Do merchants ever run out of items, or can they sell items off their shelves?

Question

Do merchants ever run out of inventory, or do they regenerate it after a certain amount of time? Also, does the merchant ever sell any of the items off of their shelves, or is that just for show?

Shelves for reference:

Answer 1

Merchants restock their inventory after 2 days in game.

The items on the shelves can be bought.

http://www.uesp.net/wiki/Skyrim:Containers#Merchant_Chests

All merchants in the game (with the exception of Hunters, Peddlers, and skooma dealers) have a merchant chest containing the merchant's gold and the goods they have available for sale. The chest does not contain the merchant's entire inventory — merchants will also sell some items sitting out in the store and unequipped items in their personal inventory — and also is not the only source of merchant gold — any personal gold will be added to the merchant's available gold.