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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 and Learning-by-Doing (with Applications to the International Aircraft Industry) by ANDY KA-PO FOK B.Sc., Simon Fraser University, 1987 M.A., The University of British Columbia, 1990 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE (BUSINESS ADMINISTRATION) in THE FACULTY OF GRADUATE STUDIES (THE FACULTY OF COMMERCE AND BUSINESS ADMINISTRATION) We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA OCTOBER, 1991 © Andy Ka-Po Fok, 1991  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  (Signature)  Department of  Commerce and Business Administration  The University of British Columbia Vancouver, Canada  Date  DE-6 (2/88)  November 10, 1991  11  Abstract Despite the non-cooperative outcome predicted by the model of Prisoner Dilemma, throughout the history of international trade, mutual conflicts leading to an equilibrium which has the lowest joint payoffs is not so frequently observed. Trade barriers have indeed been gradually removed since the end of World War II. The objective of this thesis is to investigate various policy implications for international trade under duopoly with learning effects and to examine under what assumptions of strategy adopted by the rival will result in trade disputes. Interestingly, the adoption of a "tit-for-tat" strategy can be claimed by a government to achieve free trade. In this paper, four major results are obtained. All theoretical results involve a duopolistic industry in which two firms, belonging to two different countries, attempt to export a homogeneous good to 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 render cooperation (removal of subsidies) between governments difficult to achieve. The second result shows that in a dynamic economy with infinite horizons in which a government only plans for two periods, a policy of unconditional free trade cannot provide sufficient penalties because the gains from going down the learning curve through production subsidies outweighs the losses from retaliation. The third objective of this study is to evaluate the validity of infant industry argument under duopoly. Fourth, I examine the civil aircraft manufacturing industry which has  a very close market structure discussed in this paper using two different approaches: a general descriptive case study of the industry and an empirical evaluation of its performance in the past twenty years.  iii Table of Content  Abstract ^ Table of Contents ^ List of Tables ^ List of Graph ^ Acknowledgement ^  ii iii iv v vi  Abstract ^  ii  Introduction ^  1  Other Related Literature ^  7  The Structure of the Game ^  9  The Nature of a Trade Agreement ^  10  The Modelling of Learning Effects ^  12  The Model ^ First Stage: Free Trade vs. Optimal Subsidy ^ Second Stage: Free Trade vs. the Cournot Nash Equilibrium ^ Unconditional Free Trade without Learning Effects ^ Second Stage: Free Trade vs. the Cournot Nash Equilibrium with Learning Effects ^ Implications ^ Unconditional Free Trade with Learning Effects ^ Summary of Results ^  13 15 22 28 29 37 38 40  The Infant Industry Argument ^  43  Case Study: Civil Aircraft Manufacturing ^  57  64 Empirical Evidence ^ 66 Test for Heteroscedasticity and Autocorrelation ^ Test for the Decline of the Civil Aircraft Industry ^ 68 Concluding Remarks ^  75  Appendix ^  78  Bibliography ^  94  iv List of Tables  Table 1, Payoffs in a Static Model ^  39  Table 2, Payoffs Relative to Free Trade ^  40  Table 3, Whether Free Trade is a Solution with Weak Learning Effects ^  41  Table 4, Whether Free Trade is a Solution with Strong Learning Effects ^  41  Table 5, Estimated Coefficients of Relative Weight in the Aircraft Industry ^  65  Table 6, Important Statistics of Relative Weight in the Aircraft Industry ^  65  Table 7, Estimated Coefficients of US Market Share ^  71  Table 8, Important Statistics of US Market Share ^  71  V  List of Graphs  Graph 1: Total Seats, US ^  80  Graph 2: Total Seats, Airbus ^  81  Graph 3: Total Seats, US & Airbus ^  82  Graph 4: 737, Number of Aircraft ^  83  Graph 5: Airbus 300/310, Number of Aircraft ^  84  Graph 6: Market Share of US, Number of Aircraft ^  85  Graph 7: Wages Differnece ^  86  Graph 8: Wages Ratio ^  87  Graph 9: Returns to Employee ^  88  Graph 10: Returns on Equity ^  89  Graph 11: Returns to Seat ^  90  Graph 12: Manufacturing Ratio, Aircraft and Auto ^  91  Graph 13: Manufacturing Ratio, Aircraft & Computers ^  92  Graph 14: Productivity Comparision ^  93  vi Acknowledgement  I would like to thank Professors James Brander, Keith Head, and Ilan Vertinsky as members of my thesis committee. Professor Brander has provided me with invaluable assistance to not only the completion of this paper, but also the development of my critical thinking. I would also like to thank Professors Keith Head, Tae Oum and Ilan Vertinksy for their helpful suggestions. I, of course, bear all responsibility for errors.  1 Introduction  "Should we support free trade with the U.S.?" was a question that appeared most frequently during the last election in Canada. Similar questions will perhaps be asked again when North America is facing more and more pressure from the European Community in certain subsidized industries. The purpose of this paper is to give an explanation for trade disputes under different circumstances. These circumstances include (1) the strategy that one government believes the other adopts and (2) the presence of learning effects in a duopolistic industry. Another purpose of this paper is to examine whether or not subsidies are justified in an infant industry with strong learning effects and to use the international aircraft industry as an example to explore what has happened to the aircraft industry which has a similar market structure discussed in this paper.  The investigation of the impacts of learning effects upon imperfect competition and trade policies is the first focus of this paper. Brander and Spencer (1985) offer a possible explanation for exports subsidies based on market structure. Krugman (1984) uses a generalized version of the model developed by Spence (1981) to show that there is a similarity between dynamic and static economies of scale; both studies result in a tendency for a government to adopt strategic trade policy. To the best of my knowledge, this paper is the first one which attempts to explore how the introduction of learning effects and market structure will affect the behaviour of a government in deciding on whether it should subsidize its industries. My results show that market structure, together with strong learning effects, can be used to explain certain phenomena which cannot be satisfactorily answered by market structure alone. Under the assumption that a government agrees to remove  2 subsidies only if the benefits of doing so outweigh the losses, the results generated from a model under a duopolistic market structure with strong learning effects are different from one 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 my model can be used to explain this phenomenon: because of the strategic advantage of subsidizing a high technology industry that exhibits strong learning effects, it becomes more and 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 in trade 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 next period, it is still worthwhile to subsidize the domestic industry in the current period. Such results suggest that governments should take care in selecting the industries for which they intend to provide a targeted trade policy. Governments should not simply identify an industry in which imperfect competition exists to apply a strategic trade policy; other characteristics, though not necessarily only the learning effects as this thesis discusses, may also be relevant. However, the model used in this paper clearly illustrates that a duopolistic market structure alone cannot provide an incentive for a government to subsidize its industries (if the behaviour of a government in deciding on whether it should impose subsidies 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.  3 I 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 strong empirical support. We have reasons to believe that a country will sign a trade agreement because of the fear of retaliation. In fact, how a country "thinks" the rival will behave in the second period has very important implications to the policy the country pursues in the first period. If a country thinks that the rival adopts a "tit-for-tat" strategy, the behaviour of that country is different from that if the country thinks the rival adopts a policy of unconditional free trade. However, the decision of which action to choose must reflect the costs (in the second period) of not cooperating in the first period versus the benefits of not co-operating in the first period. Cooperation, in the context of this paper, means a policy of nonintervention, i.e., not to impose any subsidies. In ongoing dynamic games, "tit-for-tat" has been shown by Axelrod (1984) to be a successful strategy. Here I focus on two periods of a larger game and I assume that country B follows a tit-for-tat strategy. I then examine the best response of country A and show that learning effects can have an important effect on whether we get "free trade" as a solution. The same result will be compared to another assumption that country B follows a policy of unconditional free trade. With the basic structure discussed in this paper, the two-period economy used here can be easily expanded to a multi-period horizon; however, for the sake of tractability, I start with a two-period economy.  4 In the past decades, a number of high technology industries have evolved which exhibit dynamic economies of scale or strong learning effects. As defined by Spence (1981), the curve "that relates unit costs to accumulated volume" is called the learning curve. 1 Learning effects are then the reduction of unit costs (or marginal costs) in proportion to past accumulated production. The semiconductor industry is one that incorporates strong learning effects. High volume production provides a firm with a strategic advantage in the long run because skills acquired in manufacturing a large-volume product help to drive the firm down a 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 markets remained closed while Japanese companies were expanding their market share. As a consequence, in 1987, the U.S. government imposed 100% tariffs on $300 million worth of Japanese consumer and office goods. 