Is there too little immigration?

"This paper presents a model of legal migration from one source country to two host countries, both of which can control their levels of immigration. Because of complementarities between capital and labor, the return on capital is positively related to the level of immigration. Consequently, when capital is immobile, host nations' optimal levels of immigration are positively related to their capital endowments. Further, when capital is mobile between the two host nations, the common return on capital is a function of the levels of immigration in both countries, meaning that immigration is a public good. As a result, when immigration imposes costs on host countries, the Nash equilibrium results in free riding and less immigration than would occur in the cooperative equilibrium. These results are qualitatively unaltered when capital mobility extends to the source nation"--Federal Reserve Bank of St. Louis web site.