Here’s a letter to an e-mail correspondent:
23 May 2013
Mr. Denis D___
Dear Mr. D___:
Thanks for your e-mail explaining your “black hole theory of the minimum wage.”
A critical part of your theory, as I understand it (with help from the link you sent to a video of Sen. Elizabeth Warren  talking about wages and worker productivity), is that the minimum wage hasn’t risen by as much as has overall worker productivity. Supply and demand, therefore, presumably aren’t working for low-skilled workers.
Ms. Warren and you are correct that worker pay in the long run is determined by worker productivity. The productivity that’s relevant, however, is marginal productivity – namely, the value that ‘the last’ worker added to a class of production projects adds to the market value of the outputs of those projects. But not all workers and not all production projects are alike. The level of aggregation at which Ms. Warren and you conduct this conversation is meaningless for the point you wish to make. You confuse trends in overall worker productivity with that of the marginal productivity of low-skilled workers.
If, all other things unchanged, consumer demand for neurosurgeons rises relative to that for general practitioners, the wages of neurosurgeons will rise relative to that of GPs. The reason is that the marginal productivity of neurosurgeons will rise relative to that of GPs. The same result will occur if, all other things unchanged, the number of GPs increases relative to that of neurosurgeons. If the average productivity of physicians as a group rises over time, nothing in economic theory says that the productivity or the wages of all physicians must rise by equal amounts – by amounts equal to the rise in average physician productivity and average physician wages. Indeed, nothing says that the wages of some kinds of physicians cannot fall even when average physician productivity is rising.
What’s true for physicians is true for workers generally. There’s absolutely no reason for Ms. Warren and you to conclude that the standard economic theory of wage determination is faulty, or fails to apply to low-skilled workers, simply because the wages of one kind of workers – the low-skilled – have not risen by as much as these wages would have risen had they been determined by the rise in average worker productivity. What matters is marginal productivity of the particular kinds of workers in question.
Donald J. Boudreaux
Professor of Economics
Martha and Nelson Getchell Chair for the Study of Free Market Capitalism at the Mercatus Center
George Mason University
Fairfax, VA 22030
Several other flaws infect Mr. D___’s and Ms. Warren’s economic analysis, but the letter above is quite long enough.