Comparative Costs, Autarky General Equilibrium, Trade Patterns, Factor Endowments, Free Trade Balances, Terms of Trade Surfaces,

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1 Comarative Costs, utary General Equilibrium, Trade Patterns, Factor Endowments, Free Trade alances, Terms of Trade Surfaces, International General Equilibrium Solutions and Factor llocations. jarne S. Jensen and Jacoo Zotti University of Southern Denmar, Det. of Environmental and usiness Economics University of Trieste, Deartment of Political and Social Sciences bstract This aer gives analytical arametric solutions for the basic, two-sector-two-factor-twocountry, (2x2x2) model of international trade. Such analytical aroach to the involved non-linear economic systems must start with the Cobb-Douglas secifications of sector technologies and consumer references. The closed-form exressions rovide a unified framewor for all traditional basic trade models. The solutions allow for international differences in country sizes, endowments, technology and references, encomassing the major ure trade theories within a systematic analytic and historical ersective. In this unified framewor, we derive the general existence conditions for the solutions under diversification and inciient country secialization. Keywords: Trade models, general equilibrium, terms of trade JEL Classification: F11, F43, E21 1

2 1 Introduction The ure theory of international trade has always been involved with the fundamental questions of what decides : 1. The commodity attern (comosition) of international trade between countries, 2. The international values, i.e., the rices of both the free traded commodities and their rimary roduction factors, 3. The gains from foreign trade. Evidently the literature is overwhelming and hence many surveys have been made, Haberler (1936,1961), Mundell (1960), hagwati (1964), Chiman ( ). The latter still surasses all other historical accounts and exositions of theory evolution (together with many references to contemorary authors/discussions). His theory chronology has three eriods of main/early contributors : I. Classical theory of comarative advantage, gains from trade (Smith, Ricardo, Mill), II. Neo-Classical theory of international trade equilibrium and the equilibrium terms of trade (Marshall, Edgeworth, Haberler), III. Modern theory of factor endowments, factor rice equalization, factor income distribution, two-sector growth models (Hecscher, Ohlin, Samuelson, Solow, Uzawa, Kem). Economic laws (theory) governing trade between two countries dawned in dam Smith - Chater 11 of restraints uon the imortation from foreign countries of goods that can be roduced at home, Smith (1776, 1961,.478): What is rudence in the conduct of every rivate family, can scarcely be folly in that of a great ingdom. If a foreign country can suly us with a commodity cheaer than we ourselves can mae it, better buy imort] it from them with some art exort] of the roduce of our own industry, emloyed roduced] in a way in which we have some advantage. y scrutinizing the rincile of cheaness and advantage in more detail with some illustrations, Ricardo (1817,.81,.175), cf. Ruffin (2002,.743), came u with the law of comarative advantage: Under a system of erfectly free commerce, each country naturally devotes its caital and labour to such emloyments industries, goods, sectors] as are most beneficial to each. This ursuit of individual advantages is admirably connected with the universal good of the whole. Precisely, the Ricardian term comarative advantage means the ability in autary to roduce a good at lower cost/rice (relative to other goods), comared to another autary country. Moreover, the law of comarative advantage (cost) says that a country exorts 2

3 (imorts) the good with the low (high) relative ( = P 1 /P 2 ) autary rice, and it can be exressed an inequality in relative autary rices : P 1 /P 2 = < P 1 /P 2 = : X 1 > 0 (1) The rediction of trade atterns - X 1 > 0 : exort of good 1 by country - in oen economies by the autary condition, (1), is (with recise assumtions) not violated in any trade model for : Two countries, two goods commodities, sectors], two factors, (2x2x2). The world equilibrium terms of trade ( ) are usually just taen (assumed, not roved) to fall strictly between the two countries relative rices (rice ratios) under autary, i.e., < < (2) excluding the case of one country (say ) being small, hence =. The bilateral rule of comaring relative rices under autary to determine trade atterns, (1), is not valid for a multicommodity (multisector, i 3) world, as demonstrated by Drabici and Taayama (1979,.217). On these higher dimensional issues, see Deardorff (1980), Shimomura and Wong (1998). We focus on a full story of the (2x2x2) model, but in contrast to the available literature so far, our objective is to deduce and finally resent exlicit analytical solutions of the world trade model (2x2x2). While comarative advantage exlains why and how trade taes lace, it does not exlain (give) the terms of trade : relative rices, in (2). Ricardo s numerical examles, cf. Chiman (1965,.482), offer no clear size of ( ) or hints to general answers. It was Stuart Mill, who first gave an analysis of the formation of international values world maret rices, determination of in (2)], that offered a rigorous answer - discussed in detail by Chiman (1965, ) - uon a ure trade theory examle left by Ricardo. Stuart Mill (1875,.352) stated: When trade is established between two countries, the two commodities will exchange for each other at the same rate of interchange in both countries, i.e. the law of one rice that will also be adhered to in our (2x2x2) model. Next Mill (1875,.359) says: ll trade, either between nations or individuals, is an interchange of commodities, in which the things that they resectively have to sell, constitute also their means of urchase: the suly brought by the one constitutes his demand for what is brought by the other. So that suly and demand are but another 3

4 exression for recirocal demand - or named the Equation of International Demand - or today: the trade balance equation with a zero constraint - which is adoted here, too. To handle the secial trade case of Ricardo, Mill assumed that consumers in both countries had identical commodity demand functions of simlest functional form, Mill (1875,.361): Let us therefore assume, that the influence of cheaness on demand conforms to some simle law, common to both countries and to both commodities. s the simlest ossible and most convenient, let us suose that in both countries any given increase of cheaness fall in rice] roduces an roortional increase of consumtion: or, in other words that value exended in the commodity, the cost incurred for the sae of obtaining it, is always the same, whether that cost exenditure] affords a greater or smaller quantity of the commodity. In short, Mill used here consumer demand functions, generated today by Cobb-Douglas utility functions, as we will do for references below. Marshall (1879, 1974) continued the study of Mill s examles with an in-deth analysis of the trade balance equilibrium determination of international values (terms of trade) by recirocal demand (offer, net-exort) curves of two countries. Let us hear, Marshall (1879, 1974,.1): The function of ure theory and models is to deduce definite conclusions from definite hyothetical remises. The remises should aroximate as closely as ossible to the facts with which the corresonding alied theory has to deal. ut the terms used in the ure theory must be cable of exact interretation, and the hyotheses on which it is based must be simle and easily handled. The ure theory of foreign trade satisfies these conditions. Marshall suorted his roositions/corollaries with 24 offer-curve diagrams; many now standard, cf. summary in Deardorff (2006,.322). While classical trade theory (Smith, Ricardo) may have assumed, cf. Chiman (1966,.18), constant factor rices and different technologies among countries, Hecscher (1919, 1991,.47) examined some : fundamental assumtions concerning the reasons for differences in comarative costs among countries, i.e. why are in (1) the autary relative costs (rices) and different? s a een economist, Hecscher correctly argued that countries with same - technologies and relative factor rices - do not trade; since then: relative costs in one country cannot ossibly differ from those in the other. Therefore trade between the countries will not arise, Hecscher (1991,.47). 4

