Intraindustry Trade Under Vertical Product Differentiation

Lambertini, Luca Working Paper Intraindustry Trade Under Vertical Product Differentiation Quaderni - Working Paper DSE, No. 233 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Lambertini, Luca (1995) : Intraindustry Trade Under Vertical Product Differentiation, Quaderni - Working Paper DSE, No. 233, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/5080 This Version is available at: https://hdl.handle.net/10419/159076 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/3.0/ INTRAINDUSTRY TRADE UNDER VERTICAL PRODUCT DIFFERENTIATION Luca Lambertini Dipartimento di Scienze Economiche* Università degli Studi di Bologna and Linacre College Oxford JEL classification: F 12, L 13 Keywords: intraindustry trade, vertical differentiation, income. Abstract The paper focuses on trade between two countries where a vertically differentiated commodityisproducedbyasinglefirmineachcountry,operatinginitiallyinautarkicconditions. It is assumed that the two countries have overlapping income distributions, giving thus rise, under certain conditions, to two-way trade, i.e., a proper intraindustry trade. It emerges that while consumers always benefit from trade, especially if two-way trade arises, firms may have conflicting preferenceson thechoice between(i)autarky andtrade, as well as (ii)one-way trade and two-way trade. Acknowledgements IwishtothankGuidoCandelaandMartinSlater forinsightfulsuggestionsanddiscussion. The responsibility for any errors or shortcomings obviously remains with me only. 1. Introduction The role of product differentiation and different consumer preferences across countries havebeenfirstadvocatedastwomajorfactorsexplainingintraindustrytradebetweendeveloped countries by Linder (1961). He argued that the priciples governing trade in manufactured goods differ from those at the basis of trade in primary goods. While accepting the idea that trade in basic goods is determined by factor endowments, he put into question the notion that factor endowments are the main determinants of trade in manufactured items. Linder highlighted instead the role of demand, stressing that usually a large intraindustry trade occurs between developed countries which have comparable factor endowments or relatively easy access to endowmentsavailableinthirdcountries,thataccordingtotheHeckscher-Ohlintheorywemight not expect to observe. Then, a cause of trade other than factor endowment must be identified. According to Linder, a manufactured good is produced by an entrepreneur in response to a perceived demand, which can be determined by the interaction of preferences and income. The roleof preferences in explaining intraindustry tradehas beenlargelyinvestigated in several contributions resorting to the Chamberlinian approach (Krugman, 1979; Helpman, 1981; Markusen, 1981, to mention only a few). Lancaster (1979, 1980) has introduced this issue in thecontext of the addressapproach. Therole of income asa determinantof trade flows has been emphasized by Hunter and Markusen (1987). In a different context, Shaked and Sutton (1984) havedescribedtheeffectoffreetradeontheextentofverticaldifferentiationandtheequilibrium number of firms able to gain positive profits after the liberalization of trade. TheissueofNorth-Southtradeinverticallydifferentiatedproductshasbeenfocused upon by Flam and Helpman (1987). They propose a model where two countries are endowed with production technologies characterized by different levels of efficiency. The authors show that the advanced country produces the top quality goods while the other supplies and exports the 1 low quality goods.1A dramatic change in the pattern of production and trade may be observed if technical progress is faster in the South than in the North. More recently, Motta (1992) has analysed a duopolistic model of trade in vertically differentiated goods between two countries which differ in size, showing that under certain conditions the small country may loose from trade liberalization. Here I want to focus on the interplay between preferences and income on one side and vertical differentiation on the other side as determinants of intraindustry trade between two countries characterized by different income distributions as well as consumer densities, extending the analysis carried out in Lambertini and Rossini (1994). The model I adopt shares many features with the one in Motta, Thisse and Cabrales (1995), though they addressacompletelydifferentquestion,namely,whetheracountrythat,underautarky,produces a good whose quality is lower than that of the good produced in the other country, can catch up after trade liberalization. They show that, when trade