Sustainability Economics — Cram Sheet

What Brundtland (1987): meeting needs of the present without compromising future generations. Sylvicultura oeconomica (1713): don't cut wood faster than the forest regrows. Baumgärtner & Quaas (2010): use scarce environmental goods and their substitutes/complements efficiently across time.

Remember Two big questions follow: how do we MEASURE sustainability, and how do we ACHIEVE it.

Remember Extreme poverty fell from >40% (1990s) to ~10% today. Electricity access: ~10% lack it (down from 25% in 1998); ~45% lack reliable energy; ~25% lack clean cooking fuels. Climate: on track for ~3.5°C by 2100; carbon-pricing coverage rose from 0.5% (1990) to 23.9% (2024).

Remember Example: $u = \sqrt{\text{coffees}} \cdot \sqrt{\text{croissants}}$. Bundle (25,4) gives $u=10$; (9,9) gives $u=9$; (4,16) gives $u=8$. Ranking: $X_2 \succ X_1 \succ X_3$.

Remember Concave utility ⇒ decreasing marginal utility with income. The poor lose more welfare per franc than the rich — foundation of equity weighting, progressive cost-sharing for climate, and intertemporal discounting (when income grows).

What Capital = stock delivering a flow of services over time.

• Human capital ($K_h$): education, health, skills.
• Physical capital ($K_p$): machines, buildings, roads.
• Natural capital ($K_n$): forests, atmosphere, oceans, mineral stocks.

Remember Comprehensive wealth $K = K(K_h, K_p, K_n)$.

What Weak (flexible) = comprehensive wealth $K$ non-declining over time; capitals can substitute. Strong (strict) = each $K_i$ stays above a critical threshold; substitution NOT permitted below.

Remember Pure question: how substitutable are man-made and natural capital? Climate: weak ⇒ pay an SCC-equal carbon tax. Strong ⇒ hold $T < 2$°C regardless of cost.

Remember ~80% of global energy still from fossil fuels. Top consumers: China 27.6%, US 15.2%, India 6.3%. Electricity is only ~20% of total energy consumption. ALL future demand growth comes from emerging markets. The "Energy Pentagon" trades off 5 dimensions: affordability, reliability, climate, particulates, fiscal sustainability.

Remember (i) Wide range of impacts; (ii) Creates winners and losers across regions/sectors; (iii) Net effect large and negative — ~5% GDP-equivalent annual loss from end-of-century warming.

What Market value of final goods/services produced within a country in a period. Three approaches: production (value-added), expenditure ($Y = C + I + G + X - M$), income (wages + profits + rents).

Remember Nominal uses CURRENT prices; real uses CONSTANT base-year prices. Rising nominal ≠ rising real! Appleville: 10M apples × €2 = €20M; if next year 9M × €3.33 = €30M nominal but real output fell.

What $$\text{PPP}_{adj} = \frac{\text{basket price in A}}{\text{basket price in B}}$$

Remember Zurich basket CHF 8,800, Schaffhausen CHF 6,710 ⇒ PPP = 1.31. A CHF 120k Schaffhausen salary = CHF 157k Zurich-equivalent. Calc question: multiply salary by PPP multiplier.

$$Y_t = A_t \cdot F(K_t, H_t), \quad H_t = L_t \cdot h_t$$

$A_t$ = TFP (tech, institutions, management). In the long run, sustained per-capita GDP growth comes only from productivity ($A_t$) growth.

$$\text{social MC} = \text{private MC} + \text{external MC}$$

Remember Optimal Pigouvian tax = marginal external cost at the efficient quantity. Positive externalities ⇒ subsidies (symmetric).

What Present value of marginal damages from emitting +1 ton CO₂ today, summed over all agents and time: $$\text{SCC}_t = \sum_{j=0}^{T_{\max}} L_{t+j} \cdot \frac{1}{(1+\rho)^j} \cdot \frac{\Delta u(c_{t+j})}{\Delta u(c_t)} \cdot \frac{\Delta Y_{t+j}}{\Delta T_{t+j}} \cdot \frac{\Delta T_{t+j}}{\Delta E_t}$$

Remember DICE-2023 baseline SCC ≈ $100/tCO₂ (2025 USD). Highly sensitive to discount rate.

