In the IEA 19th Annual Hayek Memorial Lecture, Prof. Gary Becker proposes a radical solution to the problem of immigration: sell visas to the highest bidders.
However, this "solution" is not really as radical as it sounds: it already exists in a variety of forms, legal and otherwise. For example, many countries have special fast-track visas for investors or high-net-worth individuals--a legal option. On the illegal side, many trafficking syndicates charge huge fees to move their clients across borders, fees that can be collected in a variety of permutations: cash, kind, in advance, in arrears, and so forth.
For Prof. Becker's idea to really work, nation states must completely secure their borders, something even the mightiest nations on earth seem incapable of doing.