The right rug in your studio apartment can create a new point of view for you and your guests and you don't need a genie to do it. You just have to make sure that the rug you choose makes the apartment look bigger and more open, not cramped and crowded. Here's a few rug tips to make your space stretch: 

1. First of all, make sure that the rug you choose is rectangular. When space is limited, stick with the basics! Alternatively shaped rugs will be harder to place and could make your small space seem busier and more crowded.
2. Less is more! Just have one large rug in your room. Multiple rugs will be distracting and make the room more cluttered.
3. Make sure the rug fits your room. If it fills up the entire room, it will draw attention to the fact that the room is small. If the rug is too small, your apartment will end up looking like its clothes shrunk in the dryer. A good rule of thumb is to make sure that the edges of the rug that are nearest to the wall is about 10-12 inches from the wall, making it look big enough but not too big.  
4. Remember, stripes are super! A striped rug that stretches across the room will make the room seem more elongated. If you want to spice it up, a patterned rug can bring some personality to your apartment. However, if you are going to have a patterned rug, make sure the pattern shapes are smaller so that the room seems bigger.
5. When choosing a color, remember, you never go wrong with neutrals! To find a rug that creates space, light, neutral colors are what you need. Darker rugs will absorb the space illusion and will seem too heavy for the room. Your apartment will seem smaller and more cramped. The lighter, earthy tones will fill the room without creating harsh lines that make it more obvious that the room is small. 

Rugs are also great transitional pieces to designate where the living room area verses the bedroom area is located. This division will also create the look of more space.  Your studio apartment can look sophisticated and roomy with the right accessories. That space is yours to do whatever you'd like with it and despite the fact that it may not be a ton of room, a new rug can make you feel right at home. Good luck!