hmm... interesting question. my minds going all sorts of directions.
I think there would be some brave enough to pay nothing. Probably those that could afford to buy the whole restaurant, honestly.
It would be the one's who really can't afford it and should be taking it for free that would feel to too guilty to pay nothing.
To be fair, I think I would take advantage of paying for the true cost of the ingredients plus a little for the preparation and such. Because they can buy in bulk at a lower price-point than one would pay at the grocery store, they may still have a chance of making money because obviously the restaurant would be very popular! More money left in the customer's pocket to be left for the friendly staff in tips.
Thought provoking question! do you know of a restaurant like that? I'm in!