When the production of a good creates negative externalities, which of the following leads to the socially optimal quantity of output?

Question

BlackTom AI · Accepted Answer

Internalizing a negative externality requires making private decisions reflect the social marginal cost (SMC). Define the key functions: marginal private cost (MPC), marginal external cost (MEC), and marginal social cost (MSC). By definition, MSC(Q) = MPC(Q) + MEC(Q). The socially optimal quantity Q* occurs where marginal benefit (MB, or demand) equals MSC: MB(Q*) = MSC(Q*).

Step-by-step reasoning and algebraic justification:
1. Without intervention, firms set output where MPC(Q_market) = MB(Q_market). Because MEC > 0, MPC < MSC, so Q_market > Q* (overproduction).
2. Introduce a per‑unit tax t. The firm faces an effective marginal cost MPC_t = MPC + t.
3. Choose t so MPC_t = MSC. Set t = MEC. Then MPC + t = MPC + MEC = MSC.
4. The market equilibrium with this tax satisfies MPC_t(Q) = MB(Q), which becomes MSC(Q) = MB(Q). That equality defines the social optimum Q*. Therefore a Pigouvian tax equal to the marginal external cost leads private decision makers to produce the socially optimal quantity.

Why the correct answer works: the Pigouvian tax internalizes the external cost by raising private marginal cost by exactly the external marginal damage, aligning private incentives with social welfare and eliminating the deadweight loss from overproduction.

Why the other options are incorrect:
- Price ceiling set equal to MEC: A price ceiling caps price, but does not directly adjust the producer’s marginal cost to reflect external damages; it can cause shortages or inefficiencies and does not guarantee MB = MSC.
- Price floor set equal to marginal private cost: A floor at MPC is irrelevant because firms already face MPC; it won’t internalize external costs or reduce output to Q*.
- Pigouvian subsidy equal to MEC: A subsidy lowers private cost further, exacerbating overproduction (wrong direction).
- Average cost pricing: Regulating price to equal average cost affects firm profits and possibly output, but does not target marginal external damages and generally fails to equate MB and MSC.

Conclusion: Imposing a Pigouvian tax equal to the marginal external cost aligns MPC with MSC and yields the socially optimal quantity; this confirms the correct answer: a Pigouvian tax set equal to the marginal external cost.

When the production of a good creates negative externalities, which of the following leads to the socially optimal quantity of output?Single choice

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