5 Hence behind the Ricardian inequality in (1), he saw (emhasized) as a rerequisite an inequality in autary relative factor rices, ω and ω : different relative rices of the factors of roduction in the exchanging countries, Hecscher (1991,.48). ut next oening free trade would itself affect the relative factor rices and maybe, even under some conditions, bring about not just artial, but full factor rice equalization (FPE). s to modern factor endowment theory, Ohlin (1935, endix I) re-examined and extends the general equilibrium equation systems of Walras-Cassel for the mutual interdeendence ricing of commodities and factors to trading regions (countries). He introduced and emhasized the role of different factor endowments ratios, (, ), among regions; but Ohlin (1933, ) oted in most situations for artial factor rice equalization. Next Samuelson (1948,.169) enters the discussion: In attemting to devise a rigorous roof of the artial character of factor-rice equalization, I made a surrising discovery: the roosition is false. It is not true that factor rice equalization is imossible. It is not true that factor rice equalization is highly imrobable. On the contrary, not only is factor-rice equalization ossible and robable, but in a wide variety of circumstances it is inevitable. Samuelson (1949,.182) restated verbally eight conditions for FPE. major roblem with Pareto efficient factor allocation in even two-sector economies with flexible sector technologies is that they in fact constitute miniature Walrasian general equilibrium systems. Thus early wor uon two-sector growth models in various qualitative versions addressed some of the major issues of this aer, cf. Uzawa ( ), Onii-Uzawa (1965), that were recently resolved quantitatively in Jensen (2003). Our main result is finally for internationally different technologies and consumer references to have solved exlicitly the asic Trade Model (2x2x2) for the endogenous terms of trade, ( ), and resenting analytically the international general equilibrium solutions with exlicit existence conditions uon country endowments for reserving diversification of the two trading economies. We roceed axiomatically in exosition and sections. Section 2 gives the general framewor of autary and oen economies. utary general equilibrium serves as benchmar and gives exressions of comarative advantage. Section 3 solves the world trade balance equation and gives ( ) in Proositions 1-2. Section 4 exhibit results of basic trade models. Section 5 concludes and suggests further research. 5

6 2 The Structure of Two-Sector Economies 2.1 Framewor: Factor endowments, GDP accounting There are two countries in the world, and. These countries may roduce two consumer goods (sectors), i = 1, 2, which are fully homogeneous throughout the world. In both sectors, they are using two rimary roduction factors, labour and caital. Labour endowment (suly) in country J =, is L J, while caital endowment is K J ; its factor roortion (endowment ratio) is, J = K J /L J. Migration of the rimary factors is excluded, while reallocation (mobility) among sectors is always ossible and frictionless. It is assumed that both factors are fully emloyed in each country : K 1J + K 2J = K J ; L 1J + L 2J = L J ; J K J /L J, J =, J = K J /L J = λ L1J 1J + λ L2J 2J ; ij K ij /L ij, i = 1, 2, J =, (3) λ L1J = J 2J 1J 2J, λ L2J = 1 λ L1J ; λ LiJ L ij L J, i = 1, 2 J =, (4) λ K1J = 1J J λ L1J, λ K2J = 1 λ K1J ; λ KiJ K ij K J, i = 1, 2 J =, (5) where λ LiJ, λ KiJ, are the fractions of labour (caital) of country J emloyed in sector (i), and ij is the caital-labour ratio (sometimes called caital intensity ) in sector (i), country J. It follows from (4) that a diversification condition, 0 < λ L1J < 1 - i.e., actual roduction of both goods in country J - is equivalent to a air of inequalities, 0 < λ L1J < 1 : 1J < J < 2J or 2J < J < 1J, J =, (6) Technology exhibits constant returns to scale (CRTS) in both countries. Since factor marets are assumed erfectly cometitive (zero rofit), the Euler theorem ensures that the monetary value (revenue) from roduction (Y ij ) in each sector equates the factor income of emloyed rimary factors, which is also total minimum roduction cost (C ij ), P ij Y ij = w J L ij + r J K ij = C ij, i = 1, 2, J =, (7) with the sectoral cost shares of labour and caital : ɛ LiJ = w J L ij C ij, ɛ KiJ = r J K ij C ij ; ɛ LiJ + ɛ KiJ = 1, i = 1, 2, J =, (8) 6

7 Total national income (Gross Domestic Product, GDP), (Y J ), is obtained as Y J = P 1J Y 1J + P 2J Y 2J = w J L J + r J K J, J =, (9) and the total (macro) factor income shares, δ LJ, δ KJ, in each country become, δ LJ = w J L J Y J, δ KJ = r J K J Y J ; δ LJ + δ KJ = 1, J =, (10) y (10), the shares, δ LJ, δ KJ, are identically lined to the country factor endowment ratio, ( J ), and relative factor rices, (ω J ), stated as ] J δ KJ δ LJ wj r J = δ KJ δ LJ ω J, ω J w J r J, J =, (11) Let Q ij, i = 1, 2, denote the quantitative size of the domestic final demands (absortion level) for good 1 and good 2, and they are resectively equal to domestic roduction, Y ij, (7), minus exorts X ij, (imorts = - X ij ), i.e., Q 1J = Y 1J X 1J, Q 2J = Y 2J X 2J, J =, (12) The trade balance is assumed to satisfy the constraint, P 1J X 1J + P 2J X 2J = 0 ; i.e. Y J = P 1J Q 1J + P 2J Q 2J, J =, (13) i.e., balanced trade revails with no foreign borrowing/lending allowed. The comosition of GDP, Y J, (13), into final demand (exenditure shares), s ij, is s ij = P ij Q ij /Y J ; 2 i=1 s ij 2 i=1 P ijq ij /Y J = 1, J =, (14) The macro factor income shares δ LJ, δ KJ, (10), are GDP exenditure-weighted, (39), combinations of sectoral factor (cost) shares, ɛ LiJ, ɛ KiJ, δ LJ = 2 i=1 s ij ɛ LiJ, δ KJ = 2 i=1 s ij ɛ KiJ, δ LJ + δ KJ = 1, J =, (15) The factor allocation fractions, (4), (5), can then be restated as, λ LiJ = s ij ɛ LiJ /δ LJ, λ KiJ = s ij ɛ KiJ /δ KJ, i = 1, 2, J =, (16) The total factor endowment ratio, ( J ), satisfies the identity, cf. (11), (15) : K J /L J = J = δ KJ δ LJ ω J = 2 i=1 s ij ɛ KiJ / 2 i=1 s ij ɛ LiJ ] ωj, J =, (17) which is a convenient reresentation of full emloyment and factor endowment ratio, (3). 7

