Generally, unless your incomes are identical, someone will have to pay some amount of support to someone else. Even when the incomes are identical, a support award may be made for a variety reasons. Judges don't seem to like custody cases where support isn't awarded, whether it makes sense or not. In many joint custody arrangements, the amount of child support paid is less, since the children's time is more equally divided between the two parent's housholds. The reduced support is often cited frequently by the prospective custodial parent (most often the mother) as the main reason the other parent (usually the father) is seeking joint custody.
(See Defusing Objections To Joint Custody for a more detailed write-up on this particular argument against joint custody.)