Then the relationship between changes in log wages w and profits log r depends on changes in the log price p of necessities and on the shares of capital in the production of luxuries and necessities according to:
This means that the change in the wages of workers as a function of the change in the prices of necessities will be:
The real incomes of wage-earners depend not just on what happens to wages but what happens to the prices of things they buy, and so if a share ?w of their income is spent on necessities:
And here's the catch. The necessities-share ?w of wage-earners has to be less than one, but the change in log wages is greater than the change in log prices. So wage earners' real income goes in the same direction as necessities prices--no matter how fast the prices of necessities are falling:
When Broda and Romalis assert that trade is causing the prices of tradeable necessities to fall rapidly, they are either (a) breaking the H-O framework in some way, or (b) implicitly asserting that capital is the scarce factor in the United States and thus the factor of production whose returns are reduced by globalization.
It is not clear to me how they propose to break the H-O framework. And I do not find (b) plausible.
I prefer http://www.j-bradford-delong.net/2008_pdf/20080530_stolper to break the H-O framework in a Smithian division-of-labor direction: asserting that the scarce factors that lose from trade are organizational and technological expertise and that there is substantial implicit and explicit cross-ownership of factors that together make trade nearly win-win. But I don't see Broda and Romalis going there...
