Just dropped my mac, speakers broke? I have accidentally dropped my mac in a way that it damaged my internal speakers. They're not damaged severely, but they are impared. 

Basically, without headphones the right side of my MBA 11' produces sound but the left side doesn't. This is clearly evident when I plug in headphones: The left earbud produces little noise and the right earbud produces normal amounts of noise. I have verified it is the MBA that is impaired and not the headphones.

Is it repairable? I have tried restarting my macbook and it didn't help. I don't want to take it to the apple store and pay a hefty amount. What do I do?
Yes, this is easily repairable. The speakers are relatively cheap. PBM sells them for $15 USD: http://www.powerbookmedic.com/MacBook-Air-11-Left-Speaker-p-22393.html (I have used them in the past for parts and highly recommend).

You can then hope to iFixit for a teardown of your MBA: http://www.ifixit.com/Guide/Replacing+MacBook+Air+11-Inch+Mid+2011+Left+Speaker/6312/1

Note that the MBA is actually as moderate difficulty in repairing (by iFixit), so if you are a klutz, you may elect to have someone else do the repair for you. Also, I have used general searches for your MBA model (based on the limited information you have provided), so you should ensure the parts are the exact ones you need and not go simply on my links above.