Homework 5
Climate Adaptation
Question 1. Extreme Climate Risk, Uncertainty, and Policy
Background: Extreme Climate Risk
In “normal” risk situations:
- We can list possible outcomes.
- We have probabilities that we (more or less) trust.
- We can compute an expected value and compare projects using CBA.
For extreme climate risks, things are harder:
- There may be tipping points or irreversible damages, such as:
- Large-scale species loss,
- Collapse of a major ice sheet,
- Major shifts in ocean circulation (e.g., Atlantic Meridional Overturning Circulation / Gulf Stream),
- Large methane releases from thawing permafrost.
- Probabilities of these events are:
- Highly uncertain,
- Difficult to estimate from historical data,
- Possibly changing over time.
In short: we face very large potential losses with poorly known probabilities.
Scenario: A Simple Climate Policy Choice
You are advising a government about a climate adaptation + mitigation package.
They are comparing two stylized policy options over the next 50 years.
Policy X: Moderate Protection
- Reduces annual climate damages in “normal” years, but does not fully address extreme tipping risks.
- Implementation cost (present value) of the policy: $10 billion.
- Based on current models, you estimate residual climate damages (not counting the policy cost) as:
- With probability \(0.98\), damages are $100 billion.
- With probability \(0.02\), a tipping point is crossed, leading to irreversible damages of $3,000$ billion.
- With probability \(0.98\), damages are $100 billion.
Policy Y: Strong Protection / Precaution
- Includes aggressive mitigation and robust adaptation:
- Higher upfront costs,
- But stronger effort to avoid tipping.
- Implementation cost (present value) of the policy: $40 billion.
- Rough expert judgment suggests residual climate damages:
- With probability \(0.99\), damages are $200 billion.
- With probability \(0.01\), a tipping point is still crossed, but damages are $1,500$ billion.
- With probability \(0.99\), damages are $200 billion.
In what follows, damages refer to climate-related losses only; the policy cost will be added on top when we compute total expected cost.
Calculations: Expected Damages and Total Expected Cost
Expected damages under Policy X
Here we compute the expected climate damages under Policy X:
\[ \begin{aligned} E[\text{Damages}_X] &= P(\text{no tipping}) \times \text{Damages (no tipping)} \\ &\quad + P(\text{tipping}) \times \text{Damages (tipping)} \\ &= 0.98 \times \$100\text{ billion} \;+\; 0.02 \times \$3{,}000\text{ billion} \end{aligned} \]
So expected damages:
\[ E[\text{Damages}_X] = \$98\text{ billion} + \$60\text{ billion} = \$158\text{ billion}. \]
Add the policy cost of $10 billion:
\[ E[\text{Total Cost}_X] = \$10\text{ billion} + \$158\text{ billion} = \$168\text{ billion}. \]
Expected damages under Policy Y
Here we compute the expected climate damages under Policy Y:
\[ \begin{aligned} E[\text{Damages}_Y] &= P(\text{no tipping}) \times \text{Damages (no tipping)} \\ &\quad + P(\text{tipping}) \times \text{Damages (tipping)} \\ &= 0.99 \times \$200\text{ billion} \;+\; 0.01 \times \$1{,}500\text{ billion} \end{aligned} \]
So expected damages:
\[ E[\text{Damages}_Y] = \$198\text{ billion} + \$15\text{ billion} = \$213\text{ billion}. \]
Add the policy cost of $40 billion:
\[ E[\text{Total Cost}_Y] = \$40\text{ billion} + \$213\text{ billion} = \$253\text{ billion}. \]
Homework Questions
Part A. Comparing policies by expected total cost
Based only on expected total cost (policy cost + expected damages), which policy looks better?
Explain briefly using the calculations from the Section of Calculations: Expected Damages and Total Expected Cost
Answer (1–3 sentences):
________________________________________
________________________________________
- Policy X: \(E[\text{Total Cost}_X] = \$168\) billion
- Policy Y: \(E[\text{Total Cost}_Y] = \$253\) billion
Because total expected cost is lower under Policy X, a standard CBA that uses only expected total cost would say Policy X looks better (it has the smaller expected overall loss).
Part B. Role of the rare catastrophic outcome
Does the rare but catastrophic outcome play a big role in your expected value calculations?
Why or why not? Use the numbers from Policy X as an example.
Answer (2–4 sentences):
________________________________________
________________________________________
Yes, it matters a lot.
For Policy X, the catastrophic outcome contributes $60 billion of the $158 billion in expected damages (about 38%). Even though the probability is only 2%, the loss is so large that it significantly affects the expected value. This shows how low-probability, high-loss events can still be important in EV calculations, even before adding policy costs.
Part C. Risk aversion and expected total cost
Imagine you are a risk-averse policymaker who is very worried about irreversible, catastrophic damages. Would you be comfortable relying only on expected total cost to choose between Policy X and Policy Y? Why or why not?
Answer (2–4 sentences):
________________________________________
________________________________________
Probably not.
