# Externalities and Public Goods

Business I · Microeconomics · https://tryals.app/learn/business-i/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:

$$MSB = MPB + MEB$$

| Externality | Market Outcome | Classic Fix |
| --- | --- | --- |
| Negative | Overproduction | **Pigouvian tax** = $MEC$ |
| Positive | Underproduction | **Subsidy** = $MEB$ |
| Clear rights | Bargaining | **Coase theorem** |

> **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.

## Practice questions

4 of this lesson's 13 practice questions, with answers. The full set is in the app.

### 1. Match each concept to its definition.

**Answer:**

- Negative externality → Cost imposed on third parties (e.g., pollution)
- Coase theorem → Private bargaining achieves efficiency if transaction costs are low
- Free rider → Benefits from a public good without paying
- Non-rival → One person's consumption does not diminish another's

**Why:** Externalities, bargaining, free riding, and non-rivalry, the vocabulary of market failure.

Page: https://tryals.app/practice/business-i/externalities-and-public-goods/match-each-concept-to-its-definition

### 2. A Pigouvian tax and a cap-and-trade permit system can reach the same emissions outcome. What is the practical difference between choosing them?

A. Permits are more efficient because they allow firms to trade
B. A tax fixes the price; permits fix the quantity
C. Taxes are always cheaper to administer than permit markets
D. Only permits achieve the efficient outcome; taxes merely raise revenue

**Answer:** B. A tax fixes the price; permits fix the quantity

**Why:** Each instrument fixes one blade of the scissors and lets the other move, so the choice is about which risk matters more, a hard climate threshold argues for the cap, cost certainty for the tax. Weitzman's 1974 result formalises exactly this, and it is why the EU chose an ETS while others chose carbon taxes.

Page: https://tryals.app/practice/business-i/externalities-and-public-goods/a-pigouvian-tax-and-a-cap-and-trade-permit-system-can-reach-the-same

### 3. Sort into public goods vs private goods.

**Answer:**

- Public good: National defence, Street lighting, Clean air regulation
- Private good: A sandwich, A pair of shoes, A cinema ticket

**Why:** Public goods are non-rival and non-excludable. Private goods are rival and excludable. The boundary cases (club goods, common resources) lie between.

Page: https://tryals.app/practice/business-i/externalities-and-public-goods/sort-into-public-goods-vs-private-goods

### 4. A Pigouvian tax on pollution is set equal to the marginal external cost at the socially optimal quantity.

**Answer:** True

**Why:** The tax internalises the externality: $MPC + t = MSC$ at $Q_{\text{social}}$. The firm now faces the true social cost of production.

Page: https://tryals.app/practice/business-i/externalities-and-public-goods/a-pigouvian-tax-on-pollution-is-set-equal-to-the-marginal-external