Unilateral and Multilateral Gains from Trade in International Oligopoly

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1 Unilateral and Multilateral Gains from Trade in International Oligopoly Kenji Fujiwara Graduate School of Economics, Kobe University Japan Society for the Promotion of Science Received January 2005; Final Version, June 2005 Abstract Constructing a two-agent model of international duopoly with increasing returns, this paper examines the potential gains from free trade. It is shown that under certain conditions, both agents in a country become worse off in free trade than in autarky with no redistribution. Further, the lump-sum compensation can never achieve a Pareto-improvement in such an economy. However, we can find a non-lump-sum redistributive scheme that makes nobody in the country worse off in free trade than in autarky. Keywords: Gains and losses from trade, international oligopoly, increasing returns to scale. JEL Classification: F10, F12. An earlier version of this paper was presented at the seminars held at Kobe University, the Spring 2004 Midwest International Economics Meeting and the 2004 Spring Meeting of the Japanese Economic Association. I thank David R. Collie, Fumio Dei, Yunfang Hu, Toru Kikuchi, Ngo Van Long, Kazuo Mino, Noritsugu Nakanishi, Masao Oda, Masayuki Okawa, Takashi Shibata, Kar-yiu Wong and Laixun Zhao for their comments. Among others, I would like to express special thanks to Elhanan Helpman, Murray C. Kemp and Koji Shimomura whose help substantially improved the paper. Many valuable suggestions from the editor, Harry Bloch, and the two anonymous referees are also gratefully acknowledged. Financial support from the Ministry of Education, Culture, Sports, Science and Technology of Japan (the Grantin-Aid for 21st century COE Program Research and Education Center of New Japanese Economic Paradigm ) is gratefully acknowledged. Needless to say, I am solely responsible for any remaining errors. Graduate School of Economics, Kobe University. Rokkodai-cho 2-1, Nada-ku, Kobe, , Japan. 1

2 1 Introduction The gains-from-trade proposition, i.e., there exists a domestic scheme of income redistribution which makes nobody worse off in free trade than in autarky, is one of the core theorems in trade theory and has supported trade liberalization by the GATT and its successor, the WTO. It first appeared in Samuelson (1939) and Kemp (1962), and was firmly established in the Arrow-Debreu framework by Kemp and Wan (1972). As is well known, the Arrow-Debreu model presupposes some restrictive assumptions like complete markets, perfect competition, finite agents and markets, and so forth. Wong (1995) discusses whether the gains-from-trade proposition survives when some of them are relaxed. Among others, Newbery and Stiglitz (1984) and Shy (1988) propose an extreme possibility that all agents in every country lose from trade in the presence of market incompleteness. 1 However, they allow for no possibility of introducing any income redistributive scheme among agents. Given such a scheme, Kemp and Wong (1995) prove that a lump-sum compensation scheme does exist whereby nobody becomes worse off in free trade, even in incomplete markets. Further, there is a large literature on gains and losses from trade under imperfect competition, which is another significant market distortion. 2 Here, we will refer to only 1 These authors call this phenomenon Pareto-inferior trade. 2 Helpman and Krugman (1985) and Wong (1995) provide a comprehensive survey of gains and losses from trade with imperfect competition. 2

3 two studies which are the closest to this paper and the other studies are mentioned in the final section. The first is Markusen (1981) who derives the sufficient conditions for gains from trade in international duopoly. 3 According to Markusen, a country loses from trade only if the output of the non-competitive and increasing-returns good in free trade is falls below that in autarky. 4 This result relies on the assumption of representative agents, which leaves the following open question: Is it valid even if heterogeneous agents are incorporated? Putting it another way, is it possible to obtain similar results to Newbery and Stiglitz (1984) and Shy (1988) in an imperfectly competitive model? The second is Kemp and Shimomura (2001) who prove the existence of an income redistributive scheme which makes nobody worse off in a free trade Cournot-Nash equilibrium than in an autarkic equilibrium. In addition to the high generality of their model, their result holds even under increasing returns. However, the following question is left unexplored: Is it possible to find such a proper scheme of income redistribution even in an economy such that free trade would make everyone in a country worse off without it? We shall examine these questions by formulating the simplest two-agent oligopolistic trade model with scale economies. We begin by reviewing our companion paper, Fujiwara (2004) that analytically proves that both agents in a country become worse off by starting 3 Kemp and Shimomura (2001) criticized that Markusen s (1981) treatment of profit-maximizing monopolists matters since they can consume not only the numeraire but their own product. In this paper, we overcome it by presuming that monopolists consume only the numeraire. 4 For the details of this production contraction condition, see Markusen and Melvin (1984). 3

