Externalities and Public Goods

Market Failures: Externalities

Perfect markets fail when externalities impose unpriced costs or benefits on third parties.

A negative externality like pollution means the social cost exceeds private cost:

$$MSC = MPC + MEC$$

Here $MEC$ is marginal external cost, causing overproduction ($Q_{\text{market}} > Q_{\text{social}}$) and deadweight loss. A positive externality like education means social benefit exceeds private benefit:

$$MSB = MPB + MEB$$

Common pitfall: Setting the Pigouvian tax to eliminate pollution entirely. The goal is the efficient quantity, not zero, because total abatement costs can exceed harm.

Solutions and Public Goods

The Coase theorem proves that if property rights are defined and transaction costs are low, private bargaining achieves efficiency regardless of who holds the rights; allocation affects distribution only.

Cap and trade sets a total pollution cap and issues tradeable permits, achieving the reduction target at minimum total cost.

Public goods are defined by two strict properties:

• Non-excludable: nobody can be prevented from consuming it.
• Non-rival: one person's use does not reduce another's.

Markets underprovide them due to the free-rider problem where people consume without paying.

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

Provision requires the vertical sum of individual demand curves to equal marginal cost, which justifies government intervention and taxation.