We model a competitive labour market where firms choose combinations of workers and hours per worker to produce output. If one assumes that the scale of production has no impact on hours per worker, then the change in the number of workers and hours per worker resulting from a minimum wage are inversely related. We demonstrate that total hours worked at the firm may rise for plausible parameter values if there are small fixed costs to hiring workers. Thus, in contrast to the conventional view, we show that the effect of minimum wages on employment is ambiguous.