The paper develops a general equilibrium model of migration, assimilation and trade, using a random matching framework of culture and trade. The market equilibrium and the social planner’s solution are contrasted and policy implications are given. The model predicts that the presence of immigrants who do not assimilate into the mainstream culture is economically inefficient, but whether such migration occurs depends on the underlying parameters. Because of the endogeneity of the migration decision, care must be taken to select the optimal policy instruments. In particular, subsidizing assimilation or auctioning immigration permits do not achieve the first best. Instead, a mix of selective immigration, border control and aid to the source country can be used to promote efficiency.