Classwork 7
Valuing Nature: Multiple-Choice Questions
Choose one answer for each of the 20 questions, then select Check my answers for your score, explanations, and a study plan. Each question is worth one point.
Mark any question you find difficult or tricky, or where you would like help—even if you choose the correct answer. These marks do not change your score; they help build your study plan. Download your feedback to keep it or discuss your questions with the instructor.
Use Lecture 7: Valuing the Environment as a reference. Except for the reported Classwork 6 coefficients and payment rule, the numerical examples below are simplified teaching examples.
1. What are we valuing?
Question 1 · A park with free admission
A park charges no admission fee, but visitors spend money on transportation and give up time to reach it. Which conclusion is most appropriate?
- The park’s recreation value is zero because admission is free.
- Visitors face a cost of access, and their trips can provide evidence about recreation value.
- Adding up transportation spending gives the park’s complete economic value.
- Free admission means only a stated-preference survey can provide valuation evidence.
B. The price of admission is only one part of the cost of a visit. Transportation and the opportunity cost of time also matter. A travel-cost study uses these costs and observed trips to estimate recreation demand; spending alone is not the full benefit, and visitors’ behavior does not capture all nonuse values.
Question 2 · Nature you may never see
Alex would pay to protect an endangered bird simply because knowing that the species continues to exist matters to Alex. Alex does not expect to visit its habitat. Which value is most directly illustrated?
- Recreation use value
- Option value from a possible future visit
- Travel-cost savings
- Existence value, a form of nonuse value
D. Existence value does not require personal use or a visit. By comparison, option value concerns keeping an uncertain future personal use possible, and bequest value concerns preserving nature for future generations.
Question 3 · Marginal versus total WTP
A household’s marginal willingness to pay falls in a straight line from $12 per quality-index point at the baseline to $4 per point after a four-point improvement. What is its total willingness to pay for this improvement?
- $32
- $16
- $48
- $64
A. Total WTP is the area under the marginal WTP curve over the change. Here, that area is a trapezoid:
\text{Total WTP}=\frac{12+4}{2}\times4=\boxed{\$32}.
Using $12 for every point would overstate the total because marginal WTP declines as quality improves. Using $4 for every point would understate it.
Question 4 · Compensation for losing a park
Residents currently have access to a local park. A proposal would permanently remove that access. A survey asks for the minimum compensation residents would accept for the loss. Which statement is correct?
- The question measures WTP because the park already exists.
- The question measures WTA, which must equal WTP if respondents understand it.
- The question measures WTA; limited substitutes and starting rights can help explain why it exceeds WTP.
- The question measures WTA, so any gap between WTA and WTP proves survey bias.
C. The minimum acceptable compensation is willingness to accept (WTA). Losing an existing amenity may be difficult to replace, while a household’s budget constrains how much it can pay. Starting rights and loss aversion can also matter. A WTA–WTP gap is therefore not automatically a survey error.
Asking for the maximum payment to prevent the loss would instead measure WTP. WTP can concern avoiding a loss as well as obtaining an improvement.
2. What do choices reveal?
Question 5 · Interpreting our class estimate
The Classwork 6 regression estimated a gift coefficient of 1.028 and a personal-cost coefficient of −1.507. Their ratio is 1.028/1.507\approx0.68. What does this mean?
- Exactly 68% of participants always chose to donate.
- Each extra dollar of personal cash automatically generated a 68-cent donation.
- The model’s common trade-off is about 68 cents of extra personal cash for another dollar delivered to the same organization.
- Each participant’s total willingness to pay for nature is 68 cents.
C. Dividing the gift coefficient by the magnitude of the cost coefficient expresses the estimated trade-off in personal dollars per additional dollar delivered. It is an incremental, model-based estimate from the class choices. It is not each person’s maximum donation, a percentage of participants, or the total value of an ecosystem.
Question 6 · From the card to an actual payment
A Classwork 6 card displays $15 from your cash and a $30 gift to conservation. Actual amounts are 10% of the displayed amounts. If this card and choice are selected for payment, what are the actual personal cost and total gift?
