Common wisdom holds that the introduction of a non-binding minimum wage is irrelevant for
actual wages and employment. Empirical and experimental research, however, has shown that the
introduction of a minimum wage can raise even those wages that were already above the new
minimum wage. In this paper, we analyze how these findings can be explained by theoretical wage
bargaining models between unions and firms. While the Nash bargaining solution is unaffected by
minimum wages below initially bargained wages, we show that such minimum wages can drive up
wages – and be harmful to employment – when bargaining follows the Kalai-Smorodinsky
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