Baseline emissions $E_t^{\text{Baseline}} = \sigma_t \cdot Y_t$. Abatement rate $\mu_t \in [0,1]$. Abatement cost share $\Lambda_t(\mu_t) = \theta_{1,t}\mu_t^{\theta_2}$ (convex, $\theta_2 \approx 2.6$). Damage function $D(T) = \psi T^2$ (quadratic). $$Y_t^{\text{Net}} = [1-\Lambda_t(\mu_t)]\cdot[1-D(T_t)]\cdot Y_t^{\text{Gross}}$$

Remember Key tradeoff: Higher abatement today (Λ↑, lower current GDP) ⟺ lower future damages (D↓, higher future GDP).

Remember (1) Impatience / pure time preference $\delta$; (2) Income growth + concave utility ⇒ future consumption has lower marginal utility; (3) Opportunity cost — money invested today earns real return $r$. $$U = \sum_t \frac{1}{(1+\rho)^t} u(c_t)$$

Remember (1) Direct use (whale watching), (2) Indirect use (forest carbon storage), (3) Option value (preserve future use), (4) Existence value (knowing whales exist), (5) Bequest value (leaving them for future generations).

Remember If $A$ and $B$ correlate: (1) $A$ causes $B$, (2) $B$ causes $A$ (reverse causation), (3) Third factor $C$ causes both (omitted variable / common cause).

What When the association between $A$ and $B$ misrepresents the causal effect because of an unmeasured variable that correlates with both.

Remember Classic: PM2.5 vs. health spending across countries is negatively correlated — not because pollution lowers spending, but because rich countries have BOTH less pollution AND more spending. Need quasi-experimental variation to identify causal effects.

$$\text{VSL} = \frac{\text{WTP for risk reduction}}{\text{size of risk reduction}}$$

Remember Workers paid CHF 10,000 less for 1% lower risk ⇒ VSL = $10,000 / 0.01 = $1M. NOT the value of any actual life — it's the value of a small risk reduction times the people exposed.

Remember License-plate-based driving ban removing 20% of cars on workdays. Failed! Davis (2008): NO decrease in air pollution because households bought additional, older, dirtier cars. Canonical case for why behavioural-response modelling matters.

Remember Barrage & Lee (2010): ~80% said they'd donate hypothetically, only 30–50% paid with real stakes. Contingent valuation may overstate environmental benefits.

Remember 1989 Exxon Valdez: CV estimated ~$3B in non-use values; Exxon paid >$1B. 2010 BP Deepwater Horizon: CV estimated $17.2B non-use loss; BP paid $8.8B in natural-resource damages, >$65B total. Established CV as a legally recognized valuation tool.

What WNS fungal disease hit US bats from 2006, killing ~73% of affected populations. Spread quasi-randomly across counties (event study).

Remember In WNS-affected counties: insecticide use +25% (5 years out), crop revenue −28.9%, profits ~−25%, infant mortality rose suggestively. Substitution from herbicides to insecticides ⇒ total chemical expenditure roughly unchanged.

What Indian vulture populations crashed 1995–97 when veterinary diclofenac became cheap; trace residues in livestock carcasses cause vulture kidney failure.

Remember Result: +4.7% all-cause mortality ≈ +100,000 deaths/year. Mechanisms: dissolved O₂ in water −7 to −12%, fecal coliforms +200%, rabies-vaccine sales up.

Remember Bats: farmers substituted (insecticide ↑) BUT revenue still fell 29%, profits 25%, infant mortality up. Substitution IMPERFECT ⇒ strong-sust. signature. Vultures: no man-made substitute exists in low-infrastructure settings ⇒ even cleaner strong-sust. argument.

Remember DIRECT: (1) Reduced fossil-energy spend; (2) Reduced regulatory/tax/ETS compliance costs. INDIRECT: (3) Better labor recruiting/retention; (4) Lower cost of capital; (5) Increased consumer demand.

Remember Cross-agency correlation: credit ratings 0.99 vs. ESG only 0.54 (Berg et al. 2022). Decomposition: MEASUREMENT ~56%; SCOPE 38%; WEIGHTS only 6%.

Remember Scope 1: direct. Scope 2: purchased electricity/heat. Scope 3: value chain. Pearson correlations across providers: Scope 1 ~0.97, Scope 3 as low as 0.22. High-emitting firms actually invest MORE in green-patenting (Cohen et al. 2022) — high carbon ≠ "not green."

