A1. Externalities & Market Failure
The Core Chain
Externality — Definition
A cost or benefit imposed on a third party, for which no compensation is paid. Non-capturable: no market for the effect. It is the spillover, not the third party.
Positive vs Negative
Negative: unpriced harm → activity done too much. Social cost > private cost.
- Pollution, GHG emissions, overfishing, congestion
Positive: unpriced benefit → activity done too little. Social benefit > private benefit.
- Carbon sequestration, vaccination, maintaining a shared garden
Why Externalities Cause Market Failure
Perfect competition needs all costs/benefits in prices. Externalities break this → wrong quantity → social surplus not maximised → market failure.
Optimal Level of Pollution (2025 Q1b)
Not zero. Economics answer: balance marginal benefits against marginal social damages.
MAC: cost of reducing one more unit. Rises as you clean more. Some have negative cost (save money AND reduce pollution).
MSC: harm from one more unit. Rises with pollution. For carbon, requires discounting.
QSO: where MAC = MSC. Above: MSC > MAC → abate more. Below: MAC > MSC → ease off. Area between curves = welfare loss.
Internalising the Externality
Making the spillover count in incentives. Routes: carbon pricing, Pigouvian tax, subsidy, regulation. Detail in A5.
Tragedy of the Commons (2024 Q1b)
Full private benefit, fraction of shared harm → overuse. 100 farmers each feel 1% of damage.
≠ public goods: common = rival, non-excludable. Public = non-rival, non-excludable. Exam penalises confusing these.
Welfare Concepts
CS = WTP − price (below demand, above price). PS = revenue − min acceptable (above supply, below price). Social surplus = CS + PS. Externalities → deadweight loss.
Pareto Efficiency
No one better off without someone worse off. Says nothing about fairness. "Efficient ≠ equitable" = mark-winner.
Opportunity Cost
Benefit forgone from next-best alternative. Not just cash. Central to CBA and valuation.
Key Diagram
Supply-demand cross with surplus areas. For externalities: social cost curve above supply → wedge between private and social equilibrium.
Critique
Reductionist (Peter's word). Assumes rational maximisers, perfect info. Misses norms, bounded rationality, power, intrinsic values. Powerful for diagnosing incentive problems.
2020 (aviation), 2021 (choose a market), 2024 (externalities + commons), 2025 (define + optimal pollution + intervention).
- Define externality (2–3 sentences)
- Distinguish +/− with examples
- Causal chain: no market → ignored → private ≠ social → failure
- Diagram
- Apply to context
- Critique: assumptions, distribution, measurement
- Policy sketch
A2. Non-Market Valuation
The Core Problem
Total Economic Value (TEV)
1. Direct use — personally consumed (timber, recreation). 2. Indirect use — ecological background functions (carbon seq., flood protection). 3. Non-use — option (might use), bequest (future generations), existence (glad it exists). 4. Intrinsic — worth regardless of humans.
Existence = still human-centred. Intrinsic breaks free of human frame. TEV = completeness checklist.
Shadow Prices
Price a non-market good would have at competitive equilibrium. Social cost of carbon = shadow price.
WTP and WTA
WTP: max pay. WTA: min compensation. Theory: equal. Practice: WTA ≫ WTP (loss aversion). Framing changes policy conclusions.
Revealed Preference (3 methods)
From observed behaviour. Credible but blind to non-use values.
1. Defensive expenditure — spending on protection (double glazing → noise). Floor estimate only.
2. Hedonic pricing — housing price differences. Jensen et al.: turbine view −3.15%, noise −6.69%.
3. TCM — WTP from travel costs. Assumptions: single-purpose, trip has no utility, similar households, time cost.
Stated Preference (2 methods)
From hypothetical surveys. Reaches non-use values but risks bias.
1. CVM — scenario + WTP/WTA. Biases: scope/embedding, strategic, payment vehicle, mental account.
2. Choice experiments — cards varying across attributes → individual attribute values. Needs cost attribute.
Big Picture
Complementary, not competitors. TCM: £2m (use). CVM: £8m (+ non-use). Gap = mostly non-use value.
