Pigouvian taxation and subsidies


Don't understand why pigouvian subsides shift up marginal private cost up, lead reduce the total output of firms?

I thought pigouvian subsidies will shift marginal private cost line down... but as my prof said, government intervene externality though pigouvian taxation and subsidies and both reduce firms output and the result lead to reduce pollution. but pigouvian subsidies may lead more firms enter which will increase pulltion in long term.

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Taxation: Pigouvian taxation and subsidies
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