8 2.2 Sector technologies, cost functions and relative rices For sector i = 1, 2 in country J =,, we assume standard CD technologies (F ij ) : Y ij = F ij (L ij, L ij ) = γ ij (L ij ) 1 a ij (K ij ) a ij, y ij = γ ij ( ij ) a ij, i = 1, 2, J =, (18) where Y ij is outut of sector (i) in country J - with sectoral labour roductivity, y ij Y ij /L ij, caital-labor ratio, ij K ij /L ij, and the caital intensity arameter, a ij. Free factor mobility and efficient factor allocation between sectors imose a common marginal rate of factor substitution within each country, (equal to the relative factor rices, ω J w J /r J = w ij /r ij ω ij ), which with the CD technologies (18) become : ω J = ω ij = 1 a ij a ij ij ; ij = a ij 1 a ij ω ij ; 1J = a 1J/ (1 a 1J), J =, (19) 2J a 2J / (1 a 2J ) The standard dual CD sector cost functions of (18-19) are, C ij (w J, r J, Y ij ) = 1 ] 1 aij ] aij wj rj Y ij, i = 1, 2, J =, (20) γ ij 1 a ij a ij and the sectoral cost shares (8) are : ɛ LiJ = 1 a ij, ɛ KiJ = a ij ; ɛ LiJ + ɛ KiJ = 1, i = 1, 2, J =, (21) The relative commodity (outut) rices (unit costs) are derived from (20), (19) as, where J = P 1J P 2J = C 1J/Y 1J C 2J /Y 2J = c 1J (ω J ) c 2J (ω J ) = 1 ā J γ 2J γ 1J ω J ] a 2J a 1J J (ω J ), J =, (22) ā J = (a 1J) a 1J (1 a 1J ) 1 a 1J (a 2J ) a 2J (1 a 2J ) 1 a 2J > 0, J =, (23) Relative rices J (ω J ) with CD (22) can range from zero to infinity, cf. Fig. 1, Case 1-2. Next, we can use the inverse of relative rices (22) to get the relative factor rices, ω J = γ 1J γ 2J ā J J ] 1 a 2J a 1J, J =, (24) Inserting (24) into (19), (18), give sectoral caital-labour ratios (intensities) and sectoral labour roductivities with the relative good rice ( J ) as the indeendent variable, ij ( J ) = a ij 1 a ij γ 1J γ 2J ā J J ] 1 a 2J a 1J, i = 1, 2, J =, (25) 8

9 a ij ] y ij ( J ) = γ aij γ 1J ] aij a ij ā J 2J a 1J J, i = 1, 2, J =, (26) 1 a ij γ 2J The ratios of sectoral labour roductivities within countries follow from (26), cf. (18-19), as : y 2J y 1J Next rewrite (4) - with CD technologies, (19) - as, λ L1J ( J ) = = 1 a 1J 1 a 2J J, J =, (27) J 1 2J ( J ) 1J ( J ) 1 = 2J ( J ) J 1 2J ( J ), J =, (28) a 1J /(1 a 1J ) a 2J /(1 a 2J 1 ) and use (25) to get the allocation fractions of labour (28) and caital (5) in ( J ): ] ] 1 a 2J (1 a 1J ) 1 a 2J γ1j a 1J a 2J λ L1J ( J ) = ā J J J 1 a 1J (1 a 2J ) a 2J (1 a 1J ) a 2J γ 2J (29) λ K1J ( J ) = 1J( J ) J λ L1J ( J ), J =, (30) diversified economy clearly requires that, λ L1J, (6), here satisfies the diversification condition : 0 < λ L1J ( J ) < 1, (29). Solving this inequality (29) with resect to J yields (imose after some maniulations) the following relative rice interval restriction : 0 < λ L1J < 1 J = 1 ā J γ 2J γ 1J 1 a2j a 2J J ] (a2j a 1J ) < J < 1 ā J γ 2J γ 1J 1 a1j a 1J J ] (a2j a 1J ) = J (31) where J < J for any feasible arameter set. The relative rice limits in condition (31) ] define the closed interval : J, J - cf. the two-sector geometry in Fig.1. This interval (31) is solely determined by technology arameters and by technologically (Pareto) efficient factor endowment allocation. Since the relative rices ( oortunity cost ) J (22) are always the sloe of the roduction ossibility frontier (PPF), J ( J ) in (31) is the sloe of the PPF, when roduction of sector 1 (sector 2) is zero. Condition (31) in fact, is equivalent to the diversification cone, (6). To see this, re-write (31) as ] 1 a 1J γ1j a 2J a 1J a 2J > a 1J : ā J J < J < a ] 1 2J γ1j a 2J a 1J ā J J (32) γ 2J γ 2J a 1J > a 2J : 1 a 1J a 2J 1 a 2J γ1j γ 2J ā J J 1 a 2J ] 1 a 2J a 1J < J < a ] 1 1J γ1j a 2J a 1J ā J J (33) 1 a 1J γ 2J and recall (25). Moreover, the relative rice diversification condition (31) is equivalent to the following relative factor rice interval restrictions: a 2J > a 1J : 1 a 2J a 2J J < ω J ( J ) < 1 a 1J a 1J J (34) 9

10 a 1J > a 2J : 1 a 1J J < ω J ( J ) < 1 a 2J J (35) a 1J a 2J s will be clear from Fig.1 and further exlained below, the conditions (31)-(35) are always satisfied by the general equilibrium solution (43) in autary. The intervals for the autary general equilibrium solution J ( J ), (45), are given by closed intervals of (31). Case 1, a 2J > a 1J Case 2, a 2J < a 1J J 1J J 2J J J 2J 1J J J J J J J J J J J Figure 1. Relative factor rices, ω J, caital-labour ratios, ij, (19), relative commodity rices, J (ω J ), (22), rice interval of J, (31), Walrasian autary equilibria, Ψ J (ω J ), (43). 2.3 Consumer references and demand functions In each country J =,, we have a reresentative consumer with homothetic utility function (references) of the CD form with country-secific arameters (α J ): u J = U J (Q 1J, Q 2J ) = (Q 1J ) α J (Q 2J ) 1 α J, J =, (36) where Q ij is the consumtion of final good (i) in country J. Maximization of utility (36) under the budget constraint, cf. (9), (13) : Y J = P 1J Q 1J + P 2J Q 2J, J =, (37) yields the otimal demanded quantities Q ij and exenditure shares, s ij, (14), Q 1J = α J (Y J /P 1J ) ; Q 2J = (1 α J ) (Y J /P 2J ), J =, (38) s 1J = P 1J Q 1J /Y J = α J ; s 2J = P 2J Q 2J /Y J = 1 α J ; 2 i=1 s ij = 1 (39) 10

