Demonstrating opportunity cost in production is done through possibility —specifically, the production possibilities curve or frontier (PPC/PPF).

Direct answer

  • The correct completion of the sentence
    “Demonstrating opportunity cost is done through production analysis. possibility. calculation. research. ”
    is: possibility.
  • In practice, this refers to the production possibilities curve/frontier , which shows the trade‑offs between two goods and makes opportunity cost visible.

Why “possibility” is correct

  • A production possibilities curve plots all the maximum possible combinations of two goods an economy can produce with given resources and technology.
  • Moving along this curve shows how producing more of one good requires giving up some of the other, which is exactly the definition of opportunity cost.

Why the other options are wrong

  • Analysis helps interpret opportunity cost but does not, by itself, demonstrate it; the demonstration comes from the production possibilities model.
  • Calculation (like computing per‑unit opportunity cost as ΔY/ΔX\Delta Y/\Delta XΔY/ΔX) is a numerical tool used once the production possibilities are known, not the core demonstration.
  • Research is a broad process of gathering information and is not the specific economic model used to show opportunity cost in production decisions.

So, in the multiple‑choice context, “Demonstrating opportunity cost is done through production possibility ” is the accepted and conceptually accurate choice.

Information gathered from public forums or data available on the internet and portrayed here.