2 Should a country unconditionally support free trade in 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 a duopolistic market structure and learning effects is the third focus of this thesis. For the sake of simplicity, I assume that the industry in one country is so inefficient that it is only able to survive under subsidies. If the subsidies were to be removed, this industry would be wiped out of the market and the rival would enjoy a monopolistic status. In subsidizing its industry, 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. 2 Yoffie, David B. and Helen V. Milner, "An alternative to Free Trade or Protectionism: Why Corporations Seek Strategic Trade Policy?" California Management Review (1989), 111-131.  5 phased 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 producer surplus relative to monopoly, and that loss decreases under learning effects. However, these expectations are not true as shown in my model. In other words, the presence of learning effects cannot improve a subsidized duopolistic market structure in comparison with monopoly. It should, of course, be noted that the above results are based on a very restricted set of assumptions, such as the same learning rate or the taking of only a first order Taylor's approximation. If the learning rate of the less competitive country is very high compared 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 of subsidies in the next period will also be amplified, resulting in a reduction of the level of subsidies.  6 The competition between Airbus and Boeing fits quite well into the framework described in this thesis. Hence, my fourth objective is to use the American civil aircraft manufacturing industry as an indirect example of how this industry has performed in the past two decades in which it has been subjected to subsidized competition from Europe. Although this empirical example is only loosely linked to my first three theoretical sections, the result can provide more insight into the practical side of a duopolistic industry. Such an endeavour might 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 a government to subsidize its industries include both a duopolistic market structure and strong learning effects. A duopolistic market structure alone is not sufficient to result in trade intervention 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 shifting of market share from the rival, as indicated by the decline of relative importance in the aircraft industry in the U.S..  7 Other Related Literature  International trade under imperfect competition has drawn special attention from international economists in the past decade. This attention is often linked to productivity declines in certain high technology industries, most notably in the U.S., which was once the largest free trade supporter in the world. The definite gains from free trade were first challenged in the business world; the academic field was quick to follow suit. One of the most influential papers in this area is that written by Brander and Spencer (1985) which opened a new line of thought in the field of "strategic trade policy." Traditional international economics usually ignores the impacts of participants' decisions on market prices and normally concludes that unconditional free trade is the first best optimum for not only national interests but the world as a whole. In contrast, the new strategic trade theory, with its assumption of a small number of participants in the market and its recognition of individual impacts on the market, not surprising, comes to the conclusion that trade intervention may better serve national interests. Criticism has been intense ever since the new strategic trade theory appeared. The lack of a general equilibrium approach is one of the shortcomings in the strategic trade model. Dixit and Grossman (1986) show that repercussions on other areas should not be overlooked when one considers strategic trade policy. Sensitivity to the results of small changes in assumptions is another shortcoming of the model. Eaten and Grossman (1986) adopt the assumption of Betrand (prices) rather than Cournot (quantities) competition. The policy implication is just opposite to that of Brander 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 a model of collusive intra-industry trade under a duopolistic market structure and studies its  8 important properties. He shows that collusive intra-industry trade is more sustainable if the cost differences between the producers are smaller. For this paper, cooperation is defined to involve the removal of subsidies only. For the sake of simplicity, I do not consider the collusive 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 this subject. In the civil aircraft industry, Klepper (1990) used a calibration model to show that Airbus' entry into the market reduces Boeing's profits because of learning effects. He also uses a capacity game to show that the disadvantage of late entry is overcome only after a long time and hence, market entry is unlikely without government subsidies.  9  The Structure of the Game  For the sake of tractability, the model assumes multiple time horizons. However, the government of either country formulates its trade policy based on the costs and benefits for only the next two periods. In other words, the discount rate for the next two periods is 0 and that for later periods is infinitely large. Although this assumption may be simplified, if we define each period to be four or five years, the end result will be quite close to what is observed in a democratic country where an elected leader has power to shape its policy for only a limited time period. A firm plans for an even shorter period in this model; it chooses production to maximize profits for only the next period. Firms are competing noncooperatively in terms of quantities. Hence the Cournot equilibrium is a natural outcome. Governments, however, behave in a more complicated way. Since governments of both countries are able to look at one period further than do firms (perfect information is assumed), governments recognize the benefits of producing one extra unit in the current and in the next period. These benefits stem from two sources: supernormal profits from the rival in the current period due to the duopolistic industrial organization, and the reduction in marginal costs in the next period due to the learning effects. Because of these benefits, the first 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 game in each period, while governments play a cooperative game if each of them finds that the benefits are greater than the losses; otherwise they play a noncooperative game. A cooperative game means that both governments agree not to impose any subsidies in both  10 periods. The necessary and sufficient condition for a cooperative outcome is that future losses in retaliation outweigh the present gains from noncooperation. Under a cooperative outcome, the behaviour of the two governments are fixed; subsidies will not be used as strategies.  The Nature of a Trade Agreement  Under the assumption of perfect information, both countries know that the joint beneficial outcome is free trade, as discussed by Brander and Spencer (1985), that is, when both countries do not provide industries with any production subsidies. However, if either country believes that it is worthwhile to not commit to free trade, then the noncooperative outcome is that both governments give optimal subsidies to their industries. To enforce the first best optimum (i.e. free trade), a contract or agreement that precommits the action of either country is needed. The objective of the agreement is to ensure that both countries maintain a zero subsidy level during the next two periods. For the sake of simplicity, we assumed that there is no precommitment problem -- the case in which a government does not commit to a certain promise as the environment changes in the subsequent period -- because the penalty is sufficiently large to deter either country from cheating. Suppose the agreement is being signed at t o , and the agreement will be reinforced at t 1 and t,. At t o , the decision made by a government to sign this agreement is dichotomous: a government will only sign the agreement if, after evaluating the benefits and costs of committing to the agreement in the next two periods, it is worthwhile to do so. In other words, the necessary and sufficient condition for a trade agreement to he made is that the costs of the noncooperative outcome  11 (both countries providing optimal subsidies) compared to free trade at t 2 are larger than the benefits (domestic government gives optimal subsidies and foreign government does not) compared to free trade at t 1. The cost-benefit analysis used in this paper is similar to the one used by Fung (1990) who wished to look at the possibility of cooperation in the firm level under the assumption of imperfectly substitutable goods in a duopolistic industry.  12 The Modelling of Learning Effects  The learning curve assumption is that marginal costs are a decreasing function of cumulated output. I use the following functional form to capture this idea.  f(x) = Ce "xic -  f(0) = C  where f(x) is the marginal cost after an accumulated production of x, C is the initial marginal cost, and -Ax is the elasticity of learning effects.  The first derivative of the right hand side is as follows:  f(x) = -4e "xic -  f (0) = -4  Let MC(x) represent the marginal cost in the second period, and x be the production level in the first period (since only two periods are considered in this model, accumulated production in the second period simply equals production level in the first period).  13 Since 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 - /Ix  If we use subscript 2 to represent time period 2, marginal cost at time period 2 is C2 = C 1 -  The Model  In the following section, I shall use a multi-period (in which only the next two periods are seriously taken into consideration by the government), two-country, one-good model to suggest that market structure is not the major cause of the recent standstill in trade barrier negotiations such as GATT. Recent literature, including Brander and Spencer (1981,1985), Grossman and Eaten (1986), and Krugman (1984) among others, attempts to place a strong emphasis 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 certain phenomena which cannot be satisfactorily explained by theories based on factor endowments, such as the Ricardian model or the Heckscher-Ohlin Theory. Market structure is particularly successful in explaining intra-industry trade. However, it is insufficient to conclude that market structure and imperfect competition form the only rationale of intervention in trade, an opinion which is quite popular in recent literature, and is  14 repeatedly emphasized in the book written by Krugman (1989). 