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«JEL Subject Classification: F11, F16 JEL Keywords: Specialisation, Integrated Equilibrium, Factor Price Equalisation, Inequality. *Correspondence to ...»

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Trade, Migration and Inequality in a

World without Factor Price Equalisation

Paul Oslington

Australian Catholic University


Isaac Towers

University of New South Wales

JEL Subject Classification: F11, F16

JEL Keywords: Specialisation, Integrated Equilibrium, Factor Price Equalisation, Inequality.

*Correspondence to Paul Oslington, Professor of Economics, Australian Catholic University,

7 Mount Street North Sydney, NSW 2060, Australia

Email: paul.oslington@acu.edu.au Telephone: 61 2 9739 2868 We thank seminar participants at University of New South Wales, Australian National University, and the International Economics Section at Princeton for helpful comments.


The behaviour of trading economies in the absence of factor price equalization is not well understood, although empirical evidence against factor price equalisation is overwhelming. We map regions of diversification and specialization for competitive world economies with different factor endowment partitions. Goods and factor price responses as economies move within and across different regions of specialisation are explored using a series of novel diagrams. The usefulness of endogenising patterns of specialisation is illustrated by considering the impact on inequality of migration flows (such as US-Mexico), the substitutability of trade and migration, and the impact of the entry of a large unskilled labour intensive economy (such as China) on factor prices and factor flows.

1) Introduction There have been many advances in the theory of international trade in recent years (surveyed for instance in Grossman and Rogoff (1995)), but most trade modelling and policy analysis still operates with fully diversified economies where factor price equalisation holds. This emphasis is problematic as empirical studies such as Davis and Weinstein (2001) and Schott (2003) and Debaere and Demiroglu (2003) suggest incomplete diversification and failure of factor price equalisation is the norm.

We know surprisingly little about the behaviour of trading economies in the absence of factor price equalisation, even for the simplest competitive models. Krugman (1995) in his survey comments that determining what happens outside the factor price equalisation region is a "fairly nasty business"(p1247), Dixit and Norman (1980 p113) that it is “very complicated”, and Deardorff (2001 p143) that we are “surprisingly ignorant”. Standard graduate texts such as Dixit and Norman (1980) and Bhagwati, Srinivasan and Panagariya (1998) err in their discussions of non-factor price equalisation cases. The recent text of Feenstra (2004 p22-5) offers brief comments on the complications involved.

Some work such as Wood (1994), Leamer (1995), Davis (1996) or Oslington (2002) considers specialised economies but imposes a particular pattern of specialisation rather than linking it to underlying endowment, technology, and taste parameters. An important paper which takes up the challenge of linking patterns of specialisation to underlying parameters is Leamer (1987) who considers a three-factor n-good model, showing how the range of products produced in different countries depends on their endowment ratios. While an extremely rich paper its usefulness for the problem considered here is limited by a fixed production coefficients technology, ruling out the changes in factor intensity that flow from the factor price changes which occur outside the factor price equalisation region. Another stand of the literature that endogenises patterns of production and trade is inframarginal economics (for instance Cheng, Sachs and Yang (2000), or Tombazos, Yang and Zhang (2005)) where interactions between technology, economies of scale and transaction costs generate different patterns.

The first aim of the paper is to map the regions of specialisation as for the standard competitive trade model, as no satisfactory account exists in the literature. To make the problem tractable we use Cobb-Douglas tastes and technology, and explore numerically the shapes of the regions of specialisation. For each region of specialisation we will then explore relationships between endowments, factor prices and goods prices for different trading worlds. The second aim is to clarify relationships between trade, migration and inequality outside the factor price region. For we interpret the factors of production as skilled and unskilled labour and consider migration due to factor price differentials. The third aim is to illustrate the usefulness of a world economy model with endogenous patterns of specialisation for debates about the relationship between inequality and migration flows (e.g. US-Mexico), the substitutability of trade and migration, and the impact of the entry of a large unskilled labour intensive economy (e.g. China) on factor prices and migration flows.

The paper is structured as follows. The first aim occupies sections 2 and 3, which are a series of novel diagrams showing regions of specialisation and factor prices in different regions. Sections 4 and 5 introduce the definitions of inequality and migration pressure in a non factor price equalisation world. Section 6, 7, 8, and 9 illustrate the model, meeting the third aim.

2) Integrated Equilibrium Analysis Our mapping of regions of specialisation builds on the technique of integrated equilibrium analysis developed by Dixit and Norman (1980 pp100-125), who took up Samuelson's (1949 pp194-195) parable of an angel splitting the world factor endowment between countries in different ways 1. Integrated equilibrium analysis allowed Dixit and Norman to cut through the previous debate on factor price equalisation by reframing it as a question of what joint restrictions on technology, preferences and factor endowments supported factor price equalisation 2. It has been fruitful in other ways: Deardorff (1994) further clarified the conditions for factor price equalisation; Helpman and Krugman (1985) and Kreickemeier and Some of the following draws on an unpublished paper on teaching integrated equilibrium analysis Oslington and Towers (2006).

