Lecture 7 - ECON 341

🌿 Nature, Your Choice

A conservation landscape with trees, birds, a stream, and a walking trail.

Make twelve choices between cash for yourself and support for conservation.
Two participants will be selected at random. One choice each will be carried out with real money.

Open the experiment: Nature, Your Choice

🌊 Oil Spills and Environmental Losses

Spills harm fishing, recreation, wildlife, and habitats.

Spill	Environmental valuation	Civil settlement
Exxon Valdez	About $2.8 billion (1990 dollars)	$900 million (1991)
Deepwater Horizon	At least $17.2 billion (2017 study)	$20.8 billion (2016)

Surveys include the value of wildlife and habitat even to people who never visit.
Settlement payments are not survey estimates of damages.

Does paying for cleanup compensate people for everything they lost?

Combines the spill comparison and pollution-damage categories from Fall 2024 Lecture 13. The original damage categories include fishing income, recreation, health, wildlife, habitat, coastal livelihoods, beach access, and ecosystem services. Exxon Valdez spilled about 11 million gallons in 1989. NOAA describes Deepwater Horizon as approximately 134 million gallons in 2010: https://www.noaa.gov/explainers/deepwater-horizon-oil-spill-settlements-where-money-went .

Categories organize consequences but do not establish independent values. A fishing loss can appear in recreation, ecosystems, and commercial categories. Check overlap before adding estimates. Valuation begins with an incremental change from a specified baseline rather than the total value of nature. Cleanup costs, private claims, natural-resource damages, penalties, and WTP estimates are different accounting concepts. Exxon Valdez’s approximately $2.8 billion estimate (1990 dollars) concerns values held even without direct use. The $900 million civil settlement (1991) is a different measure. The later survey slide provides its primary sources and caveats.

Deepwater Horizon: Bishop et al. (2017), “Putting a value on injuries to natural assets: The BP oil spill,” Science 356(6335), 253–254, https://doi.org/10.1126/science.aam8124 ; primary author PDF https://economics.ucsd.edu/~rcarson/papers/BP_Science17.pdf . A nationally representative survey, conducted October 2013–July 2014, elicited one-time household taxes to prevent comparable future resource injuries. A lower-bound mean WTP of $153, aggregated across 112,647,215 households, yielded at least $17.2 billion. It covers specified natural-resource services, including recreation and wildlife or habitat, rather than private commercial claims. The accessible article does not state a price-base year, so the slide identifies the publication year without labeling the estimate “2017 dollars.” The $20.8 billion civil settlement in 2016 included $8.8 billion for natural-resource damages, plus other claims and penalties. Do not add a settlement to a WTP estimate or compare the two spills as though their amounts had the same price year and coverage. NOAA settlement timeline: https://www.fisheries.noaa.gov/national/habitat-conservation/noaas-work-after-deepwater-horizon-oil-spill-timeline .

⚖️ Why Put Environmental Benefits in the Comparison?

Benefit–cost analysis: compare environmental gains with resources used to obtain them.
Damage assessment: identify lost services and guide restoration or compensation.
Leaving a benefit unmeasured does not make it zero.

If an analyst counts the cost of protecting a wetland but omits its benefits, which choice will look more attractive?

🔬 From Environmental Change to Welfare

A cleaner-river example	Step
Which change and which people?	1. Define the baseline
Fewer illnesses and healthier fish	2. Estimate physical effects
Less filtering water or avoiding swimming	3. Account for responses
Avoided costs and remaining welfare gains	4. Value the consequences

Check: could income, age, or another change explain the observed difference?

Combines Lecture 13’s damage-assessment sequence and evidence slides. Counterfactual exposure and physical-effect estimation precede valuation. Economists, environmental scientists, health researchers, and affected communities contribute different evidence. If people adapt to pollution, observed illness alone omits resources they spend avoiding harm. Count adaptation costs and residual damages consistently without adding the same avoided harm twice.

Health and environmental records, laboratory evidence, and natural experiments can help identify effects. Correlation alone does not identify a pollution effect. Compare ages, income, other exposures, and simultaneous changes. Animal-to-human extrapolation and observational identification have different uncertainties. Not all controlled human exposure research is unethical, but harmful exposure and experimental design face strict ethical limits. Interacting pollutants, incomplete data, conflicting findings, and improved methods require careful interpretation. Natural experiments also depend on assumptions that need testing. Replication and evidence across disciplines help assess credibility.

🦆 Use, Option, and Nonuse Values

1. Use	2. Option	3. Nonuse
Value from using a resource or benefiting from the services it provides.	Value from keeping future personal use possible when that use is uncertain.	Value from a resource’s existence or preservation for others, without personal use.
Examples: fishing, birdwatching, or flood protection.	Example: keeping the option to visit a forest later.	Examples: species survival and preserving nature for future generations.

\[\text{Total WTP}=\text{use}+\text{option}+\text{nonuse values}.\]

📈 Marginal WTP and the Value of an Improvement

One household's marginal willingness to pay declines as environmental quality improves.

The area under marginal willingness to pay between the baseline and the improved quality measures the household's benefit.

MWTP (marginal willingness to pay): the most a household would pay for one more unit of environmental quality.
The area under MWTP over the improvement gives total WTP for that change.

💵 Willingness to Pay and Willingness to Accept

A and B have the same money but different environmental quality. WTP is the B-to-C money gap on original well-being; WTA is the A-to-D gap on improved well-being.

At money $M$, an improvement moves A to B. A degradation moves B to A.
WTP: most to pay for the improvement while keeping A’s well-being.
WTA: least compensation to accept the degradation while keeping B’s well-being.