opens, two possible equilibria may arise. In the first, the high-quality firm maintains its leadership, while in the second, leapfrogging is observed.Thelattereventispossibleonly iftheinitialqualitygapisnotexcessivelylarge.These results hold for both integrated and segmented markets. I shall assume that the product variety offered by each firm is first determined under autarky. When trade opens, provided that quality cannot be changed due to a sunk cost, firms adjust their respective prices in order to compete in the international market. I adopt the hypothesisthatmarketsareintegrated,i.e.,firmscannotprice-discriminatebychargingdifferent prices in the two countries. This may be due to the possibility of arbitrage by consumers or to the existence of legal constraints. The two alternative cases of one-way and two-way trade are described. These settings are first assumed a priori; then, the conditions leading to the arising of one kind of trade or the other are assessed. The results obtained throughout the paper point 1. This is also confirmed by the empirical literature available, according to which poor countries usually specialize in the production of low-quality goods. See, inter alia, Tharakan (1984); Tharakan, Kerstens and Glejser (1994). 2 to a main consideration, namely that while free trade is generally preferable to autarky from a social standpoint, the choice between one and two-way trade essentially depends on the preferences of the high-quality firm, and a proper form of intraindustry trade may benefit the high-quality firm if the income difference between the consumers in the two countries is not too wide, while is not necessarily preferred to simple one-way trade by the firm located in the poorcountry, thatis specializedin theproduction ofa low-qualitygood,unlessher homemarket isvery poorascompared tothe foreign one.Neat conclusions can be reachedasfar asconsumer surplusandsocialwelfareareconcerned.Underthisrespect,two-waytradeisgenerallypreferred to one-way trade by both countries. The paper is structured in the following way. The basic model is introduced in section 2. Section3 describes the autarkic regime. Then, sections 3 and 4 deal with the alternative settings of one-way tradeand two-way trade, respectively. The issue of the choice between the two free trade regimes is tackled in section 5. Sections 6 through 8 contain a comparative evaluation of the results. Finally, section 9 provides concluding remarks and suggestions for future research. 2. The model Label the two countries as Aand B, respectively. In each country, consumers are characterized by a marginal willingness to pay for quality θand are uniformly distributed with densitysiover the interval i=A,B,with Thelatter assumptionmeans that country Ais at least as rich as country B, in that the marginal willingness to pay of the richer consumer living in country Ais not lower than that of the richest consumer in country B. The global dimension of each market is given by and I assume that with n>0, so that we shall say that country Ais larger than country Bif n>1. Each consumer buys at most one unit of the product if and only if the net surplus he gets from consumption is non negative: [0,θi], θA≥ θB. siθi,sAθA=nsBθB, U=θq−p≥0,(1 3 where qis the quality of the good and pthe price at which it is sold. Onthesupplyside,onefirmisactiveineachcountryunderautarky,offeringagoodwhose production requires a fixed cost which is convex in quality: Variable costs are assumed away. This hypothesis may be given the following justification: quality can be thought of as the result of investments in R&D, whose size is increasing in the quality level of the good being supplied, while it is completely unrelated to the scale of production. It could easily be shown that the introduction of a constant unit variable cost would not modify significantly the results that I am going to derive in the following sections. Consequently, it can be normalised to zero without loss of generality.2Finally, I shall assume that fixed costs are sunk, implying that firms choose quality once and for all. 3. The autarky equilibrium Underautarkyeachfirmoperatesasamonopolistinherownmarket.Herobectivefunction is where xiis market demand, defined as follows: F=tq2,t>0. (2 πi m=pixi−tqi2,i=A,B,(3 2. Instead, the assumption of variable costs increasing in quality would radically change the picture. This setting is investigated in Lambertini and Rossini (1994). 