3 According to the results derived from my model, it is learning effects in addition to market structure, not market structure 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 to the acceptance of a trade agreement.  The following section illustrates that cooperation between governments can be sustained if country B is believed to adopt a tit-for-tat strategy, that is, if country A believes that if it imposes an optimal subsidy in the first stage of the game, country B will impose an optimal subsidy as well in the next stage, resulting in the imposition of optimal subsidies in both countries.  3 Helpman, Elhanan and Krugman, Paul R.. Trade Policy and Market Structure. Cambridge, Mass: MIT Press, 1989.  15 First Stage: Free Trade vs. Optimal Subsidy  Let us begin with the case in which learning effects are not present. Suppose that country A and country B are exporting the same good to a third market in quantities x and y respectively, and that both countries initially have the same marginal cost. The first best optimum condition having the highest joint payoffs occurs when both countries impose zero subsidies. Assuming linear demand, p(x,y)= a-b(x+ y) and constant marginal cost, c, profit functions for A and B are r A = xp(x,y) - cx = x(a-b(x+y))-cx 7r B = yp(x,y) - cy = y(a-b(x+ y))-cy  16 First order conditions are given as follows: a - 2bx - by - c = 0 a - bx - 2by - c = 0  -2b -21{1 = [c-al -2b -2b y^c-a  x^1 [-2 1 [c-a ^1{a-c1 . i_^ b 1 -2 c-a 3b a-c Y  (1  )  Based on the gain or payoff function of the government as defined by Brander and Spencer (1985), the payoff of country A of not a adopting strategic trade policy is given by Gx NN = 77-A - xs  (2) where s is per unit production subsidies.  17 Since s = 0, if a strategic trade policy is not adopted, then (p(x,y) - c)x  GxNN = 7T A =  =(a - b(x +y) -c)x 2  =(a -c - — (a -c))x  3  9b  (3)  (a-c) c)2  Similarly, payoffs for country B under free trade are given by GYNN =  1  9b (a -c)  2  (4)  Now suppose that country A imposes a per unit subsidy s to its industry. The profit function of A becomes:  7r-A = xp(x,y) - cx = x(a-b(x + y))-cx + sx 7r-B  = yp(x,y) - cy = y(a-b(x+y))-cy  First order conditions are given as follows:  a - 2bx - by - c + s= 0 a - bx - 2by - c = 0  18 -2b -2b [x ^{c-a-1 -2b -2b^c -a  (5)  x ^1 -2 1 {c - a - s ^1 [(2-c+2.1 = y^3b 1 2 c - a^3b a - c -s  (6)  ),  —  -  The best that country A can do by adopting a strategic trade policy is to impose an optimal subsidy. Optimal subsidy is the level of subsidy that maximizes the payoff function for country A, as suggested by Brander and Spencer (1985), such that  aG xSN as  - TC^ s - X SX3 = 0 -  (7)  19  For country A,  ns= nxxs + nyYs +x nx = 0^'It s = 71  )37s + X  aGxsN_0_,It yys +x-x-sxs =0 as sopa.mat_ n YYs Xs  _ -1 ^ xs . 2 Ys- 3b' ^3b ^a2Gx^ -1 2^2 SN b()—() 3b 3b ^as 2^3b 2^2 ^s 0 =( 9b ) -( --  (8)  (9)  20  Therefore, GxsN is concave in s and if the first derivative of  GxsN  equals zero, then that  means GxsN is maximum.  From (8), .0' 1 - bxYs xs -1 1^3b = -b(—)(a -c +2s) 3 b^2  1 = — (a -c +2s)  3b  s = —1 (a-c)  1 3 ( 1 _ a c = 1 3 (a 0 _ a c ) x= 3b2‘ ti-c - 2b ; y 3b 4^4b X 1^a - c _ (a - c) 2 G^ i sN = (p(x,y)-c)x =(a -b(x -y)-cx = -,i (a -c) 2b^8 b G Y1 _ (a 0 2 From (6),  -  -  -  -  SN  16b (1 0)  21  Optimal subsidies imposed by A makes B worse off because G Y1NN > GYI SN  i.e. payoffs to country B in free trade > payoffs to country B if A imposes optimal subsidies. This is the profit-shifting motive for subsidizing a firm in a static framework. The firm in country A is doing better than that in country B because of the subsidies. This result is indeed 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 to make the impacts of learning effects easier to demonstrate.  22 Second Stage: Free Trade vs. the Cournot Nash Equilibrium  Based on the result of the previous section, I shall investigate the possible impact of a "titfor-tat" strategy by country B on the possibility of cooperation at times 1 and 2. I assume that "tat" or punishment is represented by country B playing the one-period noncooperative Nash subsidy. Cooperation (i.e. free trade) will be enforced by a trade agreement provided that 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 would evaluate the possible benefits and costs of subsidization. If I assume that country B follows a "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 of the inequality, which means losses to country A in the second period because country A thinks country B will respond with an optimal subsidy to retaliate against country A which imposed an optimal subsidy in the first stage of the game. In other words, G' ss is the payoff for country A in a Cournot-Nash equilibrium in which both country A and B impose optimal subsidies 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 stage of the game (compared to free trade) if it imposed an optimal subsidy to its industry in the first stage of the game while country B remained adopting a policy of free trade. In other words, the losses to A are based on the assumption of the adoption of a "tit-for-tat" strategy  23 by B. The right hand side of the inequality represents the gains to country A (compared to free trade) if it imposes an optimal subsidy to its industry in the first stage of the game. The interpretation of inequality (11) is simply that if relative losses in the second stage are larger than relative gains from defection in the first stage, then country A will have no incentives to deviate from cooperation; hence an agreement will be acceptable to both countries. I assume that a country defects by imposing optimal subsidies, given that the rival remains in free trade in the first period. Once an agreement is signed, cooperation (i.e., in which both countries remove all subsidies) can be enforced.  24  To find G'ss (the payoff for country A in the second stage if country B retaliates by imposing an optimal subsidy), I shall first find out the simultaneous equation of the optimal subsidy for one country in terms of that of the rival, and then solve for s and s * , which represent the optimal level of subsidy for countries A and B respectively.  Now suppose that countries B imposes per unit subsidies s to their industries. Profit functions for A and B become:  r A = xp(x,y) - cx = x(a-b(x + y))-cx + sx  yrB = yp(x,y) - cy = y(a-b(x+y))-cy+ s*y  First order conditions are given as follows:  a - 2bx - by - c + s= 0 a - bx - 2by - c + s * = 0  {-2b -2/ [1 {c-a-si 2b 2b y^c - a -s* -  -  (12)  ^  25 xi^1 -2  1 [ c-a-s  ila-c+2s-s  }  y^3b 1^-2 c-a-s *  3b a-c-s+2s*  2 ay^-1 aince Si nce —=—; --as^3b as^3b 1 A^-bx— 7V yy s 3b^3bx^a-c+2s-s* from (8) optimal s xs^2^6^6 3b 4s = a-c-s* 4s +s * =a -c  (13)  Similarly optimal s* _  -1 ^-by_ _^_ nBxxs• _ _^3b^3by^a-c+2s*-s Ys•^2^6^6  3b 4s *+s=a-c  From (13), s *+4s=a-c a-c ac 1^ ^is .^ = {a- c 1 4^ [s 1 . 115 [4 1 -41 [aa il 4  s  1{al 5 a-c 2  2  x = — (a-c); y = — (a-c) 5b^5b 2 — (a-c) 2 = GY ss G xss = (p(x+y)-c)x = (a-b(x+y)-c)x = 25b  (14) The Nash equilibrium, as represented by the payoff G' ss , is the noncooperative outcome without an agreement, in which both governments act noncooperatively. Each government attempts to maximize its gains using optimal subsidy levels, and takes the other's action as  26 given. The net consequence is an equilibrium given by the solution of reaction functions of either governments' subsidy level in terms of the rival's subsidy level. The Cournot-Nash equilibrium, despite its naive nature, is one extreme scenario which a government must consider before considering a free trade agreement; such an equilibrium tells what the payoffs would be without an agreement if the rival adopts a "tit-for-tat" strategy to retaliate against country's A defection in the first period. 4 Since marginal costs are the same in both stages 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 a binding agreement. -(Gx2 ss — G X-2 NN) > G x i sN -G x i NN  (15)  That is equivalent to show whether 2 G 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 XSN in the absence of learning effects. 2 2^1 (*) = 9b(a-c) 2- ^ (a-c) 2 -- (a-c)2 > 0 25b 8h Hence, cooperation can be enforced. —  (16)  Using the above simple cost-benefit analysis, the profit-shifting motives of a duopolistic market 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 governments have a net payoff that is less than the Nash outcome. This case, however, is inconsistent with our earlier assumption that a government is maximizing its payoff function. Thus, imposing a subsidy higher than the optimal level is ruled out.  27 question is, what other conditions, in addition to market structure, can make trade intervention relatively beneficial to a country even under the retaliation from the rival? An industrialist may claim numerous characteristics that would make trade intervention beneficial. However, one of the most relevant characteristics comes from learning in a dynamic economy: the more a worker does, the better he/she will do the job. In a twoperiod 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 this simplification, the learning effects can be easily introduced into a model with a duopolistic market structure. Hence, the first focus of this paper is to show that learning effects will change the relative payoff in the second stage, making relative gains larger than relative losses due to retaliation. As it will be shown, a government may find that the scenario in which the rival retaliates will improve under strong learning effects because subsidizing production in the first stage reduces marginal cost in the second stage. Before I illustrate the impacts of learning effects in a dynamic economy, let me first show what will result from a policy of unconditional free trade.  