2020 Q1 (TCM + computation), 2024 (via CBA), 2025 Q5d (economic framing).
- Frame: no market → invisible
- TEV
- Explain method(s)
- Apply
- Limitations
- Critique: useful but reductionist
- Connect: → CBA (A3) → instruments (A5)
A3. Cost-Benefit Analysis
The Core Chain
Definition
Social appraisal: everyone's costs/benefits, not just the project owner. Benefits = aggregate WTP. Costs = opportunity cost (not accounting cost).
NPV
Accept if > 0; highest NPV among mutually exclusive. NPV ≠ CBA. CBA = full 9-step process; NPV = Step 7 output.
Discounting
Factor = (1+r)−t. Higher rate → crushes future benefits. Rationale 1: opportunity cost of funds. Rationale 2 (Ramsey): time preference + diminishing marginal utility. δ = 0 → future counts equally → Stern (2007). Same damages, different r, opposite conclusions.
Kaldor-Hicks (2024 Q2b)
NPV > 0 → winners could compensate losers. Needn't actually happen.
The 9 Steps (2024 Q2a–b, 2025 Q3b)
- Alternatives — vs counterfactual
- Standing — whose costs/benefits?
- Identify impacts — flag omissions
- Quantify
- Monetise — A2 methods
- Discount
- NPV
- Sensitivity — vary r and key drivers
- Recommend — analysts recommend, decision-makers decide
Wind Farm — Bergmann & Hanley (2012)
| 1 mile | 20 miles | |
|---|---|---|
| Construction | €8m | €15m |
| Maintenance/yr | €0.5m | €1m |
| Electricity/yr | €3m | €4.8m |
| Dis-amenity/yr | €0.7m | €0.2m |
| Avoided carbon/yr | €1.6m | €2.9m |
| NPV | €32.6m | €62.6m |
Other Metrics
IRR: r where NPV = 0. Robustness, not scale. DBT: time to positive. B:C Ratio: gameable. NPV preferred.
Pros and Cons
Pros: transparency, comparability, non-market inclusion, widespread use.
Cons: (1) valuation limits — uncertain, non-tradeable values; (2) distribution — WTP embeds wealth, K-H hypothetical; (3) time/uncertainty — discount rate is ethical choice, small changes flip conclusions. Strong critique = combine two families.
Every year. Most tested Section A topic. 2020 (Atewa), 2021 (A2B Railway), 2024 (concept + K-H + r), 2025 (Highland wind farm).
A4. Optimisation & Linear Programming
The Core Chain
What LP Is
Optimise a linear objective subject to linear constraints. Everything proportional. "Optimal" = provably best but model-relative.
Four Building Blocks (2024 Q3b, 2025 Q2b)
1. Decision variables — quantities you choose. 2. Objective function — single expression to max/min. 3. Constraints — resource inequalities. 4. Non-negativity — x ≥ 0. Free marks.
Formulation (2024 [30], 2025 [20])
(1) Name variables, (2) objective, (3) constraints from resource sentences, (4) non-negativity. "At most" → ≤, "at least" → ≥.
2025 Worked Example
s.t. 3xd + xw ≤ 36 (labour), 2xd + xw ≤ 50 (timber), xd + xw ≤ 30 (storage), xd,xw ≥ 0
Graphical Method (2024 Q3c–d, 2025 Q2c–d)
- Axes — one per variable
- Plot constraint lines — intercepts
- Shade correct side — origin test
- Feasible region — overlap in positive quadrant
- All corners — origin, axis (tightest wins), interior (simultaneous eq.)
- Simultaneous equations — cross-multiply, subtract, solve. 3 constraints → 3 pairs, check each vs unused constraint
- Evaluate objective at every corner
- State answer + binding constraints
Binding vs Non-Binding (2025 Q2e)
LHS = RHS → binding (zero slack). LHS < RHS → non-binding. At (3,27): Labour 36/36 binding. Timber 33/50 non-binding (17 slack). Storage 30/30 binding.
Binding = real scarcity. Relax to improve. Non-binding → already surplus.
Shadow Prices (Lecture 12)
Increase in objective from one more marginal unit of a constrained resource.
