structure, together with strong learningeffects, can be used to explain certain phenomena which cannot be satisfactorily answeredby market structure alone. Under the assumption that a government agrees to remove2subsidies only if the benefits of doing so outweigh the losses, the results generated from amodel under a duopolistic market structure with strong learning effects are different fromone without. With the development of GATT (General Agreement on Tariffs and Trade)in the post-war period and the recent trade disputes in certain industries, the results of mymodel can be used to explain this phenomenon: because of the strategic advantage ofsubsidizing a high technology industry that exhibits strong learning effects, it becomes moreand more difficult than before for countries to agree on the mutual benefits of free trade.In other words, it is not necessarily true that a duopolistic market structure will result intrade disputes. However, under a duopolistic market structure and strong learning effects,a government may find that even if the rival retaliates with optimal subsidies in the nextperiod, it is still worthwhile to subsidize the domestic industry in the current period. Suchresults suggest that governments should take care in selecting the industries for which theyintend to provide a targeted trade policy. Governments should not simply identify anindustry in which imperfect competition exists to apply a strategic trade policy; othercharacteristics, though not necessarily only the learning effects as this thesis discusses, mayalso be relevant. However, the model used in this paper clearly illustrates that a duopolisticmarket structure alone cannot provide an incentive for a government to subsidize itsindustries (if the behaviour of a government in deciding on whether it should imposesubsidies is determined by the strategy of its rival); only a duopolistic market structure,together with strong learning effects, will increase the relative gains in trade intervention.3I assume the strategy adopted by the rival in the second period is "tit-for-tat". A "tit-for-tat"strategy, though not as logically coherent as a strategy based on optimization, has strongempirical support. We have reasons to believe that a country will sign a trade agreementbecause of the fear of retaliation. In fact, how a country "thinks" the rival will behave in thesecond period has very important implications to the policy the country pursues in the firstperiod. If a country thinks that the rival adopts a "tit-for-tat" strategy, the behaviour of thatcountry is different from that if the country thinks the rival adopts a policy of unconditionalfree trade. However, the decision of which action to choose must reflect the costs (in thesecond period) of not cooperating in the first period versus the benefits of not co-operatingin the first period. Cooperation, in the context of this paper, means a policy of non-intervention, i.e., not to impose any subsidies. In ongoing dynamic games, "tit-for-tat" hasbeen shown by Axelrod (1984) to be a successful strategy. Here I focus on two periods ofa larger game and I assume that country B follows a tit-for-tat strategy. I then examine thebest response of country A and show that learning effects can have an important effect onwhether we get "free trade" as a solution. The same result will be compared to anotherassumption that country B follows a policy of unconditional free trade. With the basicstructure discussed in this paper, the two-period economy used here can be easily expandedto a multi-period horizon; however, for the sake of tractability, I start with a two-periodeconomy.4In the past decades, a number of high technology industries have evolved which exhibitdynamic economies of scale or strong learning effects. As defined by Spence (1981), thecurve "that relates unit costs to accumulated volume" is called the learning curve. 1 Learningeffects are then the reduction of unit costs (or marginal costs) in proportion to pastaccumulated production. The semiconductor industry is one that incorporates strong learningeffects. High volume production provides a firm with a strategic advantage in the long runbecause skills acquired in manufacturing a large-volume product help to drive the firm downa very steep learning curve. This industry is now dominated by Japan and the U.S..Unconditional free trade becomes less and less favourable to the U.S. as Japanese marketsremained closed while Japanese companies were expanding their market share. As aconsequence, in 1987, the U.S. government imposed 100% tariffs on $300 million worth ofJapanese consumer and office goods.2 Should a country unconditionally support free tradein a duopolistic industry? The above question is the second focus of my thesis.The infant industry argument is one of the most strongest arguments against free trade.To explore whether a government really gains from subsidizing a dying industry within aduopolistic market structure and learning effects is the third focus of this thesis. For thesake of simplicity, I assume that the industry in one country is so inefficient that it is onlyable to survive under subsidies. If the subsidies were to be removed, this industry would bewiped out of the market and the rival would enjoy a monopolistic status. In subsidizing itsindustry, a government would have at least two expectations: (1) that subsidies can be'Spence, A.M., "The Learning Curve and Competition", Journal of International Economics 12 (1981), 49-70.2Yoffie, David B. and Helen V. Milner, "An alternative to Free Trade or Protectionism: Why CorporationsSeek Strategic Trade Policy?" California Management Review (1989), 111-131.5phased out in the future as the industry "learns" how to compete more effectively and (2)that the artificial maintainance of duopolistic market structure creates a loss in producersurplus relative to monopoly, and that loss decreases under learning effects. However, theseexpectations are not true as shown in my model. In other words, the presence of learningeffects cannot improve a subsidized duopolistic market structure in comparison withmonopoly. It should, of course, be noted that the above results are based on a veryrestricted set of assumptions, such as the same learning rate or the taking of only a firstorder Taylor's approximation. If the learning rate of the less competitive country is very highcompared to that of the other country, then the level of subsidies may be phased out.Similarly, if a second or third order Taylor's approximation is taken, then the effects ofsubsidies in the next period will also be amplified, resulting in a reduction of the level ofsubsidies.6The competition between Airbus and Boeing fits quite well into the framework describedin this thesis. Hence, my fourth objective is to use the American civil aircraft manufacturingindustry as an indirect example of how this industry has performed in the past two decadesin which it has been subjected to subsidized competition from Europe. Although thisempirical example is only loosely linked to my first three theoretical sections, the result canprovide more insight into the practical side of a duopolistic industry. Such an endeavourmight prove to be a very good indicator of relative growth or decline in this industry.In summary, this thesis will show the followings. (1) the necessary conditions for agovernment to subsidize its industries include both a duopolistic market structure and stronglearning effects. A duopolistic market structure alone is not sufficient to result in tradeintervention in the framework presented here. (2) If the industries in both countries "learn"at the same rate and the objective of subsidies is to remove the difference in marginal costs,then subsidies cannot be phased out in the future. Production subsidies result in the shiftingof market share from the rival, as indicated by the decline of relative importance in theaircraft industry in the U.S..7Other Related LiteratureInternational trade under imperfect competition has drawn special attention frominternational economists in the past decade. This attention is often linked to productivitydeclines in certain high technology industries, most notably in the U.S., which was once thelargest free trade supporter in the world. The definite gains from free trade were firstchallenged in the business world; the academic field was quick to follow suit. One of themost influential papers in this area is that written by Brander and Spencer (1985) whichopened a new line of thought in the field of "strategic trade policy." Traditional internationaleconomics usually ignores the impacts of participants' decisions on market prices andnormally concludes that unconditional free trade is the first best optimum for not onlynational interests but the world as a whole. In contrast, the new strategic trade theory, withits assumption of a small number of participants in the market and its recognition ofindividual impacts on the market, not surprising, comes to the conclusion that tradeintervention may better serve national interests. Criticism has been intense ever since thenew strategic trade theory appeared. The lack of a general equilibrium approach is one ofthe shortcomings in the strategic trade model. Dixit and Grossman (1986) show thatrepercussions on other areas should not be overlooked when one considers strategic tradepolicy. Sensitivity to the results of small changes in assumptions is another shortcoming ofthe model. Eaten and Grossman (1986) adopt the assumption of Betrand (prices) ratherthan Cournot (quantities) competition. The policy implication is just opposite to that ofBrander and Spencer (1985): an export tax rather than a subsidy is the appropriate policy.More recent literature includes Fung (1990) and Klepper (1990). Fung (1990) examines amodel of collusive intra-industry trade under a duopolistic market structure and studies its8important properties. He shows that collusive intra-industry trade is more sustainable if thecost differences between the producers are smaller. For this paper, cooperation is definedto involve the removal of subsidies only. For the sake of simplicity, I do not consider thecollusive result in terms of the level of output. I will touch on this subject in the appendix.However, for detailed analysis in this area, Fung (1990) offers an in-depth answer to thissubject. In the civil aircraft industry, Klepper (1990) used a calibration model to show thatAirbus' entry