He would absolutely be entitled to a rent adjustment if the property was not habitable for some or all of the month. If you had done something to affect the hot water, again, he probably would be entitled to an adjustment. Difficulties caused by Sandy, however, might result in a different answer. As you say, the storm affected everyone. I don't know if a Judge would allow a rent adjustment because the storm affected the hot water. You could agree to reduce the rent if you wished, but I can't say that you have to do so.
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While some understanding should be expected when so many people have been affected by the storm, landlords are treated as businesses and as such, it is their responsibility to shoulder the burden of restoring premises to a habitable condition.
If there is continually no hot water to take a shower on the premises you are renting out, the value of these premises has dropped. I am sure that if the apartment's value increases for some reason (like a celebrity moves in), you would have no problems raising the rent.
Your tenant's suggestion sounds reasonable and it is within his rights to demand that the new value of the premises offered be reflected in the rent. Businesses are supposed to offload some of this risk by taking out insurance rather than shifting the responsibility to tenants.
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