The effect of changes in commodity prices on factor rewards is studied in the multi-commodity, multi-factor case. It is shown that the inverse of the distributive share matrix must satisfy the following restriction: it cannot be anti-symmetric in its sign pattern. This means that one cannot partition the commodities into two groups (I and II) and factors into two groups (A and B), such that all factors in group A benefit (nominally) from all commodity price increases in group I, and simultaneously all factors in group B suffer from all commodity price increases in group II. It turns out that this is also the only sign-pattern restriction imposed by the general nature of the relationship of commodity prices and factor rewards.
Mitra, T. (2008), "Chapter 7 On Commodity Prices and Factor Rewards: A Close Look at Sign Patterns", Marjit, S. and Yu, E.S.H. (Ed.) Contemporary and Emerging Issues in Trade Theory and Policy (Frontiers of Economics and Globalization, Vol. 4), Emerald Group Publishing Limited, Bingley, pp. 125-139. https://doi.org/10.1016/S1574-8715(08)04007-4
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