Efficiency wage theory asserts that higher wages make workers more productive. In these models, wages cannot be lowered because the cost of falling productivity is larger than the savings from lower wages. Thus, lowering wages would increase costs of production.
There are various theories behind the concept of efficiency wages. The four reasons usually given for
efficiency wages are first, in poorer countries, higher wages can increase
nutrition and health leading to an increase in productivity and output. Second,
higher wages can reduce turnover decreasing hiring and training costs reducing
costs per worker. Third, the average quality of workers can depend upon the
average wage paid since lowering wages will cause the best workers to leave. Fourth, higher wages can bring forth higher effort. In these models it is optimal to pay a wage above the wage that equates the supply and demand for labor.
Focusing on the last effect, the relationship between wages and effort, it is possible that increasing the minimum wage will increase effort. If the theory that higher wages cause higher effort has validity at all, it ought to affect workers at the lower end of the wage distribution who are most likely to be discouraged and shirk on the job. Alternatively, an increase in the minimum wage might attract more productive, discouraged workers back into the labor force.
Thus, coupled with an instutitional, coordination failure, or some other story that keeps wages below their efficiency wage level initially, an increase in the minimum wage and the dignity that comes with it could increase productivity enough so that the increase actually pays for itself. [Update: Commenters are, fairly, demanding a better story here. Here's one: Suppose there are discouraged, but highly productive workers out of the labor force. If one firm raises its wage, they are still discouraged because the average wage doesn't rise. So, the firm will not benefit from raising the wage, and it doesn't. But if all firms raise the minimum wage, then the average wage increases, discouraged workers return to the labor force, productivity soars, and costs fall. The government solves this by coordinating an increase the minimum wage across all firms.]
Here's the Workers with Dignity Work Harder Curve:
And even if the producitivity effect isn't strong enough to completely offset the increase in the minimum wage, the increase in productivity would make the wage increase at least partly self-financing.
It's at least as possible as supply-side claims.