Adapted from the graph used in Lecture 15 (October 2, 2024), lec_figs/cv-ev-q.png. The original diagram places a market-good quantity on the vertical axis. This version uses money for other goods, so the WTP and WTA gaps have dollar units. M denotes original money available for other goods. Each curve represents combinations of environmental quality and money giving the same well-being. The lower curve contains A and C; the upper contains D and B. Curve forms are conceptual, not empirical estimates. WTP is willingness to pay; WTA is willingness to accept compensation. For this improvement, WTP uses initial well-being and WTA uses improved well-being. For a loss, WTA can instead compensate for enduring the loss and WTP can measure the amount paid to avoid it. Identify the direction of change and entitlement before choosing a measure. Small income effects do not eliminate a gap when substitutes are limited.

🔄 Compensating and Equivalent Variation

For an improvement, compensating variation is WTP, the B-to-C gap. Equivalent variation is WTA, the A-to-D gap. The diagram uses the same quality and money axes as the preceding slide.

For the improvement from $q^0$ to $q^1$:
Compensating variation (CV = WTP): pay after the improvement, keeping original well-being $u^0$ (B to C).
Equivalent variation (EV = WTA): receive money instead of the improvement, reaching improved well-being $u^1$ (A to D).

🌳 Limited Substitutes and WTA–WTP Differences

State-design and other U.S. quarters at face value are close substitutes, with WTA and WTP both twenty dollars. Wetland habitat and money for other goods are limited substitutes, with WTA fifty dollars and WTP about thirty-three dollars.

At face value, different U.S. quarter designs exchange dollar for dollar. Here, WTA and WTP are equal.
With limited substitutes, money may not replace a lost wetland or species. WTA can exceed WTP.

Adapted from Fall 2024 Lecture 15, October 2, 2024, lec_figs/wta-wtp-subs.jpg. The original comparison used quarters as close substitutes and mortality risk versus income as limited substitutes. This version makes both axes specific to the goods shown. Left: state-design U.S. quarters and other U.S. quarters, both measured in dollar face value. Assume no collector premium and costless exchange at face value. At A the person has $40 in state-design quarters and $100 in other quarters. B adds $20 in the former, so WTP and WTA are both $20 of the latter. Indifference curves are parallel lines with slope −1.

Right: wetland habitat (acres) and money for other goods (dollars). A and B hold money at $100 while habitat rises from 40 to 60 acres. The hypothetical curves imply WTP of $33.33 and WTA of $50. The monetary gaps are compared within each panel. WTP is not held equal across panels, and physical units differ across the two pairs of goods. These preference curves and dollar amounts are teaching assumptions, not empirical valuations. Limited substitutability can explain a WTA–WTP gap without loss aversion. Income effects, entitlements, uncertainty, and behavioral responses can also matter. For a degradation from B to A, WTA is the compensation needed to retain B’s well-being.

📉 Gains and Losses Can Feel Different

A conceptual reference-dependent value curve is steeper for losses than for equivalent-sized gains.

Prospect theory: people value gains and losses differently.

Reference point (status-quo): the situation treated as normal, such as access to your local park.
Loss aversion: losing that access can feel worse than gaining the same access feels good.
Endowment effect: already having access can raise the compensation you require to give it up, relative to what you would pay to obtain it.

🌳 Why WTA and WTP Can Differ

Limited substitutes: another purchase may not replace a lost wetland or species.
Loss aversion and the endowment effect: losing an amenity you have can feel worse than gaining it feels good.
Income and entitlements: budgets and starting rights affect the answer.
- A tight budget limits WTP to save a park, but does not cap compensation requested for losing existing access.
Responsibility and uncertainty: perceived wrongdoing or irreversible harm can affect answers.
- A household may refuse a polluter’s offer for a damaged well until long-term health risks are clearer.

🌍 Valuation and Other Decision Criteria

Why a dollar total is not enough	Why valuation still helps
Rights and nature’s intrinsic value need not be monetary.	Resources for environmental protection are limited.
WTP depends on income, and totals can hide unequal impacts.	Ignoring benefits can divert resources from effective protection.

Use valuation alongside rights, ecological limits, and distributional analysis.

Two wetland plans have similar measured net benefits, but one protects habitat whose value remains unmeasured. What evidence and decision criteria would help you choose?

🔎 Two Sources of Valuation Evidence

Revealed preference

Observed choices in related markets.
Trips, housing, jobs, and protective purchases.
Usually captures values linked to behavior.

Stated preference

Choices about a described environmental change.
Contingent valuation and choice experiments.
Can include values held by nonusers.

🗳️ A Contingent-Valuation Question

Baseline: pollution keeps a lake closed to swimming for 20 days each summer.

Would your household pay $30 per year for five years, through a local tax, for a program that prevents those closures?

If the proposal fails, the existing situation continues.
“Yes” concerns a specific change and payment, not simply support for clean water.

🧪 Survey Design: Information and Anchoring

Potential problem	A useful safeguard
Unclear or unfamiliar outcomes	Neutral descriptions, understandable units, pretests
The first number anchors answers	Test alternative bid amounts and elicitation designs
A larger project receives the same answer	Check comprehension and sensitivity to scope

💳 Survey Design: Payments and Consequences

Potential problem	A useful safeguard
Strategic answers to influence policy	A credible decision process and suitable incentives
Saying yes feels costless	Budget reminders and believable payment consequences
Objection to taxes or the institution	A plausible payment vehicle and follow-up questions

❔ A Zero Answer Can Have Different Meanings

“The improvement is not worth a payment to me.”

This may be genuine zero WTP, including a budget constraint.

“I care about the lake, but do not trust this payment scheme.”

This may be a protest response.

Use follow-up evidence. Do not automatically discard zeros.

🚢 Exxon Valdez: Survey Value and Settlement

A national survey offered an escort-ship program to prevent another spill.
Households chose yes or no at an assigned one-time tax.

