I remember reading about this in Dan Ariely's book "Predictably Irrational".
Here's summary of the relevant chapter on Wikipedia [1]: "While the effect of placebo has been knowingly and unknowingly practiced for millennia, the interesting observation Ariely and his collaborators made was that prices of the prescribed medicine can be used as a placebo as well"
The underlying paper [2] spells this out as well: "We demonstrate that marketing actions such as pricing can alter the actual efficacy of products to which they are applied. [...]"
[1] https://en.wikipedia.org/wiki/Predictably_Irrational#The_Pow...
[2] https://papers.ssrn.com/sol3/papers.cfm?abstract_id=707541