Why a minimum wage?

Back when I was in college, the economics professors displayed charts on overhead projectors showing supply and demand curves for the labor market. Where the curves intersected, this was the point that the market would set for wages, on the vertical axis, and for the level of employment, on the horizontal axis. The invisible hand of the free market would find this point, and all would be well.

But what if, asked the professor, the government were to set a minimum wage? He drew a horizontal line above the point where the supply and demand curves crossed. Now wages were slightly higher, but the number of workers exceeded the demand for them. A minimum wage increases unemployment among the poorly-compensated, and that's a bad thing. So we were to conclude that the minimum wage, while arising from good intentions, actually harmed the very people it was intended to help. It was necessary to assimilate this view in order to obtain a good grade. But it's not quite right.

If only it were enough for people to have jobs! But work is not its own reward. Nor is it sufficient for it to just stave off homelessness or starvation. If we truly value labor, it should be compensated well enough to support a certain standard of living. The federal current minimum wage of $5.15/hr is well below the $8.30/hr needed to rise above the poverty line for a family of three. If poverty is the measure, then $5.15 fails to support a minimum standard of living by a wide margin. Yes, a moderate increase in the minimum wage would likely increase unemployment slightly, but it would still increase the aggregate income of those on the low end of the income scale.