4 From the first order conditions for profit maximization w.r.t. quality and price, we have yielding as the optimal quantity and maximum profit. It appears thus that the monopolist always serves the upper (or richer) half of the market.3Besides, all equilibrium magnitudes increase as and siincrease.Thisimpliesthatthemonopolistwill finditadvantageoustoimproveproductquality as the marginal willingness to pay of the richest consumer increases. Analogously, she will increase quality as consumer density increases, provided that the burden of any increase in quality falls upon fixed costs only. These linkages between quality and marginal willingness to pay as well as consumer density entail that the higher quality good is not necessarily being produced in the richer country, unless it the following inequality is met: xi=  θi−pi qi   si,i=A,B.(4 qim=θi 2si 8t;pim=θi 3si 16t,(5 xim=θisi 2;πi m=θi 4si2 64t(6 θi 3. A social planner aiming at the maximization of social welfare would supply a higher quality as compared to the profit-seeking monopolist. Furthermore, the planner would price at marginal cost in order to serve all consumers. See Appendix A. 5 Since it appears natural to think that the possibility of serving richer consumers provides an incentive to produce a good of higher quality as compared to a market where consumers are characterized by a lower marginal willingness to pay, in the next section I will specify the conditions under which the above inequality holds. As for consumer surplus, it is defined as follows: while social welfare corresponds to the sum of consumer and producer surplus. Then, straightforward calculations show that consumer surplus and social welfare under autarky amount to 4. Free trade When trade opens between the two countries, two alternative settings can emerge. In the first, one-way trade occurs, with the firm located in country Bexporting to country A. This happens when the richest consumer in country Bis located between the levels of marginal willingness to pay associated with the consumers who are indifferent between buying either of the two varieties (h) and between buying thelow quality good or nothing (k), respectively. This situation is depicted in Figure 1. sA>sB    θB θA    2 .(7 CSim=si⌠ ⌡p/q θ(θq−p)dθ, (8 CSim=θi 4si2 64t;SWim=θi 4si2 32t.(9 6 INSERT FIGURE 1 Inthesecond,two-waytradeobtains,withbothqualitiesbeingpurchasedinbothcountries, giving rise to a proper intraindustry trade. This happens when the richest consumer in country Bis located above the marginal willingness to pay of the consumer indifferent between buying either of the two varieties (h). This situation is described by Figure 2. INSERT FIGURE 2 Under free trade, the firm located in the richer country (A) offers a good of higher quality as compared to the firm operating in country B(see below), so that their respective market demands can be indexed as Aand B, and are now defined as follows: if one-way trade occurs, and xA=(θA−h)sA;xB=(h− θB)sA+(θB−k)(sA+sB)(10 xA=(θA− θB)sA+(θB−h)(sA+sB);xB=(h−k)(sa+sB), (11 7 CLAIM1.Iftherichcountryistoosmallascomparedtothepoorcountry,one-waytradeoccurs although two-way trade would be possible. Otherwise, if the dimension of the two countries is the same, or the rich country is larger than the poor country, two-way trade generally obtains, while one-way trade is observed only if the poor country is considerably poorer than the rich country. Consider first one-way trade. Asfor the first point, notice that in such a case the following sequence of inequalities must hold:5 It can be easily established that for all admissible values of rand n. As for the first inequality in (36), it can be established through numerical calculations that (i) if n=1/2, (ii) if n=1, and (iii) if n=2, All the claims that can be found in the remainder of the paper are based on numerical simulations carried out by using the same three values adopted here for parameter n. This amounts to investigating three major cases, namely those in which country Ais (i) half the size of country B; (ii) as large as country B; and (iii) twice as large as country B. Asfor two-way trade,it turnsout thatthe inequalitiesneeded forthis kindoftrade to arise, i.e., are satisfied for all admissible values of r(see Appendix C). ConsidernowthepreferencesoffirmAasforthekindoftradethatmayarise.Byevaluating the sign of h> θB>k, θB=rθA.