4 free trade. Then, it is shown that the lump-sum compensation can no longer overcome the losses from trade, which is in contrast to Kemp and Wong (1995) mentioned above. However, even such an economy can find a proper non-lump-sum scheme of redistribution which makes its residents better off in free trade than in autarky. In addition, the existence of equilibrium is assured, which may be another contribution. 5 The simplicity of the model enables us to develop intuitions easily. Specifically, we pay a special attention to why nonnegative gains from trade are guaranteed to all agents under the scheme while they lose from trade without it. What is implied by our argument is that the concept of compensation may not be appropriate for interpreting the scheme suggested in this paper. In the case where free trade brings gains and losses, the solution is simple; the government transfers some part of the winners income to the losers. 6 On the other hand, what should be done is not so simple when all everyone loses from trade. Therefore, another interpretation is needed to discuss the role of the redistributive scheme. We will propose a distinct interpretation of the scheme which differs from compensation. Before introducing the rest of this paper, a remark is in order. This paper should not be regarded as the one belonging to the literature on strategic trade policy: Any strategic interaction and rent-shifting incentive between countries is precluded and beyond the scope of this paper. 5 Kemp and Shimomura (2001) assumed the existence. 6 Recall the case to which the Stolper-Samuelson theorem applies. 4

5 We proceed as follows. Section 2 develops a model and describes each country s autarkic equilibrium. Section 3 considers free trade without any income redistributive scheme and shows that all agents in a country lose from trade. Furthermore, Section 4 shows that gains from trade are impossible to achieve via lump-sum compensation. Then, Sections 5 and 6 present the situation where non-lump-sum income redistribution between the agents is allowed and it is derived that free trade remains potentially beneficial to them. Section 5 presents the situation where only the country that experiences losses from trade is allowed to introduce a scheme, while Section 6 considers the case where both countries do so. Section 7 sets forth our conclusions. 2 An Autarkic Equilibrium Consider a two-country (home and foreign), two-good (X and Y ), one-factor (labor), two-agent (consumer and monopolist) model. 7 Labor is fully employed and inelastically supplied by the consumer whose number is normalized to unity. The consumer demands both goods so as to maximize utility taking the prices and labor income as given. Good Y, which is the numeraire, is a competitive and constant-returns good while good X is a non-competitive and increasing-returns good. One unit of labor produces one unit of good Y. Hence, the wage rate is fixed at unity as long as good Y is positively supplied. On the other hand, good X is supplied by a monopolist, who is assumed to consume only 7 Since the analysis in this and next sections is intensively developed in Fujiwara (2004), we proceed as concisely as possible. 5

6 good Y. The consumer s utility function is specified by U = AD X 1 2 D2 X + D Y, A > 0, where U is the utility level and D i, i = X, Y is the consumption of each good. Then, letting p be the price of good X in terms of good Y, the demand function of good X is derived as D X = A p, and the autarkic inverse demand function becomes p = A X, (1) where X is the output of good X. The monopolist s cost function is given by cx + F, A > c > 0, F > 0 where c is the constant marginal cost and F is the fixed cost. 8 From these specifications, the monopolist s autarkic profit is defined as (A c X)X F. (2) 8 We assume that F is not sunk. 6

