Lecture 5 & 6 Cost Benefit Analysis & Non-renewables Flashcards
Hotelling Rule
Hotelling’s theory addresses a fundamental decision for an owner of a nonrenewable resource: Keep the resource in the ground and hope for a better price the next year, or extract and sell it and invest the proceeds in an interest-bearing security.
Because there is no dividend or interest payment in the case of resource ownership, only a resource price increase can guarantee equal return of all the assets.
Illustrate the Hotelling-rule with an appropriate equation.
Pic 7
Price path without extraction costs according to the Hoteling rule
The price and value of the resource increase over time for both functions to reflect the scarcity in supply (i.e. the opportunity cost to extract).
Price growth is steeper with a higher interest rate, and flatter with a lower interest rate.
Resource depletion is initially faster for R1 than R0
Price path without extraction costs according to the Hoteling rule:
Lower interest rate…
Slower increase in price path
Slower resource depletion
Slower decline in demand
Higher starting price
Price path without extraction costs according to the Hoteling rule:
Higher interest rate…
Faster increase in price path
Faster resource depletion
Faster decline in demand
Lower starting price
Extraction sequence associated with Hotelling path
The extraction sequence is an optimal depletion path which is characterized by decreasing demand over time
Linear and isoelastic demand with Hotelling
Linear case: firms do not let prices exceed the choke price to keep demand steady and ensure the whole resource stock is used.
There exists a level of pR for which no resource is sold.
Isoelastic case: even with indefinitely high price, a positive (though indefinitely small) quantity of resource is demanded. There is no threshold / choke price.
What happens at the choke price?
At the choke price, demand becomes zero, and there is a switch to an alternative resource or to a ‘backstop’ technology.
Explain the effects of exploration
A change in stock of the resource impacts the price
An increase in the supply leads to a lower price and higher demand
There is no change in slope of price path
Explain the effects of a backstop-technology
A backstop technology provides resources at a constant marginal cost for an indefinitely long time
pB: price of backstop technology = choke price
Do Hoteling until the point of the backstop
Hotelling rule: Monopoly
· Monopoly and perfect competition choose the same path (same Hoteling rule) because the resource constraint is binding for both market forms
· Price growth is exactly like in perfect competition: = 1 + r
· Assumption: constant elasticity of demand
Impact of market form on resource extraction and stock depletion
Pic 8
Resource depletion in competitive and monopolistic markets
Resource depletion outcomes differ between competitive and monopolistic markets. In a monopoly:
- Longer time to depletion
- Higher resource net price in early years
- Lower net price in later years.
Hotelling rule: critique / discussion of the assumptions
· Ownership guarantees: often not given
· Change in monopoly power
· Political and economic conditions in developing countries
· Which backstop technology? When?
· Perfect foresight: not realistic
· Variable extraction costs
Explain the importance of the elasticity of substitution between
non-renewable resources and capital.
Sustainability of Economic Growth
Resource Scarcity Mitigation
Incentives for Innovation
Policy Implications
Economic and Envrionmental Tradeoffs
Sustainability of Economic Growth:
A high elasticity of substitution means that capital (e.g., technology or infrastructure) can more easily replace non-renewable resources in production.
This flexibility reduces the economy’s dependence on finite resources, supporting long-term economic growth.
Resource Scarcity Mitigation:
When substitution is easier, resource depletion has a smaller impact on production costs and economic output.
A low elasticity of substitution implies that resource scarcity will significantly constrain production and increase costs.
Incentives for Innovation:
Higher elasticity encourages investment in alternative technologies and capital that can replace resource use (e.g., renewable energy systems).
Lower elasticity signals a need for urgent resource conservation and innovation in resource-efficient technologies.
Policy Implications:
Policymakers must account for elasticity when designing taxes or regulations for non-renewable resources.
Higher elasticity suggests policies should focus on promoting substitution technologies, while lower elasticity emphasizes conservation and sustainable resource management.
Economic and Environmental Trade-offs:
The ease of substitution determines how the economy balances resource depletion with environmental goals.
Greater substitution elasticity reduces environmental pressure by decreasing resource extraction, but low elasticity demands stricter resource-use controls.
Regeneration function
Pic 9
Cost of harvesting
Marginal cost = marginal utility = price
C’ = U’ = P
If Z* < MSY the market equilibrium is lower than the sustainable yield no problem
If Z* > MSYthe market equilibrium is greater than the sustainable yield economic policy is required to increase marginal cost (C’).
Economic policy to increase marginal cost curve:
Pic 11
Outcome of open access fishery that respects the regeneration function
Average cost = price
No one makes a profit
Harvest quantity > efficient solution
Biological regeneration respected
Can an optimal solution be reached under open access?
You do not have an optimal solution because you impose an externality on other users of the resource without having to pay for it.
The market is not efficient.
Compare open access and private property fisheries graphically
Pic 12
Open-access vs Private property
- PP is profitable because there is a difference between marginal
cost and marginal return. OA is not profitable. - PP equilibrium effort is lower and equilibrium harvest is higher
than under OA. Therefore, there is a higher remaining biomass
with PP. - PP has a higher return than OA.