11 2.4 Walrasian general equilibrium of two autary economies In autary, final demand for good i in country J must equate internal roduction (outut), i.e., cf. (12), Q ij = Y ij, X ij = 0, i = 1, 2, J =, (40) y combining the sectoral factor (cost) shares, ɛ LiJ, ɛ KiJ, (21), and exenditure shares, s ij, (39), our factor income shares, δ LJ, δ KJ, (15), here become, δ LJ = α J (1 a 1J ) + (1 α J )(1 a 2J ), δ KJ = α J a 1J + (1 α J )a 2J β J, J =, (41) and hence the factor allocation fractions, (4), (5), are here given as : λ LiJ = α J (1 a ij ) α J (1 a 1J ) + (1 α J )(1 a 2J ), λ K ij = α J a ij α J a 1J + (1 α J )a 2J (42) Thus with CD technologies, (18), and CD consumer references, (36), the Walrasian general equilibrium (with maret clearing rices on commodity and factor marets and Pareto efficient endowment allocations) of the autary economy is obtained by the factor endowment ( J ) - factor rice (ω J ) corresondence, satisfying the identity, (17), as a comlete Walrasian general equilibrium condition for J =,, cf. Jensen (2003,.69) : J = Ψ J (ω J ) = δ KJ(ω J ) δ LJ (ω J ) ω J = α J a 1J + (1 α J )a 2J α J (1 a 1J ) + (1 α J )(1 a 2J ) ω J = with the locus, J = Ψ J (ω J ), J =,, shown in Figures 1-2. β J 1 β J ω J (43) With factor endowment ratios ( J ) as as exogenous variables, the endogenous general equilibrium autary factor rice ratios, ω J ( J ), follow from (43) as, ω J = Ψ 1 J ( J ) = 1 α Ja 1J + (1 α J )a 2J ] α J a 1J + (1 α J )a 2J J = 1 β J β J J, J =, (44) Hence the autary relative commodity rice (rice ratio) is obtained by (44) and (22): J ( J ) = P 1J P 2J = 1 ā J γ 2J γ 1J 1 αj a 1J + (1 α J )a 2J ] α J a 1J + (1 α J )a 2J J ] a2j a 1J = 1 ā J γ 2J γ 1J 1 βj β J J ] a2j a1j (45) which are, e.g., illustrated for country and in Figure 2 - shown by ( ) and ( ). If the two autary CD economies have identical technologies, the same references, and hence only differ in endowments, the general CD rice ratio formula (45) is reduced to, J ( J ) = 1 ] a2 a γ 2 1 α a1 + (1 α) a 2 ] 1 J 1 ] a2 a γ 2 1 β 1 J, J =, (46) ā γ 1 α a 1 + (1 α) a 2 ā γ 1 β 11

12 w J = ω = ω ψ ψ ω = ω ω ( ) ω * ω ( ) J ( ) * ( ) J Figure 2. Relative rices J (ω J ), (22), cf. Case 1, Fig.1 (same technology), autary general equilibria J = Ψ J (ω J ), (43), autary relative factor rices ω J ( J ), (44), autary relative commodity rices J ( J ), (45), and terms of trade, (2). Thus the Ricardian Law of Comarative Costs (1) can be exressed by the following inequality in the bilateral autary general equilibrium relative rices (rice ratios), (45) : P 1 /P 2 = ( ) < P 1 /P 2 = ( ) : X 1 > 0 (47) Simle alications of the comarative advantage rincile for obtaining trade atterns by the general autary rule (47), (45), are : Lemma. Countries with same - technologies, references, endowments - do not trade. Countries with same - technologies and relative factor rices - do not trade. Country sizes are irrelevant for the bilateral trade attern, which are uniquely determined by : technology arameters, reference arameters, and the factor endowment ratios. Proof. If = in (46), then, ( ) = ( ), which imlies : X 1 = 0, by (47). If ω = Ψ 1 ( ) = 1 β β = 1 β β = ω in (44), then, ( ) = ( ); cf. Fig. 2. The general solution for the autary rice ratios J ( J ), (45), deend only on : technological arameters, consumer references, endowments ratios - but not v J, cf. (64). arametrically restricted version of (45) are autary rice ratios J ( J ) given by : a 1 = a 1 = a 1 ; a 2 = a 2 = a 2 ; β J ; J ( J ) = 1 ā 12 γ 2J γ 1J 1 βj β J J ] a2 a 1, J =, (48)

13 which gives the trade atterns (47) of submodels in Proosition 1 and Table 1 below. Trade atterns (47) of Hecscher-Ohlin-Samuelson (HOS) CD models follow (46), i.e. J. Lemma. If two countries differ in references and in technologies (or endowments), then endowments (or technologies) alone cannot exlain their trade atterns. Proof. It follows from (47) and autary rice exressions in (48) and the general (45). 2.5 Sector technologies, endowments and global diversification For later uroses, we will consider a arametrically constrained version of the relative rice interval restriction (31) - with a 1 = a 1 = a 1 ; a 2 = a 2 = a 2 and hence, ā = ā = ā cf. (23), (71) - for our two countries, J =, : 0 < λ L1J < 1 : J = 1 ] (a2 a γ 2J 1 1 ) a2 J < J < 1 γ 2J 1 a1 ā γ 1J a 2 ā γ 1J a 1 J ] (a2 a 1 ) = J (49) In this two-country world, the diversification condition, 0 < λ L1J < 1, J =,, (49), ] ] defines two closed rice intervals: ( ), ( ) and ( ), ( ), see Figure 3. It is excluded that any of these two closed rice intervals fully contains the other. Figure 3 a. The intersection rice interval ( ) :, ]. 0 0 Figure 3 b. The intersection rice interval ( ) :. 0 0 Figure 3 c. The intersection rice interval ( ) :, ], ] 0 0 Figure 3. The rice intervals, (49), and intersections ( ), (54-55), for countries,. 13

14 Without loss of generality: Let, cf. Fig. 3, and note that due to (49). Hence by (49), we get limits for their factor endowment ratio, ( / ), as : a 1 > a 2 : γ1 /γ 2 γ 1 /γ 2 ] 1 γ (50) a 1 < a 2 : γ1 /γ 2 γ 1 /γ 2 ] 1 γ (51) Evidently, a necessary condition for existence of a diversified international general equilibrium solution for the relative rices ( ) is that the intersection of the rice intervals: ] ],,, is non-emty. With, Fig. 3, then requires:, which stiulates that factor endowment ratios, ( / ) satisfy, cf. (49), a 1 > a 2 : a 2/(1 a 2 ) a 1 /(1 a 1 ) γ1 /γ 2 γ 1 /γ 2 ] 1 ã γ (52) a 1 < a 2 : a 2/(1 a 2 ) a 1 /(1 a 1 ) Note that, when a 1 > a 2 a 1 < a 2 ], then ã < 1 ã > 1 ]. γ1 /γ 2 γ 1 /γ 2 ] 1 ã γ (53) Thus the condition,, is met, if ( / ), cf.(50), (52), (51), (53):, a 1 > a 2 : ã γ a 2/(1 a 2 ) a 1 /(1 a 1 ) γ1 /γ 2 γ 1 /γ 2 ] 1 γ1 /γ 2 γ 1 /γ 2 ] 1 γ (54), a 1 < a 2 : γ γ1 /γ 2 γ 1 /γ 2 ] 1 a 2/(1 a 2 ) a 1 /(1 a 1 ) γ1 /γ 2 γ 1 /γ 2 ] 1 ã γ (55) If the necessary factor endowment ratio conditions (54-55) are satisfied, the intersection ] between the two rice (minimal cost) intervals is non-emty (Fig. 3 a). If the two countries have the same sector technologies (HOS-HOL models below) with γ = 1, necessary diversification conditions (54-55) for factor endowment ratios ( / ) are:, a 1 > a 2 : ã a 2/(1 a 2 ) a 1 /(1 a 1 ) < 1 (56), a 1 < a 2 : 1 < a 2/(1 a 2 ) a 1 /(1 a 1 ) ã (57) When the equality ( / ) = ã γ holds - endoint of (54-55) - then =, and hence the intersection,, between, ] and, ] is a single common oint, (Fig.3 b). When the other equality ( / ) = γ holds - endoint of (54-55) - then two intervals,, ] and, ], coincide (equal to ), (Fig. 3 c). 14