into the market reduces Boeing's profits because of learning effects. He alsouses a capacity game to show that the disadvantage of late entry is overcome only after along time and hence, market entry is unlikely without government subsidies.9The Structure of the GameFor the sake of tractability, the model assumes multiple time horizons. However, thegovernment of either country formulates its trade policy based on the costs and benefits foronly the next two periods. In other words, the discount rate for the next two periods is 0 andthat for later periods is infinitely large. Although this assumption may be simplified, if wedefine each period to be four or five years, the end result will be quite close to what isobserved in a democratic country where an elected leader has power to shape its policy foronly a limited time period. A firm plans for an even shorter period in this model; it choosesproduction to maximize profits for only the next period. Firms are competingnoncooperatively in terms of quantities. Hence the Cournot equilibrium is a naturaloutcome. Governments, however, behave in a more complicated way. Since governments ofboth countries are able to look at one period further than do firms (perfect information isassumed), governments recognize the benefits of producing one extra unit in the current andin the next period. These benefits stem from two sources: supernormal profits from the rivalin the current period due to the duopolistic industrial organization, and the reduction inmarginal costs in the next period due to the learning effects. Because of these benefits, thefirst optimal outcome with unilateral removal of subsidies is difficult to achieve.The structure of the game can be summed up as follows: firms play a noncooperative gamein each period, while governments play a cooperative game if each of them finds that thebenefits are greater than the losses; otherwise they play a noncooperative game. Acooperative game means that both governments agree not to impose any subsidies in both10periods. The necessary and sufficient condition for a cooperative outcome is that futurelosses in retaliation outweigh the present gains from noncooperation. Under a cooperativeoutcome, the behaviour of the two governments are fixed; subsidies will not be used asstrategies.The Nature of a Trade AgreementUnder the assumption of perfect information, both countries know that the joint beneficialoutcome is free trade, as discussed by Brander and Spencer (1985), that is, when bothcountries do not provide industries with any production subsidies. However, if either countrybelieves that it is worthwhile to not commit to free trade, then the noncooperative outcomeis that both governments give optimal subsidies to their industries. To enforce the first bestoptimum (i.e. free trade), a contract or agreement that precommits the action of eithercountry is needed. The objective of the agreement is to ensure that both countries maintaina zero subsidy level during the next two periods. For the sake of simplicity, we assumed thatthere is no precommitment problem -- the case in which a government does not commit toa certain promise as the environment changes in the subsequent period -- because thepenalty is sufficiently large to deter either country from cheating. Suppose the agreementis being signed at to, and the agreement will be reinforced at t 1 and t,. At to, the decisionmade by a government to sign this agreement is dichotomous: a government will only signthe agreement if, after evaluating the benefits and costs of committing to the agreement inthe next two periods, it is worthwhile to do so. In other words, the necessary and sufficientcondition for a trade agreement to he made is that the costs of the noncooperative outcome11(both countries providing optimal subsidies) compared to free trade at t 2 are larger than thebenefits (domestic government gives optimal subsidies and foreign government does not)compared to free trade at t1. The cost-benefit analysis used in this paper is similar to the oneused by Fung (1990) who wished to look at the possibility of cooperation in the firm levelunder the assumption of imperfectly substitutable goods in a duopolistic industry.12The Modelling of Learning EffectsThe learning curve assumption is that marginal costs are a decreasing function ofcumulated output. I use the following functional form to capture this idea.f(x) = Ce -"xicf(0) = Cwhere f(x) is the marginal cost after an accumulated production of x, C is the initialmarginal cost, and -Ax is the elasticity of learning effects.The first derivative of the right hand side is as follows:f(x) = -4e-"xicf (0) = -4Let MC(x) represent the marginal cost in the second period, and x be the production levelin the first period (since only two periods are considered in this model, accumulatedproduction in the second period simply equals production level in the first period).13Since a government considers the impact of its trade policy for only the next two periods,there will be no loss of generality by taking a first order Taylor's Expansion as follows:MC(x) = f(x) f(0) + x f(x) = C - /IxIf we use subscript 2 to represent time period 2, marginal cost at time period 2 is C2 = C 1-The ModelIn the following section, I shall use a multi-period (in which only the next two periods areseriously taken into consideration by the government), two-country, one-good model tosuggest that market structure is not the major cause of the recent standstill in trade barriernegotiations such as GATT. Recent literature, including Brander and Spencer (1981,1985),Grossman and Eaten (1986), and Krugman (1984) among others, attempts to place a strongemphasis on the role of market structure in explaining the incentives for trade intervention.Trade theories based on market structure can no doubt be used to explain certainphenomena which cannot be satisfactorily explained by theories based on factorendowments, such as the Ricardian model or the Heckscher-Ohlin Theory. Market structureis particularly successful in explaining intra-industry trade. However, it is insufficient toconclude that market structure and imperfect competition form the only rationale ofintervention in trade, an opinion which is quite popular in recent literature, and is14repeatedly emphasized in the book written by Krugman (1989).3 According to the resultsderived from my model, it is learning effects in addition to market structure, not marketstructure alone, that prevent a trade agreement from being acceptable to both sides.Moreover, what strategy a country "thinks" the other will adopt have strong implications tothe acceptance of a trade agreement.The following section illustrates that cooperation between governments can be sustainedif country B is believed to adopt a tit-for-tat strategy, that is, if country A believes that if itimposes an optimal subsidy in the first stage of the game, country B will impose an optimalsubsidy as well in the next stage, resulting in the imposition of optimal subsidies in bothcountries.3Helpman, Elhanan and Krugman, Paul R.. Trade Policy and Market Structure. Cambridge, Mass: MIT Press,1989.15First Stage: Free Trade vs. Optimal SubsidyLet us begin with the case in which learning effects are not present. Suppose that countryA and country B are exporting the same good to a third market in quantities x and yrespectively, and that both countries initially have the same marginal cost. The first bestoptimum condition having the highest joint payoffs occurs when both countries impose zerosubsidies. Assuming linear demand, p(x,y)= a-b(x+ y) and constant marginal cost, c, profitfunctions for A and B arerA = xp(x,y) - cx = x(a-b(x+y))-cx7r B = yp(x,y) - cy = y(a-b(x+ y))-cy16First order conditions are given as follows:a - 2bx - by - c = 0a - bx - 2by - c = 0-2b -21{1 = [c-al-2b -2b y^c-ax^1 [-2 1  [c-a^1{a-c1. i_^3b a-cb 1 -2 c-a Y(1 )Based on the gain or payoff function of the government as defined by Brander andSpencer (1985), the payoff of country A of not a adopting strategic trade policy is given byGxNN = 77-A - xs(2)where s is per unit production subsidies.17Since s = 0, if a strategic trade policy is not adopted, thenGxNN = 7TA = (p(x,y) - c)x=(a - b(x +y) -c)x=(a -c - —2 (a -c))x3(a-c)2)Similarly, payoffs for country B under free trade are given by1GYNN = 9b (a -c)2Now suppose that country A imposes a per unit subsidy s to its industry. The profitfunction of A becomes:7r-A = xp(x,y) - cx = x(a-b(x + y))-cx + sx7r-B = yp(x,y) - cy = y(a-b(x+y))-cyFirst order conditions are given as follows:a - 2bx - by - c + s= 0a - bx - 2by - c = 09b(3)(4)18-2b -2b [x), ^{c-a-1-2b -2b^c -ax^1 -2 1  {c -a -s ^1 [(2-c+2.1= —y^3b 1 -2 c -a^3b a -c -sThe best that country A can do by adopting a strategic trade policy is to impose an optimalsubsidy. Optimal subsidy is the level of subsidy that maximizes the payoff function forcountry A, as suggested by Brander and Spencer (1985), such thataG xSNTC^ (7)- s - X -SX3 = 0as(5)(6)For country A,19ns= nxxs +nyYs +xnx= 0^'It s = 71)37s + XaGxsN_0_,Ityys +x-x-sxs =0as.mat_ nYYssopaXs_ -1 ^. 