Is the asking price of the rent negotiable?

Yes, but keep in mind that there's a short supply of housing stock in NYC, so if the rent is competitively priced, you may not get very far.   On the other hand, if you plan on staying for more than one year, you might want to try locking in the rate of the first year's rent for the second year, but that can be risky if you foresee yourself having to get out of the lease before it expires.   (You can also try locking in renewal options.)   

Overall, there is no "law" that prohibits you from trying to get a better and a could agent should encourage you to try to get that better deal if it's possible.   As an example, the agent can see price changes on the unit.   Odds are, if it's listed at the lower end of the median market, it'll probably be gone at the blink of an eye.   If it's lingering and the landlord is changing the asking rent back and forth, that's a sign that it might be a good idea to negotiate.   

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