(36 θB>k h> θB h> θBh> θB ∀r∈]0,0.341325[;∀r∈]0,0.428007[; ∀r∈]0,0.466888[. θB>h>k, ∆πA 21w=π A 2w−π A 1w,(37 5. The equilibrium values of hand kfor both one and two-way trade are in Appendix C. 14 it can be established that (i) if n=1/2, (ii) if n=1, and (iii) if n=2, Thus, ifn=1/2 and consequently rlies in the interval ]0,1/2], i.e., the rich country is half the size of the poor country,but therichest consumers ofthelatter haveamarginal willingnesstopay that isatmost half the corresponding marginal willingness to pay of the richest consumers in the rich country, then in principle two way trade is possible for but firm Ais better off under one-way trade, so that she will decide not to set her price low enough to allow for the high-quality good to be purchased by consumers living in country B, since their number is not sufficient to compensate for the loss due to the decrease in the price charged by firm Aand her consequent inability to appropriate a large share of consumer surplus in her domestic market.6 Mutatis mutandis, for the cases where n=1 or n=2, it can be claimed one-way trade shall occur for or respectively. Notice that, since in such cases the parameter range where one-way trade is possible overlaps that where firm Aprefers not to exportto country B, the upper bounds of the intervals that I shall adopt in the followingsections are set according to the optimal behaviour of the high-quality firm. 6. One-way trade vs autarky In this section, I shall proceed to the comparative evaluation of the equilibrium values of individual and collective surpluses as well as the other relevant magnitudes under autarky and one-way trade. Obviously, the comparison will be carried out taking into account that rmust lie within the relevant ranges established in the previous section, for nequal to 1/2, 1 or 2, ∆πA 21w<0∀r∈]0,1/2[;∆πA 21w>0 ∆πA 21w>0∀r∈]0.328173,0.913517[;∀r∈]0.39795,1[. r∈]0.341325,1/2], r∈]0,0.328173[, r∈]0,0.39795[, 6.Thisisclearlyduetothefactthatthereisnomarketsegmentation,i.e.,firmsareassumed to be unable to price discriminate between consumers in the two countries. For an analysis of such a setting, though exclusively carried out under two-way trade, see Motta, Thisse and Cabrales (1995). 15 alternatively.7 Tobeginwith,considerpricesandquantities.Theconsequencesofone-waytradeonthese magnitudes is summarized by CLAIM2. While trade liberalization unambiguously lowers the price of the high-quality good, the price of the low-quality good may change either way. Both firms sell larger quantities after the opening of trade. Define the following differences: It is easy to verify that is always negative in the relevant range, independently of the relativesizeofthetwocountries.Asitcouldbeexpectedfromtheoutset,thecompetitionimplicit in the opening of trade lowersthe price of the high-quality good. A slightly different story must betoldaboutthepriceofthelow-quality good.Infact, itturnsoutthatifn=1/2, ispositive for all This means that the price of the low-quality good is bound to increaseafter trade liberalization ifcountryBis significantly poorer than country A. In the other two cases (n=1 and n=2), is positive over the entire parameter range. As for quantities, a quick exam suffices to conclude that both differences in (39) are positive, increasing and ∆pA 1wm =pA 1w−pA m,∆pB 1wm =pB 1w−pB m;(38 ∆xA 1wm =xA 1w−xA m,∆xB 1wm =xB 1w−xB m.(39 ∆pA 1wm ∆pB 1wm r∈]0,0.267952[. ∆pB 1wm 7. However, this need will emerge only under a few circumstances. Fortunately, in most casesno numerical simulationsare requiredin ordertoestablishthe resultsI am goingtoexpose in what follows. 16 convex in rover the relevant range. Focus now on profits. Trade exerts opposite effects on the two firms’ performances, as stated in CLAIM 3. The opening of trade decreases the profit of the high-quality firm while it increases that of the low-quality firm. Again, define It appears that is always negative. This result is intuitive and needs no further comments. I can only add that the decrease in firm A’s profit after trade liberalization is increasing (in absolute value) and concave in r, i.e., it becomes larger at a decreasing rate as the maximum willingness to pay of the poor country gets closer to that of the rich country. This happens because, as rincreases, the varieties offered by the two firms becomes more similar, enhancing thus price competition. As for , it is always positive, increasing and convex in r. The consequencesof free trade onconsumer surplus and total welfare inthe twocountries remain to be described. CLAIM 4. Trade liberalization increases both consumer surplus and social welfare in the rich country. The same generally holds for the poor country as well, with the exception that when the latter is larger than the rich country, consumer surplus may be lower than in autarky. The relevant magnitudes, and i=A,B, are defined according to the same criteria adopted above. Trade, if only one-way, increases welfare as compared to autarky over ∆πA 1wm =π A 1w−π A m,∆π B 1wm =π B 1w−π B m.(40 ∆πA 1wm ∆πB 1wm ∆CSi1wm ∆SWi1wm, 17 the whole admissible range of rin both countries. Analogously, it increases consumer surplus in the rich country. The same holds for consumer surplus in country B, except when n=1/2. In such a case, if Notice that, since is always positive, any loss suffered by consumers is always more than compensated by the increase in firm B’s profit. 