Gottfried Haberler s Principle of Comparative Advantage

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1 Gottfried Haberler s rincile of Comarative dvantage Murray C. Kem a* and Masayuki Okawa b a Macquarie University b Ritsumeiken University bstract Like the Torrens-Ricardo rincile of Comarative dvantage, Haberler s rincile rests on the imlicit assumtion that, in autarchic equilibrium, each country roduces and consumes all commodities, at least inciiently. ithout that assumtion, both rinciles must be substantially qualified. In the resent aer, which focuses on Haberler s rincile, the required qualifications are rovided in detail. JL Classification: D6, 1, 13 Keywords: Comarative advantage, Gottfried Haberler 1. Introduction Breaking away from Classical one-factor models of international trade, Gottfried Haberler (193, esecially Section 3) noted the necessity of working henceforth with nonlinear roduction frontiers. He also noted that the relative oortunity costs of roducing autarchic equilibrium quantities determine both the direction of free international trade and the manner in which the gains from trade are shared by the trading countries. Thus, in a single article, Haberler freed both descritive and normative trade theory from more than a century of Classical inhibitions. In articular, he transformed the linear Torrens-Ricardo rincile of Comarative dvantage into a more general rincile that accommodates non-linear roduction frontiers. Like the Torrens-Ricardo rincile, however, Haberler s rincile rests on the imlicit assumtion that, in autarchic equilibrium, each country roduces and consumes all commodities, at least inciiently. ithout that assumtion, both rinciles must be substantially qualified. In a comanion aer (Kem and Okawa, 26), the necessary qualifications have been attached to the Torrens-Ricardo rincile. In the resent aer, a similar service is * Contact author: Murray C. Kem, Deartment of conomics, Division of conomic and inancial Studies, Macquarie University, Sydney, NS 219, ustralia. Tel: +61 (2) mail: mkem@efs.mq.edu.au.

2 2 Murray C. Kem and Masayuki Okawa sia-acific Journal of ccounting & conomics 13 (26) 1 9 erformed for Haberler s rincile. or the most art, this aer follows Haberler in focussing on just two countries, each otentially roducing the same air of commodities by means of two rimary factors of roduction; however, the many-commodities case is briefly considered. Neither the rimary factors nor the technologies need be the same for each country, but it will be convenient to retend that the same rimary factors are available everywhere. 2. nalysis In both ngland and ortugal, cloth and wine are non-jointly roduced by labour and land under constant returns to scale, with one commodity (not necessarily the same in each country) relatively labour-intensive at all wage:rental ratios. In each country and in each industry, both factors are essential to roduction. or the time being it will be assumed that, in autarchic equilibrium, roduction and therefore consumtion is comletely secialized in each country on a country-secific commodity; for concreteness only, it will be assumed that, in autarchic equilibrium, ngland roduces and consumes cloth only while ortugal roduces and consumes wine only. inally, throughout our analysis, the references of each country are those of a rice taking reresentative agent. 1 On the other hand, no secial restrictions are laced on the utility functions of the two reresentative agents; secifically, they are not necessarily homothetic, nor need they rule out inferiority. In igure 1(a), Q Q is the nglish roduction frontier and U C is a single nglish indifference curve. The nglish autarchic equilibrium occurs at oint C. t that oint, the nglish marginal rate of transformation (MRT ) might differ from the nglish marginal rate of substitution (MRS ). If MRT = MRS then the market-clearing rice ratio is equal to MRS ; otherwise, the equilibrium rice ratio can be anywhere in the continuum bounded by MRT and MRS. e shall refer to the cone defined by (MRT, MRS ) as the nglish autarchic rice cone, not excluding the extreme case in which MRT = MRS. igure 1(a): ngland s utarchic quilibrium, with Comlete Secialization ine Q MRT MRS U Q ' C Cloth 1 This reresentation can be justified by the further assumtion that all households are identical in all resects but are unaware of the fact or by introducing a family of ost-comensation Scitovsky indifference curves.

3 Murray C. Kem and Masayuki Okawa sia-acific Journal of ccounting & conomics 13 (26) igure 1(b): ortugal s utarchic quilibrium, with Comlete Secialization ine Q C U MRS MRT Q ' Cloth Similarly, the ortuguese autarchic equilibrium is reresented in igure 1(b) by oint C, where the ortuguese marginal rate of transformation (MRT ) might differ from the ortuguese marginal rate of substitution (MRS )and where the market-clearing rice ratio must lie in the ortuguese autarchic rice cone (MRT, MRS ) not excluding the extreme case in which MRT = MRS. bandoning the assumtion of autarchy, we may consider for each country all conceivable world rice ratios; and for each rice ratio we may consider the rofit-maximizing air of oututs and the utility-maximizing consumtion air of the rice-taking reresentative agent. rom that information the nglish and ortuguese offer curves can be derived. It is aarent that, for all hyothetical rice ratios in a country s autarchic rice cone, roduction and consumtion remain secialized at the autarchic level for that country. If and only if MRT j MRS country j s offer curve has a kink at the origin as dislayed j in igures 2(a) and 2(b) for j = and j =, resectively. igure 2(a): ngland s Offer Curve, with Comlete utarchic Secialization nglish Demand for ine ' MRS MRT nglish Offer of Cloth

