Welfare Foundations, CBA & SCC

What sustainability economics is

Three justice relationships

What: Economics studies behavior as a relationship between ends and scarce means with alternative uses. Sustainability economics adds: the allocation must be not only efficient but also just along three axes.

Remember: (1) Intergenerational justice — between humans of different generations; (2) Intragenerational justice — between humans of the same generation (you here vs people across the globe); (3) Human–nature justice — between humans and non-human nature. Drupp focuses mostly on the first two. Definition (Baumgärtner & Quaas 2010): use scarce environmental goods + their human-made substitutes/complements efficiently across these justice dimensions.

The doughnut (Raworth; O'Neill et al.)

What: A social floor (inner ring — basic needs met for everyone, today and future) and a biophysical ceiling (outer ring — planetary boundaries on climate, nitrogen/phosphorus, etc.) that natural scientists say we shouldn't transgress.

Why: Boundaries are themselves normative (value judgments about risk). We want to be inside the doughnut.

Remember: O'Neill et al.'s cross-country chart — x-axis = number of biophysical boundaries transgressed, y-axis = number of social thresholds met. Rich countries (Germany, Netherlands) meet social thresholds but transgress nearly all boundaries; some poor countries respect boundaries but don't meet basic needs. The "meet needs and stay within boundaries" top-left quadrant is empty for every country — every country has a sustainability challenge.

Global risk framing (World Economic Forum)

Remember: Over a 2-year horizon, decision-makers rank geo-economic confrontation, misinformation/disinformation, conflict, cyber-insecurity, inequality. Over a 10-year horizon the top three flip to environmental: extreme weather events, biodiversity loss/ecosystem collapse, critical change to Earth systems. Lesson: these problems look non-acute short-run but dominate long-run — which is exactly what makes discounting decisive.

Why we need sustainable economic policy

The two Fundamental Theorems of Welfare Economics (FTWE)

What — 1st FTWE: In an ideal (utopian) market, every competitive equilibrium is Pareto efficient (no one can be made better off without making someone worse off). 2nd FTWE: Any Pareto-efficient allocation can be reached as a competitive equilibrium via suitable redistribution of initial endowments.

Why/Remember: The 2nd FTWE implies you can separate efficiency and equity — redistribute first, then let markets run. Trap: this separation holds in the textbook but not in the real world, and the 1st FTWE breaks down under market failures. That breakdown is the entire reason environmental policy exists.

Four canonical market failures

Remember: (1) Externalities (too little internalization — CO$_2$); (2) Public goods (too little provision — clean air); (3) Market power (distorted competition — monopoly); (4) Information asymmetries (adverse selection, moral hazard). Plus transaction costs, etc. Each justifies policy on efficiency grounds. But beware state failure — government intervention doesn't always improve things. For equity we additionally need redistribution across the three justice dimensions.

Moral compasses

Three families of moral theory

Remember: (1) Consequentialism (judge by outcomes) — its prominent case is utilitarianism (Bentham, Mill); economics operates here ~99% of the time. (2) Deontology (Kant) — judge the actions themselves; the categorical imperative: act only as you'd want everyone to act. (3) Virtue ethics (the Greeks, Aristotle) — do what a virtuous person would do (hard to operationalize: who counts as virtuous?). Some non-consequentialist concerns (a fair process) play no role in utilitarianism.

Welfarism and the Social Welfare Function

Two assumptions for utilitarianism

Remember: (1) individual utility is measurable; (2) utilities are interpersonally comparable (your 9 vs my 8). Then you sum utilities (pleasures minus pains).

Bergson–Samuelson SWF (Social Welfare Function)

What: $W = W(u_1, u_2, \dots)$, increasing in each argument. Maximizing it yields an allocation that is both efficient and socially optimal under that criterion.

• Utilitarian: $W^{\text{util}} = \sum_i u_i$. Social indifference curves have slope −1; further out = better. With identical concave utility → equal consumption. General condition for the welfare max: marginal utilities equal across people. If preferences differ, equal marginal utilities can require unequal incomes.
• Maximin (Rawlsian): $W^{\text{max-min}} = \min_i\{u_i\}$ — maximize the worst-off person's utility (Leontief-shaped, kinked indifference curves). Condition: absolute utilities equal (if feasible). Maximin does not generally imply equal incomes — with different utility functions you give different endowments.

Utility of income: decreasing marginal utility

What: Empirically (Deaton, Nobel laureate), mean life satisfaction (0–10 scale) rises with per-capita income but at a decreasing rate — each doubling of GDP gives roughly a constant increment. Rule of thumb: utility rises with income but at a decreasing rate (decreasing marginal utility of consumption).

