In this paper we study the macroeconomic effects of an inflow of low-skilled workers into an economy where there is capital accumulation and two types of agents. We find that there are substantial dynamic effects following unexpected migrations with adjustments that resemble those triggered by a sudden disruption of the capital stock. We look at the interrelations between these dynamic effects and three different fiscal systems for the redistribution of income and find that these schemes can change the dynamics and lead to prolonged periods of adjustments. The aggregate welfare implications are sensitive to the welfare system: while there are welfare gains without redistribution, these gains may be turned into costs when the state engages in redistribution.