Sustainability Economics

• Introduction to Sustainability Economics
• Economic Growth, Sustainability, Market Failures
  • Macroeconomic Refresher
  • Microeconomic Refresher
  • Integraded Assessment Models (IAMs) and the DICE Model
• Quantifying the Economic Value of the Environment, Part 1
• Quantifying the Economic Value of the Environment, Part 2
• Market Value of Firms’ Sustainability Investments
• Costs of Sustainability Investments: Basics
• Firm’s Capital Costs and Environmental Risks
• Welfare Economics
• Principles of Benefit-Cost Analysis (BCA)
• Extensions of BCA: Distribution, Substitutability, and Uncertainty
• Environmental Policy: Instrument Choice and Efficiency
• Policy: Distribution and International Cooperation
• Collapse, Resilience, and Common Pool Resources
• Measuring Sustainable Development

1. Introduction

Economics is the study of how people use scarse resources and respond to incentives.

Sustanability economics tries to understand and manage the long-term relationships between humans and nature so that scare enviromental goods, and their human-made substitues or complements, are being used efficiently.

Sustainability approaches tries to understand what do we want to preserve:

• Income, consumption
• Wealth, capital
• Utility, social Welfare
• Possibilities, opportunities
• Nature, ecosystem
• ...

An Outcome-Oriented approach seek to preserve realized human well-being over time (actual experience).
An Opportunity-Oriented approach seek to preserve means to generate welfare (potential of the future).

In relation to this, we define Capital $K$ as stock that can be used to deliver a flow of services, and we distinguish:

• $K_h$: human capital (people, education, health)
• $K_p$: physical capital (infrastructure, machines, buildings)
• $K_n$: natural capital (ecosystem, atmosphere)

Comprehensive Wealth incluse the total value of all capital stocks.

• "Weak" sustainability use and invest in natural and human-made capital stock such that comprehensive wealth doesn't decline:

• "Strong" sustainability use and invest in natural and human-made capital stock such that no stock $i\in \{h,p,n\}$ falls below a critical level:

Example: a strong approach to climate change limits temperature change below critical levels (example: limit warming at 2° no matter of the cost).
A weak approach balances costs and benefits of emissions reductions (impose carbon tax to ensure that fossil fuels are only burned when their benefit exceed social cost).

2.1 Economic Growth, Sustainability, Market Failures - Macroeconomic Refresher

GDP (Gross Domestic Product) is the market value of the final goods and services produced within the borders of a country during a particular time period.
It can be measured in 3 ways:

• the production approach
• the expenditure approach
• the income approach

The idea behind the production approach is to sum up the market value of the final goods and services produced in a year.

Example: Giacomo's Racing Bikes
Giacomo's Land is a small country with one employer (Giacomo's GmbH) that produces 100 racing bikes a year. The market price of an racing bike is $10^{\prime }000\text{ CHF}$ (yes, they are very expensive!).
All Giacomo's Land citizens work in the bike factory, that also owns all the machines, so it onlz needs to hire workers.

To determine the market value of production, we simply do:

Note that we focus to the final value at tend of the production chain (value added), so we sum the ssales revenues minus the firm's purchases of intermediate products to avoid double-counting.

The expenditure approach looks at the total value of expenditures on goods and services produced in the domestic economy by considering:

• $C$: consumption (good and servies bought by domestic households)
• $I$: new physical capital investments from domestic households and domestic firms
• $G$: government expenditures
• $X$: exports of goods and servies produced domestically and sold abroach
• $M$: imports of goods and services produced abroad and sold domestically

and calculating GDP ($Y$) as:

Nominal GDP is the total value of production using current market prices to determine the value of each unit.

• An increase in GDP will record both increases in actual production and increases in the prices of goods and services.

Real GDP is the total value of production using constant market prices_.

Real GDP allows then to compute real changes in output across time since we adjust for the price levels.

In a similar way, PPP (Purchasing Power Parity) adusted income measures adjust for differences in cost of living across locations:

A very useful tool to visualize PPP adjustments is Numbeo - Cost of Living .

For example, this comparison between Zurich and Naples shows absolute different in prices. If we want to compute PPP Adjustments, we simply do:

For example, in case we wanto to compare salaries, and we assume the following:

• average pizza-man salary in Naples: $25^{\prime }000$€
• average pizza-man salary in Zurich: $60^{\prime }000$€ we just have to re-compute the Zurich'one with the PPT adjustments:

meaning that purhcasing power of Zurich's pizza-men is actually higher.