Remember (CRRA / isoelastic): $u(y) = \dfrac{y^{1-\eta}-1}{1-\eta}$ for $\eta \neq 1$; $u(y) = \ln y$ for $\eta = 1$ (the special log case). $\eta$ = elasticity of marginal utility: if income rises 1%, marginal utility falls by $\eta$%. $\eta$ also measures inequality aversion across whatever dimension (time, space, states of nature).

Discounted utilitarianism

The standard climate-IAM welfare criterion

What: A weighted sum of utilities, where the future is down-weighted by a discount factor $D$:

$$W = u(c_1) + D\,u(c_2), \qquad D = \frac{1}{(1+\delta)^t}$$

Why: This is the standard objective inside DICE and most IAMs. $\delta$ is the PRTP (Pure Rate of Time Preference) / utility discount rate — how much we discriminate against the future just because it's the future. Lowering $D$ (raising $\delta$) shifts more of the resource pie to the present generation.

Ramsey's verdict

Remember: Ramsey (1928) called a positive $\delta$ "ethically indefensible" — he argued $\delta = 0$ (give equal weight to all generations). 100 years later, three standard arguments are made for $\delta > 0$:

• Extinction risk. Future people may not be around. If exogenous, model it as a hazard rate ≈ a PRTP. The UK government explicitly includes a societal-extinction-risk component. Illustration: a 50:50 chance of surviving the next century → $\delta \approx 0.69\%$; a 90% survival chance → $\delta \approx 0.1\%$.
• Non-discrimination / Arrow-type critique. $\delta = 0$ can demand implausibly high savings from the current generation (you can make all future generations better off).
• Descriptive argument (Nordhaus). Calibrate society's impatience against observed market interest rates — that's how markets balance these concerns.

$\eta$ as inequality aversion (across time)

Remember: In the two-generation resource-split problem, raising $\eta$ from 0.5 → 1 → 2 → 4 moves the optimal allocation toward the 45° line (equal shares across generations). Convergence to equality is faster the lower the discount rate (higher $D$). $\eta = 0$ with no aversion → give everything to generation 1. $\eta$ signals inequality aversion across time, space, and states of nature.

Critiques of welfarism

Rawls (philosopher) — three objections

Remember: (1) Offensive tastes — utility from harming others (Roman gladiator spectacle); a social evaluator shouldn't count it. (2) Expensive tastes — only happy with a Rolex; maybe don't respect it. (3) Conceptions of welfare are so diverse they're incommensurable (undercuts interpersonal comparability itself). Rawls's positive theory: equal basic liberties come lexically first, then the difference principle — socio-economic inequalities arranged to benefit the least advantaged, with positions open to all. This is a maximin-type approach.

Sen (economist) — capability approach

Remember: Adds the critique of cheap tastes — preferences formed under deprivation; the poor "learn to be satisfied with little," so a welfarist function won't give them much, which is unfair. Sen says focus not on income, not on utility, not even on Rawls's primary goods, but on functionings (being nourished, mobile, healthy, self-respecting, part of community) and capabilities (the freedom to choose among functionings). Equalize capability sets, not an index of functionings — freedom to choose has intrinsic value (book: Development as Freedom). Sen also rejects a single idealized theory of justice: we can rarely agree on the ideal, but we can agree on injustices and should work on those.

Cost-Benefit Analysis (CBA)

The basic idea

What: Do a project's benefits outweigh its costs? Choose projects with the highest benefit-cost ratio under scarcity. Utilitarian logic. The devil is in the detail: whose costs/benefits count, how to measure them, how to aggregate across states of nature, individuals, generations, and species.

Pareto → potential-Pareto chain

Remember: A Pareto improvement makes at least one person better off and no one worse off. A potential Pareto improvement raises one person's well-being by more than it lowers another's → in principle everyone could be made better off if the loser were compensated. This is the Kaldor–Hicks(–Scitovsky) compensation criterion: a reallocation is desirable if winners could compensate losers and still gain (and losers couldn't bribe winners to block it). Caveat: compensation rarely actually happens in full → you must examine distributional effects.

CBA in practice

Remember: Developed in the US (~100 yrs, Army Corps of Engineers); Reagan's executive order mandated CBA for all economically significant federal regulations; 2003 OMB guidance made benefit-cost analysis central; EPA recognized it as instrumental for sustainability decisions. Currently: the Trump administration has largely scrapped the EPA's ability to run environmentally-informed CBA. Germany: CBA is mandated in the Bundesverkehrswegeplanung for large transport projects (the biggest was the deepening of the river Elbe). Switzerland: regularly run for large transport projects — the canonical recent example is a highway expansion where the climate/CO₂ damages became a big public/media issue; BAFU updated its cost-of-emissions estimates (SCC) mid-debate, and voters ultimately rejected the highway. Shows SCC estimates matter both in regulatory analysis and public debate.

