The mechanics of this issue, economically, come down to Money Velocity.
John Whitling
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I certainly agree that raising the minimum wage to a living wage will have a positive effect on the economy. See my article: A Living-Wage Minimum Wage Will Not Materially Reduce Employment.

The point of the above post, though, is to illuminate the emotional and personality reasons behind much of the opposition to a living wage, to point out that much of that opposition has little or nothing to do with factual, economic arguments or policy but rather that it’s largely rooted in the moral philosophy of those on the other side.