7 If we assume an interior solution, the profit-maximizing output becomes X = 1 (A c), (3) 2 where the upper-bar represents the autarkic variable. 9 Substituting (3) into (1) and (2), the home autarkic equilibrium price and profit are calculated as p = 1 (A + c) (4) 2 π = 1 4 (A c)2 F, (5) where π denotes the equilibrium profit, which is assumed to be strictly positive by choosing the parameters properly. The environment in the foreign country is the same as the home environment except for the monopolist s technologies. Henceforth, an asterisk is attached to foreign variables. Throughout this paper, we make the following assumption. Assumption 1. The marginal and fixed costs of each country s monopolist satisfy c > c and F < F. 10 Some may wonder why this assumption is needed. An answer will be provided after one 9 This interior solution is ensured if A c > 2 F is imposed. 10 This assumption can be justified when the following technology is imagined. The larger fixed cost a firm pays prior to its production, the cheaper her marginal cost becomes. Further justifications are offered in Mills and Smith (1996). Also, note that this assumption implies that A > c > c since we must assume A > c for the foreign output of good X to be positive. 7

8 of the main results, Proposition 1, is proved below. By following the same procedure as in the home country s case, the relevant variables in the foreign autarkic equilibrium are obtained as X = 1 2 (A c ) (6) p = 1 2 (A + c ) (7) π = 1 4 (A c ) 2 F. (8) 3 Losses from Trade In this section, let both countries freely trade but without any redistribution scheme. The integrated market for good X clears when 2(A p) = X + X, from which the inverse demand function in the world market is obtained as p = A 1 2 X 1 2 X. (9) Thus, the monopolists profits are given by and (A c 1 2 X 1 2 X ) X F (10) (A c 1 2 X 1 2 X ) X F. (11) 8

9 The two monopolists are assumed to play a Cournot-Nash game, which leads to the following first-order conditions for an interior solution. A c X 1 2 X = 0 (12) A c 1 2 X X = 0. (13) (12) and (13) respectively give each monopolist s reaction function when each monopolist earns positive profits for any value of the rival s output. However, due to the fixed cost, this is not always the case. In particular, if F is sufficiently large, the home monopolist s reaction curve can be discontinuous. In Figure 1, the dotted line BE represents the home monopolist s reaction curve when it earns positive profits for any X 0. Let us add its zero-profit curve in this figure. It is obvious that the dotted line above the zero-profit curve is not effective because its profit is negative at any point on this segment, which makes it choose zero output. In other words, the reaction curve only below the zero-profit curve is effective and hence the home monopolist s reaction curve becomes discontinuous and consists of the segments BC and DE. 11 Formally, the home monopolist s reaction function is derived as 12 X = { A c 1 2 X if X 2(A c 2F ) 0 if X > 2(A c 2F ). (Figure 1 around here.) 11 Ito et al. (1991, Chaps 10 and 12) offer a similar argument in a context of entry deterrence. 12 Note that the length of OC equals 2(A c 2F ). 9

10 Note that the same argument straightforwardly applies to the foreign monopolist. Thus, Figure 1 shows that the foreign monopolist s reaction curve contains a horizontal segment. However, we assume in this paper that F is not as large as F so that the horizontal segment is not particularly long. Next, we add another key assumption. Assumption 2. The free trade Cournot-Nash equilibrium is unique and given by N in Figure 1. Assumption 2 is justified if F exceeds a certain value, which Fujiwara (2004) derived. 13 Roughly speaking, if F is large enough, the vertical segment of the home monopolist s reaction curve becomes longer and the resulting Nash equilibrium is more likely to be unique. At N, the home monopolist chooses zero output and the world market is monopolized by the foreign monopolist and we have X N = 0 and X N = A c, (14) where the superscript N indicates the Cournot-Nash equilibrium. Substituting this into the inverse demand function (9), the equilibrium price is determined as p N = 1 2 (A + c ). (15) Given the analysis so far, we can observe a few interesting consequences. First, com- 13 It is given by F > (A 2c + c ) 2 /8. 10