The "most important CBA": climate change

Three economists, three views

Remember: Stern — "the greatest market failure the world has ever seen." Weitzman — the climate system is "an angry beast we are poking with sticks"; treat it as an insurance problem, not standard CBA, because of large uncertainty in damages. Nordhaus — good policy lies "between wrecking the economy and wrecking the world"; it's a balancing act = CBA. They differ on how much to do — and we unpack where that comes from (parameters + evaluation framework).

Integrated Assessment Models (IAMs)

What: Couple a stylized climate model (temperature, precipitation, ecosystems) with a stylized economic model (world economy over centuries). Integrated = they're linked: production → emissions → climate change → climate damages → back to the economy. Assessment = a normative objective function (a SWF — usually discounted utilitarian) sits on top, telling us how to assess the problem.

Remember (DICE structure): mitigation cost $\Lambda_t(\mu_t)=\theta_{1,t}\mu_t^{\theta_2}$ (convex, $\theta_2\approx 2.6$); damages quadratic in temperature, $D(T)=\psi T^2$; net output $Y^{\text{Net}}=(1-\Lambda)(1-D)Y^{\text{Gross}}$. The discounted-utilitarian objective runs 500 years in 5-year steps with PRTP $\delta$ and $\tilde C$ ≈ market consumption. DICE takes the descriptive route (calibrate $\delta,\eta$ to market interest rates) but still labels a path optimal — which requires a normative model behind it.

Nordhaus vs. Stern outcomes

Remember: Nordhaus's "optimal" path → ~3.5 °C warming by 2100 (business-as-usual ~4 °C); SCC ≈ \$36/tCO₂ (rising over time). Stern's much lower PRTP → ~2 °C; SCC ≈ \$300 (≈ tenfold). The ~2 °C gap and the tenfold SCC gap come from value judgments (how much we care about future generations), not climate science. The journalist's puzzle: Nordhaus's Nobel (2018) said 3.5 °C is "economically optimal" the same morning the IPCC released its 1.5 °C special report. The Nobel committee diplomatically noted the laureate "does not deliver conclusive answers" — models translate value judgments into policy paths; moral values must complement scientific measurement on both damages and discounting.

The factor-of-20 illustration

Remember: How much would you invest today to avoid 1000 CHF of climate damages a century from now? Stern's ~1.4% discount rate → invest 250 CHF. Nordhaus's 4.5% → invest just 12 CHF. Same problem, ~20× different answer — long-term policy attractiveness is hypersensitive to discounting. (For Switzerland, SCC × emissions ≈ 1.5–13 billion CHF in annual damages, i.e. ~2%–70% of 2020 Swiss GDP depending on value judgments.)

Key formulas & one-line takeaways

Key formulas

Utilitarian SWF: $W = \sum_i u_i$; condition: marginal utilities equal.

Maximin SWF: $W = \min_i u_i$; condition: absolute utilities equal.

$$u(y)=\dfrac{y^{1-\eta}-1}{1-\eta} \quad (\eta\neq1), \qquad u=\ln y \quad (\eta=1) \quad \text{(CRRA / isoelastic utility)}$$

$$W = \sum_t D^t u(c_t), \qquad D = \frac{1}{(1+\delta)^t} \quad \text{(discounted utilitarianism)}$$

DICE net output: $Y^{\text{Net}} = (1-\Lambda(\mu))(1-D(T))\,Y^{\text{Gross}}$, with $\Lambda=\theta_1\mu^{\theta_2}$, $D=\psi T^2$.

Extinction-risk PRTP: survival prob $p$ over the century → $\delta \approx -\ln(p)/100$ (e.g. $p=0.5\to0.69\%$, $p=0.9\to0.1\%$).

One-line takeaways

• Sustainability economics = efficiency plus justice (intergenerational, intragenerational, human–nature).
• The doughnut quadrant "meet needs and respect boundaries" is empty for every country.
• 1st FTWE breaks under externalities/public goods/market power/info asymmetries — that's why we have policy; 2nd FTWE's efficiency-equity separation fails in the real world.
• Economics runs ~99% on consequentialist utilitarianism; Rawls (offensive/expensive tastes, incommensurability) and Sen (cheap tastes, capabilities/freedom) push back.
• Utilitarian SWF equates marginal utilities; maximin equates absolute utilities.
• $\eta$ does triple duty: intertemporal smoothing, inequality aversion, and (next chapter) the Ramsey discount rate.
• Ramsey (1928): $\delta>0$ is "ethically indefensible"; counter-arguments are extinction risk, non-discrimination/savings, and the descriptive market-rate view.
• CBA rests on Kaldor–Hicks (winners could compensate losers) — but compensation rarely happens, so check distribution.
• IAMs translate value judgments into policy paths; Stern → 2 °C, SCC ~\$300; Nordhaus → 3.5 °C, SCC ~\$36 — they disagree on ethics, not science.
• The discount rate alone can swing optimal climate investment by a factor of ~20.