You rented an apartment with air conditioning, which I presume was material to your choosing said apartment. Look to the lease and determine who is responsible for repairs. If the landlord is responsible, then he cannot deny his obligation to fix the air conditioning because he believes it is a "luxury item."
Additionally, in most states, there is an implied covenant in a lease called the "implied warranty of habitability." Under this implied covenant, a landlord has a duty to keep the rental premises free from defects or problems which pose serious threats to life and/or health. Things covered by an implied warranty of habitability generally include that the rental property has hot water, a working electrical system, heat in the winter, lockable doors and windows, a working toilet and smoke detectors, and be free of pests like roaches and rats.
In areas where the heat can be excessive, air conditioning may be necessary to the health and safety of occupants. Arguably, then, your landlord is responsible for fixing the a/c. You must provide written notice in writing to your landlord to correct the problem.
I'd consult with a local landlord/tenant attorney for the specific procedures in your area. If the landlord does not correct the problem within a reasonable amount of time, you may have several remedies, including a rent escrow action, available to you.
DISCLAIMER: Brandy A. Peeples is licensed to practice law in the State of Maryland. This answer is being provided for informational purposes only and the laws of your jurisdiction may differ. This answer based on general legal principles and is not intended for the purpose of providing specific legal advice or opinions. Under no circumstances does this answer constitute the establishment of an attorney-client relationship. For legal advice relating to your specific situation, I strongly urge you to consult with an attorney in your area. NO COMMUNICATIONS WITH ME ARE TO BE CONSTRUED AS ARISING FROM AN ATTORNEY-CLIENT RELATIONSHIP AND NO ATTORNEY-CLIENT RELATIONSHIP WILL BE ESTABLISHED WITH ME UNLESS I HAVE EXPRESSLY AGREED TO UNDERTAKE YOUR REPRESENTATION, WHICH INCLUDES THE EXECUTION OF A WRITTEN AGREEMENT OF RETAINER.