Thanks for contacting eXtension with this question. Without attaching images, we can only guess as to what the insect is...

One type of small beetle that is reddish brown and hard-shelled is the carpet beetle:
http://bugguide.net/node/view/18495
http://www.mississaugapestcontrol.ca/images/carpet_beetle.jpg

Another possibility is the red flour beetle:
https://upload.wikimedia.org/wikipedia/en/3/37/Tribolium_castaneum87-300.jpg

Both beetles feed on dried food products, including beans, rice, dried flower arrangements, macaroni, and similar items.  Carpet beetles will also feed on carpet backing, especially older carpets

Vacuuming up and discarding the beetles when found is the best pest control method.  Cleaning out cabinets and drawers of food debris and outdated food items is very important; discard these in an outside garbage can/dumpster.  You must be persistent, as adult beetles will emerge from cracks and crevices for a few weeks, after the apartment/home has been cleaned well.

IF my guesses are incorrect, please send in pictures for identification.
Mark