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

A steel firm's private marginal cost is MC = 20 + 2Q (₹ thousand per tonne) and the marginal external cost of pollution is a constant ₹10 thousand per tonne. The market price is ₹60 thousand, taken as given by the firm. What per-tonne tax would make the firm produce the socially optimal quantity, and what is that quantity?

The corrective tax is ₹10 thousand per tonne, equal to the marginal external cost, and the optimal output is 15 tonnes. Setting price 60 equal to social marginal cost 30 + 2Q gives Q = 15, compared with 20 tonnes without a tax.

  1. ATax ₹10 thousand; optimal quantity 20 tonnes
  2. BTax ₹10 thousand; optimal quantity 15 tonnesCorrect
  3. CTax ₹10 thousand; optimal quantity 25 tonnes
  4. DTax ₹20 thousand; optimal quantity 10 tonnes
  5. Tax ₹60 thousand; optimal quantity 0 tonnes

Explanation

Without a tax, the firm sets P = MC: 60 = 20 + 2Q, so Q = 20. Socially, MSC = 30 + 2Q, so 60 = 30 + 2Q gives Q = 15. A Pigouvian tax equal to the marginal external cost of 10 shifts the firm's MC to 30 + 2Q and gives Q = 15. Q = 20 is the untaxed outcome.

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