Abstract
We have shown in the text the crucial importance of the strong factor-intensity assumption (i.e., absence of factor-intensity reversals); here we examine formally the conditions under which reversals are present or absent. Let us begin by establishing the relationship between capital intensity and relative price of factors; for this purpose we employ the equilibrium conditions that state the equality between the value of marginal productivity of a factor and its price (this must be equal in both sectors).
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Notes
- 1.
- 2.
This is a term used by Deardoff (1982, p. 690) to denote a generalization (that he suggested) of the concept of covariance when one needs to correlate three variables symmetrically.
- 3.
The optimum conditions will give a differentiable mapping p = g(w), where p is the vector of commodity prices and w is the vector of factor prices. Global invertibility (or univalence) ensures that the inverse mapping \({\mathbf{w = g}}^{\mathbf{-1}}\mathbf{(p)}\) exists uniquely, namely a unique vector of factor prices corresponds to any vector of commodity prices exactly as a unique vector of commodity prices corresponds to any vector of factor prices; note that as we are considering global univalence, the conditions stated by the Gale-Nikaidô theorem must be satisfied.
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Gandolfo, G. (2014). Appendix to Chapter 4. In: International Trade Theory and Policy. Springer Texts in Business and Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37314-5_20
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