2Ys- 3b' x s^3b^a2Gx^-1 2^2SN --b()—()as 2^3  3b 3b2^2=( 9b ) -( ^s 0(8)(9)20Therefore, GxsN is concave in s and if the first derivative of GxsN equals zero, then thatmeans GxsN is maximum.From (8), .0'1 -  bxYsxs-11^3b= -b(—)(a -c +2s)3 b 23b= —1 (a -c +2s)s = —1 (a-c)1 3 ( 1 _ a -c = 1 3 (a -0 _ a -cx= 3b2‘ ti-c) - 2b ; y 3b 4^4bX^1^a - c _ (a - c)2G i sN = (p(x,y)-c)x =(a -b(x -y)-cx = -,i (a -c)2b^8bG Y1 _  (a -02SN 16b(10)From (6),21Optimal subsidies imposed by A makes B worse off becauseG Y1 > GYISNNNi.e. payoffs to country B in free trade > payoffs to country B if A imposes optimalsubsidies.This is the profit-shifting motive for subsidizing a firm in a static framework. The firm incountry A is doing better than that in country B because of the subsidies. This result isindeed nothing but a simplified version of the model used by Brander and Spencer (1985)in which demand is linear and marginal cost is constant. The simplification is intended tomake the impacts of learning effects easier to demonstrate.22Second Stage: Free Trade vs. the Cournot Nash EquilibriumBased on the result of the previous section, I shall investigate the possible impact of a "tit-for-tat" strategy by country B on the possibility of cooperation at times 1 and 2. I assumethat "tat" or punishment is represented by country B playing the one-period noncooperativeNash subsidy. Cooperation (i.e. free trade) will be enforced by a trade agreement providedthat the following cost-benefit analysis condition is met:- (G x2 55 - G x2 NN) > (G x1 sN-G x1NN)Let us suppose that, before making a commitment to free trade, a government wouldevaluate the possible benefits and costs of subsidization. If I assume that country B followsa "tit-for-tat" strategy, the above inequality represents such an evaluation mathematically.The noncooperative outcome for country A is represented by G"ss on the left hand side ofthe inequality, which means losses to country A in the second period because country Athinks country B will respond with an optimal subsidy to retaliate against country A whichimposed an optimal subsidy in the first stage of the game. In other words, G'ss is the payofffor country A in a Cournot-Nash equilibrium in which both country A and B impose optimalsubsidies in the second period. Gx 2NN is the payoff of a cooperative free trade equilibrium.The left hand side of the inequality represents the losses to country A in the second stageof the game (compared to free trade) if it imposed an optimal subsidy to its industry in thefirst stage of the game while country B remained adopting a policy of free trade. In otherwords, the losses to A are based on the assumption of the adoption of a "tit-for-tat" strategy23by B. The right hand side of the inequality represents the gains to country A (compared tofree trade) if it imposes an optimal subsidy to its industry in the first stage of the game. Theinterpretation of inequality (11) is simply that if relative losses in the second stage are largerthan relative gains from defection in the first stage, then country A will have no incentivesto deviate from cooperation; hence an agreement will be acceptable to both countries. Iassume that a country defects by imposing optimal subsidies, given that the rival remains infree trade in the first period. Once an agreement is signed, cooperation (i.e., in which bothcountries remove all subsidies) can be enforced.24To find G'ss (the payoff for country A in the second stage if country B retaliates byimposing an optimal subsidy), I shall first find out the simultaneous equation of the optimalsubsidy for one country in terms of that of the rival, and then solve for s and s * , whichrepresent the optimal level of subsidy for countries A and B respectively.Now suppose that countries B imposes per unit subsidies s to their industries. Profitfunctions for A and B become:rA = xp(x,y) - cx = x(a-b(x + y))-cx + sxyrB = yp(x,y) - cy = y(a-b(x+y))-cy+ s*yFirst order conditions are given as follows:a - 2bx - by - c + s= 0a - bx - 2by - c + s * = 0{-2b -2/ [1 {c-a-si(12)-2b -2b y^c -a -s*25from (8)xi^1 -2 1 }1^-2ainceS7Vs[ c-a-sc-a-s *2—=—;as^3bA^-bx—yy sila-c+2s-s3b a-c-s+2s*ay^-1y^3boptimal---as^3b13b^3bx^a-c+2s-s*xs^2^6 63b4s = a-c-s*4s +s * =a -c(13)Similarly optimal s* _-1B^-by_n xxs• _ _^3b^3by^a-c+2s*-s_^_Ys•^2^6 63b4s *+s=a-cFrom (13), s *+4s=a-c^1 a^-c4^is .^1 4 a-c= {[s 1s . 11 5 [4 1 -41  [a il1{al5 a-cx = —2 (a-c); y = —2 (a-c)5b^5bG xss = (p(x+y)-c)x = (a-b(x+y)-c)x = 25b—2 (a-c)2 = GY ss(14)The Nash equilibrium, as represented by the payoff G' ss, is the noncooperative outcomewithout an agreement, in which both governments act noncooperatively. Each governmentattempts to maximize its gains using optimal subsidy levels, and takes the other's action as26given. The net consequence is an equilibrium given by the solution of reaction functions ofeither governments' subsidy level in terms of the rival's subsidy level. The Cournot-Nashequilibrium, despite its naive nature, is one extreme scenario which a government mustconsider before considering a free trade agreement; such an equilibrium tells what thepayoffs would be without an agreement if the rival adopts a "tit-for-tat" strategy to retaliateagainst country's A defection in the first period. 4 Since marginal costs are the same in bothstages when learning effects are not present, the above payoffs are the same in both stages.From (11), if the following condition is true, then cooperation can be enforced without abinding agreement.-(Gx2 ss — G X-2 NN) > G x isN-G x iNN(15)That is equivalent to show whether 2G xNN-G XSS -G xSN > 0 (*)since Gx2NN=G xi NN =. G xNN9 G x2 55 =G x1 ss=G xss, G x2 SN =Gx1 SN =G XSNin the absence of learning effects.2^1(*) = —29b(a-c)2 25b-^ (a-c)2 --8h(a-c)2 > 0Hence, cooperation can be enforced.(16)Using the above simple cost-benefit analysis, the profit-shifting motives of a duopolisticmarket structure are not sufficient to prevent cooperation between governments. Now the'This does not imply that a government cannot do worse than a Cournot-Nash outcome. As shown earlier,the payoff function is concave in s. By imposing a subsidy higher than the optimal subsidy, both governmentshave a net payoff that is less than the Nash outcome. This case, however, is inconsistent with our earlierassumption that a government is maximizing its payoff function. Thus, imposing a subsidy higher than the optimallevel is ruled out.27question is, what other conditions, in addition to market structure, can make tradeintervention relatively beneficial to a country even under the retaliation from the rival? Anindustrialist may claim numerous characteristics that would make trade interventionbeneficial. However, one of the most relevant characteristics comes from learning in adynamic economy: the more a worker does, the better he/she will do the job. In a two-period model, "more" can be modelled by the amount of production in the first period;"better" can be modelled by the reduction of marginal cost in the next period. With thissimplification, the learning effects can be easily introduced into a model with a duopolisticmarket structure. Hence, the first focus of this paper is to show that learning effects willchange the relative payoff in the second stage, making relative gains larger than relativelosses due to retaliation. As it will be shown, a government may find that the scenario inwhich the rival retaliates will improve under strong learning effects because subsidizingproduction in the first stage reduces marginal cost in the second stage. Before I illustratethe impacts of learning effects in a dynamic economy, let me first show what will result froma policy of unconditional free trade.28Unconditional Free Trade without Learning EffectsIn the context of this paper, unconditional free trade means that a country will not imposeany subsidies to its industry regardless of what the rival has done. Would country A still findcooperation the first optimum if it knows a priori that country B adopts a policy ofunconditional free trade? The answer is no because, as it will later be shown, unconditionalfree trade reduces the penalty of deviation from cooperation. A criteria for cooperation forcountry A is given by the following inequality: 5- (G x2 sN— Gx2 NN) > (G x1sN —G x1NN)Since there is no learning effect in this model, Gx2sN GxisN, and Gx2sN = GxisN. The aboveinequality becomes an equality and hence the agreement is no longer acceptable to bothsides because the relative gains in imposing optimal subsidies are as large as the relativelosses of retaliation from the rival in the next period. Unconditional free trade, as theseresults indicate, cannot provide sufficient penalties to enforce free trade.'This inequality is the same for country B. Hence, the agreement goes both ways -- if an agreement is notacceptable to country A, then neither will it be acceptable to B.29Second Stage: Free Trade vs. the Cournot Nash Equilibrium with Learning EffectsNow let us consider how the result will change when learning effects are present. The lefthand side of (11) will become different from that under no learning effect because themarginal costs of firm A in the second stage, cc 2 are different if country A adopts differenttrade policies in the first stage. Gx 2ss is the payoff to country A in the second stage underretaliation from B if A imposes optimal subsidies in the first stage while B does not.Obviously, the stronger the learning effects, the larger G' ss is. Hence, losses in the secondstage will be smaller if a country deviates from free trade in the first period in the presenceof learning effects. I shall illustrate this point in the following section.To find Gx2ss and G' NN, I shall use a general approach in which marginal costs aredifferent in the two countries, as represented by cx 2 and cY2 for country A and B respectively.c '2 = C - AixiC 2 = c - Ary l^ (17)In the case of Gx2NN, assuming that there is no subsidy in the first stage, x 1 =yi = a - c3bInthe case of Gass, assuming that A imposes an optimal subsidy while B does not in the firststage, x 1 = --a c and y 1 = a -c2b^4b30Case 1: Both Countries Adopt Free Trade in the Second StageNow suppose that both countries adopt free trade in the first and second stages. Withlearning effects, payoffs to country A and B under free trade in the second stage (given freetrade in the first stage) are as follows:From (3)G x2 NN1b= 9—(a-c 2)2= —1b(a-c+Axi)29= —1 (a -c+ihalc_)29b^3b1= —(a-c)2(1+2-)29b^3b= G y2NN(18)The above expression, together with the payoffs due to retaliation in the second period,will be substituted to (11) to evaluate the possibility of cooperation.Case 2: A Cournot-Nash Equilibrium in the second StageNow suppose that country A imposes a per unit subsidy, s, and B imposes s * to its industryto retaliate to A's imposition of an optimal subsidy in the first stage while B remains in freetrade. Profit functions for A and B under strong learning effects become:317rA = xp(x,y) - cx = x(a-b(x+y))-cx 2x+sxirB = yp(x,y) - cy = y(a-b(x+y))-cY2y+s syThe first order condition is given as follows:a - 2bx - by - cx2x + s= 0a - bx - 2by - cY2y + s * = 032[-2b -b 1 {xl { c x2 -a-sI-b -2b y^c Y2 -a -s(19)x .^1 -2^1 c x2 -a -sy 3b 1^-2 c Y2 -a -s*1 a -2c x2 +c ) 2 +2s-s*= —3b a-2cY2 +c 2 -s+2s*ax 2 • ax -1 • ay _ 2 aySince _...