11 paring the home autarkic price with the free trade price, we see that p < p N, i.e., the free trade price exceeds the home autarkic price, which implies that the home consumer loses from trade because its labor income is unchanged in both autarky and free trade. It is obvious that the home monopolist also loses from trade because the monopolist s profit is zero in free trade while it is positive in autarky. Thus, we can restate: Proposition 1 (Fujiwara, 2004). Laissez-faire free trade worsens the welfare of both the consumer and the monopolist in the home country. Why Assumption 1 is needed is briefly remarked on here. The assumption of F > F is utilized in order for the Nash equilibrium to be given by N in Figure 1. In other words, the home monopolist will choose zero output when its fixed cost is larger than the foreign monopolist s fixed cost. On the other hand, the assumption of c < c is made use of for obtaining p N > p, i.e., the home consumer loses from trade. Therefore, Assumption 1 on cost asymmetries is essential for Proposition 1. 4 Inefficacy of Lump-Sum Compensation As Kemp and Wong (1995) prove, potential gains from free trade can still be achievable through lump-sum compensation in incomplete markets even if laissez-fair free trade is Pareto inferior. In view of their argument, it appears a natural question whether we can 11

12 find a proper lump-sum compensation scheme which makes the home country better off by the opening up of trade. This section addresses this issue and gives a negative answer. The suggested lump-sum scheme is defined as follows. Letting T M and T C denote the income transferred to the monopolist and consumer, respectively. T M is assumed to be calculated in such a way to equate the post-scheme profit to the autarkic profit, i.e., T M = π = 1 4 (A c)2 F > 0. Since the monopolist s profit under laissez-faire free trade is zero, the left-hand side stands for the post-scheme profit, whereas the right-hand side is the autarkic profit. Thus, when T M > 0 is transferred to the monopolist, it can attain the exactly the same profit as the autarkic profit. Suppose that T C is determined in the same manner; it is calculated such that the consumer can attain the same utility under post-scheme free trade as the autarkic level. Since the equilibrium price is determined as (A+c )/2 and the home consumer s autarkic utility level is (A c) 2 /8 + L, T C becomes T C = 1 8 (A c)2 1 8 (A c ) 2 = 1 8 (2A c c )(c c) > 0, by equating the autarkic utility to the post-scheme free trade utility. Note that the last inequality follows from the assumption of c > c. 12

13 The suggested scheme suffices to achieve a Pareto-improvement if and only if T M + T C 0, since it means that the government s budget constraint is satisfied or the maximum bonus is non-negative. 14 However, it is obvious that T M +T C > 0, i.e., the suggested lump-sum compensation violates the government s budget constraint and hence fails to make all agents better off in free trade than in autarky. The results obtained so far are stated in: Proposition 2. It is impossible to make nobody worse off in free trade than in autarky via a lump-sum compensation scheme. Someone may assert that Proposition 2 is self-evident and not worth stating formally. However, it has an important implication in considering gains from trade. As mentioned several times already, lump-sum compensation suffices to achieve a Pareto-improvement in the case of incomplete markets. But, Proposition 2 says that the same is no longer true in the case of imperfect competition and increasing returns. That is, it is impossible to apply Kemp and Wong s (1995) argument to the present case directly. The efficacy of lump-sum compensation crucially depends on what type of market distortion is assumed in the model. Moreover, Proposition 2 gives a rationale for why Kemp and Shimomura (2001) stated 14 The term maximum bonus follows from Wan (1965). 13

14 the following: just as the conventional gains-from-trade proposition cannot be proved without lumpsum compensation, so our theorem cannot be proved without non-lump-sum compensation. For these two reasons, it is fair to say that Proposition 2 is of some use. In the subsequent sections, we incorporate a non-lump-sum scheme of redistribution and explore the possibility of potential gains from free trade. 5 Unilateral Gains from Trade In the previous sections, we show that both agents in the home country lose from trade and a lump-sum compensation scheme can not achieve a Pareto-improvement. In order to overcome this problem, this section presents the situation where a non-lump-sum redistribution scheme is introduced in the home country to guarantee non-negative gains from trade. In particular, we consider the case in which only the home country introduces a scheme while the foreign country retains a laissez-faire policy. Before proceeding, a few preliminaries are provided. From the quadratic utility func- 14

