Unreported labour by one worker in a firm increases the probability of detection for his fellow workers, not only for himself. The firm takes this external effect into account. As a consequence, unreported work becomes rationed by the firms demand, rather than determined by demand equal supply. The gap between supply and demand increases with firm size. An empirical analysis on survey data supports theses theoretical predictions. Using a bivariate probit model, we find evidence of excess supply of unreported work in firms. We also find that the gap between supply and demand increases with firm size.