We recall that the aggregate production function for GDP is:

• $K_t$: investment and construction
• $L_t$: labor force participation
• $h_t$: education
• $A_t$: improvements in technology, institutions, management etc...

However, in the long run, the only source of sustained GDP per capita growth is the growth in productivity $A_t$. (Note that, given the right incentives, market can direct productivity improvements in almost any direction).

Starting from the aggregate production function, the Integraded Assessment Modelds (IAMs) integrade enviromental and resource dynamics into macro-economic analysis.

Firstly, we can account for the role of (fossil) energy $E£ in the GDP production:

Intuition: using more (and cheap) energy today increases GDP today.

Then, we add climate model to account for effects of fossil use energy on warking $T_t$:

and then we add $A_t$ to the GDP's formula:

Note that, in reality, energy consumption $E$ affects all the determinants of GDP, not only the productivity (for example, investments depends on depreciation rate, also affected by climate change). Most important, climate changes also has strong effects that don't affect GDP directly (non-market impacts such as elderly mortality, biodiversity etc etc...)

2.2 Economic Growth, Sustainability, Market Failures - Microeconomic Refresher

For a better review, please also refer to my microeconomic notes .

First Fundamental Theorem of Welfare Economics states that, in absence of market failures, free competitive markets lead to the economically efficient outcome.

• Intuition on the consumer side: consumers spend money on a given good until their marginal benefit from another slice is just equal to the marginal cost (the price they pay) of buying an additional unit.
• Intuition on the producer side: firms produce as much of a good until their marginal cost is just equal to the marginal revenue they sell at.

Markets allocate scarse resources efficiently because prices serve as a signal of the value and cost of using the resorces to produce a given good.

A market failure is a problem that causes the free market to deliver an outcome that is inefficient.

• Private marginal cost is the direct cost of producers of producing an additional unit.
• Social marginal cost is the private marginal cost plus any external costs or benefits of producing an additional unit.

Intuition: social marginal costs measure the full costs to society.

2.3 Economic Growth, Sustainability, Market Failures - Integrade Assessment Models (IAMs) and the DICE Model

IAMs are integrade models of the economy and the enviroment.
In macroeconomic, there are the following assumptions and behaviors:

• firms maximize profits
• households maximise well-being
• agents anticipate the future
• market equilibrium represents a solution.

Interdisciplary and policy IAMs often take these assumptions are given, but they miss the feedback loop: they calculate how growth affects the climate, but they struggle to calculate how much that climate change affects back into the economy.

The Nordhaus DICE Model (1992) is based on the Ramsey-Cass-Koopmans growth model, whose aggregate production function is:

where $Y_t^{gross}$ is the global gross output, $A_t$ the total factor productivity, $K_t$ the capital stock and $L_t$ the labor. (Note that many IAms also include energy services as production input).

The DICE models also introduce calculates the baseline industrial carbon emissions as:

where ${\sigma }_t$ is the baseline emissions intensity of the economy. (Note that, in the past ${\sigma }_t$ showed a linear-decading trend).

In addition to this baseline decarbonization trend, society can undertake additional efforts to reduce carbon emissions so, if we define ${\mu }_t\in [0,1]$ as the fraction of emissions reduced, we can model:

and then we represent the costs ${\Lambda }_t$ of emissions reductions as a share of GDP:

The Nordhaus DICE Model also accounts for CO2 emissions and, from the atmospheric carbon concentrations $M_{AT,t}$, it models the increased radiative forcing $F_t$ (measuring how much extra heat (in Watts per square meter) is being trapped at any given time $t$.)

• $\frac{M_{AT,t}}{M_{AT,1750}}$: This ratio compares the current amount of carbon in the atmosphere ($M_{AT,t}$) to the levels before the Industrial Revolution ($1750$).

• The Logarithm represents the diminishing returns of $C{O}_2$. Every time you double the concentration, you get a fixed increase in temperature.

• $\eta$ (Eta) is the climate sensitivity parameter

• $F_t^{Abate}$ & $F_t^{Ex}$: These represent forcings from sources other than $C{O}_2$ (like Methane or Aerosols).

Intuition: increasing $F_t\to$ increased temperatures.