28 Unconditional Free Trade without Learning Effects  In the context of this paper, unconditional free trade means that a country will not impose any subsidies to its industry regardless of what the rival has done. Would country A still find cooperation the first optimum if it knows a priori that country B adopts a policy of unconditional free trade? The answer is no because, as it will later be shown, unconditional free trade reduces the penalty of deviation from cooperation. A criteria for cooperation for country A is given by the following inequality: 5 - (G x2 sN G x2 NN) > (G x1sN G x1NN) —  —  Since there is no learning effect in this model, Gx2sN Gxi sN, and Gx2sN = Gxi sN. The above inequality becomes an equality and hence the agreement is no longer acceptable to both sides because the relative gains in imposing optimal subsidies are as large as the relative losses of retaliation from the rival in the next period. Unconditional free trade, as these results 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 not acceptable to country A, then neither will it be acceptable to B.  29 Second Stage: Free Trade vs. the Cournot Nash Equilibrium with Learning Effects  Now let us consider how the result will change when learning effects are present. The left hand side of (11) will become different from that under no learning effect because the marginal costs of firm A in the second stage, cc 2 are different if country A adopts different trade policies in the first stage. Gx 2ss is the payoff to country A in the second stage under retaliation 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 second stage will be smaller if a country deviates from free trade in the first period in the presence of 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 are different in the two countries, as represented by cx 2 and cY2 for country A and B respectively. c '2 C  = C - Aix i ^ 2 = c - Ary l  (17)  In the case of Gx2 NN , assuming that there is no subsidy in the first stage, x 1 =y i = a c 3b -  In  the case of Gass , assuming that A imposes an optimal subsidy while B does not in the first stage, x 1 = -a c and y 1 = a c -  -  2b^4b  30 Case 1: Both Countries Adopt Free Trade in the Second Stage  Now suppose that both countries adopt free trade in the first and second stages. With learning effects, payoffs to country A and B under free trade in the second stage (given free trade in the first stage) are as follows:  From (3) G x2 NN 1 = —(a-c 2) 2 9b 1  =— b(a-c+Axi) 2 9 1  c  = — (a -c+ihal_)2 9b^3b 1 = —(a-c) 2 (1+ 2-)2 9b^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 Stage  Now suppose that country A imposes a per unit subsidy, s, and B imposes s * to its industry to retaliate to A's imposition of an optimal subsidy in the first stage while B remains in free trade. Profit functions for A and B under strong learning effects become:  31  7r A = xp(x,y) - cx = x(a-b(x+y))-cx 2x+sx ir B = yp(x,y) - cy = y(a-b(x+y))-cY 2y+s sy  The first order condition is given as follows:  a - 2bx - by - cx 2x + s= 0 a - bx - 2by - cY 2y + s * = 0  32  [-2b -b 1 {xl { c x2 -a-sI -b -2b y^c Y2 -a -s  (19)  x y  .^  1  -  2^1  c x2 a s -  3b 1^-2 c Y2 - a -s*  s 1 a 2c x2 +c ) 2 +2s s* -  -  -  =—  3b a-2cY2 +c 2 -s+2s*  _ 2 ay = -1 -1 • ay _^ ax 2 • ax=_•^ Since _...=• ^ as 3b' as* 31,' as* 3b as 3b 1 -ux— 70 Y.,^ ^3b _3bx _ a-c+2s-s * from (8) optimal s - ^ = xs^2^6^6 3b 4s +s * = a-2cx2 +c Y2 S * Similary, s+4s*=a+c x2 - 2C Y2 -  C x2 = C - 11,X 1 C Y2 = c - ph x11 -  2b a-c Yi - ^ 4b  (20)  33 To find G x2ss under learning effects  4 1  s ^-2c 2 +c 2 +a  1 4 s* ^{c2 - 2C Y2 +a  a-c  Let o=— p.; Hence cx2 =c-2o; cY2 =c-o 4b  4 -11 r 2 c x2 + c Y21 s *j^15 {-1 4 i c x2 -2c Y2 +a  {  sl = 1  1  {  -  9c x2 +6C 2 +3a  15 6c x2 -9c 2+3a  51  -c +4 a +al -c - a +a  (21) Guess under learning effects is evaluated as follows: 1  x2 = — (-2c x 2 +c Y2 +2s -s * +a) 3b 1  9  = --L ( 2c +4 cr +c-o+- (a-c)+- o +a) 3b^5^5 -  x2 = 2 ( - c +4 a +a) 5b  2  Y2 = 5b ( - c + a + a) —  2 (a-c +4 a) 2 G ass = 25b  (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÷ 3.11) )2  (a-o2 -2 _ 2142 _ 414 + 1 + ^+ 25b 25b 3 25b 2 4b 36b 3 6b 2 =(a-c) 2 17 + ^ -  47142  100b 90b 2 900b 3  From (10) and (3), (G x1sN -G x1NN) = li (a-c) 2 - 4 (a-c) 2 =  7  (a-c) 2  (**) = (a-c) 2 17 +^ 4a._ 0  21  47/42 - 1 100b 90b 2 900b 3 72b  1124^/.2^47/12  7200b 90b 2 900b 3 (23)  35  In 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 imposing optimal subsidies in the first period) is the only necessary criteria to considering a free trade agreement, then such an agreement will not be acceptable under strong learning effects such that (**) < 0, since the steepness of the learning curve, A, would determine the sign of (**). In other words, if  -1 ,\I ^ - ( ^1 ) 2 +4 A  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 imposing an optimal subsidy in the first stage. Hence, market failure occurs in this economy. An agreement that aims to enforce free trade will not be acceptable to both countries, because of the strategic gains from strong learning effects.  36 Implications  The above results imply that if learning effects are strong, it is no longer true that cooperation between governments can be achieved by assuming the rival's adoption of a "titfor-tat" strategy; the reduction in marginal cost due to learning effects may outweigh the losses 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 a government 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 useless provided that a country still gains relative to free trade even if there is retaliation. In other words, a free trade agreement is definitely acceptable to either side (if they all use (11) to evaluate cost-benefits) with no learning effects, but whether the same agreement remains acceptable to both countries under the presence of learning effects is unclear; it depends on the steepness of the learning curve. The steeper the learning curve, the more a country will 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 in these results illustrate that in contrast to what Krugman (1984) concluded, dynamic and static economies of scale do not necessarily have the same impact on the acceptance of a free trade agreement in a duopolistic industry.  37 Unconditional Free Trade with Learning Effects  It was shown earlier that a policy of unconditional free trade results in an incentive to deviate from cooperation. How would the result change if country B adopts unconditional free 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 to deviate from cooperation. The left hand side of the inequality is evaluated as follows: 1 =— (-2c x2 +c Y2 +2s +a) 2^3b y2 = h (c x2 - 2c Y2 -s+a)  x  3 optimal subsidy is given by:  1  s = — (-2c  x2 +C Y2  +a)  1 x..^ „, = —(-2c 2 +c Y2 +a) 3b y2 =  1 (2c x2 - 3C Y2 +a) 4b  G x2sN = Vx2 +Y2) - c x0x2  =(a- ±( b  -  4c x2 +2c Y2 +2a +2c x2 -3c Y2 + a - c x 2))x2 1^2^ =—(a-c) (1+ 3,Li 2 8h^4h)  (26)  38 91b02_02(a÷ 314b)2 From (18), G 2NN = —  -(Gx2sN-Gx2NN)  =  3 41,4 ) 2 +-4(a-c) 2 (1+ 2 3 d2  81 (a-c)2(1+—  1 (a-c) 2 G x1sN -G x' NN 72b  -(G x2sN -G 2NN)-(G xi sN -G x1NN) = (a-c)  -2 ^  2 (  ^49/2  )<0 72b 10368b 3 432b 2 601122  (27) Hence, as in the results of the case without learning effects, unconditional free trade does not provide a sufficient penalty to deter the rival from deviation from cooperation in the presence of learning effects.  39 Summary of Results  The following tables are a summary of the payoffs received by countries A and B under two different assumptions -- a static and a dynamic model. While non-cooperative outcome is an equilibrium solution in the static model, in a dynamic one whether or not one will obtain free trade as a solution depends on other factors, such as learning effects and the strategy the rival is believed to adopt.  Case 1: Static Model  Payoffs = (country A, country B) Country B  S (Defect) S (Defect)  N (Not defect)  2(a c) 2 2(a c)2 25b^ 25b -  (  -  '  Country A  N (Not defect)  (a c) 2 (a c) 2 16b 8b -  (  Table 1, Payoffs in a Static Model  -  (a c) 2 (a c) 2 9b 9b -  )  )  '  -  ,  (a c) 2 (a c) 2 8b 16b  ^ (  (  -  ,  )  40  Case 2: Dynamic Model  NB: The two values in the table represent the net payoffs (cost-benefit) assuming the rival adopts (1) a "tit-for-tat" strategy and (2) a policy of unconditional free trade. If country B responds by the following strategy in  period 2  Unconditional Free Trade  Tit-for-tat Country A's action in period 1  SN (Defect)  47/12  2  (a c) 1124^ 7200b 900b 3 +^µ ) 90b 2 -^  (  (a _ 02( __  2^60111 2 72b^10368b 3 49[1 ) 432b 2  Table 2, Payoffs Relative to Free Trade in a Dynamic Model  41 Using the above table to predict whether an agreement will be signed or not, I have the following result: (yes means that an agreement that enforces free trade will be signed; no means that the same agreement will not be signed) Case 2.1: Weak learning effects If country B responds by the following strategy in period 2 Country A's action in period 1  Assumption: small  Tit-for-tat  Unconditional Free Trade  Yes  No  A  SN (Defect)  Table 3, Whether Free Trade is a Solution in the Model with Weak Learning Effects  Case 2.2: Strong learning effects, If country B responds by the following strategy in period 2 Country A's action in period 1  Assumption: large  Tit-for-tat  Unconditional Free Trade  No  No  A  SN (Defect)  Table 4 Whether Free Trade is a Solution in the Model with Strong Learning Effects  Note: large th means -1^( 1 )2+4 47 1124 90b 2^90b 2^900b 3 7200b 2(  -47 _) 900b 3  42 The above results can be summarized as follows: (1) if a country thinks that the rival adopts a "tit-for-tat" strategy, then we may find free trade as a solution only if learning effects are not strong enough; (2) if a country thinks that the rival adopts an unconditional free trade policy, then regardless of learning effects, we may not find free trade as a solution.  43 The Infant Industry Argument  In the previous sections, we have found that trade intervention depends upon what strategy a country thinks the rival will adopt and whether or not learning effects are present. In this section, we continue to investigate another explanation for trade intervention -- the protection of an infant industry. The infant industry argument is one of the most commonly used arguments against free trade. In certain high technology industries, in particular the civil aircraft manufacturing industry which is now dominated by Boeing and Airbus, there is a widely supported argument that trade intervention in the form of production subsidies from several European countries to Airbus is justified. The argument for these subsidies is that if production subsidies were removed, America might gain a monopoly status because the marginal costs differ widely in this duopolistic industry; the European aircraft industry would not be able to compete with that of America without subsidies. The costs of maintaining such a duopolistic industry are incredibly high -- more than $13 billion in the case 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 the combined profits earned by two firms in a duopolistic industry. Hence, there is a loss in producer surplus if monopoly becomes a duopoly. However, whether the same results hold true in a learning economy remains unclear. When a government subsidizes an infant high technology industry, there is always an implicit assumption that in the long run, the subsidized industry will survive on its own. One major argument in favour of subsidies in the aircraft industry is that Airbus will be able to pick up the pace and compete with Boeing once Airbus has secured a position in the market. Because of learning effects, subsidies may be gradually phased out. Unfortunately, based on the model described in this paper, the  44 opposite is true. Learning effects increase the loss of producer surplus, and in a dynamic economy, the subsidy level remains the same.  