15 Thus, we see that the resective endoints of (54), (55), (56), (57) determine the largest otential interval (range) for the factor endowment ratio, ( / ), that are comatible with reserving the roduction diversification (two sectors) in both trading countries. Let us see two case examles, cf. Fig. 1, of the endowment ratio intervals (56), (57), Case 2 : a 1 = 0.5, a 2 = 0.25; a 1 > a 2 : ã = a 2/(1 a 2 ) a 1 /(1 a 1 ) = 1/3 < 1 (58) Case 1 : a 1 = 0.25, a 2 = 0.5; a 1 < a 2 : 1 < 3 = a 2/(1 a 2 ) a 1 /(1 a 1 ) = ã (59) lthough the assumtion (hyothesis) of diversification was stressed as a necessary condition for factor rice equalization (FPE), Samuelson (1948,.175,178; 1949,.182,193), no exlicit factor endowment interval lie (56-57) for two countries was given then (later). Moreover, consumer references and country sizes will modify these intervals (54-59) - necessary, but not sufficient - of comatible endowment ratios, ( / ), cf. section 3.3. Incidentally, Figures 3a, 3b, reveal that the simle illustrative assumtion : lays a role in outlining limiting cases of inciient secialization in the two countries where nothing is being roduced of one commodity, but where it is a matter of indifference, whether an infinitesimal amount is or is not being roduced, so that rice and marginal cost are equal, Samuelson (1949,.182) ]. When condition holds, cf. (50-51), there are three ossible secialization cases: (i) Country roduces only good 2 (i.e. = ), and country does not secializes in any sector (because < < ); Fig. 3a. (ii) Country roduces only good 1 (i.e. = ), while country roduces both goods (since < < ); Fig. 3a. (iii) oth countries are secialized ( = = ), () maes good 2 (1) ; Fig. 3b. Clearly, these secialization atterns above just reverse with the assumtion : <. y the way, Samuelson (1949,.188) first used curves (qualitatively), as in Fig. 1-2, to summarize the connections between relative rices ( J = P 1J /P 2J ), relative factor rices (w ij /r ij = ω ij ), and sectoral caital-labor ratios ( ij = K ij /L ij ). ut he used, L i /K i = 1/ i, on the right horizontal axis; hence in Fig. 1-2, the rays would then be two rectangular hyerbolas: ω i = (1 a i )/a i ]/ i, cf. (19). It is more convenient with every curve ω i ( i ) in all cases to originate from: (0, 0); that also alies to: J = Ψ J (ω J ), (43). 15

16 3 International free trade and world maret rices We assume free trade between two countries, J=,, with erfect integration of the national commodity marets. Due to the absence of frictions in international trade the law of one commodity rice, P i, and hence one relative rice, () aly: P i = P i = P i, i = 1, 2 : = P 1 /P 2 = = (60) 3.1 Free trade balances and world maret equilibrium Country trades are here always balanced. s commodity marets are fully integrated, world maret equilibrium imlies, cf. (12) : X i = Y i Q i = X i = (Y i Q i ) ; i = 1, 2 (61) where X ij are exorts (imorts = - X ij ) of good (i) by country J. In order to derive the equation of the world trade balance and its terms of trade, rewrite the otimal consumtion demand for good 1 (38), using the definition of exorts in equation (61), and using (9), (13), (14), (39), to give the exenditure exressions : P 1 Q 1J = P 1 (Y 1J X 1J ) = α J (P 1 Y 1J + P 2 Y 2J ) P 1 X 1J = (1 α J ) P 1 Y 1J α J P 2 Y 2J. (62) In real (goods) terms - exorts er caita, x 1J = X 1J /L J - (62) becomes, cf. (18), (4), x 1J = X 1J /L J = (1 α J ) λ L1J y 1J α J λ L 2J y 2J, J =, (63) Let v, v reresent the country shares of world labour force (oulation), i.e., v = L /(L + L ), v + v = 1. (64) Lemma 1. For two free trading economies, with CD utility functions (36) and regular sector technologies (roduction functions), y ij, i=1,2, J=,, the international equilibrium terms of trade, = P 1 /P 2, (60), satisfies the condition: = υ α λ L2 y 2 + υ α λ L2 y 2 υ (1 α ) λ L1 y 1 + υ (1 α ) λ L1 y 1 = y 2 y 1 υ α λ L2 + υ α λ L2 (y 2/y 2) υ (1 α ) λ L1 + υ (1 α ) λ L1 (y 1 /y 1 ) (65) 16

17 and with the same sector technologies, y i = y i = y i, (i = 1, 2), in and : = y 2 y 1 υ α λ L2 + υ α λ L2 υ (1 α ) λ L1 + υ (1 α ) λ L1 (66) Proof. Inserting (63-64) in (61) gives world maret equilibrium condition (65). 3.2 Comutation of the endogenous terms of trade The ratios of sectoral labour roductivities between countries become by (26): D i = y i y i γ i γ 1 γ i γ 1 = D i ] ai γ 2 ] ai γ 2 where ā, ā, were given in (23). a 1 a 2 ( )( ) ] ai a i 1 a i ] ai a i 1 a i ], i = 1, 2 (67) a i ā ] a i > 0, i = 1, 2 (68) a ā ] 2 a 1 With (67-68), (27), (29), and (60), we have exressions to turn world maret equilibrium condition (65) into formulas for the terms of trade () exressed in its fundamental determinants : arameters of technology and reference and the exogenous factor endowments, (, ). Inserting (67-68), (27), (29): λ L2J = 1 λ L1J, into (65), we get : ] ( )( ) a υ (1 α ) (1 a 2 ) λ L1 υ α (1 a 1 ) (1 λ L1 ) 1 a 2 = ] (69) υ α (1 a 1 ) D 2 (1 λ L1 ) (1 α )(1 a 2 ) D 1 λ L1 This is an imlicit function for the terms of trade () in the factor endowments and : Ω(,, ) = 0, as the labour allocation fractions, λ L1, λ L1, in (69) also - with common rices (60) - include (,, ). Hence by (69), (29), (60), and after several maniulations, we can give the exression for the imlicit function Ω (,, ) in, Theorem 1. For (2x2x2) models of trading economies with CD sector technologies, (18), CD utility functions, (36), the international equilibrium terms of trade (relative rice), = P 1 /P 2, (2), is an imlicit function of the factor endowments, (, ) : Ω (,, ) = 0 - with solutions, (roots = > 0), given by the equation (locus) : 17

