I quote from an article in The Economist:
The economic case for migration is similar to that for free trade. Trade benefits countries by letting workers specialise in activities in which they are relatively more productive, raising output. And the larger market created by trade spreads the fixed costs of innovation more thinly, encouraging the development of new goods and ideas. Governments began the long march towards trade liberalisation after grasping that its upsides outweigh its costs, leaving a surplus large enough to compensate the losers.
Immigration is an afterthought, in both practice and theory. In traditional trade models wages converge across trading partners with similar technologies even without migration, a phenomenon winningly branded “factor-price equalization”. Sadly, factor-price equalization is a real-world rarity. As of 2000, for instance, a worker in Mexico earned a wage 40% that of a Mexican-born worker of similar education and experience working in America.
Most of this wage gap is down to productivity differences, stemming from disparities in the quality of infrastructure, institutions and skills. An individual worker, however talented, cannot hope to replicate the fertile environment of a rich economy all on his own. But transplanting a worker into rich soil can supercharge his productivity. A Mexican worker earns more in the United States than in Mexico because he can produce more, thanks to the quality of US technology and institutions.