Recent work on the economic effects of minimum wages has stressed that the standard economic model, where increases in minimum wages depress employment, is not supported by empirical work in some labor markets. We present a general theoretical model whereby employers have some degree of monopsony power, which allows minimum wages to have the conventional negative impact on employment but which also allows for a neutral or positive impact. Studying the industry‐based British Wages Councils between 1975 and 1992, we find that minimum wages significantly compress the distribution of earnings but do not have a negative impact on employment