I did some Quests for the Inn and the smith but instead of lowering the prices they increase dramatical. A friend had the same problem. I think the reputation system is at fault.

I have the same issue. There is also a thread in the Obsidian forum:

forums.obsidian.net/topic/72546-bug-reputation-level-gilded-vale/

I confirmed the bug (my post is still pending) and uploaded a savegame.

how much are your prizes from the smith?
I helped him, but still stuff costs around 4-5 times of what i get for selling it to him.
Is that how it should be?

x5 is normal. WHen you have the bug, you are paying around 85 times the normal price. I debugged this and posted a workaround on the obsidian forums:

It is a locale issue. I am using "de_DE.UTF-8" so "," is used for decimal digits and "." is used as thousand seperator. If a Obsidian tester wants to reproduce this issue, use Linux and set your locale to "de_DE.UTF-8", then do the "Late for Dinner" quest.

If you do the quest with this locale, prices are multiplied with "85" instead of "0.85", because of the wrong seperator. Changing the locale will not fix the prices afterwards, since they seem to be stored in a persistent way and are not recalculated. But it will probably fix the error from corrupting prices via reputation later in the game.

The workaround is to set your locale to "C" in start.sh:

export LC_ALL="C"

now that i see that you are all from Germany i get it ;-)
I hate those silly "." and "," problems you get with American software, i could tell tales about matlab, excel, maple and what not.
I am playing in english, so that is probably why it works for me.

I am also playing in english, but my system locale is set to german. Unity3D scripting in PoE is somehow using the locale setting for number calculations. Probably reading a "0.85" out of a config file as string and converting it to a number, which in turn uses a locale interpreting function. Therefore the bug happens ;)

very weird, how can i check what my system locale is set to?
I thought it was German :D