To illustrate the above argument, I make the following assumptions. First, a government just wants to subsidize its infant industry to make it as competitive as the industry of the other government. Second, the rate of learning is the same for the two countries. Third, there are no spill-over effects.  45  The model used in the previous sections will illustrate that subsidies which aim to maintain a duopolistic market structure (i.e., in which without subsidies, the market structure would become monopolistic) cannot be phased out in a learning economy. In addition, combined supernormal profits earned in a duopolistic industry are less than those in an equivalent monopolistic industry. More importantly, the difference in the supernormal profits between a 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 the model 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 level compared to the rival, there will be no chance of survival. The duopolistic industry structure will become monopolistic. For the sake of simplicity, let us assume that the difference in marginal 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 subsidies to its industry to make the two firms equally competitive, i.e., so that they have the same marginal costs. Based on these assumptions, the objective of this section is to show whether under a duopolistic market structure and in a dynamic economy with learning effects, subsidy level and losses in producer surplus can be reduced.  46  Profit functions for countries A and B are then:  TE A = x ip(x i +y 1 )-cxix i = x1 (a-b(x 1 +y 1 ))-cx 1x 1 n il = y1p(x 1 +y 1 ) -c Y1y1 = y1(a-b(xl+y1))-c Y1y1  an A ax 1  By Kuhn Tucker Condition:  - a - 2bX1 1- bh - C xi < 0 if xi = 0 a7,B  ay,  a-cxi < by i (*) - a-bx 1 -2by i -cY l = 0 y-  (28)  a-c y1  2b  Substitute y to (*), a-cx i < C Y- C x < cx -a+ 11^  a-c Y 1 2  a-cxi  i^2  c'' 1 -cx i < --1 (a-c Y 1 )  2  c x i -c Y i >  1 (a-c Y i ) 2  The above results indicate that if the difference in marginal costs is larger than a critical level, as given by (a-e 1 )/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.  47 Suppose now that the government of country A wishes to maintain its industry by a per unit production subsidy, s, such that 1 s = cx-cY=- (a-cY)^ C x- S  (29)  =C  Marginal costs, which are now the same under government subsidies, equal cr 1 . -2b -b1 ^{c "1 - a [ - b -2b y 1^cY 1 - a x1  1^-2^1  a -01  y 1 = 341^-2 a - c v 1 G Dm^= (p(x 1 +y 1 )-cY^= i -s)x i (a- 2 (a-c Y 1 )-c Y 1 -1 (a -c Y I )).x i  3  -1 (a-c Y i) 2 18b Dy 1 G a= — 9 b (a-c Y ) 2  (30)  48 GDX1 is the gain function to country A under subsidies that aim to keep its firm as competitive as that of country B. The net gain to country A is negative. Unlike in the case illustrated in the previous sections, subsidies that aim to maintain a duopolistic market structure because of the wide difference in marginal costs cannot provide a net positive payoff to country A. If the objective of government A is simply to prevent country B from obtaining a monopoly status, then subsidies can achieve that purpose. However, if the objective of government A is to subsidize its firm temporarily and then gradually phase out those subsidies as the firm "learn" to produce more efficiently and thus becomes more competitive, then government A will not achieve its target. I shall use a dynamic learning economy to illustrate this claim.  First of all, let us evaluate the difference between supernormal profits earned in a duopolistic industry and those earned in a monopolistic industry. The duopolistic market structure is maintained only because of the subsidies of country A. In the presence of learning effects, marginal costs will be reduced in proportion to the accumulated production (since only two periods are taken into consideration, accumulated production simply equals production in the first period). However, the reduction in marginal costs would be different in the second period if country A did not impose a subsidy to maintain its industry in the first period. This is because with subsidies, the market structure would be duopolistic in the first period, and without subsidies, it would be monopolistic. Since production level in the first period would be different under a different market structure, marginal costs would also be different in the second period. The major argument in support of subsidies in a dynamic economy is that once the subsidized industry has secured a position in the market, because of learning effects, it can survive on its own in the future. The underlying assumption is that,  49 although subsidies are not good for the world as a whole, they can be used to support the growth 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 which marginal cost can be reduced in proportion to accumulated production. First, per unit subsidies 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 monopolistic industry should be smaller in the second period than in the first period. Otherwise, the world economy would be better off without subsidies in the first place. This argument can be represented by the expression G DY 1 +G Dx1 - G M 1 < G D2 +G Dx2 - G 2  ^  (31)  The left hand side of the inequality represents the difference in relative payoffs between a subsidized duopolistic industry and a monopolistic industry in the first period; the right hand side represents that in the second period.  50 For the sake of simplicity, I shall assume that the objective of government A is to subsidize its industry so that it can be as competitive as the industry in country B, i.e., so that their marginal costs, after subsidies, are equal. To evaluate the above two expressions, I must know G m i and G M2 which represent the payoffs to country B if it can gain a monopoly status provided that country A ceases to subsidize its industry in the first and second period respectively. .CB =  y 1 (a-by 1 )-cv iy i , since x 1 =0  alt B  aY1  - a-2by i -c Y 1 = 0  a-cY 1 (32)  y1^2b  p = a - by1 = a- 1 (a-cY 1 ) 2 G m, = (p-cyx i 1 =h (a-cy 2 4  Relative payoffs between a monopolistic and a subsidized duopolistic industry in the first period are given by  G px1 +G DY i -G m1 4a-c y 1) 2 ( = (a -  ,+)  -" ,+ 1 -  c Yi)2( 3 76b )  b  (33)  51 The world economy will be better off if country A did not subsidize its industry in the first period, so that country B can gain a natural monopoly in producing y. Now the questions are, (1) whether the difference in relative payoffs can be reduced, and (2) whether per unit subsidies can be reduced if there are learning effects. To answer the above questions, I must know the relative payoffs in the second period under two different scenarios: (1) if the market structure is monopolistic in the first period, and (2) if the market structure is duopolistic in the first period.  First, if the market structure is monopolistic in the first period, then the payoffs to country B in the second period are as follows: c Y2 = c Yi -0 1 ; y 1 =  G M2  (a-c  Y2 )2^1  1 (a-c 2b  )  Y1 2  (a -c)2 (1 + -L. . 1 )2 4b 4b^2b  -^  -  (34)  52 Second, under a subsidized duopolistic market structure in the first period, if the level of subsidies in the second period is only enough to make the firm in country A as competitive as that in B, the level of subsidies, s, is calculated as follows: -c " 1 ) 2 -(cY 1 -12- (a -c Y d 2) 3b 1 (a-cY ) = c'' 1 -cx1 = S i..^2^1  S2 = C x2 C Y2 = C x i - /..4- (a 3b -  1  (35)  The above expression answers the first question in determining the level of subsidies cannot be reduced in a learning economy. If the objective of government A is to equate the marginal costs between two countries through subsidies, then it is incorrect to expect that those subsidies can be gradually phased out; marginal costs cannot be reduced in the future in proportion to accumulated production. Whatever level of subsidies government A imposes in the first period must be imposed again in the second period. If more periods are taken into consideration, it is not surprising to find that a subsidized industry remains being subsidized forever; an infant industry can never become mature. Most importantly, just as in the scenario in the first period, once subsidies are removed the industry cannot survive at all, because the difference in marginal costs in the second period is just large enough to eliminate the firm in country A from the market.  53 Now, 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 -S2X2 1/  1 (a _ c y2) = 1 (a _ c y  x=  +Axi)  3b^3b 1  ^2  1 1 =(a-cY 1 + p—(a-cY ID  (36)  ^3b^3b  1 A -(a - c Y 1 )(1 +--)  3b^3b  s2x2  =a 4(  -cY1)2(1+ i )  At G D2 = 1 (1+ — )2 (a - c Y 1) 2  9b 3b G px2 +G DY2 G 112 -  =  9b 2 3b 3b )2(a _  1 --(a-c 6b  c y 1 )2  ' 1 )2(1 -LI.)  3b  1  -- (a -c p 1 ) 2 (1 + -L I )2 4b^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  -  c  Y1)2(  36 b 1107 P8 b 14299146 ) -  -  (37)  54  The relative payoffs (between a monopolistic and a duopolistic market structure) are still negative. 6 Most importantly, the relative payoffs in the second period are smaller (i.e., more negative) than those in the first period. This implies that the payoffs to a subsidized duopolistic market structure do not improve with comparison to a natural monopolistic market structure, even in a learning economy. On the contrary, the situation worsens, mainly because marginal cost under a subsidized duopolistic market structure cannot be reduced as much as that under a natural monopoly. From the results derived in (9), namely that the gain function is concave in s, it is not surprising to find that relative gains are negative. The objective of the following is to prove that the level of subsidies used to maintain a duopolistic market structure is larger than the optimal subsidies as suggested by (26). More importantly, the optimal subsidy is zero for the firm in country A. In other words, the best that government A can do, regarding its "infant industry", is not to impose any subsidies.  From (35), c Y2  -  C  2 = 1-(a -c a l )  2 1 From (26), s = — ( -2C x2 +C Y2 +a) 4 1 1 = — ( -2- (a +cY2)+c Y2 +a) 4 2 = 0 optimal subsidy = 0 But the level of subsidies that maintains duopolistic market structure is (a -c x ) > 0; From (28) 2 1  That is because the level of subsidies that maintain duopolistic market structure is much larger than the optimal level of subsidies.  55 Since the level of subsidies that is used to maintain a duopolistic market structure is larger than 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 by market force, i.e., the government should refrain from imposing any subsidies. Although the net consequence -- that country B gains a monopoly status -- is rather unfortunate for country A, according to this model, it is ironically the best outcome.  