Remember Stated WTP ~30 EUR/tCO₂; revealed (aviation): only 4.5% of passengers offset; median WTP = 0 EUR/tCO₂. Failure modes: (1) Rebound; (2) No additionality (~52% of Indian wind CDM projects would've happened anyway, Calel et al. 2025); (3) Carbon leakage.

Remember BP: +1 SD of pre-spill green ads (~$1.6M) halves the demand impact of the spill — firms can reap reputational benefits without real change ⇒ need certification/standards. Catho (Colonnelli et al. 2023): job seekers significantly more attracted to ESG postings; magnitude ≈ 10% salary increase, driven by the ENVIRONMENTAL dimension.

Remember Scope 1/2/3 LEVELS carry significant risk premia (+13 / +23 / +30 bps per SD). Emissions INTENSITY (per $ sales) NOT significant. Key wrinkle: choice of emissions measure drives the result.

Remember Some investors prefer green securities ⇒ green firms face lower cost of capital $r$ ⇒ two effects:

• Growth effect: Green firms grow more (lower $r$ ⇒ higher capital investment).
• Reform effect: Higher $r(E)$ for fossil-heavy firms acts as an implicit tax on fossil energy: $$\frac{\partial F}{\partial E} = p_E + \frac{\partial r}{\partial E} \cdot K$$

The reform effect is bigger than it looks because $(\partial r/\partial E) \cdot K$ applies to the entire capital stock.

Remember Global sustainable AUM ~$35T by 2020 (+55% vs. 2016). Berg et al. 2023: ESG rating UPGRADES → ESG ownership +17% two years later; downgrades −13%. Environmental management scores NOT significantly affected; governance IS (course-correcting). Knaur 2024: tax-exempt pollution-control bonds DO drive sales / investment / R&D growth.

Remember Economic cost INCLUDES opportunity cost. Firms receiving FREE ETS allowances still face an opportunity cost (could have sold them). ETH using Villa Hatt has accounting cost ~0 but economic cost = market rent.

$$\text{MAC}(A^*) = \text{SCC}$$

Remember MAC curve is upward-sloping (cheap projects first). Stopping short of $A^*$ leaves money on the table; going past $A^*$ wastes resources. Deadweight loss = area between MAB and MAC curves over $[A, A^*]$.

$$\text{LCOE} = \frac{\sum_t C_t/(1+r)^t}{\sum_t q_t/(1+r)^t}$$

Remember With investment subsidy $\tau$: replace construction cost with $C^{\text{cons}}_t(1-\tau)$. With generation subsidy $s$: subtract $s \cdot q_t$ from the cost numerator. Exam calc: set $\text{LCOE}^{\text{renewable}}(\tau) = \text{LCOE}^{\text{fossil}}$, solve for $\tau$.

Remember (1) Misses intermittency / dispatchability / negative spot prices. (2) Excludes externalities (SCC, local PM, knowledge spillovers). (3) Discount rate + plant lifetime + subsidy treatment materially affects rankings.

Remember Static = cost of THIS project today. Dynamic = includes learning-by-doing. Covert & Sweeney 2022 wind turbines: doubling experience cuts costs 14–29% (own-learning), 1–2% within-firm spillovers, 0.1–0.6% cross-firm.

Remember 1st FTWE: In an ideal market (no externalities, no public goods, no market power, perfect info), every competitive equilibrium is Pareto efficient. BREAKS DOWN under market failures — that's why environmental policy exists. 2nd FTWE: Any Pareto-efficient allocation can be reached as a competitive equilibrium via redistribution of initial endowments ⇒ separation of efficiency and equity.

Remember (1) Externalities (CO₂), (2) Public goods (clean air), (3) Market power (monopoly), (4) Information asymmetries (adverse selection, moral hazard).

• Utilitarian: $W^{\text{util}} = \sum_i u_i$. With identical concave $u$ ⇒ equal consumption.
• Maximin (Rawlsian): $W^{\text{max-min}} = \min_i\{u_i\}$. Equates absolute utilities (may require unequal consumption if preferences differ).

$$u(y) = \frac{y^{1-\eta}-1}{1-\eta} \quad (\eta \neq 1); \qquad u(y) = \ln y \quad (\eta=1)$$

Remember $\eta$ does triple duty: (1) intertemporal allocation; (2) Ramsey discount rate; (3) equity weights in CBA. Optimal allocation: $c_1 = S/(1+D^{1/\eta})$. With log utility ($\eta=1$): $c_1 = S/(1+D)$.

