This paper investigates immigrants' and natives' labour supply to the firm within a semi-structural approach based on a dynamic monopsony framework. Applying duration models to a large administrative employer–employee data set for Germany, we find that once accounting for unobserved worker heterogeneity immigrants supply labour less elastically to firms than natives. Under monopsonistic wage setting the estimated elasticity differential predicts a 4.7 log points wage penalty for immigrants thereby accounting for almost the entire unexplained native-immigrant wage differential of 2.9-5.9 log points. Our results imply that discriminating against immigrants is profitable rather than costly.