56 Therefore, if the industry can only support one firm, it is ineffective for a government to work against the market forces in order to maintain a duopolistic market structure. This conclusion has very strong implications for the civil aircraft manufacturing industry. Today there are two main producers of large transport aircraft: Boeing (over 50% market share) and Airbus (30-35%). Airbus' market share has increased rapidly under European governments' heavy subsidies in the past decades. One major reason for giving these subsidies is to prevent Boeing from monopolizing in this industry. Because of its late entry into the market, Airbus could not survive without subsidies. It is expected that once Airbus has secured a position in the market, its subsidies may gradually be removed and that there may be competition in the civil aircraft industry. An airline does not have to order aircraft from the U.S. only. Unfortunately, according to the results in this section, these expectations are false. Two major effects of a subsidized duopolistic learning economy revealed by this study disprove those two conventionally accepted expectations: first, subsidies cannot be phased out; second, if learning effects are taken into account, a subsidized duopolistic market structure is worse off than a monopoly. Again, it should be noted that policy inferences from the above results are based on a restricted set of assumptions. Airbus' subsidies may be justified if it "learns" substantially faster than Boeing does. Hence the counter infant industry argument proposed here can only be applied to a very specific case: when both firms learn at the same rate. Actual inferences would depend upon crucially on the difference in the rate of learning. Without going into too much technical details in this subject, I shall turn the attention to some stylised facts in the international aircraft industry which is very close to a duopoly in the next section.  57 Case Study: Civil Aircraft Manufacturing  The aircraft manufacturing industry possesses the characteristics discussed in this paper: a duopolistic industry structure and steep learning curve. The motivation of examining the international aircraft industry is not to prove or disprove any of my theories; the purpose is simply to take a look at the practical side of duopoly and see how the aircraft industry has performed when Europe has been actively subsidizing its aircraft industry. The number of aircraft manufacturing companies has declined from more than 20 in the post-war period, to only three currently: Boeing, McDonnell Douglas (MDD), and Airbus Industrie. The relative importance of MDD in the market has gradually been replaced by Airbus, as MDD is currently almost completely involved in military aircraft manufacturing. There are much smaller 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, the aircraft manufacturing industry can be characterized as a duopoly (Airbus and Boeing together 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 very steep 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 aircraft industry 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 industry that with every doubling of the number of airplanes produced, a 20 percent reduction of direct 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.  58 becomes more gradual. Developing a new model is extremely costly and risky, though a jump in production from, say, two to four units occurs far more swiftly than is the case with a jump from eighty to a hundred units. However, this does not imply that developing a new model is more profitable than maintaining an old one. It could take five years to get a plane from the drawing board to final production. For instance, the present development of 767 by Boeing, the world's largest single private venture, involves more than ten years and almost the entire asset of the company. Because of the recession, most airlines have withdrawn their orders for new aircraft. Whether the market can absorb the expected amount of production remains unclear. In fact, through 1980, no firm broke even before 300 planes 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 not persist for too long, because Airbus is aggressively invading the market with the aid of subsidies from four European governments.  59 Airbus itself consists of only 1,500 administrative and sales staff housed in a single office building near the Aerospatiale factories. Airbus accounts are a mystery. No one really knows what Airbus has cost so far because the consortium has one peculiarity: Groupement d'Interet Economique, a French oddity which lies somewhere between a partnership and a  corporation, and which does not have to file proper accounts. 8 Costs, benefits, and work are shared according to each nation's stakes in the consortium: France's A6rospatiale and West Germany's MBB each own 37.9% of the firm, British Aerospace has 20%, and Spain's CASA has 4.2%, regardless of comparative advantage. Hence, it is not surprising that Airbus is able to get billions of dollars of subsidies from the member countries. Currently, Airbus Industrie has been criticized for competing unfairly with Boeing, a purely commercial US firm 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 that the governments of France, Germany, and Britain have handed out $13.5 billion in subsidies to Airbus. No evidence suggests that these subsidies will stop, nor is there any possibility of these investments being repaid in the future. 9  8  The Economist (September 3, 1988): 9.  9  The Economist (February 16, 1991): 51.  60 These subsidies are irrational from the viewpoint of a perfect competition model. However, two particular features of this industry explain the behaviour of the European governments sensible. First, the civil aircraft industry is part of national defence, since almost all present aircraft manufacturers started by building military aircraft. Moreover, firms that are capable of producing military aircraft can also take civil aircraft orders. For instance, McDonnell Douglas is now more involved in its military aircraft production, but if any airline should order a DC10, it could produce one of those as well. However, military orders are highly volatile. Therefore, countries which are capable of producing military aircraft tend to maintain their own civil aircraft manufacturing to act as a buffer when military orders slow down, as well as to enable a team of engineers and workers to become involved in the high technological edge of the aerospace industry. Accordingly, subsidies to aircraft manufacturing, like defence expenditures, are always linked to national security. Second, most important, there is a fear among European countries that America will become a monopoly in civil aircraft manufacturing. However, it is difficult for any individual country in Europe to compete with America because of the high capital, high risk, and long pay-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 all the risks involved in developing a new model. The success of Boeing is perhaps simply due to the timing of its entry into the market: after World War II while Europe was still recovering from wartime damage.  61 Subsidies remain the most controversial subject in the aircraft industry. Boeing estimates that the development costs of Airbus' MOO model can never be recovered and that Airbus has underpriced its latest A320 by more than 20%. 10 The US government threatens to complain to the General Agreement on Tariffs and Trade (GATT) and impose Countervailing Duties (CVD) on Airbus. However, the European Commission which was assigned the job of negotiating with the Americans on the subsidies issues is only proposing to eliminate production subsidies, and to reduce R&D subsidies from 70-90% to 45%.  11  This is a concession, although the R&D costs are the heaviest burden to an aircraft manufacturing firm. Boeing's development costs of its 767 model are now estimated to exceed $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 receive indirect 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 industry between 1978 and 1987. 12 There is no sign that a settlement concerning the trade disputes of this industry will be reached in the near future.  10  77te Economist (February 14, 1987): 60.  "The Economist (February 16, 1988): 51. 12  The Economist (September 3, 1988): 10.  62 One major prediction of this paper is that in a learning duopolistic economy, conditional free 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 Milner wrote: Following the start of formal U.S.-European negotiations in the GATT in 1987, Boeing officials said they would consider the talks successful only if Europe would eliminate all subsidies, stop political pressure in aircraft sales, and force Airbus to price in order to recoup all costs. Failing such an agreement, Boeing threatened to file an unfair trade petition (section 301), as well as anti-dumping and countervailing duty cases against Airbus, noting that "under any one of these laws, the U.S. government could negotiate with Airbus to limit the quantity of exports, eliminate subsidies, impose taxes, or reach some other solutions". 13 Such an attitude is in sharp contrast to the unconditional free trade policy supported by the industry in the past. For instance, in the 1970s, Boeing repeatedly emphasized at congressional 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 the market) and learning effects becomes more significant (the cost of launching a new design for large aircraft in the 1980s rose to $5 billion), unconditional free trade is no longer a mainstream trade policy supported by this industry. As a consequence, one finds the socalled strategic trade policy becoming the general demand of not only the industrial, but also the national interests.  Yoffie, David B., and Helen V. Millner. "An Alternative to Free Trade or Protectionism: Why Corporations Seek Strategic Trade Policy." California Management Review (summer 1989): 111-31. 13  63 Empirical Evidence  Civil aircraft industry is an important industry in the U.S. that possesses all the characteristics discussed in this paper: a duopolistic industry structure and steep learning curve. From the results of the first two sections concerning a duopolistic industry with learning effects, if one country imposes a subsidy on its industry, the industry of another country will be hurt. In the real world, the aircraft industry in the U.S. is facing a similar subsidized competition from Europe. The purpose of doing the empirical work of this industry is to check whether the aircraft industry is declining relatively in the U.S.. If there is a relative decline, the result can be used as indirect empirical evidence of some predictions made in the first two sections, as well as an indication of the existence of a problem concerning the aircraft industry in the U.S.. The relative decline is examined in two different ways: the relative weight of the aircraft industry in the non-agricultural industry and the U.S. market share in the production of total aircraft seats, i.e., the sum of all seats produced by Airbus, MDD, and Boeing.  