Remember Nordhaus: $\delta=1.5\%, \eta=1.45$ ⇒ "optimal" warming ~3.5°C, SCC ~$36. Stern: $\delta\approx0.1\%, \eta=1$ ⇒ "optimal" warming ~2°C, SCC ~$300. Same model; different ethics.

Remember Rawls: (1) offensive tastes (sadism) shouldn't count; (2) expensive tastes; (3) welfare conceptions incommensurable. Sen: capability approach — focus on FUNCTIONINGS (being nourished, mobile, healthy) and the freedom to choose them. "Cheap tastes" adapted under deprivation.

Remember Stern (SDR ~1.4%): invest 250 CHF today to avoid 1,000 CHF damage in 100 yrs. Nordhaus (SDR 4.5%): invest only 12 CHF. Same problem, factor-of-20 different policy.

$$\text{SDR} = \delta + \eta \cdot g$$

• $\delta$ = pure rate of time preference
• $\eta$ = elasticity of marginal utility (inequality aversion)
• $g$ = expected per-capita real consumption growth

Remember 81% of experts reject the simple Ramsey Rule (Drupp et al. 2018); their imputed SDR is ~1.2 pp LOWER on average.

$$\text{RPC} = \xi(g_C - g_E), \quad \xi = 1/\sigma$$ $$\text{SDR}_E = \delta + \eta g_C - \xi(g_C - g_E)$$

Remember Drupp et al. 2024: with $\xi=1, g_E=-2.8\%$ (biodiversity LPI), RPC ~4.8%/yr ⇒ PV of ecosystem services ~+1213% vs. no RPC. Drupp & Hänsel 2021: limited substitutability raises SCC by >50% in 2020, >80% by 2100.

$$w_i = (c_i/\bar{c})^{-\eta}$$

Remember Swiss BAFU 2024: SCC without equity weighting = 130 CHF/t; with weighting ($\eta=1, \delta=1\%$) = 430 CHF/t; with $\delta=0$ + weighting = 1,370 CHF/t. Equity weighting raises SCC because climate damages fall on poorer regions.

Remember Extended Ramsey Rule with growth risk: $\text{SDR} = \delta + \eta\bar{g} - 0.5\eta(\eta+1)\sigma^2$ (precautionary). Lemoine (2021): uncertainty may raise SCC >20%. Tipping points (Dietz et al. 2021): permafrost alone +8.4% to SCC; all tipping points combined +25%. Weitzman's dismal theorem: fat-tailed damages + $\eta>1$ can drive SCC to infinity.

Remember Moore et al. 2024 synthesis SCC ~$283 (95% CI $32–$874). Drivers vs. Nordhaus: damages +$20, tipping points +$19, limited substitutability +$15, PRTP +$12, growth damages +$10, distribution +$7, alt-ethics +$5.

$$\text{MAC}_i = \text{MAC}_j = p^{\text{CO}_2} = \text{marginal damages}$$

Remember Cost-effective abatement requires MACs equal across all firms AND equal to marginal damages. Bans/standards: don't equalize MACs ⇒ NOT cost-effective. ETS: trading equalizes MACs ⇒ cheapest abatement first.

Remember Weitzman 1974: TAXES preferred when MAC slope is large relative to marginal damages slope — typically flow pollutants. Karp & Traeger 2024: for STOCK pollutants like CO₂, ETS likely superior.

Remember Eco-tax price elasticity is 4–5× larger than market-price elasticity. Three mechanisms: (1) MORAL/SIGNAL effect; (2) PERSISTENCE (taxes perceived as permanent); (3) SALIENCE (media coverage at introduction). Pure income effect is NOT the answer.

Remember (1) DID: treated vs. control, before vs. after. (2) Synthetic Control Method (SCM, Abadie): construct counterfactual from weighted donor units. (3) SDID (Arkhangelsky et al.): re-weighted DID combining strengths.