Three properties:
- Internal — value to this model only
- Marginal — value of the next unit, not average
- Conditional — assumes everything else fixed
Pattern: binding → positive shadow price. Non-binding → zero (fourth leg on a three-legged stool).
≠ market price. Shadow price = ceiling on what you'd rationally pay. If shadow = £21.33 and hire at £15 → take it. At £25 → don't.
| Constraint | Binding? | Shadow Price | Interpretation |
|---|---|---|---|
| Land | Yes (75/75) | £8 | +1 acre → +£8 profit |
| Spring labour | Yes (165/165) | £21.33 | +1 hour → +£21.33 profit |
| August labour | No (57.5/65) | £0 | 7.5 hrs unused |
| Working capital | No (1800/2000) | £0 | £200 unused |
| Potato quota | No (35/48) | £0 | 13 acres unused |
Ranking: spring labour (£21.33) > land (£8) > rest (£0). Invest in spring labour first.
Allowable Range
Shadow prices hold within an allowable range. Beyond it, different constraint becomes binding → old price invalid. Spring labour: +10 allowed → £21.33 holds from 165–175. Past 175, re-solve.
Exceeding range ≠ loss. Just means old number no longer applies. Non-binding: allowable increase = ∞, decrease = current slack.
One-at-a-time. Change two simultaneously → neither reliable → re-solve.
"How to Increase Profits" (2025 Q2e [20])
- Identify binding constraints from graph
- Only binding limits profit — non-binding have slack
- Argue which to relax — target constraint restricting more profitable activity
- Acknowledge limit — improvement holds until another constraint binds
- Real-world advice — hire workers, expand storage, etc.
Tie-Lines (Lecture 12)
Enforce flow conservation in complex models. RHS = zero (accounting balances). "Tell the story" across a row and down a column. Tested in 2021 Q1 (remote); not yet in-person.
Beyond Simple LP
Dynamic LP: sequential stages. NLP: curves, no global optimum guarantee. MIP: integer decisions. Good closing sentence for limitations.
Adding a Constraint
Can only maintain or worsen the optimal. Cutting away feasible region.
Advantages (2021 [20])
- "One answer, not an argument."
- "Change a number, re-solve in seconds."
- Imposes discipline
- Output info — bottlenecks + shadow price rankings
Disadvantages (2021 [20])
- "One goal only." Hides trade-offs.
- "Straight lines in a curved world." Misses thresholds, tipping points.
- Data uncertainty. Garbage in, garbage out.
- Divisibility. Fractional answers.
- Static. One moment; misses path dependence.
- Communication difficulty.
- Construction risk. Quiet errors → confident wrong answers.
2021 (solver output + sensitivity), 2024 (formulate + draw + solve), 2025 (+ advise on increasing profits). Both recent in-person exams. 2025 part (e) tested shadow price reasoning without tables — expect recurrence. Numbers will be clean.
- (a) Formulate — variables → objective → constraints → non-negativity
- (b) Define types
- (c) Draw — labelled axes, lines, intercepts, feasible region
- (d) Solve — simultaneous equations, objective at each corner, optimum
- (e) Advise — binding/non-binding → which to relax → shadow price reasoning → real-world action → allowable range caveat
A5. Pollution Control Mechanisms
The Core Chain
A1 = problem. A5 = solution toolkit.
The Four Instruments
1. Coase (inter-agent bargaining). 2. Standards (command-and-control). 3. Pigouvian tax (market-based). 4. TPPs / cap-and-trade (market-based).
Coase Theorem
4 assumptions: clear property rights, zero transaction costs, full info, rational agents. Duke Energy: QSO reached either way; only payment direction changes.
Fails: free riders (biggest), transaction costs, info asymmetry, intergenerational equity, dispersal, strategic behaviour.
Standards
Legal cap at QSO. All firms comply equally. No reward for over-compliance.
Pigouvian Tax
T = MSC at QSO. MAC < T → abate. MAC > T → pay. Stops at MAC = T → voluntarily chooses QSO.
TPPs
Permits = QSO. Same firm logic (replace "tax" with "permit price"). Grandfathering vs auctioning — efficiency identical. Can: meet, sell surplus, buy more. Cannot "pay carbon tax."
