US/UK switch? Probably basically free for both, if both are seen as equally desirable. But citizens from "less desirable" countries would pay ($30K/yr?) to have to the right to work in the US/UK. And, for example, US/UK doctors would receive money ($30K/yr?) to work in third-world countries. The rates would vary depending on each pair of countries and relative demand.
It seems abhorrent at first to ask already-poorer third-world citizens to pay money, but the $30K/yr would presumably come out of salaries paid from the first world -- so people from third-world countries would only be able to work in the US if they were making excellent money, and therefore contributing greatly to the economy. No money is actually being "taken" from the third-world. And the $30K/yr payment to doctors, lawyers, engineers, etc. living abroad would provide a fantastic transfer of skills from the first world to the third world, helping to counteract "brain drain".
I'm not sure any governments would want to sign up for something like this, and it may feel rather questionable morally, but it could solve a lot of problems.