4 4 Murray C. Kem and Masayuki Okawa sia-acific Journal of ccounting & conomics 13 (26) 1 9 igure 2(b): ortugal s Offer Curve, with Comlete utarchic Secialization ortuguese Offer of ine MRT MRS ' ortuguese Demand for Cloth e can now move forward to consider the central questions of the aer. Suose first that the two autarchic rice cones have no oints in common. Rotating the ortuguese offer curve through 18 and then suerimosing it on igure 2(a), we obtain igure 3(a) or igure 3(b), deending on the relative ositions of the rice cones. In each figure the world equilibrium is reresented by oint, where the world excess demands for cloth and wine are equated to zero by the unique rice ratio O. Close scrutiny of the two arts of igure 3 reveals that they differ in an imortant detail: in igure 3(a), the equilibrium rice ratio lies within the close embrace of the two autarchic marginal rates of transformation whereas, in igure 3(b), it lies within the close embrace of the two autarchic marginal rates of substitution. On the other hand, each art of igure 3 brings the same glad tidings: In site of kinks in their offer curves, each country benefits from free international trade. 2 2 igures 3(a) and 3(b) are drawn on the assumtion that MRT j MRS, j =,. If that assumtion is ut j aside, we return to the familiar textbook case in which the offer curves are free of kinks so that if only MRT MRT, trade and gains from trade are assured.

5 Murray C. Kem and Masayuki Okawa sia-acific Journal of ccounting & conomics 13 (26) igure 3: The Trading quilibrium, with Comlete utarchic Secialization and Non-intersecting rice Cones (a) nglish Demand for ine ortuguese Offer of ine ' MRS MRT MRT MRS nglish Offer of Cloth ortuguese Demand for Cloth (b) nglish Demand for ine ortuguese Offer of ine MRT MRS MRS MRT nglish Offer of Cloth ortuguese Demand for Cloth Suose alternatively that the two autarchic rice cones intersect. Then, instead of igure 3(a) or 3(b), we obtain igure 4(a) or 4(b), deending on the relative ositions of the two (intersecting) cones. In each case, equilibrium world trade is zero; hence neither country benefits from free trade.

6 6 Murray C. Kem and Masayuki Okawa sia-acific Journal of ccounting & conomics 13 (26) 1 9 igure 4: The Trading quilibrium, with Comlete utarchic Secialization and Intersecting rice Cones (a) nglish Demand for ine ortuguese Offer of ine MRS MRT MRT MRS nglish Offer of Cloth ortuguese Demand for Cloth (b) nglish Demand for ine ortuguese Offer of ine MRT MRS MRS MRT nglish Offer of Cloth ortuguese Demand for Cloth roosition: Suose that under autarchy each country secializes in the roduction and consumtion of a different commodity. If and only if the two autarchic rice cones have no oints in common, free trade is beneficial to each country; moreover, each country exorts the commodity in the roduction of which it is relatively more efficient under autarchy. If the cones intersect, equilibrium world trade is zero. In deriving the roosition it was convenient to focus on the case in which, under autarchy, each country secializes in the roduction and consumtion of a articular country-secific commodity. However, the roosition is valid without that assumtion;