The model indeed estimated the global atmospheric surface temperature change over pre-industrial levels, $T_t$ as a function of the history of CO2 emissions and other forcings:

Then, the model summarizes the climate change impacts on economy with a damage function $D(T_t)$, which captures the faction of GDP-equivalent loss from warming $T_t$, so we can write:

• reducing emissions (higher ${\mu }_t$) costs money today but reduces climate damage in the future ($T_t$ decreases)
• macro-level inter-temporal trade-off are analogous to standard consumption/saving decisions.

To understand the inter-temporal tradeoffs, we consider each household's lifetime utility $U$ as:

where $u(c_t)$ is concave function of utility of each household at period $t$ and $\rho$ the discount factor.

Recall that the final goal of the DICE model was to estimate the social cost of carbon (SSC), defined he total damage that one extra ton of carbon emitted today causes to the world for the rest of time.

Intuition: $SC{C}_t$ sums all the discounted future changes in utility (wealth effect), weighted by the effect on future GDP changes (economic damage) and the effect of future temperature changes (climate damage).

Furthermore, regarding the DICE model, we can consider 5 different scenarios:

1. Baseline: Current policies + trends
   • Global carbon price of $6/tCO2 in2020, growing 2.5% per year
2. Paris Extended:Reach 2030 goals + continue
   • Emissions control rate growing ≈0.5p.p./yr from2030-2100
3. Cost-Benefit Optimal: Maximize welfare function
4. 2◦Target: Maximize welfare + temperatur econstraint
5. Alt. Discounting: Modify utility parameters to yield (near) constant discount rates of 1%, 2%, ... 5% per year

3. Quantifying the Economic Value of the Environment, Part 1

Methods to value the enviroment include:

• statistical methods
• experiments
• structural models
• structured surveys

If two variables $A,B$ are correlated, it may be the case that:

• $A$ causes $B$
• $B$ causes $A$
• a third factor $C$ causes both $A,B$

The omitted variable bias occurs when the association of $A,B$ gives an iaccurate (biased) impression of the causal impact of $A$ on $B$ (or viceversa) because of an omitted third variable.

Cross-sectional analysis implies comparing outcomes across unit at a given point in time. (example: evaluating different countries parameters in the same year).

The omitted variable bias is particularly common in the cross-sectiona analyses since it is difficult to isolate effects of a specific variable out of all the other things (ceteris paribus concept, please refer also to my Econometrics Notes about that).

Time-series analysis, in contrast, compares outcomes across time.

Pane analysis tracks and compares outcomes across both time and units. It casn easily control for some omitted variables such as time-invariant differences across units or shocks that affected everyone.

In general, even with carefully designed analyses of sample data, we cannot guarantee that there are not omitted variables (bias), one way to ensure better accuracy is to couple laboratory experiments in controlled settings with field experiments in real world. Example: randomized control trials (RCTs).

Experiments and quasi-experimental analyses of sample data can provide precise insights from specific settings, but they cannot provide any intelligence regardging:

• interactions/effects not-observed in historical data
• effects on a larger scale
• welfare impacts of enviromental changes beyond immediate monetary costs.

Structural models can help us provide a broader measure of economic value of the enviromental capital.

Strictly related to that, we can define the Value of Statistical Life (VSL) as the additional cost that invididuals would be willing to pay for improvements in satefy that, in the aggregate, reduce the expected numbers of fatalies by one.

VLS represents the value of the mortality risk reduction.
Examples: how much are you willing to pay to travel in airplan with higher safety standards? How much are you willing to pay to go to the doctor for regular health-cancer checks?

Lets' consider this example: look at the labor market compensation for fatality risk:

• Job $1$: annual fatality risk: $2$, Salary: $60000\text{CHF}$
• Job $1$: annual fatality risk: $1$, Salary: $50000\text{CHF}$ $⟹$ workers are paying $10000\text{CHF}$ to reduce fatality risk by $1$.

If we consider 100 workers, 1 life would be saved statistically, so we can derive:

Structural model, in this context, often rely on VSL to estimate the impacts of a factor.

For example, the APEEP (AP2, AP3) Model analyzed the total PM2.5 mortality health damages caused by each sector in the US economy, with the following steps:

• models pollution emissions from almost 10'000 sources across US
• models each flow of pollution present in each county, independently on where the pollution originates
• combines demographic data for each county with pollution, using a Dose-Response function to estimate how pollution correlates with mortality. For example:

• translate mortality impacts into monetary terms based on the VSL approach.

