Now the government is considering imposing extra tax on polluting industry. From the first table, what is the optimal tax?

Question

BlackTom AI · Accepted Answer

Understanding the question: we’re told to look at the first table and determine the optimal tax on a polluting industry. The goal of a Pigouvian tax is to set the tax equal to the marginal damage (external cost) at the socially optimal level of pollution, so that the polluting firm internalizes the externality and emits the quantity that aligns private costs with social costs. Now, let’s evaluate the options one by one.

Option A: $30. In many standard problem sets, the table lists marginal damage (or external cost) at different emission levels. If the first table shows that the marginal damage at the socially optimal emission level equals $30, then a $30 tax would internalize the externality and lead to the optimal quantity. This would be consistent with the Pigouvian approach. We would need to verify that $30 exactly matches the marginal damage at the optimal point described in the table.

Option B: $45. If the table’s marginal damage at the optimal emission level is lower than $45, then a $45 tax would overprice pollution, causing firms to reduce emissions more than optimal and resulting in a welfare loss relative to the social optimum. Conversely, if the table showed marginal damage rising steeply and crossing at $45, then $45 could be correct, but that would depend on the specific values given. Absent that alignment, $45 is unlikely to be the precise optimal Pigouvian tax.

Option C: $35. Similar to the previous point, unless the table indicates that the marginal damage at the optimal emission level equals $35, this option would generally misprice the externality. If the table’s damage figure at the optimal point is not exactly $35, using $35 would lead to a suboptimal quantity and welfare loss.

Option D: $40. The logic mirrors the above: only if the table specifies that the marginal damage at the socially optimal emission equals $40 would this be the correct Pigouvian tax. Without that explicit match, $40 would be an incorrect internalization level.

Putting it together, each option’s correctness hinges on the specific numerical value of the marginal damage at the socially optimal pollution level as shown in the first table. The key check is whether the tax equals the marginal damage at that optimum. If the table indeed shows $30 as the marginal damage at the socially optimal point, then $30 would be the correct Pigouvian tax; all other values would diverge from the optimal taxation rule and lead to either under- or over-internalization of the externality.

In summary, to determine which option is correct, compare each candidate tax to the marginal damage value presented in the first table at the socially optimal emission level. The option whose value matches that marginal damage figure is the one that aligns with the concept of the optimal Pigouvian tax. If the table indicates $30 as that figure, then $30 is the tax that achieves the social optimum; if the table shows a different figure, the corresponding match among the options would be the correct choice.

Now the government is considering imposing extra tax on polluting industry. From the first table, what is the optimal tax?单项选择题

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