Lecture 10: Public Goods and Externalities

Learning Objectives

By the end of today you should be able to:

Define non-rival and non-excludable and use them to classify any good
Explain why public goods lead to free-riding and market underprovision
Distinguish positive from negative externalities, and production from consumption externalities, with examples
Show how a negative production externality creates deadweight loss using a supply-and-demand diagram

Where We Are

Last lecture: taxes and price controls can create DWL — but those are government-imposed distortions

Today: market failures that need no government interference to go wrong

Public goods and externalities — two different ways the price mechanism breaks down

Both share the same root cause: the price carries incomplete information

Game: The Flex Pass Fund

You start with a balance of flex passes
Decide how much to contribute to a shared public pot
- Your contribution is immediately deducted from your balance
- The total contribution to the pot is multiplied: $\text{Pot} = 1.5 \times (\text{Your Contribution} + \text{Other Contributions})$
- Every player receives an equal share of the pot — even if they contributed nothing

Goal: maximize your own final flex pass balance

Log in to the app (shiny.kylecoombs.com/coordination-games), enter your contribution, and submit

Game Rules

\[\text{Your Final Flex Pass Balance} = \text{Your Starting FP} - \text{Your Contribution} + \\ \frac{1.5 \times (\text{Your Contribution} + \text{Other Contributions})}{N}\]

Pick $\text{Your Contribution}$ in steps of 0.5
What is your “best response” or best strategy?

Best response if others contribute a lot: contribute less, free-ride
Best response if others contribute nothing: also contribute nothing

We may play two rounds — second round may include communication

Debrief: What Happened?

Did total contributions reach the maximum possible pot?

Who contributed a lot? Who contributed little or nothing?

Would round 2 (with talking) change anything? Why?

The individually rational strategy (contribute less) leads to a collectively bad outcome

This is the essence of the public goods problem — and it explains why markets systematically underprovide certain things

What Makes a Good “Public”?

Two dimensions define how goods work in markets:

Rivalry: Does one person’s use reduce availability to others?

Rival: your slice of pizza means less for everyone else
Non-rival: your enjoyment of a radio broadcast doesn’t reduce anyone else’s

Excludability: Can non-payers be prevented from consuming?

Excludable: a concert requires a ticket — no ticket, no entry
Non-excludable: once a lighthouse is lit, any passing ship benefits

The Four Types of Goods

Figure 1: Two dimensions — rivalry and excludability — yield four categories of goods

Radio Signals: A Pure Public Good

Non-rival: Your radio doesn’t reduce anyone else’s signal quality

Non-excludable: Once the signal is broadcast, there is no way to stop people from tuning in

So how does commercial radio make money?

Advertisers pay for your attention — the station bundles a rival, excludable product (ads) with the non-excludable broadcast

Before the advertising model: early stations relied on donations or government funding — or they simply went dark

The Free Rider Problem

If I can enjoy the good without paying, why would I pay?

Rational individual strategy: wait for others to provide the good, then consume for free

The problem: when everyone reasons this way, no one provides the good

Connection to our game:

Strategy	Your payoff	Group payoff
Contribute maximum	Low (you paid)	High
Free-ride completely	Highest individually	Collapses if everyone does it
Nash equilibrium	Zero contribution	Zero pot

Why Prices Can’t Fix This

In a normal market, prices work because:

Buyers reveal willingness to pay through purchases
Firms produce up to where $P = MC$
Mutually beneficial trades happen; others don’t

With a public good, preferences stay hidden:

If I admit I value the lighthouse at $100, you’ll expect me to help pay
Rational strategy: claim $0 and free-ride
The market “sees” reduced WTP → doesn’t provide the good

Prices exclude non-payers, but public goods are non-excludable.

Example: The Final Question Game

Each revealed bonus question is a public good:

Non-rival: everyone can attempt it once revealed
Non-excludable: everyone sees the question once revealed

The payoff: a 5 point question appears with probability 50% → 2.5 points on average

The cost: increases. Cost of question $q$ = $q^2 + 11$ flex passes:

Question	Cost (flex passes)	Your expected gain	Worth it alone?
1	12	2.5	No
2	15	2.5	No
3	20	2.5	No

No individual ever pays to reveal a question — private benefit (2.5) is always below private cost (≥ 12)

Worksheet 10 — Parts A & B

Work through the worksheet before the next slide.

Part A: expected value of a bonus question Part B: fill in the cost table and decide — worth it alone?

The Social Calculation

Figure 2: Private benefit (flat at 2.5) never clears the cost. Social benefit (2.5 × Number of students) clears it for several questions. The gap between Q_private = 0 and Q_social is the market failure.

