Pushing Economies (and Students) Outside the Factor Price Equalization Zone

Abstract

Despite overwhelming empirical evidence of the failure of factor price equalization, most teaching of international trade theory (even at the graduate level) assumes that economies are incompletely specialized and that factor price equalization holds. The behavior of trading economies in the absence of factor price equalization is not well understood, and some major textbook treatments err. The authors map regions of specialization and diversification for standard competitive economies and show how outputs, goods, and factor prices change as economies move within and across different regions of diversification and specialization. Two examples of how the analysis can enrich graduate-level trade teaching are given: the substitutability of goods trade and factor movements, and debates over the trade and inequality.

Keywords:

• factor price equalization
• integrated equilibrium
• teaching
• trade

JEL codes:

• A20
• F11
• F16

Paul Oslington is a professor of economics at Australian Catholic University and a visiting fellow in the Crawford School of Economics and Government, Australian National University, Sydney, Australia (e-mail: [email protected]). Isaac Towers is a lecturer in mathematics at the University of New South Wales/Australian Defence Force Academy, Australia. The authors thank seminar participants at the University of New South Wales, the Australian National University, and Princeton University and the anonymous referees for helpful comments.

Notes

1. A common approach in the trade literature is to construct McKenzie (1955) cones of diversification and argue that economies with endowment combinations inside the cones will be diversified, whereas those outside the cone will specialize. This is simple and sometimes useful, but will be misleading to the extent that goods prices change (as they will in a global economy when endowments or other parameters change), altering the position of the cones. This shortcoming was one of the reasons Dixit and Norman (1980) developed integrated equilibrium analysis.

2. In correspondence on this issue, Avinash Dixit and Victor Norman (1980) mentioned that their colleague Gene Grossman independently realized the error in the Dixit and Norman textbook (see Grossman 1990; and Grossman and Helpman 1991, 190). My letter to Avinash Dixit contained an error about the shape of one of the regions, and I thank him and Gene Grossman for pointing this out. Deardorff (1994, 169) included a diagram dividing the area outside the factor price equalization region into six regions, but drew linear boundaries that apply in the special case of fixed production coefficients. Courant and Deardorff (1992) considered the conceptually similar issue of lumpiness within countries, but with fixed goods prices.

3. For purposes of exposition, assume the starting point is above (i.e., where A has more labor) the junction of the diversification and extreme specialization regions.

4. The property of the standard model is that, at constant prices, an increase in the endowment of one factor increases the output of the industry that uses that factor relatively intensively and reduces the output of the other (or some other) industry (Deardorff 2006).

5. If the production technology had fixed coefficients, then the boundaries of the extreme specialization region would be straight-line extensions of the factor usage vectors that enclose the diversification region. However, for other technologies where factor proportions are influenced by the factor price changes that occur outside the factor price equalization region, the closure of the Y industry in A that brings us into the extreme specialization region will be delayed.

6. The boundary of the specialization and extreme specialization regions is the locus of L^A K^A obtained from solving Conditions 10–17 when setting Y^A = 0 in Conditions 13 and 14. Needless to say, it is an ugly expression even for the Cobb-Douglas case.

7. The other way of getting wage effects from trade is to vary the numbers of goods and factors, for instance, the three-factor-two-good model mentioned in the Extensions section and explored by a number of trade economists (e.g., Leamer 1995).