What is the common law principal that allows the state to assume a parental role and to take custody of a child when he or she becomes delinquent, is abandoned, or is in need of care that the natural parents are unable or unwilling to provide?

Parens Patriae

Explanation:

Parens patriae refers to a legal term that refers to the authority of the government to intervene on behalf of those who are unable to take care of themselves. The doctrine of  Parens Patriae has found its strongest use in the care of infants, mentally ill persons and those who are legally incompetent to handle their affairs. The State is the sole protector of all children under its jurisdiction, and the State courts have the absolute authority to interfere and protect the best interests of children whose well being is compromised by conflicts between parents.

the answer is:

c. economic output