To find empirical evidence that supports the theory proposed by this paper in the civil aircraft industry is difficult, though not necessarily impossible. The main reason for the difficulty is that Airbus, unlike its American counterpart, does not disclose its information to 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 aircraft industry. The implication is indicated by the expression that —Y a < o , where y can be as  64 perceived as the production level in the aircraft industry of the U.S. and s can be perceived as European subsidies to Airbus. In other words, the relative weight of the civil aircraft industry declines in the U.S. because of subsidies to Airbus. Let R t be the relative weight of the monthly production index of the civil aircraft industry in the entire manufacturing industry. These data were downloaded from Citibase.  Rt  =  flo  (38)  The following tables represent the regression results of 234 observations. R t = airt /manu t where air s is the monthly production index of the aircraft industry and manu t is the monthly production index of all manufacturing industries. The performance of the civil aircraft industry can be evaluated as follows: if 13 1 < 1 then next month's ratio of civil aircraft production to all manufacturing industries is less than this month's.  65  Coefficient  Variables  t-Ratio  Standard Error  R t4  0.97  0.012  84  constant  .0041  .0021  1.98  Table 5, Estimated Coefficients of Relative Weight of Aircraft Industry  Statistics  Values  R2  0.96721  Durbin-h  .5  Breusch-Pagan  1.383  Table 6, Important Statistics of Relative Weight Of Aircraft Industry  66  Test for Heteroscedasticity and Autocorrelation  To ensure the correctness of the model, I shall test for the presence of heteroscedasticity and autocorrelation. It is important to check whether these problems exist because the consequences of applying OLS to a relationship with heteroscedastic or autocorrelated disturbances are (1) an unbiased but inefficient estimation and (2) invalid inference procedures. To test for heteroscedasticity I shall use the Breusch-Pagan test. The test is described as follows:  Model: y = XB + u  where the disturbances ti t are assumed to be normally and independently distributed with variance ail = h(X t'a) and where h(.) denotes some unspecified functional form. a is a 4x1 vector of coefficients unrelated to B and X t is a 2x1 vector of variables (i.e., 1, R t _ i , t, t 2 ) thought to influence the heteroscedasticity. The first element in X t is assumed to be 1.  67 Thus the null hypothesis H o : a 1 =a 2 =0 specifies homoscedasticity since a 1 2 = 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 x 2 with 1 degrees of freedom. If Q > x .95 (1), one would 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 represented by h, is calculated from the procedure presented in Econometric Methods, pp. 318. h calculated in this empirical model is .5. If h >1.645, reject the null 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 .5 and is less than 1.645; hence, the null hypothesis is not rejected.  68 Test for the Decline of the Civil Aircraft Industry  (1) Relative Weight of Aircraft Industry The first test I shall perform is to check whether B i < 1. If it does, then the relative importance of the aircraft industry in all manufacturing is declining.  Ho: fi i <1 H1 : 13 1 21 If tcac >terit then reject Ho^ At a =.05, tcrit =1.65 tcak-  .012  (39)  -2.5<tcrit  Therefore, the null hypothesis is not rejected. The implication of the above result is that given this period's R t and t, R t+1 will be less than R t . In other words, there is a downward trend observed in the civil aircraft industry.  a  69 Therefore, the ratio of the civil aircraft manufacturing industry to all other manufacturing industries has been declining. There may be many reasons for this decline. To find out precisely what factors cause this decline would be quite a challenging task, and one that is outside the scope of this paper. This study has offered several positive theories to explain the incentive for a government to subsidize its industry. One of the conclusions derived from the results found in this paper implies that subsidies from foreign government will unambiguously have a negative impact upon production in the domestic industry. The relative decline of the civil aircraft industry in the U.S. is one major empirical result found in this paper and can be used as indirect evidence to support my theories. This evidence is insufficient to definitively prove what I claim, because I cannot show that the decline is caused by Airbus. However, I hope that the efforts I have made so far can be used as a foundation to investigate further empirical evidence in the context of international trade under learning effects.  70 (2) Market Share Apart from the relative weight of the aircraft industry in the U.S., the trend of U.S. market share in the production of civil aircraft would be another useful indication of the decline of this industry. Market share used in this paper is defined to be the percentage of total seats produced by the U.S. (i.e. MDD and Boeing altogether) in the sum of all seats produced by Airbus, Boeing, and MDD. The total number of aircraft produced for a particular model is printed yearly in Civil Aviation Statistics. For each model, there are a range of seats. To calculate the total number of seats produced in the U.S., I simply used the median of the range of seats available and multiplied it by the total number of aircraft produced for each model. I added up all the seats produced by MDD and Boeing. I did the same thing for Airbus. The market share of the U.S. is the ratio of the total seats produced by the U.S. to those produced by Airbus and the U.S.. To test whether the market share of the U.S. is declining in the international aircraft industry, I use the following regression model:  Mt = Yo iMt i -  where TA is the market share of the U.S. in the production of civil aircraft (in the units of seats). If the market share of the U.S. is declining, then y < 1. The following tables represent the regression results of 15 annual observations.  71  Variables  Coefficient  Standard Error  t-Ratio  Mt-1  0.51501  0.28528  1.79  constant  .24351  1.6467  .44  Table 7, Estimated Coefficients of US Market Share  Statistics  Values  R2  0.2255  Durbin-h  -.0154  Breusch-Pagan  .133  Table 8, Important Statistics of US Market Share  Using the similar tests for heteroscedasticity and autocorrelation, I have the following results. If Q > x .95 (1), one would reject the hypothesis of homoscedascity at the 5 percent level. x .95 (1)=3.841. Q=.133. Hence, the hypothesis of homoscedascity is not rejected at the 5 percent level. Durbin-h calculated in this empirical model is -.0154. If h > 1.645, reject the null hypothesis at the 5 percent level of significant in favour of the hypothesis of a firstorder autocorrelation. Calculated in this empirical model, h is -.0154 and is less than 1.645; hence, the null hypothesis is not rejected.  72  Ho : y1< 1 H1 : y i l If tcdc >tcrit then reject Ho At a =.05, tcrk =1.65 t„k  (41)  1 -1 '5.29 --1.75<tcrk  Therefore, the null hypothesis is not rejected. The implication of the above result is that given this period's M t , M4 +1 will be less than M. In other words, there is a downward trend observed in the market share of the U.S. in terms of the total number of seats produced.  73  Apart from the rigorous tests used above, one can also use other indicators to evaluate overall performance in the aircraft manufacturing industry in the past decades. Several graphs indicate a similar problem in this industry: there has been a relative decline in the past decade. From the graph concerning total seats sold by MDD and Boeing versus those sold by Airbus, we can find that the number of seats sold by Airbus is rising faster than those 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 are very similar in terms of range and the number of seats available, the competition between the two models is very close to a duopoly. From 1981 to 1984 and from 1987 to 1989, the total 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 while those of Boeing and MDD together increased twice only. From the graph concerning the wages of the aircraft industry to other non-agricultural industries (graph 8), we know that the ratio was rising from 1971 to 1981, but remained the same since 1981. From the graph concerning 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 has been falling since 1984, the level of returns to seat was still less than the level in 1983 in constant (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 weight in the U.S. in 1990 was indeed lower that in 1971. Note that graph 12 also indicates a similar decline observed in the automobile industry. In comparison with a more successful industry, such as the computer industry in graph 13, the relative weight of the computer industry in all manufacturing industries has been increasing rapidly. The last indicator is  74 productivity (see graph 14), as represented by the total number of seats produced by each employee in Boeing and MDD. In general, the level of productivity between 1982 and 1989 was less than that between 1975 and 1989. Moreover, the level of productivity in 1989 is only less than half of that in 1981. Again, it would be quite hasty to blame the decline entirely on European subsidies, but different pieces of evidence, together with the theories proposed by this paper, may be used as a reference in formulating a better trade policy in targeted industries such as the civil aircraft industry to better promote national interests.  