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IAI Actuarial Core Principles · Business Economics · Government intervention in a market

A steel firm in Odisha has marginal private cost MPC = 20 + 2Q (₹ thousand) and each unit of output causes pollution damage of ₹10 thousand, so MSC = 30 + 2Q. Demand (marginal benefit) is P = 80 − Q. What per-unit tax, in ₹ thousand, makes the market output socially efficient?

The efficient per-unit tax is ₹10 thousand, equal to the marginal external damage. Adding it to private marginal cost gives the social marginal cost curve, so the firm produces where price equals marginal social cost, about 16.67 units rather than the unregulated 20.

  1. A5
  2. B10Correct
  3. C15
  4. D20
  5. 30

Explanation

Market output: 80 − Q = 20 + 2Q gives Q = 20. Efficient output: 80 − Q = 30 + 2Q gives Q = 16.67. A Pigouvian tax equal to the marginal external cost of 10 shifts the firm's cost to MSC, so it yields the efficient output. A tax of 30 or 20 would overcorrect, as it exceeds the external damage.

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