Lecture 5 & 6 Cost Benefit Analysis & Non-renewables

Question 1

Hotelling Rule

Answer 1

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.

Question 2

Illustrate the Hotelling-rule with an appropriate equation.

Answer 2

Pic 7

Question 3

Price path without extraction costs according to the Hoteling rule

Answer 3

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

Question 4

Price path without extraction costs according to the Hoteling rule:
Lower interest rate…

Answer 4

Slower increase in price path
Slower resource depletion
Slower decline in demand
Higher starting price

Question 5

Price path without extraction costs according to the Hoteling rule:
Higher interest rate…

Answer 5

Faster increase in price path
Faster resource depletion
Faster decline in demand
Lower starting price

Question 6

Extraction sequence associated with Hotelling path

Answer 6

The extraction sequence is an optimal depletion path which is characterized by decreasing demand over time

Question 7

Linear and isoelastic demand with Hotelling

Answer 7

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.

Question 8

What happens at the choke price?

Answer 8

At the choke price, demand becomes zero, and there is a switch to an alternative resource or to a ‘backstop’ technology.

Question 9

Explain the effects of exploration

Answer 9

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

Question 10

Explain the effects of a backstop-technology

Answer 10

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

Question 11

Hotelling rule: Monopoly

Answer 11

· 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

Question 12

Impact of market form on resource extraction and stock depletion

Answer 12

Pic 8

Question 13

Resource depletion in competitive and monopolistic markets

Answer 13

Resource depletion outcomes differ between competitive and monopolistic markets. In a monopoly:

1. Longer time to depletion
2. Higher resource net price in early years
3. Lower net price in later years.

Question 14

Hotelling rule: critique / discussion of the assumptions

Answer 14

· 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

Question 15

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

Answer 15

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.

Question 16

Regeneration function

Answer 16

Pic 9

Question 17

Cost of harvesting

Answer 17

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’).

Question 18

Economic policy to increase marginal cost curve:

Answer 18

Pic 11

Question 19

Outcome of open access fishery that respects the regeneration function

Answer 19

Average cost = price
No one makes a profit
Harvest quantity > efficient solution
Biological regeneration respected

Question 20

Can an optimal solution be reached under open access?

Answer 20

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.

Question 21

Compare open access and private property fisheries graphically

Answer 21

Pic 12

Question 22

Open-access vs Private property

Answer 22

1. PP is profitable because there is a difference between marginal
   cost and marginal return. OA is not profitable.
2. PP equilibrium effort is lower and equilibrium harvest is higher
   than under OA. Therefore, there is a higher remaining biomass
   with PP.
3. PP has a higher return than OA.

Question 23

Cost-Benefit Analysis (CBA)
4 bullets

Answer 23

▪ 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

Question 24

Social optimum

Answer 24

▪ 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

Question 25

Cost-benefit analysis: Problems

Answer 25

▪ 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

Question 26

Measuring Environmental Benefit How? Direct Expression Indirect Expression

Answer 26

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

Question 27

Direct expression of preferences (CV, Choice modeling)

Answer 27

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

Question 28

Direct expression of preferences (CV, Choice modeling) Assessment Positive

Answer 28

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

Question 29

Direct expression of preferences (CV, Choice modeling) Assessment Negative

Answer 29

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

Question 30

Indirect expression of preferences (Avoidance cost method)

Answer 30

▪ 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

Question 31

Assessment of the avoidance cost approach Pos and Negative

Answer 31

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!

Question 32

Indirect expression of preferences (Travel Cost)

Answer 32

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.

Question 33

Discussion travel cost method

Answer 33

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

Question 34

Indirect expression of preferences (Hedonic Prices)

Answer 34

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

Question 35

Assessment of hedonic prices

Answer 35

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).

Question 36

Measuring costs (Types of Costs)

Answer 36

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.

Question 37

Objection to the Cost-benefit analysis for environmental issues

Answer 37

▪ 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?