15 tion, the consumer s indirect utility function is V (p, L) 1 2 (A p)2 + L, (16) where L, the home labor endowment, represents the labor income because of the unitary wage rate. Since p = (A+c)/2, the consumer s utility in the autarkic equilibrium becomes V 1 2 (A p)2 + L = 1 ( A A + c ) 2 + L 2 2 = 1 8 (A c)2 + L. (17) On the other hand, the utility in post-scheme free trade is obtained by substituting the inverse demand function, p = A X/2 X /2, into (16) and adding the compensatory transfer, say Γ, to the income: [ ( 1 A A X 1 )] 2 2 X + L + Γ = 1 8 (X + X ) 2 + L + Γ. (18) We assume that the transfer is determined so that the utility in post-scheme free trade is exactly the same as that in autarky, which yields Γ = 1 8 (X + X ) (A c)2, (19) by equating (17) to (18). Therefore, we have only to show that the monopolist s postscheme profit exceeds its autarkic profit for achieving a Pareto-improvement. 15

16 The home monopolist seeks to maximize its profit taking into account the effect of X on the scheme. Thus, the monopolist s post-scheme profit becomes = (A c 1 2 X 1 2 X ) X F Γ (A c 1 2 X 1 2 X ) X F (X + X ) (A c)2. (20) That is, the home monopolist s objective function changes from that in laissez-faire free trade. The associated first-order condition is A c 3 4 X 1 4 X = 0. (21) (13) and (21) give a new output pair in post-scheme free trade as X T = 2 5 (3A 4c + c ), X T = 2 5 (A + 2c 3c ), (22) where the superscript T denotes the post-scheme Cournot-Nash equilibrium. Substituting (22) into (9) yields the equilibrium price: p T A 1 2 XT 1 2 X T = 1 5 (A + 2c + 2c ), (23) and the home monopolist s profit is re-calculated as (p T c)x1 T F (XT 1 + X1 T ) 2 1 (A c)2 8 = [ ] (A + 2c + 2c ) c 5 (3A 4c + c ) F + 1 [ (3A 4c + c ) )] 5 (A + 2c 3c 16

17 1 (A c)2 8 π T. Invoking that the home monopolist s autarkic profit is π (A c) 2 /4 F, the difference between the two profit levels is given by π T π = [ ] (A + 2c + 2c ) c 5 (3A 4c + c ) + 1 [ (3A 4c + c ) )] 5 (A + 2c 3c 1 8 (A c)2 1 4 (A c)2. Based on the analysis so far, we are ready to state: Proposition 3. By introducing the income redistribution scheme defined in (19), free trade with this scheme is Pareto-improving for the home country. Proof. For our purpose, it suffices to show that π T > π for any A, c and c which satisfy c (c, A). To do this, setting c = αc + (1 α)a, α (0, 1), substituting it into π T π given above and some arrangements yield = = π T π [ 2 25 (3 2α)(4 α) (1 + α)2 3 8] (A c) 2 ( 6 25 α α ) (A c)

18 f(α)(a c) 2. It is immediately seen that f(α) is always positive for any α (0, 1) because the discriminant of the quadratic equation f(α) = 0 is negative. This establishes Proposition 3. Proposition 3 can be interpreted diagrammatically by using Figure 2, which describes the post-scheme trading equilibrium. After the home country introduces the scheme, the home monopolist has an incentive to re-optimize and its reaction curve will shift to the right while the foreign monopolist s is unchanged. Thus, it is fair to say that the scheme plays a role in changing the home monopolist s strategic position favorably since the home monopolist will expand its output. The resulting Cournot-Nash equilibrium is given by T, which tends to promote international competition and the price may be lower than in autarky. This raises the consumer s utility and the consumer subsidizes the monopolist. Thanks to this subsidy, the home monopolist can gain from trade despite the decrease in price. (Figure 2 around here.) Remark 1. One may feel that a similarity exists between our argument and that of the strategic trade policies such as Dixit and Kyle (1985) because the scheme makes the home country better off while it may make the foreign country worse off. In other words, it seems to have a rent-shifting role by improving the home monopolist s strategic 18