18 with : ] 1 a 1 a 2 1 γ a 2 2 a 1 υ α (1 a 1) + (1 α ) (1 a 2)] (1) a 2 (1 a 1 ) ā γ 1 a 1 a 2 a1 (1 a 2 ) υ (1 a 1 ) (1 a 2 ) a 2 (1 a 1 ) (1 a 1) α + (1 a 2 ) 1 α ] (2) D 2 D 1 ] 1 a 1 a 2 1 a 2 1 γ a 2 2 a 1 1 α + υ + 1 a ] 1 α (3) 1 a 1 a 2 ā γ 1 D 1 1 a 2 D 2 a 1 a 2 υ a 2 (1 a 1 ) α a 1 + (1 α ) a 2 ] = Ω (,, ) = 0 (70) 1 a 2 a 1 a 1 a 2 (1) a = 1 a 2, (2) (a = 1 a 2 )(a 1 a 2), (3) = a 1 (1 a 2 ) a 2 (1 a 1 ) (a 1 a 2 )(a 1 a 2 ) and where, (ā, ā ), were given by, (23), and, (D 1, D 2 ), by (68). Proosition 1. asic World Trade Model - The imlicit function, Ω(,, ) = 0, (70), becomes an exlicit analytic terms of trade function (surface), = Φ(, ), if the CD sector technologies, (18), in both countries have arameter restrictions, cf. (23), (49) : a i = a i = a i, i = 1, 2 : ā = ā = ā (71) ] 1 ] 1 = Φ(, ) = 1 γ a γ υ 2 2 a 1 γ a γ 1 1 β ] + υ 2 2 a 1 γ 1 1 β ] (72) ā γ υ β + υ β where : ā aa 1 1 (1 a 1 ) 1 a 1 a a 2 2 (1 a 2 ) 1 a ; γ 2 γ2 γ 2 ] a1 γ1 γ 1 ] a2 ] 1 (73) β J α J a 1 + (1 α J ) a 2, J =, (74) and factor endowments, (, ), satisfy diversification conditions in Proosition 2 below that imose relevant restrictions (intervals) for the the factor endowment ratios, ( / ). Proof. With, a i = a i = a i by (71), we get in (70): (1) = (3) = 1 a 1 a 2, i.e. a common rice exonent, and (2) = 0 = 1. y (71), the last two comonents of D i, (68) and D 1,D 2 in (70)], dros out. Hence (71) imlies a drastic simlification of (70), which with further comilations, cf. (73-74), become the exlicit relative rice function (72). The equilibrium value of the terms of trade (72) is ositive, since β J, (74), is less than one for any 0 < a i < 1 and 0 < α J < 1, which is sufficient for a ositive in (72), (when feasible exist, cf. Proosition 2.) In comarison to the general imlicit solution,, (70), in Theorem 1, solution,, (72) in Proosition 1 has the advantage to be in closed form, and yet encomass some degree of heterogeneity ( γ), (73), in the sector technologies across the trading countries. 18

19 The international terms of trade exression,, (72) - illustrated geometrically as surfaces (contours) in Figures 4a-4b - deends as a GE solution on four sets of Determinants: 1. Factor endowment ratios (exogenous variables), 2. ll sectoral technology arameters, 3. ll consumer reference arameters, 4. Relative country sizes (arameters). Figure 4 a. Terms of trade surface: = Φ(, ), (76), Case 1: a 1 = 0.25, a 2 = 0.5, with: ā = , γ 1 = 2, γ 2 = 2.6, α = 0.4, α = 0.8, υ J = 0.5, β = 0.4, β = 0.3, ] = Φ(, ) = 1 a2 a γ 2 υ (1 β ) +υ (1 β ) 1 ā γ 1 υ β +υ β = ] 0.25 * Figure 4 b. Terms of trade surface: = Φ(, ), (76), Case 2: a 1 = 0.50, a 2 = 0.25, with: ā = , γ 1 = 2, γ 2 = 2.6, α = 0.4, α = 0.8, υ J = 0.5, β = 0.35, β = 0.45, ] = Φ(, ) = 1 a2 a γ 2 υ (1 β ) +υ (1 β ) 1 ā γ 1 υ β +υ β = / ] 0.25 *

20 w J ω 1 = ω 1 ψ ψ ω 2 = ω2 ω ( ) * ω * ω ω ( ) J * * * ** ** ( ) ( ) 1 2 J Figure 5. Relative commodity rices, J (ω J ), (22), cf. cases in Figure 1, Walrasian autary equilibria, J = Ψ J (ω J ), (43), autary relative factor rices, ω J ( J ), (44), autary relative commodity rices, J ( J ), (48), size of terms of trade, = Φ(, ), (72), and the diversification cone boundaries, J, J, by inserting solution (72) into (32), (33). straightforward Corollary of Proosition 1 gives a ersective on simle submodels. Corollary 1. If CD sector technology arameters ( total factor roductivity ), γ ij, (18), γ i = γ i = γ i, i = 1, 2 : γ = 1 (75) are also the same in both countries, then (72) becomes : = = Φ(, ) = 1 ] a2 a γ 2 υ (1 β ) + υ (1 β ) 1 (76) ā γ 1 υ β + υ β i.e, the terms of trade solution ( ) with same CD sector technologies in both countries. With the same tastes, CD references, utility functions, cf. (36), and (74), the terms of trade (76) becomes : β = β = β α a 1 + (1 α) a 2 (77) = = Φ(, ) = 1 γ 2 ā γ 1 1 β β (υ + υ )] a2 a 1 (78) With the same size of two countries, υ = υ = 1, then (78) gives a HOS model solution: 2 = = Φ(, ) = 1 ] a2 a γ 2 1 β 1 ā γ 1 2 β ( + ) (79) 20