=•^ =_•^ _^ = -1as 3b' as* 31,' as* 3b as 3b= ^3b _3bx _ a-c+2s-s1-ux—70 Y., *from (8) optimal s - ^xs^2^6^63b4s +s * = a-2cx2 +c Y2 -S *Similary, s+4s*=a+c x2-2C Y2C x2 = C - 11,X1C Y2 = c - phx1 -1 2ba-cYi - 4^b(20)33To find G x2ss under learning effects4 1 s ^-2c 2 +c 2 +a1 4 s* ^{c2 -2C Y2 +aLet o=—a-c p.; Hence cx2 =c-2o; cY2=c-o4b{sl = 1 4 -11 r2c x2 +c Y21s *j^15 {-1 4 i c x2 -2c Y2 +a1 -9c x2 +6C 2 +3a15 6c x2 -9c 2+3a{51 -c +4 a +al-c - a +aGuess under learning effects is evaluated as follows:x2 = —1b (-2c x 2 +c Y2 +2s -s * +a)3= --L (-2c +4 cr +c-o+-1 (a-c)+-9 o +a)3b^5^5x2 = 2 ( -c +4 a +a)5b2Y2 = —5b ( -c +a +a)Gass = 25b2  (a-c +4 a)2(21)(22)34(11) becomes -(G x2ss-G x2NN)-(G x1sN-G x1NN) (* *)(G x2 SS - Gx2Nd^252b (a-c)2(1+ /.)2 +(a:2 (1÷ 3.1) )2(a-o2 -2 _ 2142 _ 414 + 1 +^+25b 25b 3 25b 2 4b 36b 3 6b 2=(a-c)2  17 +^ - 47142100b 90b 2 900b 3From (10) and (3), (G x1sN-G x1NN) = li(a-c)2 -4(a-c)2 = 7 (a-c)2(**) = (a-c)2  17 +^ - 47/42 - 1100b 90b 2 900b 3 72b4a._ 021  1124^/.2^47/12 7200b 90b 2 900b 3(23)35In contrast to (16), (* *) is not necessarily greater than zero. This implies that if (* *) 0 (i.e.the losses due to retaliation in the second period are larger than the gains from imposingoptimal subsidies in the first period) is the only necessary criteria to considering a free tradeagreement, then such an agreement will not be acceptable under strong learning effects suchthat (**) < 0, since the steepness of the learning curve, A, would determine the sign of (**).In other words, ifA-1^ - (,\I ^1  ) 2 +4  47  1124 90b 2^90b 2^900b 3 7200b-47 2(^ )900b 3(24)then the costs of retaliation in the second stage no longer outweigh the benefits of imposingan optimal subsidy in the first stage. Hence, market failure occurs in this economy. Anagreement that aims to enforce free trade will not be acceptable to both countries, becauseof the strategic gains from strong learning effects.36ImplicationsThe above results imply that if learning effects are strong, it is no longer true thatcooperation between governments can be achieved by assuming the rival's adoption of a "tit-for-tat" strategy; the reduction in marginal cost due to learning effects may outweigh thelosses due to retaliation. In contrast to the case in which learning effects are not present,as illustrated in (16), the case under sufficiently strong learning effects may induce agovernment to deviate from cooperation in the first period, or result in mutual mistrust.Mutual mistrust is a net consequence of the strong learning effects, as indicated by (24).Because of strong learning effects, each country believes that an agreement will be uselessprovided that a country still gains relative to free trade even if there is retaliation. In otherwords, a free trade agreement is definitely acceptable to either side (if they all use (11) toevaluate cost-benefits) with no learning effects, but whether the same agreement remainsacceptable to both countries under the presence of learning effects is unclear; it dependson the steepness of the learning curve. The steeper the learning curve, the more a countrywill gain by subsidizing its industry. It should be noted that both the results of (16) and (24)are derived under the assumption of duopolistic industrial organization. The difference inthese results illustrate that in contrast to what Krugman (1984) concluded, dynamic andstatic economies of scale do not necessarily have the same impact on the acceptance of afree trade agreement in a duopolistic industry.37Unconditional Free Trade with Learning EffectsIt was shown earlier that a policy of unconditional free trade results in an incentive todeviate from cooperation. How would the result change if country B adopts unconditionalfree trade under learning effects? I shall investigate the change using the following criteria:-(Gx2SN-Gx2 NN) > (Gx1SN -Gz1 NN)As in (11), if the above inequality holds, then there is no incentive for a government todeviate from cooperation. The left hand side of the inequality is evaluated as follows:x2^3b= —1 (-2c x2 +c Y2 +2s +a)y2 = h (c x2 -2c Y2 -s+a)3optimal subsidy is given by:s = —1 (-2c x2 +C Y2 +a)1x..^3b„, = —(-2c 2 +c Y2 +a)y2 = 1 (2c x2 -3C Y2 +a)4bG x2sN = Vx2 +Y2) -c x0x2=(a-±( -4c x2 +2c Y2 +2a +2c x2 -3c Y2 + a - c x 2))x2b1^2^3,Li 2=—(a-c) (1+8h 4h)(26)38From (18), G 2NN = —91b02_02(a÷ 314b)2-(Gx2sN-Gx2NN) = 81 (a-c)2(1+—G x1sN-Gx' NN 7 12b (a-c)2-(G x2sN-G 2NN)-(G xisN-G x1NN)= (a-c)2( -2 ^601122^49/2 ) < 072b 10368b 3 432b 2(27)Hence, as in the results of the case without learning effects, unconditional free trade doesnot provide a sufficient penalty to deter the rival from deviation from cooperation in thepresence of learning effects.3414, )2 +-4(a-c)2(1+23d239Summary of ResultsThe following tables are a summary of the payoffs received by countries A and B undertwo different assumptions -- a static and a dynamic model. While non-cooperative outcomeis an equilibrium solution in the static model, in a dynamic one whether or not one willobtain free trade as a solution depends on other factors, such as learning effects and thestrategy the rival is believed to adopt.Case 1: Static ModelPayoffs = (country A, country B)Country BS (Defect) N (Not defect)Country AS (Defect)2(a -c)2(2(a -c)2 (a - c)2(^'(a - c)225b^' 25b 8b )16bN (Not defect)(a - c)2((a - c)2)(a - c)2((a - c)2,16b 8b ,9b )9bTable 1, Payoffs in a Static Model40Case 2: Dynamic ModelNB: The two values in the table represent the net payoffs (cost-benefit) assuming the rivaladopts (1) a "tit-for-tat" strategy and (2) a policy of unconditional free trade.If country B responds by the following strategy inperiod 2CountryA'sactioninperiod 1Tit-for-tat UnconditionalFree TradeSN (Defect)-^2( 1124^47/12 2^601112(a _02( __(a c)7200b 900b 3+^µ )72b^10368b 349[1)90b 2 432b 2Table 2, Payoffs Relative to Free Trade in a Dynamic Model41Using the above table to predict whether an agreement will be signed or not, I have thefollowing result:(yes means that an agreement that enforces free trade will be signed; no means that thesame agreement will not be signed)Case 2.1: Weak learning effectsIf country B responds by the followingstrategy in period 2Country A'sactionin period 1Assumption: smallATit-for-tat UnconditionalFree TradeSN (Defect) Yes NoTable 3, Whether Free Trade is a Solution in the Model with Weak Learning EffectsCase 2.2: Strong learning effects,If country B responds by the followingstrategy in period 2Country A'sactionin period 1Assumption: largeATit-for-tat UnconditionalFree TradeSN (Defect) No NoTable 4 Whether Free Trade is a Solution in the Model with Strong Learning EffectsNote: large th means-1^(  1  )2+4  47  1124 90b 2^90b 2^900b 3 7200b2(  -47 _)900b 342The above results can be summarized as follows: (1) if a country thinks that the rival adoptsa "tit-for-tat" strategy, then we may find free trade as a solution only if learning effects arenot strong enough; (2) if a country thinks that the rival adopts an unconditional free tradepolicy, then regardless of learning effects, we may not find free trade as a solution.43The Infant Industry ArgumentIn the previous sections, we have found that trade intervention depends upon what strategya country thinks the rival will adopt and whether or not learning effects are present. In thissection, we continue to investigate another explanation for trade intervention -- theprotection of an infant industry. The infant industry argument is one of the most commonlyused arguments against free trade. In certain high technology industries, in particular thecivil aircraft manufacturing industry which is now dominated by Boeing and Airbus, thereis a widely supported argument that trade intervention in the form of production subsidiesfrom several European countries to Airbus is justified. The argument for these subsidies isthat if production subsidies were removed, America might gain a monopoly status becausethe marginal costs differ widely in this duopolistic industry; the European aircraft industrywould not be able to compete with that of America without subsidies. The costs ofmaintaining such a duopolistic industry are incredibly high -- more than $13 billion in thecase of Airbus. In a static economy the tradeoff between monopoly and duopoly is obvious:supernormal profits earned by a monopolistic firm are unambiguously higher than thecombined profits earned by two firms in a duopolistic industry. Hence, there is a loss inproducer surplus if monopoly becomes a duopoly. However, whether the same results holdtrue in a learning economy remains unclear. When a government subsidizes an infant hightechnology industry, there is always an implicit assumption that in the long run, thesubsidized industry will survive on its own. One major argument in favour of subsidies in theaircraft industry is that Airbus will be able to pick up the pace and compete with Boeingonce Airbus has secured a position in the market. Because of learning effects, subsidies maybe gradually phased out. Unfortunately, based on the model described in this paper, the44opposite is true. Learning effects increase the loss of producer surplus, and in a dynamiceconomy, the subsidy level remains the same.To illustrate the above argument, I make the following assumptions. First, a governmentjust wants to subsidize its infant industry to make it as competitive as the industry of theother government. Second, the rate of learning is the same for the two countries. Third,there are no spill-over effects.45The model used in the previous sections will illustrate that subsidies which aim to maintaina duopolistic market structure (i.e., in which without subsidies, the market structure wouldbecome monopolistic) cannot be phased out in a learning economy. In addition, combinedsupernormal profits earned in a duopolistic industry are less than those in an equivalentmonopolistic industry. More importantly, the difference in the supernormal profits betweena monopolistic and a duopolistic market structure increases if learning effects are present.As shown throughout this paper, the basic determinant of a government's behaviour in themodel is the difference in marginal costs. In one extreme case, as this section will illustrate,if the industry in one country has a marginal cost higher than a certain critical levelcompared to the rival, there will be no chance of survival. The duopolistic industry structurewill become monopolistic. For the sake of simplicity, let us assume that the difference inmarginal costs is just large enough to make country A unable to produce anything, i.e. x 1 =0.Let us also assume that the objective of government A is to provide just enough subsidiesto its industry to make the two firms equally competitive, i.e., so that they have the samemarginal costs. Based on these assumptions, the objective of this section is to show whetherunder a duopolistic market structure and in a dynamic economy with learning effects,subsidy level and losses in producer surplus can be reduced.46Profit functions for countries A and B are then:TEA = xip(xi +y1)-cxixi = x1(a-b(x1 +y 1))-cx1x 1n il = y1p(x1 +y1) -c Y1y1 = y1(a-b(xl+y1))-c Y1y1By Kuhn Tucker Condition:anA- a -2bX1 1-bh -C xi < 0 if xi = 0ax1a-cxi < by i (*)a7,Bay,a-c y1y-2ba-c Y 1Substitute y to (*), a-cx i <2C Y-C x < cx -a+a-cxi11^i^2c''1 -cxi < --1 (a-c Y 1)2c xi -c Y i > 1(a-c Yi)2The above results indicate that if the difference in marginal costs is larger than a criticallevel, as given by (a-e1)/2, then country A cannot compete at all, and x 1 =0. In other words,if we assume that e i -cYi =(a-cY1 )/2, then x1=0.