Does monopsony on the labor market in itself justify the implementation of a minimum wage when it would not be used in a competitive economy? This issue is studied in a model of optimal taxation. We find that there is no room for the minimum wage when there are a continuum of skills with no isolated mass point at the bottom of the wage distribution. Accordingly, in the empirically relevant situation, where there is a continuum of wages at the bottom of the distribution, the minimum wage is not helpful. This article is protected by copyright. All rights reserved.