From Ayn Rand Answers:
What is your attitude toward immigration? Doesn’t open immigration have a negative effect on a country’s standard of living?
AYN RAND: You don’t know my conception of self interest. No one has the right to pursue his self-interest by law or by force, which is what you’re suggesting. You want to forbid immigration on the grounds that it lowers your standard of living–which isn’t true, though if it were true, you’d still have no right to close the borders. You’re not entitled to any “self-interest” that injures others, especially when you can’t prove that open immigration affects your self-interest. You can’t claim that anything others may do–for example, simply through competition–is against your self interest. But above all, aren’t you dropping a personal context? How could I advocate restricting immigration when I wouldn’t be alive today if our borders had been closed?