Figure	What it represents
About $2.8 billion 1990 dollars	Conservative estimate of nonuse values
$900 million 1991 agreement	Civil settlement for restoration and damages

The survey valued nonuse losses, including wildlife and habitat valued by people who never visit.

Combines Fall 2024 Lecture 15’s Exxon Valdez design, results, and implications, with the legal-payment distinction from Lecture 13. Carson, Mitchell, Hanemann, Kopp, Presser, and Ruud (2003), “Contingent Valuation and Lost Passive Use: Damages from the Exxon Valdez Oil Spill,” Environmental and Resource Economics 25, 257–286. Original 1992 report: https://econweb.ucsd.edu/~rcarson/papers/AlaskaReport.pdf . The main survey predates the 1993 NOAA panel. Do not say it followed guidelines issued later. Clear information, visual aids, pretesting, and referendum-style choices were central to its design.

The approximately $2.8 billion figure is a one-time, conservative lower-bound aggregate based on estimated median WTP and the study’s aggregation conventions. It does not imply that every WTP estimate is below WTA. The 1991 civil settlement was payable over ten years. Legal history: Exxon Shipping Co. v. Baker, 554 U.S. 471 (2008), https://www.govinfo.gov/content/pkg/USREPORTS-554/pdf/USREPORTS-554-471.pdf . Its $303 million figure concerns voluntary payments to private parties, not just fishermen. A survey estimate, cleanup bill, and legal payment answer different questions. Legal recognition of nonuse damages does not mean every survey estimate should automatically determine an award.

🐻 A Choice About Brown-Bear Protection

A proposed trust would fund measures expected to prevent the loss of one brown bear per year, on average.

Bear-cam viewers received one of 11 annual donation amounts, from $5 to $500.
The payment would continue for five years.
Contributions would be refunded if the funding threshold was not reached.

Source bridge: Fall 2024 Lecture 16, “Example 2: WTP to Protect Brown Bears,” survey-design and valuation-question slides. Richardson, L., and Lewis, L. (2022), “Getting to know you: Individual animals, wildlife webcams, and willingness to pay for brown bear preservation,” American Journal of Agricultural Economics 104(2), 673–692, https://doi.org/10.1111/ajae.12249.

The paper fielded this survey from July 10 through October 25, 2019. A broader research program also collected bear-cam data in 2020, but this paper’s administration section describes the 2019 fielding. The scenario concerned an average avoided loss of one bear per year, not necessarily a named bear. The provision-point rule returned contributions if the threshold was not met. Interpret values as contingent on the proposed trust, protection measures, payment duration, and funding rule.

📉 Brown-Bear Responses and WTP

Among bear-cam viewers, acceptance of the annual donation generally falls as the proposed amount rises.

The response-screened sample is added. Both samples show lower acceptance at higher donation amounts.

Response screening: remove protests, misunderstandings, and beliefs that answers cannot affect protection.
Effect: 14% excluded. The remaining sample generally had a higher share saying yes. A “no” alone was not excluded.
Estimated WTP: $70–$140/year per bear-cam viewer.

Combines Fall 2024 Lecture 16’s response graph and interpretation. Primary source: Richardson and Lewis (2022), https://doi.org/10.1111/ajae.12249 ; author-uploaded full text https://www.researchgate.net/publication/353925852_Getting_to_know_you_individual_animals_wildlife_webcams_and_willingness_to_pay_for_brown_bear_preservation . Plotted percentages are approximate whole-number readings from Figure 1 as reproduced in the supplied textbook, not raw data. The authors excluded 9% as protests, such as believing government should pay or distrusting the trust fund, another 3% for not understanding the information, and another 2% who believed survey answers could not affect protection decisions. The last number reflects overlap with previous exclusions. In total, 14% were screened out. Figure 1’s remaining-sample acceptance percentages generally rise, while the downward relationship with the bid remains. Six percent still accepted the $500 bid. This procedure does not exclude every zero or “no,” and it cannot make self-selected bear-cam viewers representative of U.S. households.

Acceptance falling with the offered donation is consistent with demand and supports theoretical construct validity. That pattern alone does not establish representativeness, remove hypothetical bias, or validate every model choice. Preferred nonparametric and spike estimates yield roughly $70–$140 annually per respondent. The authors’ conservative aggregation uses $70 and the analysis sample, yielding more than $260,000 per year. They do not multiply by all U.S. households. A large sample does not cure self-selection.

The result concerns a specified protection program, rather than a market price for a bear. The paper discusses damage assessment and regulations affecting a small number of animals. Economic WTP, ecological replacement cost, and legally owed compensation are distinct concepts.

🧩 A Water-Quality Choice Experiment

Change from baseline	B	C
Acceptable nutrients (pp)	+5	+1
Water clarity (m)	+1	+0.5
Recreation suitability (pp)	+6	+8
Cost (NZ$/month)	6	3

pp = percentage points. Which plan would you choose?
Estimated WTP: NZ$12.10/household/year for 10 cm more clarity.

Combines the New Zealand choice-card and clarity-trade-off slides from Fall 2024 Lecture 16. Walsh, P. J., Guignet, D., and Booth, P. (2023), “Eliciting policy-relevant stated preference values for water quality: An application to New Zealand,” Agricultural and Resource Economics Review 52(2), 347–378, https://doi.org/10.1017/age.2023.20 . Earlier working paper: U.S. EPA Working Paper 2022-02.

Nutrients means the percentage of rivers with acceptable nutrient levels. Recreation suitability concerns the percentage of rivers meeting the E. coli-related recreation standard. The original card described improvements by 2025 and a permanent increase in monthly household cost of living. It is a historical example, not a current forecast. Neither B nor C dominates across all attributes. Designed, repeated cards across respondents allow estimation. One student’s response does not identify a complete WTP schedule.

