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      Question

      A government levies a Pigouvian tax t = 40. Firm A:

      MAC_A = 20 + 2q_A; Firm B: MAC_B = 10 + 3q_B. What are optimal abatement levels?
      A q_A = 10, q_B = 10; total abatement = 20 Correct Answer Incorrect Answer
      B q_A = 15, q_B = 10; total abatement = 25 Correct Answer Incorrect Answer
      C q_A = 10, q_B = 10; MAC_A = MAC_B = 40 — confirming cost-effective allocation Correct Answer Incorrect Answer
      D Both (A) and (C) are correct and equivalent descriptions of the same outcome Correct Answer Incorrect Answer

      Solution

      Each firm abates until MAC = tax rate: Firm A: 20 + 2q_A = 40 ⇒ q_A = 10. Check: MAC_A = 20 + 20 = 40 ✔ Firm B: 10 + 3q_B = 40 ⇒ q_B = 10. Check: MAC_B = 10 + 30 = 40 ✔ Total abatement = 20. MAC_A = MAC_B = 40 — cost-effective condition satisfied. Options (A) and (C) describe the same outcome differently. The Pigouvian tax automatically equalises MAC across all firms without the regulator needing to know individual MAC functions.

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