A risk-averse policymaker cares especially about worst-case scenarios, not just the average total cost. Even though Policy X has a lower expected total cost, its higher probability and severity of the worst-case outcome might be seen as unacceptable. A risk-averse decision-maker might still favor Policy Y, because it reduces the worst-case damages, even though its expected total cost is higher.
Part D. Risk vs. uncertainty
Give one reason why extreme climate risks are closer to uncertainty (in the economist’s sense) than to well-defined risk.
Answer (1–3 sentences): ________________________________________
In economics, risk means we know (or can estimate) the probabilities of different outcomes, while uncertainty means we do not. Extreme climate events—like sudden ice-sheet collapse or large methane releases—often have poorly known or widely debated probabilities, so they fit better under uncertainty than under well-defined risk.
Part E. Link to the Precautionary Principle
In 2–4 sentences, explain how extreme climate risks (tipping points, irreversible damages, uncertain probabilities, very large losses) can justify:
- Following a precautionary principle, and/or
- Adopting a safe minimum standard for climate policy.
Answer (2–4 sentences):
________________________________________
________________________________________
Extreme climate risks involve irreversible damages and very large potential losses (e.g., major sea-level rise or ecosystem collapse), but we do not know their probabilities with confidence. Because the consequences might be catastrophic and cannot easily be reversed, relying only on expected total cost is risky. This justifies using the precautionary principle and setting safe minimum standards (for emissions, conservation, etc.) to avoid worst-case outcomes, even if we lack precise probability estimates.
Question 2. Moral Hazard and the National Flood Insurance Program (NFIP)
Instructions
- Answer Parts A–D using average (expected) annual cost as your decision rule.
- Show your calculations and briefly explain your reasoning in words.
Scenario
A homeowner is choosing between two locations:
- Location S (Safe):
- Annual housing cost (rent/mortgage, etc.): \(20{,}000\)
- No flood risk.
- Annual housing cost (rent/mortgage, etc.): \(20{,}000\)
- Location F (Flood-prone):
- Annual housing cost: \(18{,}000\)
- Each year, there is a \(10\%\) chance of a flood causing \(100{,}000\) in damage to the house.
- Annual housing cost: \(18{,}000\)
Assume the homeowner cares only about minimizing their average annual cost.
You can think of:
Average annual cost without insurance \(=\) housing cost
\(\;\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad +\) average (expected) flood damage cost
Average annual cost with insurance \(=\) housing cost
\(\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad +\) any insurance premiums paid.
Part A. No insurance
There is no flood insurance available.
- Compute the homeowner’s average annual cost in Location S.
- Compute the homeowner’s average annual cost in Location F.
- Which location is cheaper on average?
- If the homeowner wants to minimize average annual cost, which location will they choose?
Location S (Safe):
- No flood risk.
- Average annual cost: \[ \text{Cost}_S = 20{,}000 \]
- No flood risk.
Location F (Flood-prone):
- Housing cost: \(18{,}000\)
- Each year there is a \(10\%\) chance of \(100{,}000\) in damage.
- Average (expected) flood damage: \[ 0.10 \times 100{,}000 = 10{,}000 \]
- Average annual cost: \[ \text{Cost}_F = 18{,}000 + 10{,}000 = 28{,}000 \]
- Housing cost: \(18{,}000\)
Comparison:
- Location S: \(20{,}000\)
- Location F: \(28{,}000\)
👉 Cheaper location: Location S.
A cost-minimizing homeowner chooses Location S (Safe).
Part D. Moral hazard and NFIP policy
Answer in words (no new calculations needed):
- Using your results from Parts A–C, explain how subsidized NFIP premiums can create moral hazard in location choices (deciding where to live).
- Explain how risk-based premiums (and measures like premium discounts for elevating buildings or floodproofing) could help reduce moral hazard in the NFIP.
- Give one concrete policy idea for the NFIP (for example, a rule about rebuilding or premium discounts) that could discourage risky behavior while still helping people manage flood risk.
- Subsidized NFIP premiums and moral hazard
- Moral hazard: When people take more risk because they do not bear the full cost of that risk.
- With subsidized NFIP premiums, homeowners in flood-prone locations:
- Pay only \(2{,}000\) instead of the true average damage of \(10{,}000\).
- Do not feel the full cost of living in a risky place.
- Pay only \(2{,}000\) instead of the true average damage of \(10{,}000\).
- As a result:
- More people may choose to live in floodplains.
- People may rebuild in the same risky place after floods because insurance keeps paying.
- More people may choose to live in floodplains.
So subsidized NFIP can encourage riskier location choices, increasing total flood damages and program costs.
- Risk-based premiums and mitigation incentives
- Risk-based premiums make the homeowner pay a premium equal to the true average flood risk.
- This makes high-risk locations financially less attractive.
- Mitigation incentives (e.g., premium discounts for elevating houses, installing flood barriers, or for communities that improve drainage) can:
- Reward risk reduction
- Encourage safer building practices and better local flood management.
- Reward risk reduction
Together, these tools reduce moral hazard by making risky choices more expensive and safe choices cheaper.