19 position in the international market. However, it has been assumed that the government solves no optimization problem in our argument, which makes our argument differ from that found in the strategic trade policy literature. Remark 2. One may already notice that the scheme in this paper does not correspond to that in the traditional gains-from-trade proposition. In the previous studies, the scheme is completely captured as compensation: the government transfers winners income to losers. Of course, the scheme presented in this paper shares this aspect. However, its role goes beyond compensation since it shifts the home monopolist s reaction curve. 6 Multilateral Gains from Trade From Proposition 3, we can safely say that free trade is potentially beneficial for the home country. In deriving it, we have presumed that the foreign country maintains a laissez-faire regime a priori. However, as pointed out in Remark 1, the suggested scheme may be a beggar-thy-neighbor policy for the foreign country. If this is true, the foreign country may retaliate. Then, what if the home country and the foreign country both introduce similar schemes? This section is devoted to addressing this situation. Let the foreign country introduce the same scheme as the home country s, which is 19

20 defined as the foreign consumer s compensating variation: Γ 1 8 (X + X ) (A c ) 2. Given this scheme, the foreign monopolist s post-scheme profit becomes (A c 1 2 X 1 2 X ) X F (X + X ) (A c ) 2. (24) Hence, the home monopolist has the objective function (20) and the foreign monopolist (24). As a result, each monopolist s first-order condition will alter to A c 3 4 X 1 4 X = 0 (25) A c 1 4 X 3 4 X = 0, (26) which gives the new Cournot-Nash equilibrium output pair: X M = A 3 2 c c, X M = A c 3 2 c, (27) where the superscript M means the Cournot-Nash equilibrium when both countries introduce the scheme. Then, the world price is determined as p M A 1 2 XM 1 2 X M = 1 2 (c + c ). Since each country s autarkic price is p = (A + c)/2 and p (A + c )/2, respectively, we can see p > p M and p > p M, i.e., the world price under both countries schemes is 20

21 lower than each country s autarkic price. Hence, the consumer in each country becomes better off and subsidizes each country s monopolist so as to keep the consumer s utility at an autarkic level. Therefore, the next task is to examine whether the monopolist s profit is greater than the autarkic level. Substituting (27) into (20) and (24) yields each monopolist s profit after both countries implement the scheme: π M = 1 [ 2 (c c) (A c) + 1 ] 2 (c c) [(A c) + (A c )] 2 1 (A c)2 8 F π M = 1 [ 2 (c c) (A c ) 1 ] 2 (c c) [(A c) + (A c )] (A c ) 2 F. (28) Subtracting (5) from (28), the difference between the home autarkic profit and postscheme free trade profit becomes π π M π = 1 [ 2 (c c) (A c) + 1 ] 2 (c c) [(A c) + (A c )] (A c)2, (29) while the foreign monopolist s counterpart is π π M π = 1 [ 2 (c c) (A c ) 1 ] 2 (c c) [(A c) + (A c )] (A c ) 2. (30) 21

22 Fortunately, it can be shown that both π and π become positive for any A, c and c, which is summarized in: Proposition 4. Assume that both countries introduce the income redistribution scheme Γ and Γ, respectively. Then, it is possible to make nobody in each country worse off in post-scheme free trade than in autarky. Proof. The proof follows that of Proposition 2. Setting c = αc + (1 α)a, α (0, 1), substituting this into (29) and (30) and rearrangements give π = π = [ 1 4 (1 α)(3 α) (1 + α)2 3 8] (A c) 2 [ 1 4 (1 α)(3α 1) (1 + α)2 3 8 α2 ] (A c) 2. The terms in the square brackets in each equation are simplified to 1 4 (1 α)(3 α) (1 + α)2 3 8 = 3 8 α2 3 4 α g(α) 1 4 (1 α)(3α 1) (1 + α)2 3 8 α2 = 1 2 α2 3 4 α h(α). Again, both g(α) and h(α) turn out to be positive for any α (0, 1) since their discriminant is negative, which establishes π > 0 and π > 0. The intuitions for Proposition 4 can be explained by referring to Figure 2. When both 22