The published Model 1 national average marginal WTP is NZ$12.10 per household per year for a 10-centimeter increase in average regional river clarity. The ratio of the clarity coefficient to the negative of the cost coefficient converts the modeled preference trade-off into money. Retain the exact attribute, unit, and period. The estimate is neither the price of a whole river nor the value of all possible improvements. Nutrient and E. coli improvements have their own estimates and units. The authors compare a modeled Auckland package with a NZ$66 targeted water-quality rate but explain that the projected environmental effects of that rate are insufficiently specified for a formal convergent-validity test.

🏛️ Valuing the National Park Service

Annual stated willingness to pay totals 92 billion dollars: 62 billion for National Park Service lands, waters, and historic sites, and 30 billion for programs.

Households chose between park-land sales or program cuts, paying to avoid some losses, or paying more to retain current protection.
Each option specified the losses and an additional federal income tax every year for ten years.
$92 billion/year is stated WTP, rather than revenue.

Combines Fall 2024 Lecture 16’s National Park Service survey design and value slides. Haefele, M., Loomis, J., and Bilmes, L. (2016), “Total Economic Valuation of the National Park Service Lands and Programs: Results of a Survey of the American Public,” Harvard Kennedy School Faculty Research Working Paper RWP16-024, https://heep.hks.harvard.edu/sites/g/files/omnuum8116/files/heep/files/dp71_haefele-loomis-bilmes.pdf .

The survey’s hypothetical scenario was inspired by occasional proposals rather than a current announcement. Three options offered different land sales or program cuts and annual federal income-tax costs for ten years. The largest reduction carried no tax, smaller reductions required some tax, and full protection carried a higher tax. A budget reminder preceded choices, rather than a generic post-question cheap-talk script.

The authors report $62 billion per year for parklands, waters, and historic sites, plus $30 billion for programs, totaling $92 billion. Their calculation scales estimated marginal values beyond the 20–40% reductions in the survey and multiplies sample household WTP by only 18% of U.S. households, assigning zero WTP to the remainder. Explain these assumptions when interpreting the aggregate.

This annual stated-WTP welfare estimate includes recreation and nonuse values. It is not revenue, tourism spending, an asset sale price, or a complete moral value of nature. Comparing it with annual appropriations alone does not produce a valid benefit-cost ratio because the objects and assumptions differ. The next slide compares receipts, which measure a different concept.

🏞️ Park Fees, Revenue, and Value

Measure	National parks	Disneyland Park
2026 admission	Yosemite: $35/vehicle U.S.-resident rate, seven days	Disneyland: $104–$224 Per person (ages 10+), one park, one day
Annual receipts (2024)	$378 million NPS-wide recreation fees FY2024 reported	≈ $2.8 billion 2024 total estimate Tickets, food, merchandise and other park receipts

Disneyland estimate: 17.3m visits × assumed $160/visit.
Receipts leave out consumer surplus and nonuse values.

Discussion: If Disneyland generates more revenue than national parks, does that necessarily mean it creates greater economic value for U.S. society?

Admission sources: Yosemite entrance fees, NPS, updated January 9, 2026; Disney’s January 19, 2026 ticket-price explanation, linking to the official ticket calendar; Disney’s standard ticket and age guide. These are dated standard-admission figures, excluding discounts, add-ons, and travel costs. Yosemite’s vehicle fee covers passengers for seven days at the U.S.-resident rate; nonresident surcharges and passes can change the amount paid. Disneyland’s range is for ages 10+ and varies by date. The admission units differ, so do not calculate a value ratio from them.

Disneyland attendance source: the 2024 TEA Global Experience Index, original report, printed pp.16 and 35, published by TEA, Entertainment + Culture Advisors, and The Park Database in October 2025. The report estimates 17.337 million visits to Disneyland Park in Anaheim during calendar 2024. These are park visits, including repeat visits, not 17.337 million distinct customers. Disney California Adventure is a separate park and is excluded from this calculation.

Working total-revenue estimate, not a Disney disclosure: assume $160 in revenue per Disneyland Park visit, comprising $100 from admissions and premium attraction access, $30 from food and beverages, $20 from merchandise, and $10 from other park-related receipts. Every component is an assumption, not an observed Disneyland average. Then 17.337 million visits × $160/visit = $2.77392 billion, rounded to about $2.8 billion.

This estimates Disneyland Park’s revenue rather than profit. Include only purchases attributable to that park and its assumed share of shared services, such as parking and photo services, within the $10 allowance. Exclude all California Adventure admissions and purchases, hotel rooms and hotel purchases, Downtown Disney, cruises, surrounding businesses, and the rest of the Disney company. The allocation of shared receipts is uncertain. The admissions assumption allows for the unknown mix of annual passes, multiday tickets, discounts, and premium access. The posted one-day ticket range is neither the observed average nor a lower bound on revenue per park visit.

Source and calibration limits: Disney’s FY2024 annual report, printed pp.12 and 45–46, reports $11.171 billion in theme-park admissions and $8.039 billion in merchandise, food, and beverage revenue across its broader operations. The latter category includes resorts and cruise ships, so its roughly 72% ratio to admissions is not a clean Disneyland Park spending ratio. Disney’s park-spending metric covers ticket sales and in-park food, beverages, and merchandise, but it publishes regional growth rates rather than a Disneyland dollar level. Do not mechanically assign company-wide sales to this park or describe the assumed $30/$20/$10 components as measured data.

For a rough admissions-only cross-check, the 2024 TEA report’s ten main Disney parks excluding Tokyo total 114.937 million visits. Dividing the company’s $11.171 billion admissions by that total gives about $97 per visit. This supports the order of magnitude of the assumed $100 but does not identify Disneyland’s yield: the periods and counting conventions differ, park prices and pass mixes differ, and the company category is broader than this ten-park sum.