Economists generally prefer looking at what people do instead at what people say (revealed preferences vs stated preferences).

Example: the hypotetical biasis: people generally exaggerate their willingness to pay for enviromental protection.

However, in some csases surveys can still be useful.
Consider this example: the non-use values for specific species (how do you value the life of 250'000 sea birds killed by a oli company?)

Contingent valuation (CV) is a highly structured survey used to understand values for very specific good and scenarios.

4. Quantifying the Market Value of Firms’ Sustainability Investments – Part 2

One common metric to classify how much a firm is sustainable is the ESG (enviromental, social, governance) Rating.

ESG rating method may differ across providers and they are usuaolly proprietary up to some level but, while credit ratingds from different providers show high correlation ($\approx 0.99$), correlation of ESG ratings is lower ($\approx 0.54$)

This disagreement comes from different factors:

• different agencies consider different attributes (38% od the divergence)
• different agencies measure same attributes with different methods :(56% of divergence)_
• different agencies weight them differently (6% of divergence).

A potentially more objective and more directly climate-relevant indicator may be the firm's carbon emissions.

• Scope 1: direct emissions: emissions from the firm's production (the apprea highly consistent across data providers).
• Scope 2: indirect emissions: emissions from purchased heat, electricity, stea, cooling etc (slightly less but still highly correlated across providers).
• Scope 3: indirect emissions from productio of purchased materials, activities and services (data are more noisy, substantial disagreement).

However, often the carbon emissions are not a good indicator of how much a firm is green.
For example, firms with higher carbon emissions and low ESG scores are also the most active innovators in low carbon technologies.

Another potential solution is to measure greenes at the product level.

How can we distinguish the effects of firm sustainability from potential other factors (such as skilled management or external factors)?

If we collect data on corporate bonds spreads (measure of borrowing costs or cost of capital) and ESG scores, we can estimate the following specification:

${\beta }_1$ is the "Sustainability" factor, in other words it is the coefficient that tells you the relationship between the overall spread and the ESG ratings. If ${\beta }_1$ is negative and statistically significant, it suggests that as ESG scores go up, borrowing costs go down.

The basic intuition behind this strategy is that if some other firms can reduce their gas emissions cheaper than a specific firm, that firm could pay the others to reduce its emissions, so everyone can benefit. (Indeed, many companies use carbon offsets to hekp neutralize carbon emissions that are very expensive or impossible to eliminate).

Some possible negative consequences:

• Rebound effect: people may increase energy/resources consumètion in response to the offset.
• Lack of additionality: the "paid"/sold emissions would have been reduced even with out carbon offset program payments.
• Carbon Leakage: tree planting in one country may increase emissions inn other countries throguth displacement of agricultural land and increase imports.

Market Valuation of Firm Sustainability: Insights:

With these challenges and potential problems in mind, let's study 5 general insights on indirect benefits behind sustainability:

1. (Some)Consumers are often willing to pay more for sustainable products. Intuitively, this is easy to observe with products that differ only from an enviromental point of view (same price, dimension, quality etc...). Also note that estimating demand curves (how demand changes depending on sustainability) may be very difficult and require lot of data.

For example, in Switzerland, organic products have around $12$ share of the total grocery expenditure, very high compared to the rest of Europe.

2. Consumers are not always willing to pay more, especially for CO2 emissions reductions or offsets. For example, considering 64k online bookings at a Swiss Airlin where $82$ of the buyers could have paid for "carbon tax/offset" for less than $30$ EUR/Ton, only $5$ actually offset their emissions. The median willingness to pay for offsets as $0$ EUR.

3. Consumers sometimes respond even to unverified claims of greeness, providing incentives for green-washing.

4. Labor recruitment and retention may benefit fro corporate social responsibility, even if evidence is still limited. This is particularly hard to proove since more sustainable firms may also have better management and other reasons why they might have better labor outcomes. However, experimental evidence shows that kobs seekers (on average), give importance to ESG signals.

5. Capital costs are likely lower for more sustainable firms, even if evidence is mixed. In 2021, for example, Bolton and Kapcerzyk analyze the associatoin of firm's carbon emissions and stock returns in the US:

(However, it is not clear what measure for carbon emissions is the best for this use).

