Final answer:
The production possibilities frontier shows both scarcity and productive efficiency.
Step-by-step explanation:
The statement that the production possibilities frontier is useful for demonstrating scarcity but not productive efficiency is False.
The production possibilities frontier (PPF) is a graph that shows the different combinations of two goods that can be produced given the available resources and technology. It represents both scarcity and productive efficiency.
Scarcity is demonstrated because the PPF illustrates the limited resources and choices that society faces when deciding how to allocate those resources. Productive efficiency is demonstrated because points on the PPF represent the maximum possible output that can be achieved given the available resources and technology.