2 marks, −0.667MicroeconomicsMarket failure, externalities and public goodsPigouvian taxes and corrective policyHardabout 2 min

IIT JAM 2021 Question 18: Market failure, externalities and public goods

A paper mill has $TB = 120Q - Q^2$ and $TC = 20Q$ , and its effluent creates an environmental cost $EC = Q^2$ . The government imposes a production tax $t$ per unit. The value of $t$ that achieves the socially optimal level of production is

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Answer and worked solution

Answer: (C)

Private marginal benefit is $120 - 2Q$ and private marginal cost is $20$ , giving the private optimum $Q = 50$ . The social marginal cost adds the marginal external cost $2Q$ , so the social optimum solves $120 - 2Q = 20 + 2Q$ , giving $Q = 25$ .

A per-unit tax $t$ makes the mill choose where $120 - 2Q = 20 + t$ ; setting $Q = 25$ gives $70 = 20 + t$ , so $t = 50$ . The answer is (C).

The trap: (B) 25

The optimal tax equals the marginal external cost at the social optimum, $2Q = 2(25) = 50$ , not the output level 25 itself.

Plain-text version

A paper mill has TB = 120Q - Q² and TC = 20Q, and its effluent creates an environmental cost EC = Q². The government imposes a production tax t per unit. The value of t that achieves the socially optimal level of production is (A) 6 (B) 25 (C) 50 (D) 70

Also written as: A paper mill has TB = 120Q - Q^2 and TC = 20Q, and its effluent creates an environmental cost EC = Q^2. The government imposes a production tax t per unit. The value of t that achieves the socially optimal level of production is

Market failure, externalities and public goods has come up 114 times in 7 exams since 2006.

What this question tests

This question is on Pigouvian taxes and corrective policy, part of Market failure, externalities and public goods in Microeconomics.

Using taxes or subsidies to make people face the social cost of their actions.

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