Take a look at this link for better understanding on usage of certain prepositions.
The definition of "OF" as a preposition-
Used for belonging to, relating to, or connected with:
Examples of "of" as a preposition-
The secret of this game is that you can’t ever win.
The highlight of the show is at the end.
The first page of the book describes the author’s profile
In context of this definition, look at your first sentence.
Audi Cuts Prices of Spare Parts in China
The preposition "OF" is used here to indicate that the price belongs to/is used in relation with prices of spare parts.
Now, the definition of "FOR" as a preposition-
Used to indicate the use of something:
Some examples of "for" as a preposition-
This place is for exhibitions and shows.
I baked a cake for your birthday.
I put a note on the door for privacy.
She has been studying hard for the final exam.
And now, looking at your second statement-
Starbucks to Raise Prices for Packaged Coffee, Other Products
Ask yourself- Starbucks is raising prices for what? Intuitively, "for" is a better fit here than "of".