Sensitivity scenarios for assumed revenue per visit: $115 ($80 admissions + $20 food/beverages + $10 merchandise + $5 other) gives about $1.99 billion. The central $160 case gives $2.77 billion. A $225 case ($140 + $40 + $30 + $15) gives about $3.90 billion. Thus roughly $2–$4 billion describes these chosen scenarios, not a statistical confidence interval or evidence-backed bounds on actual revenue. Actual sales and the park’s accounting allocation could differ.

NPS source: FY2026 U.S. Budget Appendix, Department of the Interior, printed p.550, “Recreation Fee Permanent Appropriations,” account 014–9928, receipts line 1130. The FY2024 actual recreation-fee receipt is $378 million. The $380 million total adds the $2 million opening balance and is not the receipt amount. These are reported fee receipts for the National Park System, not all NPS income, entrance fees alone, surrounding tourism spending, congressional funding, or the preceding study’s annual WTP estimate. The NPS period is fiscal 2024, while the Disneyland attendance period is calendar 2024.

The NPS figure is reported fee revenue, whereas the Disneyland figure estimates its broader park receipts, including sales. NPS concessioners’ sales and other NPS revenue are not included in the $378 million. The figures therefore have different coverage even aside from the different pricing systems and geographic scopes. They do not establish a head-to-head ranking of economic benefits. Low public entrance fees can coexist with high willingness to pay, substantial visitor consumer surplus, and preservation benefits to nonvisitors. Disneyland may also generate consumer surplus, attachment, or bequest values. A comparable valuation needs a defined change, the same population and period, and consistent treatment of costs and external effects if comparing net social benefits. Do not add receipts to WTP already covering the same services.

Ask whether making a park free would eliminate its benefits, and whether increasing its fee would increase the benefits people receive. Use those answers to distinguish payments from benefits without asserting that either destination is intrinsically more valuable.

🏞️ A Free Recreation Site Still Has a Price of Access

Travel-cost step	What the analyst uses
Observe behavior	Trips, transport expense, travel time, and visitor characteristics
Estimate demand	How visits change as generalized trip cost changes
Measure benefit	Consumer surplus under the estimated recreation-demand curve

Travel spending helps identify demand. Spending itself is not the full recreation value.

📈 Travel Cost and Annual Visits

Five equal-sized regions. Trips per 1,000 residents/year.

Five observations show fewer annual trips per one thousand residents at higher generalized trip costs.

Five scattered observations lie on either side of fitted recreation demand, Q-hat equals 188 minus 1.8 times generalized trip cost P.

\[\underbrace{\widehat Q}_{\text{predicted annual visits}}=188-1.8P\]

Source bridge: Fall 2024 Lecture 17, “Travel-Cost Demand Function: Step 1, Data Collection,” “First Variant of TCM,” the regression scatterplot, and “Example Regression Result.” These are invented teaching data. The five origins A–E have annual visits per 1,000 residents of 164, 98, 92, 26, and 20 at generalized trip costs of $20, $40, $60, $80, and $100. Residuals of 12, −18, 12, −18, and 12 sum to zero and have zero covariance with price, preserving the exact OLS intercept and slope while making observations visibly differ from fitted values. Equal populations and normalized visit rates prevent a larger origin from appearing to have greater individual demand merely because it contains more people.

Generalized cost combines relevant transport expense, fees, and the opportunity cost of travel time. Regressing Q on P by ordinary least squares gives the displayed intercept of 188 and slope of −1.8. Its more general form is Q_i = alpha + beta P_i + epsilon_i, with beta < 0. The error term includes other influences on visits. This is a fitted relationship, not evidence establishing that price causes the observed differences. Applied travel-cost models normally account for substitute sites, income, site quality, population at risk, and other demand shifters. Visit counts or rates often require count-data or zonal models rather than this simple linear example.

🔺 Visits and Consumer Surplus

\[P=\$60:\qquad \widehat Q=188-1.8(60)=80\]

At a sixty-dollar generalized trip cost, predicted annual trips are eighty per one thousand residents. The shaded triangle above cost and below fitted inverse demand is consumer surplus.

\[CS\approx\$1{,}778\text{ per 1,000 residents/year}\]

Source bridge: Fall 2024 Lecture 17, “Step 4: Predict Visitation” and “Step 5: Estimate Consumer Surplus.” The predicted 80 annual visits are a rate per 1,000 residents, not a count for every community. Apply an appropriate population base before converting a rate to a total.

Invert the estimated demand relation Q = 188 − 1.8P to obtain P(Q) = (188 − Q)/1.8. The implied choke price is about $104.44. At a $60 generalized trip cost and Q = 80, the triangle has value 0.5 × (104.444… − 60) × 80 = $1,777.777… per 1,000 residents per year. The plotted inverse is the algebraic inverse of the Q-on-P regression, not a separately estimated P-on-Q equation. Rounding the intercept and slope before calculating can create a slightly different result.

Consumer surplus measures the net recreation benefit above generalized access cost under the assumed model. It is neither total travel spending nor total economic value including nonuse motives. It inherits the demand and access-cost assumptions. If a broader survey estimate already includes the same recreation benefit, do not add this value again.

🗺️ Site Choice and Substitution

A visitor compares sites using trip cost, access, and environmental quality.
The model predicts the site that gives that visitor the highest utility.
After a closure or quality loss, the visitor may choose another site, take fewer trips, or stop visiting.
The trip-cost coefficient converts the modeled utility change into a money measure of welfare.

🌊 Recreation Loss From Lower Quality

Before a quality loss, six annual visits at a twenty-dollar trip cost yield ninety dollars of consumer surplus.

After quality deteriorates, recreation demand shifts inward and consumer surplus falls.

The lost consumer-surplus area measures the recreation welfare loss from lower environmental quality in the classroom example.

Compare welfare before and after, allowing behavior to change.

