The answer is, it depends. Only when both parents earn the same amount of income and either pay their own child care expense or have no child care expense, will there be no exchange of child support. In my practice, I have few couples who earn equivalent salaries. In order to equalize the amount of money available to provide for the children in both households, child support is usually paid, even when there is 50/50 parenting time.
The other side of 50/50 parenting time that many parents fail to consider is that by splitting the time in each household, many of the supplies needed to care for the children have to be duplicated. For example, each household needs a wardrobe. Hopefully, the parents can coordinate buying just one of the major expense items, like winter coats. In higher conflict homes, even such items need to be duplicated. The children need a computer in each home and other expensive toys, like bicycles. What is saved on child support is generally spent (and then some) on providing the duplicates.
Even when reduced child support is paid, it may not be sufficient to permit the lower income parent to provide adequately for the children. We often see in such situations that the parents agree to share the costs for clothing and activities in addition to paying child support.
As mentioned in the preceding article, the amount of child support to be paid should not be the driving force in deciding how much parenting time you can successfully handle. Consider the needs of the children and the needs of the parents in determining parenting time, then calculate the support needed to implement the plan.