Minimum Wage vs. Human Capital

So while I was out running today, I had an idea. Suppose that there is a difference between the wage clearing rate and the current minimum wage. What if that difference could be captured and invested in human capital?

Let me back up here a minute. Human capital is the stuff that makes you more valuable as a person (think economically, not in terms of virtue). Education, training, and experience are all good examples of this.

What if there were to be some sort of massive government scholarship fund with this difference which could be used to invest in human capital for workers who meet certain requirements?

The Bureau of Labor Statistics (BLS) reports that there are 2 million workers earning minimum wage. Let's suppose that the wage clearing rate is w. With full time workers, 40 hours / week x 50 working weeks / year = 2000 working hours / year. Therefore (2,000,000)(2,000)(5.15 - w) would be placed into this fund each year. Even if this difference were 50 cents, that would still be $2 billion placed into this fund. At $40,000 / worker, this could improve 50,000 workers, or 2.5% of those working at minimum wage. In general, for each cent of difference between 5.15 and w, you would improve .05% of the workforce, which is quite significant for a penny.

When workers would leave this class (minimum wage class) of work, they would lower that supply of workers which would, in turn, raise the clearing wage price. Eventually, in the limit, this would actually raise the clearing wage (w) to the minimum wage ($5.15 in my scenario above).

Problems with this scenario would include:

Where would the money come from?
Probably a tax on the corporations paying the workers minimum wage. They're already losing the money via the minimum wage itself, so I'm not sure exactly what their objection to this would be. Most likely, they would prefer to train their own workers, and take the training costs as a tax deduction. Perhaps this could work as well.

Who would train the workers?
By providing a scholarship-esque program, this could utilize the currently existing capital improvement facilities (colleges, universities, trade schools, community colleges, etc.) for education. The burden shouldn't be too heavy on them (at 50 cents difference, that only makes for an additional 50,000 students nationwide).

Other odd results?
Well, I would suggest having some sort of wage-to-scholarship amount scale, or else you'll have people intentionally trying to work at minimum wage for the scholarship benefits. Intead, perhaps workers could receive scholarship amounts based on how much they earn, decreasing as their pay got farther from minimum wage. Someone working at a wage above (5.15 - w) + 5.15, for example, would receive no assistance.

This was some random idea I had, so please feel free to comment, especially with economic ideas. Remember, anyone can post on this blog.