⚠️ Travel-Cost Estimates Depend on Modeling Choices

Question	Risk if ignored
Was this a multipurpose trip, and what is travel time worth?	Assigning the entire vacation cost to one site can overstate access cost.
Which substitute sites were available?	A nearby alternative can reduce the loss from a closure.
Who never visited?	Trip behavior cannot reveal their existence or bequest values.

🧩 A Random Utility Model for Our Experiment

A random utility model (RUM) combines utility from observed attributes with an unobserved component, such as personal attachment to conservation. Assumptions about that component let the model predict choice probabilities.

One actual choice card	Cash you keep	Conservation gift
Ducks Unlimited	$7.50	$1
Trout Unlimited	$7	$1
Keep all cash	$8	$0

Across cards, the analysis estimates how the recipient, cash forgone, and total gift affect choices.
The resulting trade-off concerns cash and conservation giving.

The table reproduces version 11 card C05 from assets/js/econ-341-forest-choice-design.js using actual dollars rather than the ten-times display scale. Ducks Unlimited receives $0.50 of personal cash plus $0.50 of instructor support; Trout Unlimited receives $1 of personal cash and no support. Both gifts total $1. A selected participant pays no money from their wallet. Keeping $8 remains available. Everyone receives the same twelve menus, with shuffled card order and organization positions; their choices can differ. “Random” describes the analyst’s unobserved component of utility, not an assumption that participants choose without preferences.

The course analysis fits a conditional-logit RUM (scripts/forest-choice/model.R): recipient-specific constants, actual personal cash forgone, and actual gift delivered explain utility relative to keeping all cash. Choice-set strata define menus; participant-clustered uncertainty accounts for repeated choices. The model estimates pooled cash–donation trade-offs under the experiment’s incentives, not separate individual WTP or total ecological values. Finite estimates require appropriate choice variation. Monetary ratios can be unstable when the personal-cost coefficient is near zero. No fitted coefficients or empirical findings are asserted on this slide.

🏖️ Minorca Beach Closures and Site Substitution

573 visitors surveyed at 51 beaches in 2008.
Site choices varied with beach attributes and trip costs.
Researchers used a RUM to simulate oil-spill closures.

Closed beaches	€/visit	€/day
West beaches	€0.24	€6,000
West and north beaches	€1.73	€43,250

2008 euros; daily totals refer to peak season. These are users’ losses, not vendors’ losses.

Source bridge: Fall 2024 Lecture 17, “Using the TCM to Estimate Recreational Value: Beaches in Minorca, Spain.” Primary source: Riera, P., McConnell, K. E., Giergiczny, M., and Mahieu, P.-A. (2011), “Applying the travel-cost method to Minorca beaches: Some policy results,” in J. Bennett (ed.), International Handbook on Non-Market Environmental Valuation, pp.60–73. Working-paper PDF: https://www.obsam.cat/wp-content/uploads/2014/05/Applying-travel-cost-method-51-beaches-Menorca.pdf.

The study reports three simulated closure scenarios. The middle scenario closed western and Ciutadella-north beaches, with €0.46 per visit and €11,500 per peak-season day. The aggregate uses about 25,000 visitors per day. The primary source explicitly excludes losses to beach-service vendors. Do not add vendor revenue losses to visitor WTP without a consistent welfare framework.

🏠 Environmental Quality Is Part of a Housing Bundle

Otherwise similar homes near cleaner water have a higher illustrative price. The environmental contribution must be separated from the rest of the housing bundle.

A hedonic property model separates an environmental attribute from the rest of the housing bundle.

Sources: Tietenberg and Lewis (2023), Environmental and Natural Resource Economics, 12th ed., Chapter 4, pp.93, 95, 97–99; Fall 2024 Lecture 18, hedonic-property introduction. The plotted $320,000 and $300,000 are fictional teaching values, not observed matched sales or a published coefficient. Homes bundle structure, lot, schools, commuting, neighborhood amenities, and environmental quality. An unadjusted price gap does not identify the environmental effect.

The slope of a hedonic price schedule with respect to an environmental attribute is a marginal implicit price. Under the relevant equilibrium, information, and choice assumptions it can reveal marginal willingness to pay at the chosen bundle. It is not automatically the average treatment effect of a policy, the value of a large change, or the whole population’s total willingness to pay. A house-price difference is capitalized into an asset price; do not add it each year as though it were an annual flow.

🔎 What Makes a Hedonic Comparison Credible?

\[\begin{aligned} \text{HomePrice}_i&=\alpha+\beta\,\text{Environmental quality}_i\\ &\quad+\gamma\,\text{Home features}_i+\delta\,\text{Location}_i+\varepsilon_i \end{aligned}\]

Other price determinant	Evidence to seek
Different homes	Size, age, lot, and repeat sales
Different locations	Schools, commuting, and nearby amenities
Other changes over time	A credible comparison group and timing

$\beta$ measures the association between environmental quality and home price, holding other measured factors fixed.
$\varepsilon_i$ is the error term: influences on home $i$’s price that the model does not measure.

Sources: TL pp.95, 97–99; Fall 2024 Lecture 18, hedonic-regression explanation. A regression can adjust for measured differences but cannot promise to control every relevant factor. Repeat-sales or property fixed effects can remove time-invariant property characteristics; common time effects and a credible comparison help address other price changes. Identification still requires assumptions about omitted changes, sorting, information, and exposure measurement.

Optional board notation: $P_{it}=\alpha_i+\lambda_t+\beta E_{it}+\gamma X_{it}+\varepsilon_{it}$, where $E$ measures the relevant environmental exposure or information. This is a framework, not a claim that every cited study uses this exact specification. An equation alone does not establish a before-and-after design. GIS visibility, proximity, buffers, and environmental layers improve measurement but are not separate valuation methods. Paterson and Boyle’s viewshed example and the chapter’s Edwards Dam example illustrate why proximity, visibility, and credible comparison locations matter.