75 Concluding Remarks  Based on the framework of a duopolistic industry selling the same good to a third market similar to the one first presented by Brander and Spender (1985), I introduced learning effects into a model having infinite horizons. Although only two periods are taken into account by a government which formulates an appropriate trade policy, deciding whether or not it should cooperate with another government to remove all production subsidies, the model can be modified to incorporate an economy with infinite horizons. The basic structure would not change as long as we focus on a strategy that involves two period only -- a strategy of "tit-for-tat" and unconditional free trade. I show that cooperation (i.e. free trade with 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: if relative losses in the second period (as both countries impose optimal subsidies) are larger than 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 found four major results. First, under a duopolistic industry with weak learning effects, cooperation can still be achieved between governments, if each one believes the other adopts a "tit-fortat" strategy. But if unconditional free trade is adopted, the losses become smaller compared to free trade in the second period, and hence cooperation cannot be achieved. Second, if learning effects are strong, then regardless of whether free trade is conditional or unconditional, cooperation between government cannot be achieved because a subsidy imposed in the first period results in two sources of gain: profit-shifting in the first period and reduction of marginal cost in the second period. Third, if a duopolistic market structure can only be maintained under the subsidies of a government, then learning effects will not  76 make the industry more competitive in the future. Subsidies cannot be phased out. If market force determines the nature of an industry to be monopolistic, then a government cannot use subsidies to change this. It may be better off for the world as a whole not to move against market force. According to the model discussed in this thesis, the hope that subsidies can be gradually removed because of learning effects is unrealistic. It should be noted that the above results are based on a very restricted set of assumptions. Among those restricted assumptions, same learning rates and the definition of cooperation restricted to the level of subsidies rather than output are the most sensitive ones. If one country has a learning rate substantially higher than the other country, then the level of subsidies may be phased out.  14  If the definition of cooperation is not restricted to the removal of subsidies, but is defined to be the level of output, then a positive level of subsidies may be beneficial to both countries because of learning effects. More importantly, for the efficiency of the world economy, a single country having all the production will be able to get the maximum benefits of learning effects. 15 Furthermore, the assumption of exporting the same good to a third market with no domestic consumption is also quite restrictive. Using the international aircraft industry as an example, we do observe quite substantial domestic  14  For the sake of simplicity, I assume that the country with no subsidies adopts a policy of unconditional free trade. If that country adopts a "tit-for-tat" strategy, then the effects of different learning rates, together with the 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 counterproductive to the benefits one can get from learning effects. No doubt one country being a monopoly of all production is the most efficient one in terms of learning effects. However, assuming that each country is selfinterest, no one is willing to stop producing. Each country will claim that the other should be removed from the market. As long as there is no central government, the most likely outcome remains a duopoly. Apart from a central government, the presence of other cross-boundary institution, such as a multi-national corporation can also achieve the most efficient outcome (i.e. a natural monopoly). That is because a multi-national corporation does not need to pay attention to the country specific cost-benefit analysis. It will make the best advantage of the presence of learning effects. In contrast, no government which makes decision based entirely on the gain function of its country will not allow the other country to gain a monopoly status, a scenario which is ironically the most efficient one. See appendix for details.  77 consumption in this market. However, using the above assumptions, I can prove the validity of an argument with high tractability. Fourth, while the civil aircraft manufacturing industry possesses all of the characteristics discussed in this paper, according to the ratio of the monthly production of this industry to other manufacturing industry in the U.S., this industry has been declining in the past decades. Whether or not this decline is caused by the European subsidies to Airbus Industrie is outside of the scope of this thesis. However, this question would be an interesting starting point for future research on duopoly in the context of international trade.  78 Appendix 2 From equation 27, the highest joint payoffs are 2G x2 ,,, = — (a c) 2 (a+) 2 , but the 9b^ -  3b  payoffs for a monopoly are G m2 . = 1 0 _ 02 (a+ L )2 and hence from the world 4b^3b  economy's point of view, it is better for only one country to produce the good to capture all the benefits of learning effects. However, which country should abandon its production is the critical issue. There is no solution in a model which is based on the self-interest of a country 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 allocation of production pattern. In a profit-maximizing economy, the evolution of multi-national firms perhaps is the only solution to the inefficient allocation of production pattern.  Graphs  Total Seats, US Graph 1 Thousands 160 140 120 100 80 60 40 20 0 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89  Year Total Seats (US) Source: Civil Aviation Statistics  Total Seats, Airbus Graph 2 Thousands 30 ' -  25 20  15 10 5  -  -  _/ -  -  0 ^  1^1^1^1^1^1^1^1^1^1^1^1^1  75 76 77 78 79 80 81 82 83 84 85 86 87 88 89  Year Total Seats (Airbus) Source: Civil Aviation Statistics  Total Seats, US & Airbus Graph 3 Thousands 200 ' -  75 76 77 78 79 80 81 82 83 84 85 86 87 88 89  Year Total Seats (US) Source: Civil Aviation Statistics  Total Seats (Airbus)  B737  Graph 4, Number of Aircraft B737#  75 76 77 78 79 80 81 82 83 84 85 86 87 88 89  YEAR B737 Source: Civil Aviation Statistics  Airbus 300/310 Graph 5, Number of Aircraft A300/310# 120 100 80 60 40 20 0  IMII IPP  ,t...d•^.441^  ,AIII^./11^  -4,•■^. /!.; .:5411^.....0:41111  75 76 77 78 79 80 81 82 83 84 85 86 87 88 89  YEAR A300/310 Source: Civil Aviation Statistics  Market Share of US  Graph 6, Number of Aircraft % OF 8737 in (B737+A300/310) 100%  75% -  50% -  25%  0% 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89  YEAR B737 Source: Civil Aviation Statistics  M, A300/310 --  Wages Difference Graph 7, Aircraft to Non-agriculture Hourly Wages (Deflated)  7  1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111  71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90  Year — Wages, others^1^ Wages, aircraft Source: Citibase  Wages Ratio Graph 8, Aircraft to Non-agriculture Wages Ratio (non agr=1) -  1  1111111111111111111111111111111111111M111711 1111111111111I1111111111111111111111111111111111111111111111111111111MIMT1111111 1111111111111111T111111111[TTIIIR11 11111 1111111111111111111111111111111111111111111111111111111111111 -  71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90  Year * Ratio (air/non-agr) Source: Citibase  Returns to Employee  Graph 9, Profits of Boeing & MDD 20  $Thousands/Employee  20  15  15  10  10  5  5  0^ 0 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90  Year 1^ Returns to Employee Source: Compustat  Returns on Equity Graph 10, Profits of Boeing and MDD Returns on Equity  71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89  Year  Returns to Seat  Graph 11, Profits of Boeing & MDD 400  $Thousands/Seat  400  300  200  100  0  71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90  Year Returns to Seats Sou rce: Compu stat  0  Manufacturing Ratio Graph 12, Aircraft Industry Base•All Manufacturing  0  111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111(1111111111111111I1M111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111  71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90  Year ---- Aircraft Ratio^I^ Auto Ratio Source: Citibase  Manufacturing Ratio Graph 13, Aircraft Industry Base•All Manufacturing  »111111111111111111111M111111111111111111111111111111111111»111111111111111)11111111111111111111111f1111111111M111111111111111111M111111111111111111111111111111111111111111111111111111111111111111111111111111111111111  71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90  Year Aircraft Ratio^*^ Cmpt Ratio Source: Citibase  Productivity Comparision Graph 14 1600  Manufacturing  Aircraft Industry  1400  600 500  1200 400  1000 800  300  600  200  400 100  200  ^ I^i^I^I^I^I^I ^0 0 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89  Year prod manu Source: Citibase  ^ prod air  94 Bibliography  Axelrod, Robert. The Evolution of Cooperation. New York: Basic Books, Inc., 1984. "A Better Way to Fly?" The Economist (April 16, 1988): 78-80. "Aerospace Takes off," The Economist (April 8, 1989): 71-2. "Airbus Industrie Expects to Make Profit This Year for First Time." Aviation Week & Space Technology (September 10, 1990): 67-8. "Airbus Pins Itself Down." The Economist (January 30, 1988): 50-1. "All Shapes and Sizes." The Economist (September 8, 1988): 52-60. "Boeing, Airbus Brace for Fight over Wide-Body Twin Market." Aviation Week & Space Technology (January 22, 1990): 27-8. Brander, James A. and Spencer Barbara J.. "Export Subsidies and Market Share Rivalry." Journal of International Economics 18 (1985): 83-100. Brander, James A.. "Rationales for Strategic Trade and Industrial Policy." Strategic Trade and New International Economics, Cambridge: MIT Press, 1986. "Dispute over Trade Practices Simmers as Competition from Europe Increases." Aviation Week & Space Technology (September 5, 1988): 65-94. "Dissecting Airbus." The Economist (February 16, 1991): 51-2. Dixit, Avinash K. and Grossman, Gene M.. "Targeted Export Promotion with Several Oligopolistic Industries." Journal of International Economics 21 (1986): 233-50. Eaton, Jonathan, and Grossman, Gene M.. "Optimal Trade and Industrial Policy under Oligopoly." Journal of International Economics 24 (1988): 331-44. Fung, K.C.. "Collusive Intra-Industry Trade." Canadian Journal of Economics 24 (1991): 391-404. Gunston, Bill. Airbus. London: Osprey Publishing Limited, 1988. Helpman, Elhanan and Paul R. Krugman. Trade Policy and Market Structure. Cambridge, Mass.: MIT Press, 1989. Johnston, J.. Econometric Methods. U.S.: McGraw-Hill, Inc., Third Edition, 1984. Krugman, Paul R.. "Import Protection as Export Promotion: International Competition in the Presence of Oligopoly and Economics of Scale." in: Henryk Kierzskoskowski, eds., Monopolistic Competition and International Trade. Oxford: Clarendon Press, 1984. Hayward, Keith. 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