Deriving The Private Marginal Benefit of Pollution Curve

The Private Marginal Benefit of Pollution

• How can pollution have any benefits? • Consider a firm that produces steel. One of the by-products of

steel production is pollution. Dumping the pollution in the air (and water) is the cheapest way for the firm to dispose of the pollution.

• If the firm were to choose to be socially responsible by reducing pollution by 1 tonne, it would have to develop and implement an abatement technology. – This might be as simple as choosing to burn a cleaner form of coal to

produce coke, – or it might be as complicated as investing in a new smelting technology.

• Abatement of pollution is not costless.

The Private Marginal Benefit of Pollution• As the firm attempts to abate more and more pollution, stronger and more expensive interventions (such

as stack scrubbers) must be employed → increasing marginal costs to abatement.• If we were to graph the private marginal costs of abatement (PMCB) for firm B, it might look like:

• qB is the amount of abatement necessary to eliminate all of the firm’s current level of pollution. • The total cost for the cutting its pollution in half would require the firm to abate ½qB tonnes of pollution. • The total abatement cost to firm B to cut its pollution in half would be the area under the PMC B curve

from 0 to ½qB . This is illustrated above as the area of the shaded triangle.

PMCB

qB

Tonnes of Pollution Abatement 0

$/Tonne

½qB

Abatement

The Private Marginal Benefit of Pollution

• If the marginal cost of abatement is increasing for the firm, then the marginal costs of abatement effort falls as pollution rises. For the firm, this reduction of abatement effort is its private marginal benefit from polluting.

• With no abatement effort, the firm would pollute qB tonnes of pollution.

• The private marginal benefit from pollution PMBB for firm B is simply the marginal cost of abatement avoided. This is illustrated below. To cut pollution in half as illustrated below would mean an increase in abatement costs and a loss of the benefit from cheaply disposing the waste biproduct of iron production as pollution. The cost of cutting pollution in half is, as before, the area of the shaded triangle.

The Private Marginal Benefit of Pollution• The private marginal benefit of pollution is illustrated below. • To cut pollution in half as illustrated below would mean an increase

in abatement costs and a loss of the benefit from cheaply disposing the waste bi-product of iron production as pollution.

• The cost of cutting pollution in half is, as before, the area of the shaded triangle.

PMBB

qB Tonnes of Pollution 0

$/Tonne

½qB

Abatement