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How do you calculate the net social welfare loss due to a negative externality in production?

If there exists a negative externality in the production of a good or service (eg. coal power station emitting greenhouse gases) the Marginal Social Cost (MSC) to society of producing the good will exceed the Marginal Private Cost (MPC) paid by the producer. This is due to the fact that the producer is does not have to pay compensation to society for the external cost. Because of the fact that the producer takes only its own interests into account when deciding how much to produce, the market mechanism will result in overproduction of the externality good, producing where Marginal Private Benefit = MPC instead of the socially optimum position where Marginal Social Benefit = MSC. This overproduction will lead to a net loss in social welfare, which can be calculated by multiplying the difference between MPC and MSC by half of the difference between the market level of production and the socially optimum level. This is more easily demonstrable diagrammatically, where the net welfare loss is equal to the area of a triangle formed by continuing a line up from the market level of production to the MSC line.

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