Community cohesion and assimilation equilibria

We study the assimilation behavior of a group of migrants who live in a city populated by native inhabitants. We conceptualize the group as a community, and the city as a social space. Assimilation increases the productivity of migrants and, consequently, their earnings. However, assimilation also brings the migrants closer in social space to the richer native inhabitants. This proximity subjects the migrants to relative deprivation. We consider a community of migrants whose members are at an equilibrium level of assimilation that was chosen as a result of the maximization of a utility function that has as its arguments income, the cost of assimilation effort, and a measure of relative deprivation. We ask how vulnerable this assimilation equilibrium is to the appearance of a "mutant" - a member of the community who is exogenously endowed with a superior capacity to assimilate. If the mutant were to act on his enhanced ability, his earnings would be higher than those of his fellow migrants, which will expose them to greater relative deprivation. We find that the stability of the pre-mutation assimilation equilibrium depends on the cohesion of the migrants' community, expressed as an ability to effectively sanction and discourage the mutant from deviating. The equilibrium level of assimilation of a tightly knit community is stable in the sense of not being vulnerable to the appearance of a member becoming better able to assimilate. However, if the community is loose-knit, the appearance of a mutant will destabilize the pre-mutation assimilation equilibrium, and will result in a higher equilibrium level of assimilation.