Microeconomics 2 – Chapter 16 Study Notes: Externalities, Property Rights & Coase Theorem

Externalities & Market Efficiency

• Guiding question: “How much of activity x should society undertake?”
  • Basic economic rule: Continue an activity until marginal cost (MC) equals marginal benefit (MB).
  • Individual illustration: Keep buying cake slices as long as the extra slice’s pleasure > its price.
  • Market illustration: In perfect competition, producers supply output where MC = P (price equals individual demand) ⇒ private markets yield Pareto-efficient allocations when no externalities are present.
• Problem: If producing a cake (or any good) inflicts unpriced health damage on nearby residents, market prices no longer capture social cost ⇒ competitive outcome becomes inefficient.
• Formal efficiency condition
  • Society should undertake activity x if SB(x) > SC(x), where SB and SC are social benefit and social cost functions.
  • Without externalities: SB =\text{private benefit}, SC =\text{private cost} ⇒ markets efficient.
  • With externalities: divergence appears ⇒ markets allocate too much (negative externality) or too little (positive externality) of the activity.

Defining Externalities

• Broad idea: An externality exists when actions by one economic actor directly affect the utility or profit of another without compensation through market prices.
• Not an externality: a demand shift that raises a good’s price (effect occurs through the price system).
• Refined definition (captures decision calculus):
  • Activity carried out by Agent A imposes non-priced costs/benefits on others that A does not consider when choosing her optimal level.
• Examples
  • Negative: Chemical plant pollutes river → downstream fishery’s catch falls.
  • Positive: Beekeeper adds hives → adjacent apple orchard yields rise.
  • Nuisance: Food plant smell lowers nearby residents’ utility.
• Counter-examples (no externality under property internalization):
  • Chemical firm and fishery are owned by same company ⇒ pollution cost enters joint profit calculation.
  • Chemical firm purchased pollution rights from fishery.
  • Fishing company bought downstream site at a discount, fully aware of pollution.

Negative Externalities

• Definition: Unaccounted-for costs imposed on third parties.
• Consequences: Over-production / over-consumption relative to social optimum.
• Policy justification: Taxes, regulations, liability rules to align private incentives with social welfare.
• Stylised 2-firm model (Firm 1 pollutes, Firm 2 suffers)
  • Firm 2’s effective cost: \tilde C2(x2,x1)=C2(x2)+a x1, a>0 captures marginal damage per unit of Firm 1’s output.
  • Competitive outcome x1^M ignores a; efficient outcome x1^{PE}<x_1^M.

Positive Externalities

• Definition: Unpriced benefits conferred on others.
• Consequences: Under-production (e.g., education, vaccination).
• Policy tools: Subsidies, public provision.
• Example cost shift: \tilde C2(x2,x1)=C2(x2)-b x1, b>0 ⇒ Firm 1’s activity lowers Firm 2’s costs.

The Reciprocal Nature of Externalities (Coase 1960 Insight)

• Classic story: Doctor vs. Confectioner in same building; noise impairs doctor.
• Key idea: Harm is mutual — stopping noise harms confectioner’s livelihood.
• Efficient solution minimizes total harm, not necessarily the harm to a single party.
• If negotiation is costless, parties can bargain to efficient allocation regardless of initial liability assignment.

Numerical Illustrations (Examples 16.1–16.5)

• 16.1: Payoff(Confectioner noise)=40; Cost to Doctor=60 → Efficient: shut down factory.
  • Whether confectioner is liable or not, bargaining (or liability) leads to shutdown; transfers differ.
• 16.2: Gain to confectioner=60; Cost to doctor=40 → Efficient: continue operating; again, legal rule changes only transfers.
• 16.3: Noise gain=40; Noise cost=60; Soundproofing cost=20 → Efficient: install soundproofing and keep operating (Total NB=80). Occurs under either liability regime.
• 16.4: Same as 16.3 plus doctor can rearrange office for 18 (even cheaper) → Efficient: doctor rearranges (Total NB=82). Happens under both regimes; side payments ensure correct party bears cost ( 18≤P≤20 ).
• 16.5: Gain=60; Cost=40; Soundproof=20; Negotiation cost=25 → Efficient: install soundproofing, but only achieved if confectioner liable because costly bargaining prevents agreement when not liable. Demonstrates importance of transaction costs.