The study prooved that there's an increasing risk premium based on emissions levels:

• $+1\text{ std dev}$ Scope 1 Total Emissions $⟹+1.5$ annual increase in stock return
• $+1\text{ std dev}$ Scope 2 Total Emissions $⟹+2.8$ annual increase in stock return
• $+1\text{ std dev}$ Scope 3 Total Emissions $⟹+3.6$ annual increase in stock return

However, the study failed to capture significant effect of carbon emissions intensity (emissions per unit of sales).

5. Market Value of Firms’ Sustainability Investments

In the last chapter, we saw tha there's some evidence that greener firms may face lower capital costs.

According to the Global Sustainable Investment Alliance, in the last years, there has been a increasing trend in sustainable investments:

• global sustainable investment grew $+55\%$ from 2016-2020, reaching around $35.3$ trillion dollar.
• $35\%$ of AuM is made by sustainable investments in 2020.
• "Green bonds", issued to support specific enviromental projects, represent also a growing market (even if the methods to certificate them is still challenge).

So, if some investors prefer "green securities" and there are enough of them, green investments may lower the cost of capital, leading to two potential outcomes:

• cause greener firms to growth relatively more (growth effect)
• incentivize firms to become greener (reform effect).

Consider thenm the following Partial Equilibium profit-maximization model.

Consider any firm maximizing profits by choosing capital $K$ with cost $r$, labor $L$ with wage-cost $w$, fossil energy $E$ with energy price $p_e$:

Without green investors, if we normalize the price $p$ to $p=1$ and hold labor constant for an easy rappresentation, we obtain the following simplication:

that, if we put the partial derivatives of the profit function equal to zero, brings to the following maximizing conditions:

That, in ecomomic terms, translates into:

(Generally speakiog, we assume that, holding other inputs costant, the marginal product of capital is decreasing).

We now introduce green investment, by saying that green investors can lower capital costs. For example, $r$ (cost of capital) may become an increasing function of the energy consumption $E$:

In this case, the maximizing conditions become:

If then a firm is green enough to face lower capital cost $r(E)<r$, we would expect to increase its capital investments, resulting in the growth effect:

Furthermore, the new equilibrium coming from the marginal product of fossil energy acts an an effective tax on fossil inputs, incentivizing firms to reduce the use of fossil energy (reform effect).

But... _how do esg rating changes affect who owns shares in a firm?_A

Recent research shows that ESG funds and individual investors are reponsiveto their mandate:

• 2 years after a rating upgrade $⟹17\%$ higher ownership
• 2 years after a rating downgrade $⟹13\%$ lower ownership

However, changes in the ESG ratings do NOT affect firms' ESG strategy and actions.

Florian Berg shows then that, while stock market and ESG asset managers are sensible to ESG rating upgrades/downgrades, there's no evidence that these have some economic impact.

• Climate risk effect on borrowing costs has been increasing in both slope and magnitude ($\approx$ cost of debt is rising for entities highly exposed to climate risk).

• Climate risk capitalization remains incomplete in many markets ($⟹$ financial markets have not yet fully priced the true cost of climate change into asset values)

  • Example: consider two identical homes in the same location, but one is more exposed to flood risk then it should be priced less thanks to the presentvalue of future insurance/flood costs. However, often one key issue in similar scenarios is that there are limited information regarding enviromental risks.

• Climate risk effects can be incorrectly measured by conventional methods that rely on historicla data.

  1. often there no measure of an asset's physical climate and enviromental risk exposure
  2. climate risks are correlated with other factors for asset prices.

6. Costs of Sustainability Investments: Basics

• Accounting cost: actual expenses + capital depreciation
• Economic cost: social cost of utilizing resources (taking into consideration also the opportunity cost)

• Average cost: _cost per unit produced ($\text{Total Cost}/Q$)
• Marginal cost: _cost of an additional unit produce (${\text{Total Cost}}_N-{\text{Total Cost}}_{N-1}$)

In sustainability, we already mentioned marginal cost considering the abatement cost curves, representing the costs of redcution of $C{O}_2$ emissions by an additional ton.

The curve, given the actual technologies and resources, order all the actions we can do, from the cheapest to the most expensive, to reduce emissions.
Also, te curve takes into consideration negative costs.

