Questioner: “What is your attitude towards open immigration and what is your attitude towards the effect it may have upon the standard of living in this country? And does not this require that the answer is that you are, uh, opposed to both—aren’t you asking a person to act against his own self-interest ...”?
Ayn Rand: “You don’t [understand] 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 grounds that it lowers your standard of living – which certainly is not true, though if it were true you’d still have no right to close the border to others. Therefore to claim it’s your self-interest is an irrational claim: You are not entitled to any self-interest that injures others, and the rights of others, especially when you can't prove that open immigration affects your self-interest. You cannot claim that anything that others may do – for example, simply through competition – is against your self-interest, and therefore you [would] want to stop competition dead. That is the kind of [alleged] self-interest you are not entitled to. It is a contradiction in terms and cannot be defended.
But above all, aren’t you dropping a more personal context? How could I ever advocate that immigration should be restricted when I wouldn’t be alive today if our borders were closed.”
~ Ayn Rand, from the book Ayn Rand Answers
[Hat tip Mother of Exiles]