Remember Sweden carbon tax (Andersson 2019): ~−11% transport CO₂ 1990–2005. German eco-tax (Basaglia et al. 2025): CO₂ −15%, PM₂.₅ −25%, NOx −13%; health benefits ≈ 2/3 of monetized benefits. EU ETS: −14 to −16% CO₂ in regulated firms, NO contractions in activity (Colmer et al. 2024).

Remember Lump-sum "climate dividend" KEEPS the steering effect intact. Subsidising polluting goods WATERS DOWN the effect. Nesje et al. (2025) expert survey: when picking multiple, green R&D 59%, affected households 56%, distortionary taxes 43%, lump-sum 25%. Experts prefer a portfolio.

Remember Ahonen & Palanne 2025 (Finland): income deciles explain only ~1.5% of variation in fuel-tax burdens. Horizontal heterogeneity (lifestyle: car-ownership, rural residence) DOMINATES. With per-capita rebate, lower deciles can gain on net.

Remember Switzerland: ⅓ to building program; ⅔ rebated — households via health insurance (equal per-capita), firms proportional to wage bill. Austria Klimabonus: 145 EUR base + 0/50/100/145 EUR regional adder (rural gets most).

Remember (1) Egalitarian/per-capita: equal atmospheric rights. (2) Sovereignty/grandfathering: permits ∝ current emissions. (3) Polluter-pays: ∝ historical responsibility. (4) Ability-to-pay: ∝ GDP.

Remember 4 conditions: (1) Shared public-resource good; (2) Cooperative arrangement makes members better off; (3) Non-members can be EXCLUDED OR PENALIZED at low cost; (4) Stability. Quantitative: ~$50/tCO₂ + 2–10% tariff sustains broad participation. NO tariff ⇒ no country joins. CBAM (transitional 2023, full 2026): covers iron/steel, cement, fertilizer, aluminium, hydrogen, electricity.

Remember Both non-excludable. CPRs (fisheries, groundwater) are RIVALROUS. Cooperation breaks down FASTER in CPR than VCM because defectors can actively undo others' contributions.

Remember (1) Clearly defined boundaries; (2) Rules match local conditions; (3) Collective-choice arrangements; (4) Monitoring; (5) GRADUATED SANCTIONS; (6) Conflict-resolution mechanisms; (7) Minimal recognition of right to organise; (8) Nested enterprises.

Remember MSY: effort $E_{MSY}$ maximizes biological growth ($S_{MSY} = K/2$, $Y_{MSY} = rK/4$). Efficient effort $E_e$ < $E_{MSY}$ (effort is costly). Open-access $E_c$ > $E_{MSY}$ (rents to zero). Ordering: $E_e < E_{MSY} < E_c$. Under open access, the shadow price of the stock = 0.

Remember Regime shifts in both ecological (lake eutrophication, coral collapse) AND economic systems (financial crises, poverty traps). HYSTERESIS: recovery may require much LARGER reversal than the original perturbation.

Remember 5 factors: (1) Environmental damage, (2) Climate change, (3) Hostile neighbours, (4) Loss of trading partners, (5) Society's response. Key: "conflict between short-term interests of those in power and long-term interests of society as a whole."

• Monetary composites (inclusive wealth, CWON): aggregate to $; one number; needs shadow prices.
• Dashboards (SDGs, Swiss MONET): transparent; no single comparable score.
• Composite indices (HDI, OHI, EPI): single score; sensitive to normalization + aggregation.

$$W = \sum_i p_i \cdot K_i$$

Remember Hartwick rule: invest exhaustible-resource rents in reproducible capital. Currently a WEAK-sustainability measure. 1992–2010: global W per capita +50%; NATURAL capital per capita ~−2%/yr.

$$M_r(x) = \left(\sum_i w_i x_i^r\right)^{1/r}$$

Remember Special cases: $r=1$ (arithmetic, $\eta=0$, perfect substitutes — HDI pre-2010); $r\to0$ (geometric, $\eta=1$ — HDI post-2010); $r=-1$ (harmonic, $\eta=2$, stronger complementarity); $r\to-\infty$ (minimum, $\eta\to\infty$, Leontief/strong sustainability).

Remember $N > 6{,}000$ participants, 12 coastal countries. Median $\eta \approx 3$ — most people see goals as COMPLEMENTS (beyond harmonic mean). Recomputed OHI DROPS by ~20%. Standard arithmetic-mean indices paint too rosy a picture of sustainability.