Children and adults alike will have to pay the full price for Broadway shows. There are no reduced price tickets for children. Even if the child will be on an adult's lap, the Box Offices require you to pay for the child.
Please note that Disney Productions aside, many theaters do not allow children under the age of 4 to attend. The only exception to this is the show Frozen, which is only for children over the age of 8. We request you to check the website carefully for age restrictions before bookings tickets for your children.