7 Murray C. Kem and Masayuki Okawa sia-acific Journal of ccounting & conomics 13 (26) that is, it is valid even if, under autarchy, the two countries secialize in roducing and consuming the same commodity and even if, under autarchy, only one country secializes. Thus we may confidently conclude that Haberler s rincile of Comarative dvantage survives if and only if the two autarchic rice cones are discrete, with no oints in common. In this section we have followed Haberler in focussing on the familiar two-country, two-commodity case. e now turn our attention to more amle world economies with more than two member countries. 3. More Than Two Countries Suose that ngland and ortugal are joined by rance, each country caable of roducing cloth and wine but under autarchy comletely secializing in the roduction and consumtion of cloth and therefore ossessing its own autarchic rice cone. Three cases will be considered in detail: [1] No two of the autarchic rice cones intersect. [2] Two of the autarchic rice cones intersect. [3] ach autarchic rice cone intersects at least one of the other cones. Case [1] This case is illustrated by igure 5. It is not difficult to see that any equilibrium world rice ratio must lie in the cone (MRT, MRS ), which we will call the world rice cone, for any other rice ratio would fail to induce a ositive net suly of each commodity. igure 5: Non-Intersecting utarchic rice Cones orld rice Cone C C C / MRT MRT MRS MRS MRT MRS C Suose next that the equilibrium world rice ratio lies in the sub-cone (MRT, MRS). t that rice ngland imorts cloth from ortugal and rance in exchange for wine; there is no trade between ortugal and rance. Similarly, if the equilibrium world rice ratio lies in the sub-cone (MRS, MRT ), rance imorts wine from ngland and ortugal in exchange for its exorts of cloth; there is no trade between ngland and ortugal. In each sub-case all three countries gain from trade. So far, there are no surrises. If, however, the equilibrium world rice ratio lies in the remaining sub-cone (MRT, MRS ), the outcome is quite different. or that sub-cone coincides with ortugal s autarchic rice cone, imlying that, in the world equilibrium, ortugal does not trade. ngland and rance, on the other hand, trade in nglish wine and rench cloth. Thus, although the three autarchic rice cones have no oints in common, only two countries gain from trade. vidently our roosition needs modification to accommodate an additional country.

8 8 Murray C. Kem and Masayuki Okawa sia-acific Journal of ccounting & conomics 13 (26) 1 9 Case [2] This case is illustrated by igure 6, in which the autarchic rice cones of ortugal and rance intersect. ny equilibrium world rice ratio must lie in the new world rice cone (MRS, MRT). If the equilibrium rice ratio falls in the sub-cone (MRS, MRT), ngland exorts wine to ortugal and rance in exchange for cloth. ortugal and rance do not trade with each other. ll countries gain from trade. If, on the other hand, the equilibrium world rice ratio lies in the sub-cone (MRS, MRS ) and therefore in ortugal s autarchic rice cone, ortugal does not trade with ngland or rance. The latter trade with each other in nglish wine and rench cloth, to the advantage of each country. igure 6: Two utarchic rice Cones Intersect orld rice Cone C MRT MRS MRT C C / MRS MRT MRS C Thus in cases [1] and [2], we encounter essentially the same list of ossible outcomes. No new ossibilities are created by Case [2] s limited intersection of autarchic rice cones. Case [3] This case is illustrated by igures 7(a) and 7(b). In igure 7(a), the nglish and rench autarchic rice cones intersect the ortuguese cone but do not intersect each other; in igure 7(b) the three autarchic rice cones have a common intersection that coincides with the rench cone. In the sub-case deicted in igure 7(a), any equilibrium world rice ratio must lie in the world rice cone (MRT, MRS ); any other rice ratio can be ruled out because no two countries would trade on oosite sides of the market. Since any equilibrium rice ratio lies in ortugal s autarchic rice cone, ortugal does not trade. ngland exorts wine to rance in exchange for cloth, to the benefit of each country. igure 7(a): Multile Intersections of utarchic rice Cones orld rice Cone C MRT MRS MRT C / C MRT MRS MRS C igure 7(b): Multile Intersections of utarchic rice Cones with No orld rice Cone C C MRT MRT MRT MRS MRS C / MRS C

9 Murray C. Kem and Masayuki Okawa sia-acific Journal of ccounting & conomics 13 (26) In the sub-case deicted in igure 7(b), on the other hand, there is no ossibility of trade. t each imaginable rice ratio, either no country wishes to trade or those countries willing to trade are all on the same side of the market. Summarizing, in a world of three countries with non-intersecting autarchic rice cones, the oening of trade might benefit all countries or it might benefit only the extreme countries, that is, those countries with autarchic rice cones in terms of the largest and smallest marginal rates of substitution and transformation. This remains true if some but not all of the autarchic rice cones intersect. Only if the three autarchic rice cones have a common intersection is all trade ruled out, as in our roosition. In each of our three cases, it has been assumed that under autarchy all countries secialize in cloth roduction. However, that assumtion does not rule out mutually rofitable trade. In fact, all of our conclusions can be derived without that assumtion. References Haberler, G., 193, Die Theorie der komarativen Kosten und ihre uswertung für die Begründung des reihandels, eltwirtschaftliches rchiv 32: 349 7; translated and rerinted as The Theory of Comarative Costs and its Use in the Defense of ree Trade in nthony Y.C. Koo (ed.), Selected ssays of Gottfried Haberler, Cambridge, M: MIT ress (1985): Kem, M.C. and M. Okawa, 26, The Torrens-Ricardo rincile of comarative advantage: an extension, Review of International conomics, 14: