A model is set up where migrants must choose a level of social traits and consumption of ethnic goods. As the consumption level of ethnic goods increases, the migrants become ever more different to the local population and are less assimilated. Less assimilation affects the reaction of the local population to the migrants and their willingness to accept the newcomers. This social phenomenon and affects wages and unemployment. We show that the growth in the unemployment and social benefits of legal migrants increases the consumption of ethnic goods, thus creating a trap wherein the willingness of the local population to accept the migrants into the economy decreases. This process also increases the probability of the migrants' dependence on the welfare state. On the other hand, illegal migrants could play an important role in the assimilation of the legal migrants.