- a-bx1 -2by i -cYl = 0(28)47Suppose now that the government of country A wishes to maintain its industry by a perunit production subsidy, s, such thats = cx-cY=-1 (a-cY)^ (29)C x-S = CMarginal costs, which are now the same under government subsidies, equal cr1 .x 1 1^-2^1341^-2a-01y1 = a -c v 1 (30)G Dm^= (p(x1 +y1)-cY^= (a-2 (a-c Y1)-c Y1 -1 (a -c YI )).x ii -s)x i3 -1 (a-c Yi)218bG Dya 9= —1b (a-c Y )2-2b -b1^{c "1 -a[ -b -2b y 1^cY 1 -a48GDX1 is the gain function to country A under subsidies that aim to keep its firm ascompetitive as that of country B. The net gain to country A is negative. Unlike in the caseillustrated in the previous sections, subsidies that aim to maintain a duopolistic marketstructure because of the wide difference in marginal costs cannot provide a net positivepayoff to country A. If the objective of government A is simply to prevent country B fromobtaining a monopoly status, then subsidies can achieve that purpose. However, if theobjective of government A is to subsidize its firm temporarily and then gradually phase outthose subsidies as the firm "learn" to produce more efficiently and thus becomes morecompetitive, then government A will not achieve its target. I shall use a dynamic learningeconomy to illustrate this claim.First of all, let us evaluate the difference between supernormal profits earned in aduopolistic industry and those earned in a monopolistic industry. The duopolistic marketstructure is maintained only because of the subsidies of country A. In the presence oflearning effects, marginal costs will be reduced in proportion to the accumulated production(since only two periods are taken into consideration, accumulated production simply equalsproduction in the first period). However, the reduction in marginal costs would be differentin the second period if country A did not impose a subsidy to maintain its industry in thefirst period. This is because with subsidies, the market structure would be duopolistic in thefirst period, and without subsidies, it would be monopolistic. Since production level in thefirst period would be different under a different market structure, marginal costs would alsobe different in the second period. The major argument in support of subsidies in a dynamiceconomy is that once the subsidized industry has secured a position in the market, becauseof learning effects, it can survive on its own in the future. The underlying assumption is that,49although subsidies are not good for the world as a whole, they can be used to support thegrowth of a domestic industry in a learning economy under a duopolistic market structure.The above argument can be analyzed by two expressions in a learning economy in whichmarginal cost can be reduced in proportion to accumulated production. First, per unitsubsidies in the second period are smaller than that of the first period, i.e., s 2 < s 1 . Second,the difference in relative payoffs between a subsidized duopolistic industry and monopolisticindustry should be smaller in the second period than in the first period. Otherwise, theworld economy would be better off without subsidies in the first place. This argument canbe represented by the expressionG DY1 +G Dx1 -G M1 < G D2 +G Dx2 -G 2^ (31)The left hand side of the inequality represents the difference in relative payoffs betweena subsidized duopolistic industry and a monopolistic industry in the first period; the righthand side represents that in the second period..CB = y1(a-by 1)-cviyi, since x1 =0alt B- a-2by i -c Y1 = 0a-cY1y1^2bp = a -by1 = a-1 (a-cY 1)2G m, = (p-cyx i=-1h (a-cy24aY1(32)50For the sake of simplicity, I shall assume that the objective of government A is to subsidizeits industry so that it can be as competitive as the industry in country B, i.e., so that theirmarginal costs, after subsidies, are equal. To evaluate the above two expressions, I mustknow Gmi and GM2 which represent the payoffs to country B if it can gain a monopoly statusprovided that country A ceases to subsidize its industry in the first and second periodrespectively.Relative payoffs between a monopolistic and a subsidized duopolistic industry in the firstperiod are given byG px1 +G DYi -G m1 4a-c y1)2( -" +, 1 -, + )b=(a -c Yi)2( 376b )(33)51The world economy will be better off if country A did not subsidize its industry in the firstperiod, so that country B can gain a natural monopoly in producing y. Now the questionsare, (1) whether the difference in relative payoffs can be reduced, and (2) whether per unitsubsidies can be reduced if there are learning effects. To answer the above questions, I mustknow the relative payoffs in the second period under two different scenarios: (1) if themarket structure is monopolistic in the first period, and (2) if the market structure isduopolistic in the first period.First, if the market structure is monopolistic in the first period, then the payoffs to countryB in the second period are as follows:c Y2 = c Yi -01; y1 =2b1 (a-c Y1 )2(a-c Y2)2^1G M2 -^ - 4b (a -c)2(1 + - .L.1 )24b 2b(34)52Second, under a subsidized duopolistic market structure in the first period, if the level ofsubsidies in the second period is only enough to make the firm in country A as competitiveas that in B, the level of subsidies, s, is calculated as follows:S2 = C x2 -C Y2 = C xi -/..4-- (a -c "1)2 -(cY 1 -12-1 (a -c Yd2)3b 3b= c''1 -cx1 = Si -1 (a-cY )..^2^1(35)The above expression answers the first question in determining the level of subsidiescannot be reduced in a learning economy. If the objective of government A is to equate themarginal costs between two countries through subsidies, then it is incorrect to expect thatthose subsidies can be gradually phased out; marginal costs cannot be reduced in the futurein proportion to accumulated production. Whatever level of subsidies government A imposesin the first period must be imposed again in the second period. If more periods are takeninto consideration, it is not surprising to find that a subsidized industry remains beingsubsidized forever; an infant industry can never become mature. Most importantly, just asin the scenario in the first period, once subsidies are removed the industry cannot surviveat all, because the difference in marginal costs in the second period is just large enough toeliminate the firm in country A from the market.53Now, let me investigate how relative payoffs will be changed under subsidies.G D.K2 .4 (a-cy2)2.4 (1÷i)2(a_c Y 1)2 -S2X21 /x = 1 (a _c y2) = 1 (a _c y 1+Axi)^2  3b^3b 1=-1 (a-cY1 + p—(a-cY ID^3b^3b--1 (a -c Y1)(1 + A--)3b^3bs2x2 = 4 (a -cY1)2(1+i)G D2 = 1 (1+ —A t )2 (a - c Y 1)29b 3bG px2 +G DY2 - G 1122 3b )2(a _c y1)2=9b 3b16b--(a-c '1 )2(1 -L3bI.)--1 (a -c p1)2(1 + -LI )24b^2b_ (a _cy1)2(0+ Az x 2 + 2,u _ 1 )_ 1 (1+ A )2)3b 9b 27b 2 6b 4b 2b= (a -cY 1)2(----7— +---5 - +  2/2  -  112 - li )36b 54b 2 81b 3 16b 3 4b 2= (a -cY1)2(  36b - 1107 8Pb - 14299146 )(36)(37)54The relative payoffs (between a monopolistic and a duopolistic market structure) are stillnegative.6 Most importantly, the relative payoffs in the second period are smaller (i.e., morenegative) than those in the first period. This implies that the payoffs to a subsidizedduopolistic market structure do not improve with comparison to a natural monopolisticmarket structure, even in a learning economy. On the contrary, the situation worsens, mainlybecause marginal cost under a subsidized duopolistic market structure cannot be reducedas much as that under a natural monopoly. From the results derived in (9), namely that thegain function is concave in s, it is not surprising to find that relative gains are negative. Theobjective of the following is to prove that the level of subsidies used to maintain aduopolistic market structure is larger than the optimal subsidies as suggested by (26). Moreimportantly, the optimal subsidy is zero for the firm in country A. In other words, the bestthat government A can do, regarding its "infant industry", is not to impose any subsidies.From (35), c Y2 -C 2 = 1-(a -c al)2From (26), s = —1 ( -2C x2 +C Y2 +a)4= —1 ( -2-1 (a +cY2)+c Y2 +a)4 2= 0 optimal subsidy = 0But the level of subsidies that maintains duopolistic market structure is(a -c x1 ) > 0; From (28)2 That is because the level of subsidies that maintain duopolistic market structure is much larger than theoptimal level of subsidies.55Since the level of subsidies that is used to maintain a duopolistic market structure is largerthan the optimal subsidy, relative gains should be negative; as was shown above, in such a"infant industry", the best that government A can do is to let the industry be determined bymarket force, i.e., the government should refrain from imposing any subsidies. Although thenet consequence -- that country B gains a monopoly status -- is rather unfortunate forcountry A, according to this model, it is ironically the best outcome.56Therefore, if the industry can only support one firm, it is ineffective for a government towork against the market forces in order to maintain a duopolistic market structure. Thisconclusion has very strong implications for the civil aircraft manufacturing industry. Todaythere are two main producers of large transport aircraft: Boeing (over 50% market share)and Airbus (30-35%). Airbus' market share has increased rapidly under Europeangovernments' heavy subsidies in the past decades. One major reason for giving thesesubsidies is to prevent Boeing from monopolizing in this industry. Because of its late entryinto the market, Airbus could not survive without subsidies. It is expected that once Airbushas secured a position in the market, its subsidies may gradually be removed and that theremay be competition in the civil aircraft industry. An airline does not have to order aircraftfrom the U.S. only. Unfortunately, according to the results in this section, these expectationsare false. Two major effects of a subsidized