23 countries introduce the scheme, both monopolists have an incentive to expand the output and the international market becomes more competitive since both reaction curves shift up. The resulting world price is lower than each country s autarkic price and hence the consumer gains and subsidizes the monopolist. As a result, both countries monopolists can increase profits despite the declining price. Thus, free trade with the multilateral introduction of the scheme is Pareto-improving for both countries. Remark 3. Proposition 4 has an important implication in considering gains from trade. As Proposition 1 says, the distribution of trading gains is extremely biased towards one country and it is impossible to remedy it through lump-sum compensation as Proposition 2 asserts. However, when both countries adopt the scheme, free trade can benefit both countries. Note that we have assumed that no policy coordination between countries exists although both agents in both countries gain from trade. Therefore, Proposition 4 stands out and it is the core message at the heart of Kemp and Shimomura s (2001) gains-from-trade proposition; there exists a domestic scheme of income redistribution such that no agents become worse off in a free trade Cournot-Nash equilibrium than in an autarkic equilibrium. 23

24 7 Summary and Conclusions This paper has constructed a two-agent model of international duopoly and increasing returns to address gains and losses from trade. The main results can be summarized as follows. (1) Under certain conditions related to the monopolists cost structure, laissezfaire free trade worsens all agents welfare in one country, say, the home country, (2) lumpsum compensation can no longer achieve a Pareto-improvement, and (3) nevertheless, even such a country can still find an appropriate redistributive scheme which takes a nonlump-sum form and makes nobody worse off in post-scheme free trade than in autarky. Our argument is comparable to the argument for protection by Graham (1923). As is well-known, he claimed that protection could be justified in the presence of increasing returns. Ethier (1982) discussed Graham s proposition by constructing a formal two-country model with increasing returns. Although the present paper has considered internal economies of scale and imperfect competition, which differs from Ethier (1982), our argument could provide some insight into Graham s assertion. Let us close the paper by making several comments on extensions of this study. First, we must recognize that the clear-cut results in this paper depend on a highly specified model. Though it is quite difficult to extend our analysis to the general model in Kemp and Shimomura (2001), applications to the two-country, two-good, two-factor models of Markusen (1981), Lahiri and Ono (1995) and Shimomura (1998) may be possible. 24

25 Second, we have assumed that no strategic interaction between each country s government occurs. When such a factor is allowed for, the model is reformulated as a two-stage game one like that of strategic trade policy. Thus, this task may useful in reconciling the issues of potential gains from trade and strategic trade policy. Third, our analysis is confined to Cournot-Nash oligopoly. To our knowledge, Clarke and Collie (2003) are the first to examine gains from trade under differentiated Bertrand oligopoly. The extension to their analysis is of great interest and importance. The final point is related the work by Collie (1996), who examined the welfare consequences of unilateral free trade in a model of market segmentation; only one country, say, the home country allows imports from the foreign firm. Collie s idea was not explored in this paper since we have assumed the existence of an integrated market. All of these extensions are left as future topics of research. 25

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28 [16] Markusen, J. R. and J. R. Melvin (1984), The Gains-from-Trade Theorem with Increasing Returns to Scale, in H. Kierzkowski, Monopolistic Competition and International Trade, Clarendon Press, Oxford, [17] Mills, D. E. and W. Smith (1996), It Pays to Be Different: Endogenous Heterogeneity of Firms in an Oligopoly, International Journal of Industrial Organization, 14, [18] Newbery, D. M. G. and J. E. Stiglitz (1984), Pareto Inferior Trade, Review of Economic Studies, 51, [19] Samuelson, P. A. (1939), The Gains from International Trade, Canadian Journal of Economics and Political Science, 5, [20] Shimomura, K. (1998), Factor Income Function and an Oligopolistic Heckscher- Ohlin Model of International Trade, Economics Letters, 61, [21] Shy, O. (1988), A General Equilibrium Model of Pareto Inferior Trade, Journal of International Economics, 25, [22] Wan, H. Y., Jr. (1965), Maximum Bonus: An Alternative Measure for Trading Gains, Review of Economic Studies, 32,

29 [23] Wong, K. (1995), International Trade in Goods and Factor Mobility, MIT Press, Cambridge, MA. 29

30 X 2(A c) B A c N C D O π = 0 E 2F A c 2(A c ) Figure 1: X 30

31 X 45 N M T O Figure 2: X 31

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