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Pigouvian tax and externalities

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The private marginal benefit for commodity X is given by 10 - X where X is the number of units consumed. The private marginal cost of producing X is constant at $5. For each unit of X produced, an external cost of $2 is imposed on members of society. In the absence of any government intervention, how much X is produced? What is the efficient level of production of X? What is the gain to society involved in moving from the inefficient to the efficient level of production? Suggest a Pigouvian tax that would lead to the efficient level. How much revenue would the tax raise?

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