Neoclassical economists, using a competitive demand/supply model of labour markets, typically conclude a legislated minimum wage is harmful to economic efficiency and social welfare. The major theoretical counter-attack by proponents of a minimum wage is to argue that low-wage labour markets are better modelled as monopsonistic. This article develops and formalizes a second theoretical defence for a legal minimum wage law. This defence rests on the concept of the social cost of labour, as originally popularized by Sidney and Beatrice Webb and then further developed by American institutional economists. This analysis is unique in that it continues to use the competitive demand/supply model but nonetheless demonstrates that a legislated minimum wage often simultaneously increases both economic efficiency and fairness, unlike the neoclassical prediction.