Cost-Benefit Analysis (CBA)
4 bullets
▪ Used for social appraisal of investment
projects
▪ Aims to appraise the projects that address
(and potentially correct) market failures
▪ Explicitly accounts for future effects of a
project/policy
▪ Public projects consider environment
* Take into account environmental
impacts
* Aim at providing environmental
services
Social optimum
▪ Maximize present-value stream of net
benefits
▪ Theory: characterize optimal allocation
* optimal use of the environment
* use of discount rates
▪ Practice: try to approximate the value
* social welfare is unobservable
* use either direct or indirect
expressions of preferences
Cost-benefit analysis: Problems
▪ How to measure costs/benefits
▪ Choice of discount factor r and the observation period T
▪ How to deal with uncertainty
▪ Consideration of distribution and fairness
▪ Ethical considerations
Measuring Environmental Benefit
How?
Direct Expression
Indirect Expression
NPV = SUM t=1 T [(B_t - C_t) / (1+r)^t]
B_t:
▪ Direct expression of preferences (stated preferences)
Environmental benefit is estimated based on surveys on the hypothetical willingness to pay
▪ Indirect expression of preferences (revealed preferences) Estimation of environmental benefit through the market prices of related goods
Direct expression of preferences (CV, Choice modeling)
Contingent valuation (CV) method:
1. People are questioned about their
willingness to pay for certain environmental goods.
2. In these surveys, hypothetical scenarios correspond to the appraised environmental projects
3. The responses are analysed to infer the value of environmental goods and services
Choice Modelling Method
▪ Persons surveyed are presented with a menu of choices
Direct expression of preferences (CV, Choice modeling)
Assessment Positive
Assessment of direct methods
Advantages
▪ Takes into account both use and non-use values (here it would be difficult to use revealed preferences
▪ Responds relate directly to the theoretical willingness to pay
▪ Survey can be customized to specific issue at hand
Direct expression of preferences (CV, Choice modeling)
Assessment Negative
Disadvantages
▪ Hypothetical Bias: Respondents are asked to state their WTP in hypothetical scenarios
▪ Framing Effects: CV responses may be influenced by the context of the valuation questions or framing
▪ Protest Bids: Some respondents may provide protest bids, stating extremely high or low values
▪ Sample Bias: The sample of respondents may not be
representative of the larger population
▪ Validity and Reliability: The validity and reliability of CV
results can be debated, especially if the survey design is not carefully executed
Indirect expression of preferences (Avoidance cost method)
▪ Avoidance cost method:
* Reacting to negative environmental influences, people
can spend money to avoid these: water filter, medicine,
etc.
* Conclusions can be drawn on the benefit of the
elimination of negative environmental influences
Assessment of the avoidance cost approach
Pos and Negative
Assessment of the avoidance cost approach
Positive
▪ Simple approach to estimate the benefit of an environmental measure (e.g. reduction of air pollution)
Negative
▪ Problem: goods used to reduce negative environmental
influences also generate other, additional benefits.
* Air conditioning does not only reduce the influence of air pollution, it also produces a “pleasant” climate.
* A water filter not only produces clean water, it also makes better tea.
* It is difficult to distinguish these different effects!
Indirect expression of preferences (Travel Cost)
Travel cost method:
* To generate a demand curve for a private good one can measure the amount demanded at a certain price.
* To measure e.g. the benefit of a clean beach, instead of using the explicit cost, one can measure the travel costs (direct cost and opportunity cost) that tourists are willing to pay to spend time at the beach.
Discussion travel cost method
Pos
Relatively easy to apply and hence used quite often
Neg
However, certain methodological problems persist:
▪ Travel and opportunity costs are difficult to measure
(correctly)
▪ How can substitutes (e.g. amusement parks near the
beach) be accounted for?
▪ As in every poll, sample selection problems can appear
(e.g. regular visitors of the nature reserve can be overrepresented)
▪ The poll can only record the use-value and not the nonuse value of environmental goods
Indirect expression of preferences (Hedonic Prices)
Hedonic prices method:
* Measures the value which people accord to different
features of a good
* Real estate price = price of the house’s different features
(number of rooms, location, environmental quality,
climate risk exposure, etc.)
* Regression analysis derives correlation between
environmental quality and house prices
Assessment of hedonic prices
Pos
This model is extremely intuitive, as it allows a monetary valuation of environmental factors directly through market prices.
Neg
But: empirical models are extremely complex. There are also problems of getting together such extensive data on the product characteristics. If important attributes are missing, this could lead to considerable biases (omitted variable bias in case of regression analysis).
Measuring costs (Types of Costs)
Types of costs:
* Fixed cost of construction: costs of the construction of
infrastructure, change of processes, etc.
* Variable costs of maintenance: maintenance and
operating costs of the facility.
* Other costs: lost jobs, not used resources, etc.
For example, lost jobs because of a new environmental
law. These costs are only considered, if workers cannot
be integrated into other sectors.
Objection to the Cost-benefit analysis for
environmental issues
▪ Are consumer preferences the correct benchmark for social decisions?
▪ Is it right to only consider humans’ position? Should animals and plants be awarded an own ethical value in the cost/benefit analysis?
▪ How do we incorporate risk and irreversibility in the analysis? Which scenarios to rely on?
▪ How do we incorporate distributional concerns?