7. Two-way trade vs autarky Ishallnowfocusonthesettingwherebothvarietiesaretraded.Theprocedureandmethods I shall adopt here are completely analogous to those explained in the previous section, so I can proceed rather quickly. The parameter ranges within which the comparison between two-way trade and autarky makes sense are: (i) if n=1, (ii) if n=2, Noticethatifn=1/2,intheviablerangeofparametersonlyone-waytrademayoccur(seesection 5). As before, I start by treating prices and quantities. CLAIM 5. Under two-way trade, prices are always lower and quantities are always larger than under autarky. Define: as the differences between two-way trade and autarky, as far as prices and quantities are concerned.Itturnsoutthat and forbothcountriesoverthewholeadmissible rangeofparameters.Thisleadsonetothinkthattheconsequencesoftwo-waytradeonproducer r∈]2−√3,0.341325[.∆CSB 1wm >0∆WSB 1wm r∈]0.328173,1];r∈]0.39795,1]. ∆pi2wm =pi2w−pim;∆xi2wm =xi2w−xim;i=A,B,(41 ∆pi2wm <0∆xi2wm >0 18 and consumer surplus, and thus also on social welfare, should be clearcut. Actually, this is not exactly the case, at least as far as firms’ profits are concerned. These results are summarized in the following: CLAIM 6. Two-way trade unambiguously decreases both firms’ profits if the two countries have the same size. If the rich country is larger than the poor one, then trade increases the profit of the high-quality firm if the poor country is sufficiently rich, while it increases the profit of the low-quality firm under the opposite circumstances. CLAIM7.Two-way tradeincreasesboth consumer surplusand socialwelfareinboth countries as compared to autarky. I take into account firstly the case where n=1, i.e., where both countries have the same overall dimension, so that any market size-effect is ruled out. In such a case, it can be verified that foralladmissible values ofr. Theresultsdisplayed in(42) arefullyin linewith intuition.Things goa slightly different way if the rich country is larger thanthe poor country, e.g., ifn=2.In such a case, although one reaches the same conclusions as above as for consumer surplus and social welfare, two-way trade happensto increase both firms’ profits in two distinctparameter ranges: ∆πi 2wm =π i 2w−π i m<0; ∆CSi2wm =CSi2w−CSim>0; ∆SWi2wm =SWi2w−SWim>0,i=A,B,(42 ∆πA 2wm >0iff r ∈]0.5877,0.938364[;(43’ 19 Condition (43’) implies that the high-quality firm may profit from two-way trade roughly over the upper half of the admissible range for r, while condition (43") says that the same happens to the low-quality firm if her own domestic consumers are sufficiently poor as compared to foreign consumers. The effect involving firm Acan be given the following explanation: if the poor countryis smaller but not significantly poorer than the richcountry, when trade opens firm A,whosellsahigh-qualitygood,profitsfromanon-trivialincreaseinthedemandforherproduct by high-income consumers living abroad, while exactly the opposite happens to firm B. As for the situation described by (43"), it may be thought to work like this: if the poor country is both appreciably smaller and significantly poorer than the rich country, when trade opens the low-qualityfirm’s profit increases because she is now able to serve a large number of relatively richer consumers who cannot though afford to buy the high-quality good being sold by firm A. On the contrary, the latter looses from trade because the increase in the overall market size and demand is not sufficient to make up for the decrease in profits due to competition. 8. Two vs one-way trade The comparison between two-way trade and one-way trade remains to be carried out. Obviously, it shall be limited to the restricted range of parameters where both kinds of trade are possible. It hasalready been established in section 5 that the arising of one type of tradeor the other dependsupontherelativeperformanceofthehigh-qualityfirminthesetwosettings.Inparticular, we know thatif the rich country is considerably smaller than the poor country (n=1/2), two-way trade shall not occur. This implies that the comparison between one and two-way trade is ∆πB 2wm >0iff r ∈]0.39795,0.471026[. (43" 20 meaningful only when the two country are of about the same size (n=1) or the rich country is larger than the poor country (n=2). As for prices’ and quantities’ behaviour in the two settings, I can state the following: CLAIM 8. Both prices are lower under two-way trade than under one-way trade. The quantity soldby the high-quality firmis higher under two-way trade, whilethatsold by the rivalis higher under one-way trade. Again, define One quickly checks that for both firms, while and over the entire range of parameter r. Furthermore, as far as the low-quality firm’s performance is concerned, the following holds: CLAIM 9. The low-quality firm is always better off under one-way trade than under two-way trade. This obtains by checking that for all admissible values of r. Under two-way trade, the loss due to the competition by the ∆pi21w=pi2w−pi1w;∆xi21w=xi2w−xi1w;i=A,B.