🦺 Jobs Also Bundle Pay, Conditions, and Risk

\[\text{Wage}_i=\alpha+\beta\,\text{Fatality risk}_i+\gamma\,\text{Worker traits}_i+\delta\,\text{Job features}_i+\varepsilon_i\]

Otherwise similar jobs	Safer job	Riskier job
Known workplace risk	Lower	Higher
Compensating pay	Lower	Higher

A hedonic wage model estimates the pay–risk trade-off, holding other job and worker characteristics constant.
$\beta$ measures the additional pay associated with a higher fatality risk, holding other measured factors fixed.

Sources: TL p.95 and pp.105–108; Fall 2024 Lecture 18’s property-versus-wage hedonic comparison. This is a conceptual compensating-differential table, not a claim that every risky job pays more. Skill, hours, benefits, working conditions, unionization, worker selection, and risk information can affect the observed wage difference. A credible estimate needs meaningful measures of the risk people perceive and face. Labor-market constraints and imperfect information can weaken the simple interpretation.

The displayed regression is a conceptual linear model, not an estimated equation or a claim that every study uses this exact specification. Fatality risk must use the same time period as the wage, such as annual wages and annual mortality risk. Worker traits can include education and experience; job features can include hours, benefits, and other hazards. The coefficient has units of additional pay per unit of mortality probability. Hedonic wages identify a marginal money–risk trade-off. Do not call the wage gap the value of an identified worker’s life or assume willingness to accept a large risk is identical to willingness to pay to avoid it.

🚰 Averting Expenditures

Monthly coping costs comprise ten dollars for bottled water, five for filters, and five in time. Remaining illness is an additional loss.

Averting means trying to avoid harm. Households spend money or time to reduce exposure to pollution or unreliable services.
Buying bottled water, filtering tap water, or collecting safer water uses resources—even if illness is avoided.
These costs can miss remaining harm. Low spending may reflect a tight budget, not little concern.

Sources: TL pp.97–98, 100–101; Fall 2024 Lecture 18’s averting-expenditure discussion. The $10, $5, and $5 are fictional monthly teaching values, not Kathmandu study findings. Households may buy, filter, pump, store, collect, or boil water. Time has an opportunity cost even when no cash changes hands. Define cost categories so the same input does not appear twice.

Protection may reduce illness while leaving other welfare losses. Counting only remaining illness omits resources spent avoiding it. Counting coping spending as the entire damage can omit residual harm. Coping expenditures can inform a lower bound on willingness to pay under suitable assumptions, including informed voluntary choices, effectiveness, and appropriate treatment of other purchase benefits. Bottled water may also provide taste or convenience benefits. Constraints, corner solutions, and imperfect substitutes complicate the interpretation.

Small spending does not establish small harm or weak concern when households cannot afford protection. Replacement engineering costs are not automatically public willingness to pay. Include affordability and distribution alongside the aggregate value, and avoid claiming that each observed dollar of spending equals a dollar of compensating variation.

🇳🇵 Kathmandu: A Low Water Bill Did Not Mean Low Costs

People with water containers collect and wait for water at Tanga Hiti, a stone spout in Patan, Kathmandu Valley. — Collecting water at Tanga Hiti, Patan, Kathmandu Valley.

Study: a 2001 survey of 1,500 households in five Kathmandu Valley municipalities.
Unreliable supplies led households to collect, pump, treat, store, or purchase water.
Average coping cost: $2.94/month, about 1% of income and almost twice the utility bill.
Stated WTP for improved service was higher than coping costs.

Primary source: Pattanayak, S. K., Yang, J.-C., Whittington, D., and K. C. Bal Kumar (2005), “Coping with unreliable public water supplies: Averting expenditures by households in Kathmandu, Nepal,” Water Resources Research 41, W02012, https://doi.org/10.1029/2003WR002443 ; full paper https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2003WR002443 . The random household sample covered Kathmandu, Lalitpur, Bhaktapur, Kirtipur, and Madhyapur. Table 3 reports mean total coping cost of $2.94/month across 1,500 households, with means of $1.39 for poor and $4.00 for nonpoor households. Dollar amounts are U.S. dollars. Do not add the five behavior-specific conditional means: their participation samples differ. The 2001 survey studied collecting, pumping, treating, storing, and purchasing water. Values are historical, not current Kathmandu costs. Coping costs were significantly below stated willingness to pay for improved service.

Photo: Jude Lee (IchStyle), “Tanga Hiti, Patan” (June 18, 2015), CC BY 2.0, unmodified, via Wikimedia Commons: https://commons.wikimedia.org/wiki/File:Tanga_Hiti,_Patan_18913936015.jpg ; license https://creativecommons.org/licenses/by/2.0/ . The image supplies place-and-activity context; it does not depict the households in the 2001 survey.

A monthly coping-cost total divided by a utility bill is not marginal WTP per unit of water. Quantity, reliability, quality, time, residual harm, and the proposed service change matter. Wealth and education affect the ability to cope. A subsequent comparison of 2001 and 2014 surveys documents changing coping costs: Gurung et al. (2017), “The costs of delay in infrastructure investments,” https://doi.org/10.1002/2016WR019529 . This is evidence that historical findings must not be presented as current conditions, rather than an extra unsourced current estimate.

📚 Benefit Transfer and Uncertainty

Benefit transfer: use existing estimates for a new policy.
Meta-analysis: study why published estimates differ.
Match the change, population, units, and time period.
Low, Central, and High are alternative benefit estimates for the same policy, not different groups. Cost stays at $50,000. Does the estimate change the decision?

A low benefit estimate is below the fixed policy cost, so net benefit is negative.

With the central benefit estimate, the same policy has positive net benefit.

