The universal Scandinavian welfare model offers generous tax financed social benefits. The scheme is associated with workfare elements as a targeting device to direct benefits to those considered deserving. Thereby social insurance and egalitarian outcomes are achieved while work incentives and thus a high employment rate crucial for the financial viability of the model are maintained. The scope for this policy may depend critically on the characteristics of the population (abilities and preferences) and thus be significantly affected by immigration affecting the distribution of characteristics, especially if the model attracts immigrants with particular characteristics. The paper develops a simple model capable of capturing the rationale and essence of the above-mentioned redistribution model and considers its sensitivity and robustness to immigration, which may change the composition of the population in the ability and/or preference dimension.