Every language has perfunctory linguistic tokens meant to accompany or acknowledge an act of some kind. The expression of thanks and its customary retort are perhaps the most common such species in the class of what are called performative speech acts. Sometimes these tokens are old enough to have grown opaque to the point of meaninglessness, as with the word welcome uttered by itself or in the phrase from which it is derived, you are/ you’re welcome, as a polite formula used in response to an expression of thanks. This formulaic utterance seems to have originated in American English in the beginning of the 20th century but has since spread to other varieties of English.
All the European languages also have some variety of acknowledgement of thanks that is equivalent to English not at all, don’t mention it, e.g., Spanish de nada, German (das) macht nichts, Russian ne stoit (не стóит [благодарности]), etc. In contemporary colloquial American English one also often hears no problem with the same function.
The linguistically most interesting of these specimens is undoubtedly you’re welcome because welcome has such a wide range of meanings. Here is its etymology from The Oxford English Dictionary Online:
Etymology: Originally Old English wilcuma ( < wil- , will- will, desire, pleasure + cuma comer, guest) = Old High German willicomo , Middle High German and Middle Low German willekome , -kume (whence Old French wilecome ), with subsequent alteration of the first element to wel- well adv. and n.4, and identification of the second with the imperative or infinitive of the verb come, under the influence of Old French bien venu, bien veigniez, Latin bene venisti, bene venias, etc., . . . .
Why welcome as a response to the expression of thanks? The first interpretation that comes to mind is the gloss “your thanks are welcome,” wherein the component “your thanks” is understood to have become identified with the UTTERER, hence “you’re/you are welcome.” In other words, just as in the case of “thanks” as a reduced form of “my thanks” or “I thank you,” you’re welcome is at bottom a product of TRUNCATION. Otherwise it makes no grammatical sense. But such quasi-meaninglessness is typical of linguistic tokens that are purely performative.
MICHAEL SHAPIRO
It’s not just in colloquial American English that one hears “no problem” with the same function. It’s become all-pervasive, and I’m at a loss to know what its function actually is. It’s become a verbal tic which serves only to cause annoyance when there really is a problem. One calls the bank to get a constantly recurring problem rectified, and even if one hasn’t been robotic oneself and said thank you, thus prompting the tic, out comes “no problem”. Useless to say “but there IS a problem” (actually a meta-problem, I suppose), as the immediate response is “no problem”. Even pointing out that the problem is the expression “no problem” seems to constitute further conditioning of the reflex.
On the other hand this use of “you’re welcome” seems less mysterious to me. I have always taken it to be a truncated form of “you’re welcome to my services” or such.
Actually I don’t think thanks as such are supposed to be welcome! Hence some of the other expressions you mention, to which I would add Ger “bitte”, It “prego”, which I take to mean “please don’t thank me” (which sounds a bit rude in English, as if we were to say “oh pur-lease”, or “no thanks, pray”) or Jap “dou itasimasite”, which is more like “for what?” than say Fr “de rien” (which again has a comical echo in Eng “thanks for nothing”). Personally I like Esperanto “ne dankinde” (“not worth thanking for”. Or saying “thank you” back (for giving me the opportunity to be of service), like Ch “xièxie n?”. This last seems to be gaining ground, in the UK at any rate.
I think it actually functions to reassure the recipient that the gift is given free of hidden charge/debt/or obligation, as in “You are welcome to the gift”, thus, implying that no thanks are necessary or that the “thank-er” should feel welcome to take possession of what has been given at the pleasure of the giver.