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Externalities and market failure

October 15, 2011

The first theorem of welfare economics tells us that a competitive market will produce an efficient level of output, but this is not true when an externality exists. This is because the externality means there is a difference between the private marginal cost (PMC) and the social marginal cost (SMC). When there is a negative externality, it means the cost to society is greater than the private marginal cost incurred by the firm producing the externality. When there is a positive externality it means there is some benefit to society so the social marginal cost is lower than the private marginal cost.

Here we have a market where a firm produces a negative externality (eg some pollution). In a competitive market, the firm will produce where demand = private marginal cost (D = PMC), the PMC is basically the firm’s supply curve, so you will get a competitive output of Qc and a price of Pc. However when you take into account the negative externality, the SMC is higher than the PMC at all positive levels of output. The socially optimal output, Qs is where D = SMC and this is at a lower level than Qc.

Notice that just because there is pollution, the social optimum is not to produce at the level where there is no pollution because that is also the level at which there is no output either. There is a benefit produced by creating extra output, and there is damage produced by creating the externality that comes with the output. A cost-benefit analysis will find the efficient point at the level where the marginal benefit of producing another unit of output equals the marginal damage of producing another the amount of externality that comes with producing another unit of output.

Again this leads us to the socially optimal point, it is just another way of thinking about it.

When there is a negative externality a competitive market will produce an inefficiently large amount of output. Conversely, when there is a positive externality, a competitive market would produce an inefficiently small amount of output.

We can look at the welfare effects of the externality by breaking it down into consumer and producer surplus.

At the competitive price-quantity combination:
Consumer surplus = A + B + C + D
Private producer surplus = F + G + H
Externality cost = C + D + E + G + H
Welfare = consumer surplus + private producer surplus – externality cost = A + B + F – E

At the socially optimal price-quantity combination:
Consumer surplus = A
Private producer surplus = B + C + F + G
Externality cost = C + G
Welfare = consumer surplus + private producer surplus – externality cost = A + B + F

The difference in welfare between the competitive output and the socially optimal output is E, this is the deadweight loss of the externality in a competitive market.

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