The difference between the marginal social cost curve (supplier plus society) and the supply/marginal cost curve is the:
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The difference between the marginal social cost curve and the marginal cost curve is the negative externality.
Social marginal cost (supplier plus society) is given by the combined marginal costs of the supplier (Private marginal cost) and the society (marginal external cost).
SMC = PMC + MEC
So, SMC - PMC = MEC.
Marginal external cost is the negative externality because it is incurred from an economic transaction by a third party (i.e. Neither the producer nor the consumer).
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