duopolistic learning economy revealed by thisstudy disprove those two conventionally accepted expectations: first, subsidies cannot bephased out; second, if learning effects are taken into account, a subsidized duopolisticmarket structure is worse off than a monopoly.Again, it should be noted that policy inferences from the above results are based on arestricted set of assumptions. Airbus' subsidies may be justified if it "learns" substantiallyfaster than Boeing does. Hence the counter infant industry argument proposed here can onlybe applied to a very specific case: when both firms learn at the same rate. Actual inferenceswould depend upon crucially on the difference in the rate of learning. Without going intotoo much technical details in this subject, I shall turn the attention to some stylised facts inthe international aircraft industry which is very close to a duopoly in the next section.57Case Study: Civil Aircraft ManufacturingThe aircraft manufacturing industry possesses the characteristics discussed in this paper:a duopolistic industry structure and steep learning curve. The motivation of examining theinternational aircraft industry is not to prove or disprove any of my theories; the purposeis simply to take a look at the practical side of duopoly and see how the aircraft industry hasperformed when Europe has been actively subsidizing its aircraft industry. The number ofaircraft manufacturing companies has declined from more than 20 in the post-war period,to only three currently: Boeing, McDonnell Douglas (MDD), and Airbus Industrie. Therelative importance of MDD in the market has gradually been replaced by Airbus, as MDDis currently almost completely involved in military aircraft manufacturing. There are muchsmaller manufacturers in developing countries, and the USSR does produce civil aircraft,however, they have almost no influence on the demand in the world market. Thus, theaircraft manufacturing industry can be characterized as a duopoly (Airbus and Boeingtogether have more than 80% of the world's market share in the civil aircraft industry).Moreover, it is well known in this industry that the manufacturing process involves a verysteep learning curve; labour costs decline steadily with the number of units produced,because workers learn as they work. One more unit manufactured in the civil aircraftindustry is crucial to the business, since throughout the entire life cycle of an aircraft model,at most only a few hundred units can be sold. There is a general rule in the aircraft industrythat with every doubling of the number of airplanes produced, a 20 percent reduction ofdirect labour can be achieved.' The learning curve initially decreases very rapidly, and then'Newhouse, John. The Sporty Game, 18-9. New York: Alfred A. Knopf Inc., 1982.58becomes more gradual. Developing a new model is extremely costly and risky, though ajump in production from, say, two to four units occurs far more swiftly than is the case witha jump from eighty to a hundred units. However, this does not imply that developing a newmodel is more profitable than maintaining an old one. It could take five years to get a planefrom the drawing board to final production. For instance, the present development of 767by Boeing, the world's largest single private venture, involves more than ten years andalmost the entire asset of the company. Because of the recession, most airlines havewithdrawn their orders for new aircraft. Whether the market can absorb the expectedamount of production remains unclear. In fact, through 1980, no firm broke even before 300planes were sold. Since 1952, no European jetliner has reached that level, and only six U.S.planes have attained that goal. So far, the only really profitable model is the Boeing 747,because of its unique position in the market. However, such a unique position may notpersist for too long, because Airbus is aggressively invading the market with the aid ofsubsidies from four European governments.59Airbus itself consists of only 1,500 administrative and sales staff housed in a single officebuilding near the Aerospatiale factories. Airbus accounts are a mystery. No one really knowswhat Airbus has cost so far because the consortium has one peculiarity: Groupement d'InteretEconomique, a French oddity which lies somewhere between a partnership and acorporation, and which does not have to file proper accounts. 8 Costs, benefits, and work areshared according to each nation's stakes in the consortium: France's A6rospatiale and WestGermany's MBB each own 37.9% of the firm, British Aerospace has 20%, and Spain'sCASA has 4.2%, regardless of comparative advantage. Hence, it is not surprising that Airbusis able to get billions of dollars of subsidies from the member countries. Currently, AirbusIndustrie has been criticized for competing unfairly with Boeing, a purely commercial USfirm which formerly dominated more than 54% of the civil aircraft manufacturing market.Boeing's dominance is declining because of the competition from Airbus. It is estimated thatthe governments of France, Germany, and Britain have handed out $13.5 billion in subsidiesto Airbus. No evidence suggests that these subsidies will stop, nor is there any possibility ofthese investments being repaid in the future. 98The Economist (September 3, 1988): 9.9The Economist (February 16, 1991): 51.60These subsidies are irrational from the viewpoint of a perfect competition model.However, two particular features of this industry explain the behaviour of the Europeangovernments sensible. First, the civil aircraft industry is part of national defence, sincealmost all present aircraft manufacturers started by building military aircraft. Moreover,firms that are capable of producing military aircraft can also take civil aircraft orders. Forinstance, McDonnell Douglas is now more involved in its military aircraft production, butif any airline should order a DC10, it could produce one of those as well. However, militaryorders are highly volatile. Therefore, countries which are capable of producing militaryaircraft tend to maintain their own civil aircraft manufacturing to act as a buffer whenmilitary orders slow down, as well as to enable a team of engineers and workers to becomeinvolved in the high technological edge of the aerospace industry. Accordingly, subsidies toaircraft manufacturing, like defence expenditures, are always linked to national security.Second, most important, there is a fear among European countries that America willbecome a monopoly in civil aircraft manufacturing. However, it is difficult for any individualcountry in Europe to compete with America because of the high capital, high risk, and longpay-back period in the civil aircraft industry. One major reason that Britain, France,Germany, and Spain formed a consortium is that none of them alone is able to absorb allthe risks involved in developing a new model. The success of Boeing is perhaps simply dueto the timing of its entry into the market: after World War II while Europe was stillrecovering from wartime damage.61Subsidies remain the most controversial subject in the aircraft industry. Boeing estimatesthat the development costs of Airbus' MOO model can never be recovered and that Airbushas underpriced its latest A320 by more than 20%. 10 The US government threatens tocomplain to the General Agreement on Tariffs and Trade (GATT) and imposeCountervailing Duties (CVD) on Airbus. However, the European Commission which wasassigned the job of negotiating with the Americans on the subsidies issues is only proposingto eliminate production subsidies, and to reduce R&D subsidies from 70-90% to 45%. 11This is a concession, although the R&D costs are the heaviest burden to an aircraftmanufacturing firm. Boeing's development costs of its 767 model are now estimated toexceed $4 billion. However, taxpayers in the US are not required to share this burden.Airbus has countered in the subsidy row by claiming that American companies receiveindirect aerospace subsidies in the form of huge government defense and space contracts.One report estimated that some $23 billion had been paid to the American aircraft industrybetween 1978 and 1987. 12 There is no sign that a settlement concerning the trade disputesof this industry will be reached in the near future.1077te Economist (February 14, 1987): 60."The Economist (February 16, 1988): 51.12The Economist (September 3, 1988): 10.62One major prediction of this paper is that in a learning duopolistic economy, conditionalfree trade would be more mutually acceptable to both sides than unconditional free trade.In the aircraft industry, this behaviour is exactly what is observed. As Yoffie and Milnerwrote:Following the start of formal U.S.-European negotiations in the GATT in1987, Boeing officials said they would consider the talks successful only ifEurope would eliminate all subsidies, stop political pressure in aircraft sales,and force Airbus to price in order to recoup all costs. Failing such anagreement, Boeing threatened to file an unfair trade petition (section 301),as well as anti-dumping and countervailing duty cases against Airbus, notingthat "under any one of these laws, the U.S. government could negotiate withAirbus to limit the quantity of exports, eliminate subsidies, impose taxes, orreach some other solutions". 