A common approach in the literature is to construct cones of diversification, following McKenzie (1955) and argue that economies with endowments inside the cone will be diversified, while those outside the cone specialised. This is sometimes useful, but cones are drawn for particular goods prices, which are endogenous in a world economy model.

Nelson (2006) have extended it to consider trading worlds with imperfect competition; Davis (1998) called it a truly global approach when deriving some startling results about the consequences for different countries factor markets of factor accumulation in different parts of the world.

The simplest and most widely used model with two countries, two factors and two goods will be used, along with standard assumptions of perfect competition, concave constant returns to scale technology that is the same across the world, and identical homothetic preferences. It will be assumed that equilibrium factor proportions are unique, and degenerate combinations of technology, endowments and tastes which mean a good is produced nowhere in the world will be ruled out.

An equilibrium for a world not divided into countries (or equivalently with free movement of goods and factors between countries) is shown in figure 1 3. The dimensions of the box are the world endowment of the factors, unskilled labour L and skilled labour K 4. Equilibrium factor usage vectors for the two products X and Y are shown. X is relatively unskilled labour intensive.

Now consider splitting the world endowment of the factors between countries A and B in the proportions represented by V in figure 2. Since V is within the shaded parallelogram (the area enclosed by the factor usage vectors from figure 1) both countries produce both goods using the same factor proportions as the undivided world. Factor prices and goods prices will be identical to the undivided world. Since preferences are identical and homothetic individuals in the countries will consume the products in the same proportions as the undivided world, so the factor content of consumption in the two countries will be a point on the diagonal of the box such as C.

The factor content of trade will thus be the vector VC. This is the factor price equalisation case.

For splits of the endowment outside the shaded parallelogram in figure 2 such replication of the integrated equilibrium is not possible and factor price equalisation breaks down. This has been widely noted in the literature, but there is considerable uncertainty about what exactly happens.

Dixit and Norman comment "In order to be able to say what happens outside the factor price equalization region, we need more information concerning technology and demand functions" (p113) and that this can "make matters very complicated" (p113).

Equilibrium conditions are given in the appendix Capital can be thought of an intersectorally and internationally mobile third factor.

None of the discussions in the literature of what happens outside the factor price equalisation region are completely accurate. Dixit and Norman's textbook, an excellent and widely used reference, errs in suggesting that there are four regions of specialisation outside the factor price equalisation region 5 (see Dixit and Norman (1980) pp113-114 and especially figure 4.4). As will be shown below there are in fact six regions - they miss the possibility that both countries specialise completely in different goods. Bhagwati, Srinivasan and Panagariya (1998 87-90) repeat the error that there are four regions and miss the regions where both countries specialise.

There seems to be no satisfactory account in the literature of what happens outside the factor price equalisation region.

3) What Happens Outside the Factor Price Equalisation Region?

As suggested by Dixit and Norman (1980 p113) the analysis outside the factor price equalisation region is “very complicated” and we will follow their approach of numerical simulation with a particular production technology to map the regions. The case illustrated has Cobb-Douglas production and utility functions, production share of K in X α =.45, share of K in Y β =.55, and consumption share σY =.5, but we have experimented with a range of parameter values 6.

The six regions of specialisation and diversification are shown in Figure 3 7. The regions are best explained by tracing how a trading world switches between equilibria as endowments change. Begin with an endowment split in the diversification region marked +.

Give country B more skill and country A correspondingly less, so that we move through the region from + in the direction of the arrow. In country B, factor and goods prices do not change and the output of the labour intensive good X will fall, and Y rise following the Rybczynski In correspondence on this issue Avinash Dixit mentioned that his colleague Gene Grossman independently realised the error in the Dixit and Norman text (see Grossman (1990), and Grossman and Helpman (1991) p190), as well as a related error in the earlier Helpman and Krugman book. My letter to Avinash Dixit contained an error about the shape of one the regions and I thank him and Gene Grossman for pointing this out. Deardorff (1994 p169) includes a diagram that divides the area outside the factor price equalisation region into six regions, but draws linear boundaries for the special case of fixed production coefficients.

The figures have been generated using Matlab, after some initial experimentation with Mathematica.

Equilibrium conditions for the different regions are given in the appendix.

Theorem. Eventually the output of X in country B will fall to zero at the boundary of the diversification and specialization regions. Further increases in the endowment of skill in country B will make it impossible for B to fully employ its endowment of both factors producing both products at the integrated equilibrium factor proportions. There is not enough labour to absorb all country B’s skill, and to maintain full employment in B production of the labour intensive good X must cease and Y alone be produced in B. The reverse effects will occur in country A, and production of Y in A ceases.

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