Final answer:
Implied authority is the unwritten power allowing a producer to perform necessary incidental acts in an agency agreement. It is distinct from express, apparent, or acknowledged authority.
Step-by-step explanation:
The unwritten authority given to a producer to carry out necessary incidental acts of the agency agreement is called implied authority. Implied authority refers to the power to perform acts that are reasonably necessary to accomplish the purpose of an agency agreement, even if not specifically stated in the agreement. This contrasts with express authority, which is the authority expressly given by one party to another, apparent authority, which is the power a third party assumes an agent has based on the principal's behavior, and acknowledged authority, which would refer to authority recognized by all parties involved.