13Such an attitude is in sharp contrast to the unconditional free trade policy supported bythe industry in the past. For instance, in the 1970s, Boeing repeatedly emphasized atcongressional hearings that it opposed import restrictions or other trade barriers. However,as the market structure becomes closer to a duopoly (as MDD partially withdraws from themarket) and learning effects becomes more significant (the cost of launching a new designfor large aircraft in the 1980s rose to $5 billion), unconditional free trade is no longer amainstream trade policy supported by this industry. As a consequence, one finds the so-called strategic trade policy becoming the general demand of not only the industrial, but alsothe national interests.13 Yoffie, David B., and Helen V. Millner. "An Alternative to Free Trade or Protectionism: WhyCorporations Seek Strategic Trade Policy." California Management Review (summer 1989): 111-31.63Empirical EvidenceCivil aircraft industry is an important industry in the U.S. that possesses all thecharacteristics discussed in this paper: a duopolistic industry structure and steep learningcurve. From the results of the first two sections concerning a duopolistic industry withlearning effects, if one country imposes a subsidy on its industry, the industry of anothercountry will be hurt. In the real world, the aircraft industry in the U.S. is facing a similarsubsidized competition from Europe. The purpose of doing the empirical work of thisindustry is to check whether the aircraft industry is declining relatively in the U.S.. If thereis a relative decline, the result can be used as indirect empirical evidence of somepredictions made in the first two sections, as well as an indication of the existence of aproblem concerning the aircraft industry in the U.S.. The relative decline is examined in twodifferent ways: the relative weight of the aircraft industry in the non-agricultural industry andthe U.S. market share in the production of total aircraft seats, i.e., the sum of all seatsproduced by Airbus, MDD, and Boeing.To find empirical evidence that supports the theory proposed by this paper in the civilaircraft industry is difficult, though not necessarily impossible. The main reason for thedifficulty is that Airbus, unlike its American counterpart, does not disclose its informationto the public. However, one simple test of the results derived from this paper can be made,namely that the subsidies for Airbus worsen the general performance of the civil aircraftindustry. The implication is indicated by the expression that —Ya < o , where y can beas64perceived as the production level in the aircraft industry of the U.S. and s can be perceivedas European subsidies to Airbus. In other words, the relative weight of the civil aircraftindustry declines in the U.S. because of subsidies to Airbus. Let R t be the relative weightof the monthly production index of the civil aircraft industry in the entire manufacturingindustry. These data were downloaded from Citibase.Rt = flo (38)The following tables represent the regression results of 234 observations. R t = airt/manutwhere airs is the monthly production index of the aircraft industry and manu t is the monthlyproduction index of all manufacturing industries. The performance of the civil aircraftindustry can be evaluated as follows: if 13 1 < 1 then next month's ratio of civil aircraftproduction to all manufacturing industries is less than this month's.65Variables Coefficient StandardErrort-RatioRt4 0.97 0.012 84constant .0041 .0021 1.98Table 5, Estimated Coefficients of Relative Weight of Aircraft IndustryStatistics ValuesR2 0.96721Durbin-h .5Breusch-Pagan 1.383Table 6, Important Statistics of Relative Weight Of Aircraft Industry66Test for Heteroscedasticity and AutocorrelationTo ensure the correctness of the model, I shall test for the presence of heteroscedasticityand autocorrelation. It is important to check whether these problems exist because theconsequences of applying OLS to a relationship with heteroscedastic or autocorrelateddisturbances are (1) an unbiased but inefficient estimation and (2) invalid inferenceprocedures. To test for heteroscedasticity I shall use the Breusch-Pagan test. The test isdescribed as follows:Model: y = XB + uwhere the disturbances tit are assumed to be normally and independently distributed withvariance ail = h(Xt'a) and where h(.) denotes some unspecified functional form. a is a 4x1vector of coefficients unrelated to B and Xt is a 2x1 vector of variables (i.e., 1, R t_ i , t, t2)thought to influence the heteroscedasticity. The first element in X t is assumed to be 1.67Thus the null hypothesisHo: a 1 =a2 =0specifies homoscedasticity since a 12 = h(a 1 ) is constant over all i. Breusch-Pagan statistics,as represented by Q, are calculated from the procedure presented in Econometric Methods,pp. 300. For the empirical model used in this paper, Q =1.383 with 1 degrees of freedom.Under the null hypothesis, Q is distributed x2 with 1 degrees of freedom. If Q > x .95(1), onewould reject the hypothesis of homoscedascity at the 5 percent level. x.95(1) =3.841.Q =1.383. Hence, the hypothesis of homoscedascity is not rejected at the 5 percent level.To test for autocorrelation, I shall use the Durbin-h test. Durbin-h statistics, as representedby h, is calculated from the procedure presented in Econometric Methods, pp. 318. hcalculated in this empirical model is .5. If h >1.645, reject the null hypothesis at the 5percent level of significant in favour of the hypothesis of a first-order autocorrelation.Calculated in this empirical model, h is .5 and is less than 1.645; hence, the null hypothesisis not rejected.68Test for the Decline of the Civil Aircraft Industry(1) Relative Weight of Aircraft IndustryThe first test I shall perform is to check whether B i < 1. If it does, then the relativeimportance of the aircraft industry in all manufacturing is declining.Ho: fi i<1H1 : 131 21If tcac>terit then reject Ho^ (39)At a =.05, tcrit =1.65tcak-.012 -2.5<tcritTherefore, the null hypothesis is not rejected. The implication of the above result is thatgiven this period's Rt and t, Rt+1 will be less than R t . In other words, there is a downwardtrend observed in the civil aircraft industry.a69Therefore, the ratio of the civil aircraft manufacturing industry to all other manufacturingindustries has been declining. There may be many reasons for this decline. To find outprecisely what factors cause this decline would be quite a challenging task, and one that isoutside the scope of this paper. This study has offered several positive theories to explainthe incentive for a government to subsidize its industry. One of the conclusions derived fromthe results found in this paper implies that subsidies from foreign government willunambiguously have a negative impact upon production in the domestic industry. Therelative decline of the civil aircraft industry in the U.S. is one major empirical result foundin this paper and can be used as indirect evidence to support my theories. This evidence isinsufficient to definitively prove what I claim, because I cannot show that the decline iscaused by Airbus. However, I hope that the efforts I have made so far can be used as afoundation to investigate further empirical evidence in the context of international tradeunder learning effects.70(2) Market ShareApart from the relative weight of the aircraft industry in the U.S., the trend of U.S. marketshare in the production of civil aircraft would be another useful indication of the decline ofthis industry. Market share used in this paper is defined to be the percentage of total seatsproduced by the U.S. (i.e. MDD and Boeing altogether) in the sum of all seats producedby Airbus, Boeing, and MDD. The total number of aircraft produced for a particular modelis printed yearly in Civil Aviation Statistics. For each model, there are a range of seats. Tocalculate the total number of seats produced in the U.S., I simply used the median of therange of seats available and multiplied it by the total number of aircraft produced for eachmodel. I added up all the seats produced by MDD and Boeing. I did the same thing forAirbus. The market share of the U.S. is the ratio of the total seats produced by the U.S. tothose produced by Airbus and the U.S.. To test whether the market share of the U.S. isdeclining in the international aircraft industry, I use the following regression model:Mt = Yo iMt- iwhere TA is the market share of the U.S. in the production of civil aircraft (in the units ofseats). If the market share of the U.S. is declining, then y < 1. The following tablesrepresent the regression results of 15 annual observations.71Variables Coefficient StandardErrort-RatioMt-1 0.51501 0.28528 1.79constant .24351 1.6467 .44Table 7, Estimated Coefficients of US Market ShareStatistics ValuesR2 0.2255Durbin-h -.0154Breusch-Pagan .133Table 8, Important Statistics of US Market ShareUsing the similar tests for heteroscedasticity and autocorrelation, I have the followingresults. If Q > x .95(1), one would reject the hypothesis of homoscedascity at the 5 percentlevel. x .95(1)=3.841. Q=.133. Hence, the hypothesis of homoscedascity is not rejected at the5 percent level. Durbin-h calculated in this empirical model is -.0154. If h > 1.645, reject thenull hypothesis at the 5 percent level of significant in favour of the hypothesis of a first-order autocorrelation. Calculated in this empirical model, h is -.0154 and is less than 1.645;hence, the null hypothesis is not rejected.72Ho: y1< 1H1 : y i lIf tcdc>tcrit then reject HoAt a =.05, tcrk=1.651t„k  '5.29-1 --1.75<tcrk(41)Therefore, the null hypothesis is not rejected. The implication of the above result is thatgiven this period's M t, M4 +1 will be less than M. In other words, there is a downward trendobserved in the market share of the U.S. in terms of the total number of seats produced.73Apart from the rigorous tests used above, one can also use other indicators to evaluateoverall performance in the aircraft manufacturing industry in the past decades. Severalgraphs indicate a similar problem in this industry: there has been a relative decline in thepast decade. From the graph concerning total seats sold by MDD and Boeing versus thosesold by Airbus, we can find that the number of seats sold by Airbus is rising faster thanthose sold by Boeing and MDD together (see graphs 1 and 2). The next indicator (graph 6)is the market share of Boeing 737 comparing to Airbus 300/310. Since the two models arevery similar in terms of range and the number of seats available, the competition betweenthe two models is very close to a duopoly. From 1981 to 1984 and from 1987 to 1989, thetotal number of B737 sold was falling while the total number of A300/310 was rising.Particularly in the last two years (1988-89), the sales of Airbus increased five times whilethose of Boeing and MDD together increased twice only. From the graph concerning thewages of the aircraft industry to other non-agricultural industries (graph 8), we know thatthe ratio was rising from 1971 to 1981, but remained the same since 1981. From the graphconcerning total returns (the sum of profits, in constant dollars, of both Boeing and MDD)to seat (the sum of all seats produced by Boeing and MDD), we can find that the trend hasbeen falling since 1984, the level of returns to seat was still less than the level in 1983 inconstant (1982) dollars. Similar pattern can be observed in the graph of "Returns on Equity"(see graph 10). Despite the strong learning effects in the aircraft industry, its relative weightin the U.S. in 1990 was indeed