I just noticed that there is an achievement for autopricing your shop.

How does autopricing work? What is the basis for the prices it chooses?

And is there a button someplace to autoprice? If so, I cannot seem to find it.

autoprice can only be used by Gold ACcount users, and bases its prices by going below or at the lowest market price.

That would be very convenient! I thought it might be a Gold Account perk... Thanks! :)

It will price everything under 1 mill sP at the cheapest shop price for each of them according to the shop search. You can do this once a day. You can only access it with a Gold Account.