The Coase Theorem & Property Rights

• Statement: If property rights are well-defined and transaction costs are zero, private bargaining leads to an efficient allocation of resources, independent of who initially holds the rights.
• Logic: Rights create tradable entitlements (e.g., “right to make noise” vs. “right to silence”). Parties negotiate to the outcome maximizing joint surplus.
• Real-world caveats:
  • Transaction costs (information, bargaining, enforcement) often non-negligible and rise with number of parties.
  • Defining complete, enforceable rights may be infeasible (e.g., air quality, biodiversity).
  • Hence governments use taxes, quotas, liability laws, standards.
• Distributional note: Initial rights affect who pays/receives compensation, though not efficiency (with zero T-costs).

Application: Public-place Smoking Ban

• Two assumptions underlying bans:
  1. Negotiations with strangers in public are impractical ⇒ high T-costs.
  2. Societal valuation of nonsmokers’ clean air > smokers’ utility from smoking.

Government Intervention I: Pigouvian Taxation

• Principle: Levy tax t on externality-causing agent equal to marginal external damage \frac{\partial C2}{\partial x1}=a.
• In 2-firm model, tax t=a induces Firm 1 to choose efficient x_1^{PE}.
• Requirements & pitfalls:
  • Government must know marginal damage function (informational challenge).
  • Might mis-target the party with lowest avoidance cost ⇒ inefficient.
  • When bargaining is costless, Pigouvian tax may distort (over-correct) because private negotiations would have solved problem.
• Example 16.9: Doctor can self-protect for 18 (cheapest), but tax on confectioner forces alternative, raising costs.

Government Intervention II: Tradable Emission Certificates

• Mechanism: Authority sets total emissions cap Q and issues Q certificates; market determines price.
  • Firms with high abatement costs buy certificates; low-cost firms sell after reducing emissions.
  • In equilibrium: MC_{abatement} equalized across firms ⇒ cost-effective attainment of cap.
• Advantages
  • Achieves target at minimum total cost without government knowing each firm’s abatement cost.
  • Creates explicit price signal; compatible with heterogeneous firms.
• Disadvantages / prerequisites
  • Cap must be binding (below baseline emissions).
  • Does not itself decide “optimal” cap level; government still needs social-cost information.
• Example with two firms & five technologies (A–E)
  • Unregulated choice: both use A (4 t/day).
  • Policy comparisons:
  1. Uniform 50 % mandate: each firm moves to C ⇒ total abatement cost = 150.
  2. Tax =10: too low, no abatement.
  3. Tax =25: only Firm 1 switches to C; emissions cut by 2 t.
  4. Tax =41 (smallest achieving 50 % cut): Firm 1 chooses D, Firm 2 B ⇒ abatement cost 110 (plus tax revenue).
  5. Certificate trading (4 certificates): Market allocates 3 to Firm 2, 1 to Firm 1 → same emission pattern as Policy 4 but at minimum private cost 110; monetary transfers depend on initial allocation.
• Relation to Coase: Unlike pure bargaining, government pre-sets cap; certificates trade only among emitters, not with victims of pollution. Efficiency stems from quota, not free-market internalization.

Positional Externalities

• Definition: Externalities arising from relative (rank-based) competition — one agent’s improvement reduces others’ relative standing.
• Example puzzle: Hockey players seldom wear helmets voluntarily but support mandatory rule.
  • Each player gains agility from skating without helmet, fearing competitive disadvantage if others abstain.
  • Collective helmet rule removes positional arms race, improving joint safety.
• General environments: Job hours race, conspicuous consumption, academic grading curves.
• Institutional responses that curb positional races:
  • Work-week limits (labor law).
  • State pension systems (force savings, reduce savings competition).
  • Workplace safety standards.
  • Anti-doping regulations in sports.

Ethical & Practical Implications

• Externalities justify government intervention beyond laissez-faire on welfare grounds.
• Property-rights approaches stress rule-of-law foundations and distributional consequences.
• Pigouvian instruments target marginal damages but demand information; certificate trading solves cost-minimization yet not optimal-level dilemma.
• Positional externalities spotlight domains where absolute welfare conflicts with relative status; efficient regulation may need to coordinate restraint.

Key Equations & Symbols (LaTeX format)

• Social efficiency rule: SB(x)=SC(x) at optimum.
• Negative externality cost shift: \tilde C2(x2,x1)=C2(x2)+a x1,\; a>0.
• Positive externality benefit shift: \tilde C2(x2,x1)=C2(x2)-b x1,\; b>0.
• Pigouvian tax: t^*=\frac{\partial C_{external}}{\partial x}.

Connections & Further Reading

• Builds on earlier micro topics: consumer/producer surplus, welfare theorems, public goods.
• Coase’s insight bridges economics & legal scholarship; foundational for Law & Economics.
• Positional externalities link to behavioral economics and social choice.
• Recommended text: Frank & Cartwright (2013), Microeconomics and Behavior, Ch. 13.