(44 ∆pi21w≤0∆xA 21w>0∆xB 21w<0 ∆πB 21w=π B 2w−π B 1w<0(45 21 high-quality firm in country B, the low-quality firm’s home market, adds to the loss due to the competitive regime associated with trade, so that firm Balways prefers one-way trade. Theopposite preferencesobviouslycharacterizeconsumerslivingin bothcountries,since is always positive. As for social welfare, while isalways positive, ispositive for allvaluesof rif thetwocountrieshave the sime size (n=1), while, if n=2, two-way trade is socially preferable to one-way trade only if country Bis sufficiently rich, and precisely for r>0.49218. Otherwise, the loss suffered by the low-quality firm outweighs the gain in terms of consumer surplus. Accordingly, I can finally state CLAIM10.Two-way trade ispreferable to one-way trade fromthe consumers’ viewpoint. The same applies to social welfare in the rich country, while it holds forthe poor country if the latter is not excessively poor or small as compared to the rich country. 9. Conclusions and suggestions for future research I have investigated the issue of free trade in vertically differentiated goods between two countries characterized by different dimensions and income distributions, in a framework suitable to describe North-South trade. Several results have been derived. First, according to the relative size as well as wealth of their respective domestic markets, firms may have conflicting interests as for (i) the opening oftrade, be that oneor two-way, as against theautarkic status quo ante; and (ii) one vs two-way trade. The conclusions that the model suggests in terms of consumer surplus and social welfare arerather clearcut.Under bothperspectives, tradeisgenerally preferredtoautarkyand two-way tradeispreferredtoone-waytrade,sincetheformerimpliesthatduopolisticcompetitionextends to both countries, while in the latter the low-quality firms competes against the high-quality ∆CSi21w=CSi2w−CSi1w∆SWA 21w=SWA 2w−SWA 1w ∆SWB 21w=SWB 2w−SWB 1w 22 firm in the richer market while keeping her monopolistic position at home. Thepresentanalysiscan beextendedandamendedunder severalaspects.First,ithasbeen carried out under the hypothesis that firms set the quality of their respective products under autarky,so that aftertrade liberalizationthey canonly adjust prices.Ina richermodel, thiscould be considered as the short run or impact effect of trade liberalization, letting firms reoptimize with respect to quality thereafter.8Alternatively, if one prefers to maintain the assumption that quality must beset once and for all due to the existence of sunk costs, then it can be figured that firms choose quality under autarky, anticipating that at some date trade shall open, so that they set quality in order to maximize a discounted flow of profits over a time interval that stretches beyond the time at which liberalization occurs. This would properly embed the analysis in a dynamic perspective. Finally, the general setting presented here opens the way to the analysis of strategic trade policy by the governments of the countries involved. Some instances of the effects exerted by tariffs and quotas are already described by Krishna (1987, 1990) and Lambertini and Rossini (1994), where it is shown that the introduction of a tariff on imports by therichcountry maybenefit bothfirmsand increaseboth countries’welfare.The issueof export rivalry on the world market between firms operating in countries characterized by different levels of economic development is tackled by Chang and Kim (1989) and Chang and Chen (1994). In these two papers, the firm operating in the developed country is appointed the Stackelberg leadership, and the follower relies on an imported key input which is needed for the production of a low-quality good that is exported to the world market. The authors establish thatthegovernmentofthedevelopingcountryshouldeitherintroduceatariffontheinputimports or tax its final good exports. 8.This is done by Motta, Thisse and Cabrales (1995) by introducing a convex adjustment cost which is completely absent under autarky. However, this is not fully satisfactory, since it seems to imply that firms face two different technologies under the two market regimes. 23 Figure 1. One-way trade Figure 2. Two-way trade 30