Low, central, and high benefits imply different net benefits despite an unchanged policy cost.

Sources: TL pp.95–97; Fall 2024 Lectures 18–19 on benefit transfer and different methods. Benefit transfer uses existing evidence when a new primary study is too costly or slow. The study site supplies evidence for a policy site’s decision. Value transfer may adjust a per-household number using justified income and price-year changes. Function transfer uses estimated relationships together with characteristics of the policy setting.

Meta-analysis synthesizes multiple studies. A meta-regression can relate estimates to ecological, population, and methodological characteristics, potentially yielding a transfer function. It is not simply the average of every available dollar figure. Multiple estimates within one paper may be correlated. Study quality, publication bias, heterogeneity, and extrapolation affect the result.

Match baseline and size of change, environmental service, substitutes, geography, affected population, currency and price year, and payment period. Current-dollar conversion does not repair a poor ecological or preference match. One-time WTP, annual WTP, per-visitor-day values, and per-household values are not interchangeable. Do not scale a value by an unrelated population. Dated EVRI inventory counts and transfer-error percentages do not establish universal current counts or accuracy guarantees. Combining estimates requires checking overlap in populations, services, periods, and value components.

Sensitivity graph combines the previous uncertainty slide. Benefits of $40,000, $60,000, and $80,000 are compared with a fixed $50,000 policy cost; net values are −$10,000, +$10,000, and +$30,000. These are assumed scenarios, not empirical estimates, a confidence interval, or probabilities. Ask whether the sign of net benefit changes. Uncertain evidence can still be more informative than assigning zero benefit. Use consistent present-value or time-period units.

The categories do not describe different demographic groups, study sites, or policies. They are low, central, and high estimates of the same policy’s benefits. Such alternatives could reflect uncertainty about WTP or the size of an environmental improvement, but this graph assigns no particular empirical cause or probability to the scenarios.

❄️ Comparing Polar-Bear Values

A log-scale point plot compares four annual estimates in million 2009 Canadian dollars: preservation 6320, viewing 7.2, sport hunting 1.3, and subsistence hunting 0.6.

Transfer quality: a different species or setting may be a poor match.
Coverage: check overlapping benefits and missing cultural values.

Primary source: EcoRessources Consultants (2011), Evidence of the Socio-Economic Importance of Polar Bears for Canada, prepared for Environment Canada, June 11, Table 14 and discussion, https://publications.gc.ca/collections/collection_2012/ec/CW66-291-2011-eng.pdf ; official HTML https://www.canada.ca/en/environment-climate-change/services/species-risk-public-registry/related-information/socio-economic-importance-polar-bears.html . The four estimates use different valuation methods and all refer to million 2009 Canadian dollars per year. They are not current dollars or a price per bear. The logarithmic scale displays ratios rather than equal dollar distances.

Preservation is transferred willingness to pay to avoid the loss of Canada’s polar-bear population, not a new representative contingent-valuation survey. Viewing combines visitor consumer surplus and tour-provider net income. Subsistence hunting draws on replacement/market evidence. The sport-hunting transfer uses older evidence about a different big-game or grizzly hunting experience. Annual values for another hunt may poorly match a rare polar-bear trip. Geographic, cultural, ecological, population, and timing differences matter.

Do not mechanically sum these components. Preservation WTP may include scientific, educational, iconic, or other motives. The report did not separately monetize research or educational value because spending did not adequately measure public WTP. Its preservation transfer could exclude recreation but could not exclude every indirect motive. This identifies a risk of overlap, not proof that separately calculated scientific values had been double-counted. Important Inuit cultural, spiritual, community, and food-security values remain unmonetized. Small dollar estimates for hunting do not establish small importance. The limitations do not imply that unmeasured values are zero or that valuation evidence has no use.

🩺 Value of Statistical Life (VSL)

At annual mortality risk two in ten thousand, ten thousand people face two expected deaths per year.

Reducing each person's annual risk to one in ten thousand lowers expected deaths from two to one among ten thousand people.

VSL values reductions in mortality risk, not an identified person’s life.

Suppose each person would pay $100 to reduce annual risk by 1 in 10,000.

\[\begin{aligned}VSL&=\frac{\$100}{1/10{,}000}\\&=\$1\text{ million}.\end{aligned}\]

Source: Fall 2024 Lecture 19, introduction to valuing life and the risk-reduction approach. VSL means value of statistical life. It values small mortality-risk changes, not an identified person’s life. Both graphs refer to the same annual risk period and the same population of 10,000. Individual annual mortality risk falls from 2/10,000 to 1/10,000. That reduction implies one fewer expected death across the group, not an identified saved individual.

If each person would pay $100 for this annual reduction, aggregate WTP is 10,000 × $100 = $1 million per expected death avoided. Equivalently, divide individual WTP by the individual risk change. The $1 million is an assumed teaching example, not an agency recommendation. The same denominator and risk period must apply to the WTP numerator. Students who took ECON340 can explain the statistical distinction to classmates.

Optional board checks from the older lecture: $700 in additional annual wages divided by 1/10,000 additional annual risk implies $7 million, but interpretation requires comparable workers and jobs and credible risk information. Paying $100 for 1/100,000 less risk implies $10 million. These are alternative exercises, not additional empirical estimates.

🚗 Speed vs. Safety: Travel Time and Fatal Crash Risk

The instructor's research route map compares a red fastest route with a blue safer feasible route, with fatal-crash locations marked along the road network. — Fastest route (red) and a safer feasible route (blue). Dots mark fatal crashes.

Byeong-Hak Choe and Stephen Newbold

Do faster journeys save enough time to justify added fatal-crash risk?
Time benefit: time saved × value of travel time.
Risk cost: added expected fatalities × VSL.
We use VSL as an input, rather than estimate it here.