Why the Market Gets It Wrong

Private decision: Is $2.5 \geq q^2 + 11$? → Never. Q = 0.

Social decision: Is $2.5 \times N \geq q^2 + 11$? → Yes, for N = 20, up through Q6. Q* = 6.

The problem: when you pay to reveal a question, you capture only your own 2.5 expected points

But every classmate also gets 2.5 expected points — and you can’t charge them

The market sees your private WTP (2.5). The social WTP is $2.5 \times N$ (50). Prices aggregate the wrong thing.

Public Goods: Summary

Property	What it means	Market failure
Non-rival	MC of one more user = 0	Hard to set efficient price
Non-excludable	Can’t stop non-payers	Free-riding destroys revenue

Market outcome: firms can’t capture enough revenue → underprovision or zero provision

Policy responses:

Government provision (funded by taxes)
Subsidies to private providers
Intellectual property law (creates excludability — imperfectly)

What Is an Externality?

An externality occurs when a transaction imposes costs or benefits on someone not party to the transaction

A buyer and a seller agree on a price — but a third party bears consequences they never consented to

Key insight: Market price only reflects what buyer and seller care about

\[\text{Private cost} \neq \text{Social cost}\] \[\text{Private benefit} \neq \text{Social benefit}\]

Four Types of Externalities

Negative externalities

Impose costs on third parties

Factory discharge → downstream river users pay
Driving → traffic congestion for other drivers
Cigarette smoke → bystanders pay

Positive externalities

Confer benefits on third parties

Vaccination → herd immunity protects neighbors
Beekeeper’s bees → pollinates nearby farms
Education → more informed voters and workers

Each can arise from production (making something) or consumption (using something)

Externality Examples: A 2×2 View

	Production	Consumption
Negative	Beef production creates methane	Cigarette smoking in public
Positive	Beekeeper pollinates neighbor’s crops	Getting vaccinated (herd immunity)

Today’s focus: negative production externality

Beef production generates methane — a potent greenhouse gas. Climate damages are borne by everyone, but the cost never appears in the price of a steak.

Market Failure with a Negative Externality

When production creates external costs:

\[MSC = MPC + \underbrace{\text{external cost per unit}}_{\text{damage to third parties}}\]

Market equilibrium: the firm sets $P = MPC$ (doesn’t pay for the external cost)

Social optimum: efficiency requires $P = MSC$

Result: the market overproduces — quantity exceeds the socially efficient level

The Externality Diagram: Beef and Methane

Figure 3: Negative production externality: MSC lies above MPC by the external cost per unit. Market produces Q_m = 6; social optimum is Q_s = 5. DWL (red) is the efficiency loss from overproduction.

Before and After: The Externality

Figure 4: Left: market ignores MSC — equilibrium at Q_m = 6, P_m = $8. Right: social optimum at Q_s = 5 reveals the DWL triangle from overproduction.

Same Formula, Different Cause

DWL from a tax (Lecture 9):

\[DWL = \frac{1}{2} \times t \times \Delta Q\]

DWL from a negative externality:

\[DWL = \frac{1}{2} \times \text{external cost} \times \Delta Q\]

Our example: $DWL = \frac{1}{2} \times \$2 \times 1 = \$1$

Source of DWL	Mechanism	Who bears the loss?
Tax	Gov’t creates wedge	Buyers and sellers
Monopoly	Firm restricts output	Society (lost trades)
Externality	Missing price on spillover	Third parties + society

Question: what could the government do to fix the externality? (hint: compare the DWL formulae)

What Can Policy Do?

Pigouvian tax: tax the producer by the external cost per unit ($2 here)

Firm now faces: effective $MPC' = MPC + tax = MSC$
Market equilibrium shifts to $Q_s = 5$, $P = \$9$
DWL eliminated; revenue redistributed

Regulation: mandate all firms produce $Q = 5/N$ (where $N$ is the number of firms), so total $Q_s=5$

Cap-and-trade/permits: fix quantity cap at $Q_s = 5$ and let firms trade emission rights

Coase Theorem: if affected parties can negotiate costlessly and property rights are clear, they will reach $Q_s$ on their own — without government

Lecture 10 Summary

Public goods

Non-rival + non-excludable

Free-rider problem
Underprovision (possibly zero)
Price cannot aggregate all WTP

Externalities

Unpriced third-party spillovers

Negative → overproduction
Positive → underproduction
Price ignores social cost/benefit

Common thread: prices carry incomplete information → market quantity ≠ socially efficient quantity

Both are cases where the invisible hand reaches the wrong equilibrium

Advanced Topic: information asymmetries create market failures