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      Question

      For a firm with Total Cost function TC = 100 + 6Q +

      2Q², which of the following statements is CORRECT? (I) MC = AC at the minimum of AC (II) The minimum of AC occurs at Q = 5 (III) At Q = 5, MC = AC = 26 (IV) The fixed cost does not affect the MC but shifts the AC curve upward
      A I and IV only Correct Answer Incorrect Answer
      B I, II and IV only Correct Answer Incorrect Answer
      C I, III and IV only Correct Answer Incorrect Answer
      D I, II, III and IV Correct Answer Incorrect Answer

      Solution

      Minimum AC: Set dAC/dQ = 0 ⇒ −100/Q² + 2 = 0 ⇒ Q = √50 ≈ 7.07 (NOT Q = 5). ∴ Statement II is FALSE. At Q = √50: AC = MC = 6 + 20√2 ≈ 34.28 (NOT 26). ∴ Statement III is FALSE. Statements I (✔) and IV (✔) are correct. Answer: (A).

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