21 Finally, with the same factor endowments ratios, J = =, then (79) becomes : = = Φ( J ) = 1 γ 2 ā γ 1 ] a2 a 1 β 1 J (80) β i.e., the secial Walrasian (general) equilibrium relative rice ratio in autary, (46). 3.3 Existence of international general equilibrium solutions Proosition 2. Existence of international GE solutions to asic Trade Model. The solution (72) of the (2x2x2) model exists economically as a feasible GE solution, when the factor endowments, (, ), satisfy the GE diversification cone conditions : (84-92) - exressed, cf. (54-55), in terms of the comosite arameters: ( γ), (73); ( γ), (50); (ã), (52), together with the comosite arameters, ( ϑ), ( ϑ), ( ϑ), defined by, ϑ = υ υ 1 α α 1 a 2 1 a 1 (81) ϑ = υ (1 β ) a 2 γ υ α (a 1 a 2 ) + υ β (1 a 2 ) (82) ϑ = γ υ β (1 a 1 ) υ (1 α ) (a 1 a 2 ) γ υ (1 β ) a 1 (83) When a 1 > a 2, the restrictions (intervals) uon the ratio, ( / ) are given by: ϑ γ, γ ] = a 1 > a 2 : If γ < ϑ, then (84) υ (1 β ) a 2 γ1 /γ 2 γ υ (a 1 a 2 ) α + υ β (1 a 2 ) γ 1 /γ 2 ] 1, γ1 /γ 2 γ 1 /γ 2 ] 1 ] a 1 > a 2 : If γ > ϑ, then (86) ] 1 ] 1 ] ϑ γ υ β (1 a 1 ) υ (1 α ) (a 1 a 2 ) γ1 /γ a 2 2 a 1 γ1 /γ a 2 2 a 1 γ, γ]=, (87) γ υ (1 β ) a 1 γ 1 /γ 2 γ 1 /γ 2 (85) a 1 > a 2 : If γ = ϑ, then = ϑ γ = ϑ γ = ã γ = a 2/(1 a 2 ) a 1 /(1 a 1 ) γ1 /γ 2 γ 1 /γ 2 When a 1 < a 2, the restrictions (intervals) uon the ratio, ( / ) are given by: ] 1 (88) γ, ϑ γ ] = γ1/γ 2 γ 1 /γ 2 a 1 < a 2 : If γ < ϑ, then (89) ] 1, υ (1 β ) a 2 γ υ (a 1 a 2 ) α + υ β (1 a 2 ) γ1 /γ 2 γ 1 /γ 2 ] 1 ] (90) 21

22 a 1 < a 2 : If γ > ϑ, then (91) ] 1 ] 1 ] γ, ϑ γ1/γ a 2 2 a 1 γ υ β (1 a 1 ) υ (1 α ) (a 1 a 2 ) γ1 /γ a 2 2 a 1 γ]=, γ 1 /γ 2 γ υ (1 β ) a 1 γ 1 /γ 2 (92) a 1 < a 2 : If γ = ϑ, then = ϑ γ = ϑ γ = ã γ = a ] 1 2/(1 a 2 ) γ1 /γ a 2 2 a 1 (93) a 1 /(1 a 1 ) γ 1 /γ 2 Proof. See endix. Note that in contrast to conditions (54-55), reference arameters and country sizes aear in (81-83), and hence also aear in GE diversification intervals (84-92) for the endowment ratio ( / ), (sufficient conditions, to ensure with diversification exists). Corollary 2. The GE diversification cone restrictions (intervals) for factor endowment ratios ( / ) corresonding to Corollary 1, ssumtion, (75), are given by, cf. (84-92) : a 1 > a 2 : If 1 < ϑ, then υ (1 β ) a ] 2 υ (a 1 a 2 ) α + υ β (1 a 2 ), 1 a 1 > a 2 : If 1 > ϑ, then υ β (1 a 1 ) υ (1 α ) (a 1 a 2 ) ], 1 υ (1 β ) a 1 a 1 < a 2 : If 1 < ϑ, then a 1 < a 2 : If 1 > ϑ, then 1, υ (1 β ) a 2 υ (a 1 a 2 ) α + υ β (1 a 2 ) 1, υ β (1 a 1 ) υ (1 α ) (a 1 a 2 ) ] υ (1 β ) a 1 The two cases in Fig. 4a-4b have GE endowment ratio intervals, cf. (81-83), (97), (95), Case 1 : a 1 = 0.25, a 2 = 0.5; a 1 < a 2 : 1 > ϑ = 1/3 ; 1 < = ϑ (98) Case 2 : a 1 = 0.5, a 2 = 0.25; a 1 > a 2 : 1 > ϑ = 3/4 ; ] (94) (95) (96) (97) ϑ = < 1 (99) which are smaller than the corresonding autary endowment ratio intervals in (59-58). The analysis of the effects on factor rices of free international trade in a few goods by Samuelson (1948,1949) was suosedly extended to any number of goods and factors in general equilibrium, by a succinct summary of the Walrasian statical model of general equilibrium in its cometitive asects, Samuelson ( ,.1). However, it mostly deals with the interrelations between the factor rices and commodity rices of Pareto efficient (cometitive) resource allocations mainly belonging to roduction sector equilibria. ut interrelations between localisation (countries) and international trade are only addressed by giving formal equation systems, Samuelson ( ,.13). No existence roof of an international general equilibrium is rovided - as in Proositions

23 4 International Free Trade Models and Results The international trade models of Proositions 1-2 with solution : = Φ(, ), (72) allow for countries differing in sizes, endowments, technologies and references. They constitute a comrehensive framewor for seeing how these elements affect the existence and the quantitative asects of a world trade equilibrium. Moreover, if countries have the same size, v J = 0.5, they may be considered as the unified model of traditional trade models with two roduction factors. ll well-nown models can be obtained as secial cases of the asic Model of Proositions with six submodels reorted in Table 1. The table indicates by (x) asects, which differ across countries. For examle, international differences in technologies are seen in Ricardian models (Model I). This Table 1 also give information about arameters that are assumed identical internationally. In model V (HOS), for instance, these are technology and reference arameters. Table 1. Models in trade theory as submodels of the asic Model : Proositions 1-2. Models Technology Endowments Preferences I Ricardo x II Mill x III Marshall x x IV Hecscher-Ohlin (HO) x x V Hecscher-Ohlin-Samuelson (HOS) x VI Hecscher-Ohlin-Linder (HOL) x x VII asic Model x x x 4.1 International terms of trade with diversification For each model, the exlicit exression of the international terms of trade can be easily obtained from equation (72). Table 2 resents the exlicit analytic exressions of the terms of trade ( ) for the six models under the general assumtion that countries also differ in size, v J. The simler formulas for same country size follow immediately by using υ J = 0.5. Comlying with (84-97), all terms of trade values ( ) from Table 2 lie between the relative autary general equilibrium rices (45); see,, and in Tables