lower that in 1971. Note that graph 12 also indicates asimilar decline observed in the automobile industry. In comparison with a more successfulindustry, such as the computer industry in graph 13, the relative weight of the computerindustry in all manufacturing industries has been increasing rapidly. The last indicator is74productivity (see graph 14), as represented by the total number of seats produced by eachemployee in Boeing and MDD. In general, the level of productivity between 1982 and 1989was less than that between 1975 and 1989. Moreover, the level of productivity in 1989 is onlyless than half of that in 1981. Again, it would be quite hasty to blame the decline entirelyon European subsidies, but different pieces of evidence, together with the theories proposedby this paper, may be used as a reference in formulating a better trade policy in targetedindustries such as the civil aircraft industry to better promote national interests.75Concluding RemarksBased on the framework of a duopolistic industry selling the same good to a third marketsimilar to the one first presented by Brander and Spender (1985), I introduced learningeffects into a model having infinite horizons. Although only two periods are taken intoaccount by a government which formulates an appropriate trade policy, deciding whetheror not it should cooperate with another government to remove all production subsidies, themodel can be modified to incorporate an economy with infinite horizons. The basic structurewould not change as long as we focus on a strategy that involves two period only -- astrategy of "tit-for-tat" and unconditional free trade. I show that cooperation (i.e. free tradewith zero subsidies) can be achieved if one country believes the other adopts a "tit-for-tat"strategy. The decision rule of whether or not free trade will be adopted is as follows: ifrelative losses in the second period (as both countries impose optimal subsidies) are largerthan gains from defection in the first period (only one country imposes an optimal subsidy),then cooperation can be enforced. Using the above simple cost-benefit analysis, I have foundfour major results. First, under a duopolistic industry with weak learning effects, cooperationcan still be achieved between governments, if each one believes the other adopts a "tit-for-tat" strategy. But if unconditional free trade is adopted, the losses become smaller comparedto free trade in the second period, and hence cooperation cannot be achieved. Second, iflearning effects are strong, then regardless of whether free trade is conditional orunconditional, cooperation between government cannot be achieved because a subsidyimposed in the first period results in two sources of gain: profit-shifting in the first periodand reduction of marginal cost in the second period. Third, if a duopolistic market structurecan only be maintained under the subsidies of a government, then learning effects will not76make the industry more competitive in the future. Subsidies cannot be phased out. If marketforce determines the nature of an industry to be monopolistic, then a government cannotuse subsidies to change this. It may be better off for the world as a whole not to moveagainst market force. According to the model discussed in this thesis, the hope that subsidiescan be gradually removed because of learning effects is unrealistic. It should be noted thatthe above results are based on a very restricted set of assumptions. Among those restrictedassumptions, same learning rates and the definition of cooperation restricted to the level ofsubsidies rather than output are the most sensitive ones. If one country has a learning ratesubstantially higher than the other country, then the level of subsidies may be phased out. 14If the definition of cooperation is not restricted to the removal of subsidies, but is definedto be the level of output, then a positive level of subsidies may be beneficial to bothcountries because of learning effects. More importantly, for the efficiency of the worldeconomy, a single country having all the production will be able to get the maximumbenefits of learning effects. 15 Furthermore, the assumption of exporting the same good toa third market with no domestic consumption is also quite restrictive. Using theinternational aircraft industry as an example, we do observe quite substantial domestic14For the sake of simplicity, I assume that the country with no subsidies adopts a policy of unconditionalfree trade. If that country adopts a "tit-for-tat" strategy, then the effects of different learning rates, together withthe impact of retaliation, may not lead to the phasing out of subsidies.15This result can be used to explain the phenomenon that the presence of national boundaries is counter-productive to the benefits one can get from learning effects. No doubt one country being a monopoly of allproduction is the most efficient one in terms of learning effects. However, assuming that each country is self-interest, no one is willing to stop producing. Each country will claim that the other should be removed from themarket. As long as there is no central government, the most likely outcome remains a duopoly. Apart from acentral government, the presence of other cross-boundary institution, such as a multi-national corporation canalso achieve the most efficient outcome (i.e. a natural monopoly). That is because a multi-national corporationdoes not need to pay attention to the country specific cost-benefit analysis. It will make the best advantage ofthe presence of learning effects. In contrast, no government which makes decision based entirely on the gainfunction of its country will not allow the other country to gain a monopoly status, a scenario which is ironicallythe most efficient one. See appendix for details.77consumption in this market. However, using the above assumptions, I can prove the validityof an argument with high tractability. Fourth, while the civil aircraft manufacturing industrypossesses all of the characteristics discussed in this paper, according to the ratio of themonthly production of this industry to other manufacturing industry in the U.S., this industryhas been declining in the past decades. Whether or not this decline is caused by theEuropean subsidies to Airbus Industrie is outside of the scope of this thesis. However, thisquestion would be an interesting starting point for future research on duopoly in the contextof international trade.78AppendixFrom equation 27, the highest joint payoffs are 2G x2 ,,, = —2 (a - c)2(a+)2, but the9b^3bpayoffs for a monopoly are G m2. = 1 0 _02(a+ L )2 and hence from the world4b^3beconomy's point of view, it is better for only one country to produce the good to capture allthe benefits of learning effects. However, which country should abandon its production isthe critical issue. There is no solution in a model which is based on the self-interest of acountry as discussed in this paper. Each country wants to be a monopoly. In other words,the presence of countries in this model automatically rules out the most efficient allocationof production pattern. In a profit-maximizing economy, the evolution of multi-national firmsperhaps is the only solution to the inefficient allocation of production pattern.Graphs16014012010080 -60 -40200Total Seats, USGraph 1Thousands75 76 77 78 79 80 81 82 83 84 85 86 87 88 89YearTotal Seats (US)Source: Civil Aviation Statistics_/1^1^1^1^1^1^1^1^1^1^1^1^1Total Seats, AirbusGraph 2Thousands30 -'25 -20 -15 -10 -5 -0 ^75 76 77 78 79 80 81 82 83 84 85 86 87 88 89YearTotal Seats (Airbus)Source: Civil Aviation StatisticsTotal Seats, US & AirbusGraph 3Thousands200 -'75 76 77 78 79 80 81 82 83 84 85 86 87 88 89YearTotal Seats (US)   Total Seats (Airbus)Source: Civil Aviation StatisticsB737Graph 4, Number of AircraftB737#75 76 77 78 79 80 81 82 83 84 85 86 87 88 89YEARB737Source: Civil Aviation StatisticsIMII IPP,t...d•^.441^ ,AIII^./11^ -4,•■^./!.;.:5411^....0:41111Airbus 300/310Graph 5, Number of AircraftA300/310#12010080 -60 -40 -20 -075 76 77 78 79 80 81 82 83 84 85 86 87 88 89YEARA300/310Source: Civil Aviation Statistics100%75% -50% -25%0%Market Share of USGraph 6, Number of Aircraft% OF 8737 in (B737+A300/310)75 76 77 78 79 80 81 82 83 84 85 86 87 88 89YEARB737 M--, A300/310Source: Civil Aviation StatisticsWages DifferenceGraph 7, Aircraft to Non-agricultureHourly Wages (Deflated)7 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111171 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90Year— Wages, others^1^ Wages, aircraftSource: CitibaseWages RatioGraph 8, Aircraft to Non-agricultureWages Ratio (non -agr=1)1 1111111111111111111111111111111111111M111711 1111111111111I1111111111111111111111111111111111111111111111111111111MIMT1111111 1111111111111111T111111111[TTIIIR11 11111 -111111111111111111111111111111111111111111111111111111111111171 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90Year* Ratio (air/non-agr)Source: Citibase20151052015105Returns to EmployeeGraph 9, Profits of Boeing & MDD$Thousands/Employee0 ^  071 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90Year1^ Returns to EmployeeSource: CompustatReturns on EquityGraph 10, Profits of Boeing and MDDReturns on Equity71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89Year4000Returns to SeatGraph 11, Profits of Boeing & MDD$Thousands/Seat400300200100071 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90YearReturns to SeatsSou rce: Compu stat0 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111(1111111111111111I1M111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111Manufacturing RatioGraph 12, Aircraft IndustryBase•All Manufacturing71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90Year---- Aircraft Ratio^I^ Auto RatioSource: Citibase»111111111111111111111M111111111111111111111111111111111111»111111111111111)11111111111111111111111f1111111111M111111111111111111M111111111111111111111111111111111111111111111111111111111111111111111111111111111111111Manufacturing RatioGraph 13, Aircraft IndustryBase•All Manufacturing71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90YearAircraft Ratio^*^ Cmpt RatioSource: CitibaseManufacturing1600140012001000800600400200Aircraft IndustryProductivity ComparisionGraph 146005004003002001000^I^i^I^I^I^I^I  ^071 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89Yearprod manu ^ prod airSource: Citibase94BibliographyAxelrod, Robert. 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