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Mithral weapons cost 500gp/lb. Fighting fans have no weight. Mathematically, a mithral fighting fan cost the same as a normal fighting fan.
I'm certain this is wrong.
How much should mithral fighting fans cost? Is there a minimum cost of making a weapon mithral? I'm assuming it's a plain minimum of 500 gp (so it's that much more expensive than masterwork).

Darth Grall |

Firstly, why do you want a mithral fan? It won't have a benefit aside from the silver typing, which you can get for much cheaper and easier with alchemical silver. It's largely made from silk, so it's "hafted" and won't benefit from its hardness either. Sure you'll get the masterwork but otherwise having a fan be mithral seems like an all around bad idea aside.
That said, since there is no real mechanical benefit I'd say there is little to no reason to pump it's cost to the absurd. Obviously it has to be masterwork(300 gp base) and the cost of the weapon(5 gp). And even if it has no listed weight, it has to have some weight, however negligible.
So what's "negibible" in terms of weight? *.5 pounds as you guys said* The item is also mostly silk drapped over the folding metal frame, which in and of itself should detract from it's weight but lets say it doesn't:
At .5 lbs * 500 gp/lbs + 300 Masterwork + 5 weapon cost = 555 gp.
So a mithral fighting fan would cost 555 gp. And that's a lot for essentially a few mithral needles with a hinge, supported by a lot of silk.
Now, I'm keeping the masterwork component in the cost of the materials; since the metal only makes up a portion of the item(the silk must be masterwork too mind you) and that's ALWAYS 300 gp.
Edit'd for missed posts!

asthyril |

Note that all mithral weapons are automatically masterwork.
So you add the mithral components AFTER the masterwork component.==Aelryinth
Cost: Weapons or armors fashioned from mithral are always masterwork items as well; the masterwork cost is included in the prices given below.
masterwork costs are included in the price you pay for the item, you don't add more for it

Darth Grall |

Yes, we all get that Masterwork is supposed to be factored into the cost of this item made from this Material. However:
What does a Masterwork Fan made of Steel and Silk cost?
305 gp
What does a Mithral and Silk Fan cost?
255 gp
Does that seem right to you?
In this case the RAW fails us, thus its up us to make the call. At the very least, I would implore them to charge 305; if not more so in the range of a 500 gp, to compensate for the rarity of Mithral or at the least the value of Masterwork Goods.