24 Table 2. Terms of trade (72) from the asic Model of trade theory in Proosition 1. I Ricardo = 1 ] 1 β ā β ] 1 ] 1 γ γ υ 2 γ γ 1 + υ 2 γ 1 γ υ + υ γ 2 γ 1 II Mill = 1 ā III Marshall = 1 ā υ 1 β ] + υ 1 β ] υ β + υ β ] a2 a 1 ] 1 ] 1 γ γ υ 2 γ γ 1 1 β ] + υ 2 γ 1 1 β ] γ υ β + υ β IV HO = 1 ] 1 β ā β ] 1 ] 1 γ γ υ 2 γ γ 1 + υ 2 γ 1 γ υ + υ V HOS = 1 ā VI HOL = 1 ā γ 2 1 β γ 1 β γ 2 γ 1 VII asic Model = 1 ā ] a2 a 1 υ + υ ] υ 1 β ] + υ 1 β ] υ β + υ β ] 1 ] 1 γ a γ υ 2 2 a 1 γ γ 1 1 β ] + υ 2 γ 1 γ υ β + υ β ] a2 a 1 1 β ] HO=Hecscher-Ohlin, HOS=Hecscher-Ohlin-Samuelson, HOL=Hecscher-Ohlin-Linder 4.2 Factor rice equalization The asic Model of international trade allows an exact analysis of the conditions under which factor rice equalization occurs. We distinguish between cases when both countries are diversified - their exogenous endowment ratios (, ) belong to the intervals (84-92) of Proosition 2 - and some cases with inciient secialization in the two countries. Without secialization, both countries roduce two goods and equalization of free trade commodity rices (unit costs), (22), gives their factor rice ratio: ω J ( ) by (24). Corollary 3. With incomlete secialization in both countries (84-92), factor rice equalization occurs only and always, when CD technologies are internationally identical. Hence FPE diversification intervals for the factor endowment ratios, ( / ), must here be restricted to the closed intervals (94-97) of Corollary 2. FPE imlies : i ( ) = i ( ). 24

25 Proof. Simly observe that relative factor rices (24) with J = solely deends on technology arameters - only if they are identical in the two countries are : ω = ω. Thus, the wage-rental ratios (ω, ω ) are equal - FPE - in the international general equilibrium solutions of the Mill, HOS, HOL, trade models, cf. Table 3,5, irresective of different consumer references and different endowments (but satisfying Corollary 2). 4.3 World General Equilibrium llocations and Net Exorts Using the analytical framewor of both autary and world trade models, we show - in Tables 3-6, for autary and free international trade ] - the general equilibrium (GE) solutions of selected endogenous variables : (43), (48) autary], and : (24), (25), (29-30), (63) governed by the world maret terms of trade: J = = Φ(, ), (72) ]. In Tables 3-6, we have always chosen : a 1 = 0.50 > a 2 = 0.25, cf. Case 2, Fig. (1,4b,5). In Tables 3-5, the relative rice intervals (49) are the same, being unaffected by (α, α ). First it is shown that references (the demand-side of the economy) are as imortant in affecting sectoral factor allocations and the trade atterns, (trade flows, net-exort) as the suly-side is. Thus Table 3 gives numerical examles about the roles of tastes in Table 3. Selected GE solutions of the extended Mill trade model - Table 2. Parameters and Endowments : J 0.5 ; a ; a ; 1 2 ; ; J 2 PRICE INTERVL : (49) UTRKY : (44), (45) INTERNTIONL EQUILIRIUM : (72), (24), (25), (29-30), (63) L 1 L 1 K 1 K 1 x shaing the trade atterns and the size of net exorts. The two columns from left contain the size of the reference arameters, α and α. Note that references need here to be different across nations, since there would be no trade otherwise (as seen in three rows). In the first two rows, consumers in country relatively dislie good 1 in comarison 25

26 to their counterarts in country (α < α ), while in rows 4-5 they refer good 1. For this reason, in rows 1-2, country is a net exorter of good 1, i.e. X 1 > 0 (last column), and a net imorter in rows 4-5. Evidently, the comarative cost (advantage) rincile for obtaining trade atterns by the general autary rule (47) changes this inequality relation with (48) in rows 4-5. Moreover, as the international ga in references rises, the traded quantities increase. s indicated by the terms of trade exression for the Mill s Model (Table 2, Model II), ( ) also deends on reference arameter α J via : β J = α J a 1 + (1 α J ) a 2, J =,, cf. (74). The higher α J (J =, ) are, the higher is here, (72), as an increase in α J is resonsible for a larger demand of good 1 on the world level. Note that the suly sides of the two economies are identical (γ 1 = γ 1 = γ 1, γ 2 = γ 2 = γ 2 ) in the Mill s model. Thus sectoral factor allocations in the two economies are in fact the same after trade, i.e. λ L1 = λ L1 and λ K1 = λ K1, Table 3 - demonstrating that international differences in consumers tastes can overwhelm the effect due to technology or endowments. Similar results for trade atterns and factor allocations are illustrated in Tables 4-6. Table 4 considers countries with differences in technologies and references. In this Marshall model (combining Ricardo and Mill), we have: γ 2 /γ 1 > γ 2 /γ 1, i.e., country is technologically relatively more efficient in good (sector) 2. Preferences are only identical in the boldface cases. ut once national consumers tastes start to diverge, trade atterns are affected even to the oint in which they are reversed. If consumers in country start referring good 1, trade atterns remain unchanged with increasing imorts of good 1. This is true, if references of country s consumers remain unchanged or dislie for good 1 increases in country. However, if consumers in country () sto referring (disliing) good 1, trade atterns may be reversed. Country becomes a net exorter of good 1. ut the comarative cost/rice rincile (47), (45), never fails. Let us briefly loo into the logic behind the results of HOS-HOL models in Table 5. Here trade atterns and factor allocations are determined by endowments and references. Countries have different factor endowments (country is more labour-abundant than country ), but are equied with the same technologies (γ i = γ i ). s sector/good 2 is more labour intensive than sector 1, country should tend to exort commodity 2. 26

27 Table 4. Selected GE solutions of the extended Marshall trade model - Table 2. Parameters and Endowments : J 0.5 ; a ; a ; ; ; ; ; J 2 PRICE INTERVL : (49) UTRKY : (44), (45) INTERNTIONL EQUILIRIUM : (72), (24), (25), (29-30), (63) L 1 L 1 K 1 K 1 x Table 5. Selected GE solutions of the extended HOS - HOL trade models - Table 2. Parameters and Endowments : J 0.5 ; a ; a ; 1 2 ; ; 1.8 ; 2.2 PRICE INTERVL : (49) UTRKY : (44), (45) INTERNTIONL EQUILIRIUM : (72), (24), (25), (29-30), (63) L1 L1 K1 K1 x ut such trade attern can again be reversed, if the dislie (reference) for good 1 by consumers in country (country ) is sufficiently high. Note again that comarative cost (rice) rincile (47), (45), never fails. Table 6 rovides some examles from HO trade models. In all cases, country is relatively labour abundant ( < ), and sector (good) 1 is caital intensive (a 1 > a 2 ). Under these assumtions, country should traditionally be exorter of good 2 (the labour-intensive commodity) and imorter of good 1 - as seen in all rows, excet one. Note that the interaction between the technological efficiency arameters (γ i, γ i ) of sectors in the two countries affects the size of net exorts of country and thus all other variables. If the relative technological efficiency, (γ 2 /γ 1 ), in country becomes very large (very favourable for good 2), as in row 2, Table 6, the comarative cost advantage 27