Three-Firm Comparison
TPP vs Tax
TPP: quantity certainty, inflation-proof, industry-friendly. Tax: simple, double dividend, polluter-pays, no hoarding.
Enforcement
Leakage: production moves to unregulated jurisdiction. CBAM (EU, Jan 2026). Info asymmetry: incentive to cheat.
Case Studies
EU ETS: crashed to <€4 (2008); reforms → >€80 (2022). BP: internal trading, met 2010 target 9 years early. Montreal Protocol: ban correct when optimal = zero.
2020 Q3 (aviation), 2025 Q1c (intervention). Often 30-mark subpart.
- Frame (link A1)
- Name & classify
- Mechanism
- Three-firm argument
- Pros/cons
- Evidence
- Enforcement
- Critique
B1. Sustainability Frameworks Pending
IPAT (I = P × A × T). EKC (shape + critique). Strong vs weak sustainability.
IPAT: 2020, 2025. EKC: 2020. Strong/weak: 2020.
B2. Ecology Fundamentals Pending
Limiting nutrients. Diversity response to nutrient addition. Trophic levels.
2024 Q5. Mechanism-based.
B3. Agriculture & ILUC Pending
Organic vs conventional. ILUC. Land sparing vs sharing. Mitigation hierarchy.
2020, 2021, 2024, 2025. HIGH frequency.
B4. Urban Biodiversity Pending
Abiotic factors. Mechanisms. Policy links.
2021 Q6, 2025 Q5a.
B5. Resource Curse Pending
Definition. Mechanisms. Counter-examples.
2021, 2024.
B6. Corporate Influence Pending
Macro strategies. Legg et al. (2021) 5 methods. Examples.
2024 Q4c, 2025 Q6a.
B7. Behaviour Change Pending
Policy tools. Crowding in/out. Judge et al. 5-stage model.
2020 Q6b, 2025 Q6b. Know the graph.
B8. Circular Economy Pending
Lower frequency. Keep brief.
Key Linkages
A-Section Pipeline
- A1 → A2 → A3 → A5: externalities → valuation → CBA → instruments
- TCM → demand curve → CS → CBA benefit stream
- Shadow price of carbon = MSC at QSO = internalisation price = CBA damage cost = Pigouvian tax rate
Welfare & Fairness
- Kaldor-Hicks ↔ Pareto: K-H relaxes "no losers"
- Discount rate ↔ MSC estimation: same parameter, same debate
- WTP/WTA gap → CBA critique: wealth bias
A1 → A5 Bridge
- A1 = problem, A5 = solution
- Coase ↔ commons: fails for same reason commons exist
- EU ETS €4 ↔ social cost ~$100: market failing to price
Optimisation Connections
- Binding constraints → policy advice: bottlenecks = where to intervene. Shadow prices rank priorities.
- LP shadow prices (A4) ≠ non-market shadow prices (A2): LP = marginal constraint value from solved model. A2 = hypothetical market-clearing price. Both internal and marginal, but different sources. Don't confuse in exam.
- LP ↔ CBA critique: both precise-looking from uncertain inputs, both compress into one metric
- LP formulation ↔ A1: both force defining "best"
- Three-firm (A5) ↔ CBA (A3): cheapest option does the work
Section B (to expand)
- IPAT → EKC → Strong/weak sustainability
- Organic/ILUC → Land sparing vs sharing → Mitigation hierarchy
- Corporate influence → Policy failure → Behaviour change
Progress Tracker
- ✅ A1. Externalities & Market Failure
- ✅ A2. Non-Market Valuation
- ✅ A3. Cost-Benefit Analysis
- ✅ A4. Optimisation — Lectures 11 + 12 complete (formulation, graphical, binding, shadow prices, allowable ranges, tie-lines, extensions)
- ✅ A5. Pollution Control Mechanisms
- ○ B1–B8 — awaiting Alfy lecture reviews
- ○ Lecture 10 (JB) — lower priority
- ○ Answer templates — Phase 2
- ◐ Cross-cutting — partially updated (LP ≠ A2 shadow price distinction added)