(Teorically, we could draw the marginal-benefit curve in the first initial abatement graph to understand where the optimal equilibrium lies, however, costs and benefits are really dinamic and hard to solve).

• Static costs: costs of a specific project (could be measured via present discounted valoue)
• Dinamic costs: overall costs of a project, including future effects and spillovers (learning-by-doing, scale effects, positive externalities etc...)

Example: in the wird-turbines sector, doubling manufacturing experience lowers costs by $14-29\%$.

However, note that the costs reduction can be given by two factors (correlation $\ne$ causation): increase in experience or increase in supply, so it's hard to draw conclusions.

• Partial equilibrium: focus on one market in isolation
• General equilibrium: consider effects on other markets.

Example: airline depaiting bunying sustainable aviation fuel:

• PE cost: extra cost of sustainable aviation fuel (fuel cost only)
• GE cost: _also consider changes in cost of labor and capital cost (it this change attracts workers/investors)

How can we measure the costs of different electricity generating technologies in a comparable way?

The levelized cost is the (constant, real) price of power that would equate the net present value of revenue from a plantís output with the net present value of the cost of production.

Assuming that a plant existas for $N$ periods and produces $q_n$ units per period $n$, the present value of costs is:

were $C_n$ is the cost of producing in period $n$ including also the capital costs.

With the same assumptions, the net present value of revenue is:

If we equate the expressions we can solve for $p_{LCOE}$:

The LCOE (levelized cost of energy) provides a easy way to compare cost of energy... but, there are two key facts about the electricity market that we must consider:

• it's costly to trasport and store
• demand is higly volatile in space and time

$⟹$ .The value of electricity depends critically on the timing, location, and controllability (dispatchability) of its production.

With increasing share of variable resources sources, some markets show zero or negative spot prices for electricity.

Sould subsidies and tax beneifts be included in the estimation?

• from private (investor) perspective: yes
• from public (economist) perspective: no

Should externalities be included in LCOE?

• Public (economist) perspective: yes

Note: GHG cost: greenhouse gas emissions cost, Non-GHG: particulate matter.

7. Firm’s Capital Costs, Sustainability, and Environmental Risks

9. Welfare Economics

The sustainability challenge implies meeting basic needs today while safeguarding opportunities for future generations:

All market equilibria (in a ideal-utopian market) are Pareto-efficient.

Any Pareto efficient allocation can be achieved as a competitive equilibrium through a suitable redistribution of initial endowments, allowing for a separatio of efficiency and distribution concerns.

$⟹$ as the conditions for a perfect market are not usually satisfied, governmental actions should be considered.

In particular, economic policy is both needed to correct market failures:

• too little internalization of external effects
• too little provision of public goods
• distorted competition due to market power or information asymetry

or to enable a "fair" distribution between:

• humans of different generations (intergenerational justice)
• humans of the same generations (intragenerational justice)
• humans and the non-human nature (interspecies justice)

To select and analyze the right economic policy, we firstly need to define a moral compass (moral theory):

• Consequentialism: justed the moral worth of the effects of an action.
• Deontological values: focus on judjing the actions themselves.
• Virtue Ethics: considers as the right action what a virtuout person whould do in that scenario.

Given the assumption that individual utilities are measurable and comparable, utilitarism sums um all the values of all the pleasures on the one oe side and those of all the pains on the other.

According to different theories, the welfare function $W$ can have different shapes but it's always increasing in all its arguments.

The 2015 Nobel Prize for analyzed the relationship between life satisfaction and Per Capita GDP, showing that each doubling of GDP is associated with a costant increases in satisfaction.

However, the relationship between income and utility is not so simple. Assuming all other aspects fixed, common findings say that utility increases with income at decreasing rate:

where $\eta$ determines the elasticity of marginal utility income:

Intuition: if income increases by by $1\%$, marginal utility decreases by $\eta \%$.

In the case of $W^{utilitarism}$ for $n=2$ in a pure distribution probel ($y_2=S-y_1$), the maximization of the welfare function brings to:

If both individuals have identical preferences, equal incomes are welfare-optimal.

If we want to maximize the utility of the worst-off individual, that is:

that, if it feasible, to:

Note that, in this csase, maximin optimization doesn't always bring to equal incomes.

