Externalities and Public Goods

When Markets Fail

Perfect competition achieves Pareto efficiency — but only when there are no externalities (costs or benefits that fall on third parties).

Negative externality (e.g., pollution): the private cost of production is less than the social cost. The firm ignores the damage to others:

$$MSC = MPC + MEC$$

where $MEC$ is the marginal external cost. The market overproduces: $Q_{\text{market}} > Q_{\text{social}}$. The gap is deadweight loss from overproduction.

Positive externality (e.g., education, vaccination): the private benefit is less than the social benefit. The market underproduces.

$$MSB = MPB + MEB$$

Solutions:

• Pigouvian tax (Pigou): tax the externality-generating activity at a rate equal to $MEC$ at the social optimum. This internalises the externality — the private cost becomes the social cost.
• Pigouvian subsidy: for positive externalities, subsidise to close the gap between private and social benefit.
• Coase theorem (Coase): if property rights are well-defined and transaction costs are low, private bargaining between the parties can achieve the social optimum regardless of who holds the property right. The allocation of rights affects distribution but not efficiency.
• Cap and trade: set a total pollution cap, issue tradeable permits. Firms that can abate cheaply sell permits to firms that find it expensive — achieving the target at minimum total cost.

Public goods have two properties:

• Non-excludable: you cannot prevent someone from consuming it (national defence, lighthouse).
• Non-rival: one person's consumption does not reduce another's.

Markets underprovide public goods because of the free-rider problem: individuals benefit without paying. Government provision, funded by taxes, is the standard solution.

$$\text{Optimal provision}: \sum MB_i = MC$$

The social optimum requires the vertical sum of individual demand curves (because all consumers enjoy the same unit) to equal marginal cost.

Externalities and their fixes

Common pitfall: Setting the Pigouvian tax to eliminate the externality entirely. The efficient tax equals marginal external cost at the optimum — some pollution is efficient when abating it costs more than the harm it does. The goal is the right quantity, not zero.