We examine the effect of borrowing constraint facing new immigrants on the process of their assimilation in the new society. We shall do so in a two-period model. In period one, immigrants invest, with some costs to them, in trying to assimilate. The probability of success in this endeavor depends on the amount invested and also on the level of the provision of a 'public' good paid for by lump-sum taxation of 'natives'. Those who succeed enjoy a higher level of productivity and therefore wages in period 2. The level of investment is endogenously determined. Assimilation also affect remittances by immigrants. Given this framework, we examine the effect of public support on the degree of assimilation and income repatriation. We do so under two scenarios regarding the credit market facing new immigrants. In the first, they can borrow as much as they want in period 1 at an exogenously given interest rate. In the second scenarios, there is a binding borrowing constraint. We compare the equilibrium under the two scenarios.