Do I still need to write e.g. "willingness to pay (WTP)" when there is already a list of abbreviations containing WTP at the beginning of my paper?
I would say that it isn't essential, but it might be a service to your readers to do that. They will, then, see the term used in context as well as its abbreviation.
I agree with Buffy 100% that it is not strictly necessary. However, the question is raising a red flag for me.
The purpose of academic writing is to communicate ideas as clearly as possible to other human beings. If you include the full words, does it increase the clarity of the sentence? If you're unsure, ask a colleague to read over a bit of the paper. My strong suspicion is that they will prefer to see the word written out the first time, and will want to use the key only secondarily (if they forget an abbreviation.)
Always keep the four C's in mind when you write: Clarity, Clarity, Clarity, and Clarity. All else is just formatting.1
1 - And as De Novo observed, formatting is also clarity. ;)