Final answer:
The platysma is the muscle responsible for pulling the lower lip down and tensing the skin of the neck.
Step-by-step explanation:
The muscle that pulls the lower lip inferiorly and tenses the skin of the neck is the platysma. The platysma is a broad sheet of muscle arising from the fascia of the chest and deltoid muscles and ascending over the collarbone to the face. It contributes to facial expressions by depressing the lower jaw and lip. This action is essential for expressions of surprise or fear, and also for the tension of the skin of the neck. In contrast, muscles like the depressor anguli oris and depressor labii inferioris are primarily involved in the movement of the mouth and lips, but not in tensing the neck skin.