If we want to maximize the weighted sum of utilites with $D$ utility discount factor (useful in the case of 2 generations, but could also work for the intertemporal utility of a single individidual), we write:

In this scenario, consider now the utility discount factor $D=\frac{1}{(1+\delta {)}^t}$ that, for different values parameters, assumes different meanings:

• $\delta =0⟹D=1$: Impartial Consequentialism

• Arguments $\delta >0⟹D<1$:

  • risk of humankind's exinction (i.e. the change of surviving in the next 100 years) brings to:
  $$\mathbb{P}(\text{surviving})=0.5=D=\frac{1}{(1+\delta {)}^{1}00}⟹\delta \approx 0.69$$ $$\mathbb{P}(\text{surviving})=0.9=D=\frac{1}{(1+\delta {)}^{1}00}⟹\delta \approx 0.11$$

  Intuition: the greater probability of surviving, the utility discount factor $D$.

Coming back at the maximization problem, it rewrites as:

in the case of maximal distribution of a resource $S$:

that brings to the following welfare maximizing condition:

John Rawls gave the following the main key critiques:

• some people derive welfare from "offensive tastes"
• some people derive welfare from "expensive tastes"
• the conception of welfare are so diverse and cannot be measurable

In 1971, he then propose the Theory of Justice:

1. each person is to have an equal right to the most extensive basic liberty compatible with a similar liberty ofr others.
2. socio-economic inequalities are to be arranged so that they are (a) reasonably expeted to be everyone's advantage, (b) attached to positions open to all.

Intuition: equalization of equal liberty must be complete and is prior to the distribution of the other primary goods, then maximize the remaining three primary social goods starting to the lwast well-off.

In contrast, Amartya Sen argued that Rawls went too far in the opposite direction of welfarism since primary goods are not the right maximanda. Instead, the focus should be on what goods to for people (capability approach).

In this debate, if the various institutional primary goods were equally supplied:

• Rawls would call for equalizing the remaining one (income)
• Sen would call for distributing income in order to equalize the functionoing that people can achieve with that income.
  • Sen defined a person's capacility as the set of vectors of functionings available to him $⟹$ he suggests not to equalize the indec of functionings, but rather for equalizing the capabilities across all people.
  • Also, since there are multiple measures of humand advantage and capability, Sen claims there's no single recipes for justice and proposes and ideal theory of justice to reduce clear inequalities.

9. Principles of Benefit-Cost Analysis in the Climate Context

A cost-benefit analysis is based on the idea of potential Pareto improvements and the Kaldor-Hicks-Scitovsky compensation criterion.
In this context, a reallocation is desirable if:

• the winner could compensate the losers and still be better off
• the losers could not compensate the winners for the reallocation not occuring and still be as well off as they would have been if it did not occur.

Note that, in realty, these compensation rarely take place and don't necessarily balance out across different projects!.

In simple BCA terms, we want to balance avoided climate damages with mitigation costs, defined as:

• ${\theta }_1(t)$: fraction of economic output that is required to reduce emissions to zero.
• $\mu (t)$: emission control rate.
• ${\theta }_2$: cost convexity parameters

Furthermore, we model the famage function as:

• $\psi$: aggregate scaling parameter for the damages on consumption via production-damages.

_Note that there's a quadratic Scaling: in the DICE model, damages scale quadratically with $T(t)$ (change in atmospheric temperature compared to pre-industrial levels).

As we seen before, the welfare function is then calculate as:

• $L_t$: population size in period $t$.
• $\delta$: rate of pure time preference, it reflects how much less we value the utility of future generations compared to the present.
• $\eta$: the (minus) elasticity of the marginal utility of comprehensive consumption, it represents society's desire for consumption smoothing or inequality aversion.
• ${\tilde{c}}_t$: index of generalized (per capita) consumption.

Following the DICE model, we can end up with the following estimation:

• Swiss contribition to global climate costs amounts between 2% (Nordhais) and 17% (Stern) of the 2020 Swiss GDP.
• The difference between the estimates is due to the different discounting terms. $\implies% choosing yher right long-term discount rate for CBA is one of the most critical problems in economics.

10. Extensions of Benefit-Cost Analysis: Distributional Weights, Limited Substitutability, and Uncertainty

11. Environmental Policy: Instrument Choice, Efficiency and Effectiveness

12. Environmental Policy: Distribution, Re-distribution and International Cooperation

13. Collapse, Resilience and the Sustainable Management of Common Pool Resources

14. Measuring Sustainable Development