- $1.50 personal cost and a $3 gift
- $15 personal cost and a $30 gift
- $3 personal cost and a $3 gift
- $1.50 personal cost and a $1.50 gift
A. Multiply each displayed amount by 10%. The selected participant gives up $1.50 of the $8 available cash, keeps $6.50, and sends a total of $3 to conservation. Donation support supplies the other $1.50 of the gift. Giving up cash creates a real opportunity cost.
Question 7 · Can we infer a downward-sloping marginal WTP curve?
Our class regression uses a constant coefficient on personal cost and a constant coefficient on the gift delivered. Does its estimated 68-cent trade-off establish that marginal WTP falls as gifts grow?
- Yes; every positive WTP estimate proves diminishing marginal WTP.
- Yes; a negative personal-cost coefficient is the slope of the marginal WTP curve.
- No; marginal WTP must increase as gifts grow.
- No; this specification assumes a constant trade-off, so changing marginal WTP requires a model that allows it and supporting evidence.
D. With constant cost and gift coefficients, their ratio is constant. The model therefore produces a horizontal marginal WTP line by construction; it does not prove that people’s true marginal WTP is constant.
Allowing the effect of an additional gift dollar to depend on the gift’s size would let us investigate a downward slope. A lower probability of choosing an offer when its personal cost rises is a different relationship from declining marginal WTP as the amount delivered grows.
Question 8 · Why use several choice cards?
A survey presents river-management plans that vary in water clarity, recreation access, and household payment. Each card also includes an option with no change and no additional payment. Why vary these attributes across cards?
- To make the most expensive plan the correct answer.
- To learn the trade-offs people make among environmental attributes and money.
- To ensure that every respondent has the same willingness to pay.
- To avoid having to describe the environmental baseline.
B. A choice experiment learns from comparisons among bundles of attributes. Variation in attributes and cost helps separate their influences on choice. The baseline, payment arrangement, and proposed changes still need clear descriptions, and the design needs enough independent variation.
3. How credible is survey evidence?
Question 9 · What does a zero answer mean?
A respondent reports zero WTP for a lake improvement and explains, “I care about the lake, but I do not trust this agency to collect and spend the tax.” What is the most appropriate next step?
- Treat the response as proof that the lake has no value to this person.
- Use follow-up evidence to understand the payment objection and document how such responses are treated.
- Automatically delete the response because it lowers the average WTP.
- Replace zero with the average positive answer.
B. This may be a protest response about the payment arrangement rather than zero value for the environmental improvement. Other zeros can reflect genuinely low value or a tight budget. Researchers should investigate and report their treatment of these responses, rather than automatically removing or replacing them.
Question 10 · Does a bigger improvement mean four times the WTP?
Program A prevents five swimming-closure days per summer. Program B prevents twenty at the same lake. The population, payment method, and payment period are the same. Which statement is most appropriate?
- WTP for Program B must be exactly four times WTP for Program A.
- Similar answers prove that respondents place no value on swimming.
- A scope test should also change the lake and payment method.
- Comparing responses can test sensitivity to the size of the improvement, but WTP need not rise proportionally.
D. A scope test asks whether respondents distinguish the size of the specified environmental change. Diminishing marginal benefits, budgets, and substitutes mean four times the improvement need not produce four times the WTP. Similar answers deserve investigation of what people understood and valued; they do not by themselves establish that the responses are invalid.
Question 11 · A costless “yes”
In a survey, some respondents say they would pay for conservation because they believe no payment will ever be required. Which design change most directly addresses this concern?
- Explain the payment and its consequences accurately, remind respondents of their budgets, and follow up on how certain their answers are.
- Tell respondents that a larger WTP is the preferred answer.
- Remove the payment from every choice so respondents can focus on nature.
- Promise that the payment is binding even when no payment will occur.
A. This concern is hypothetical bias: an answer may differ when a payment feels costless. Clear, credible consequences and budget reminders can help, and certainty questions provide additional evidence. None guarantees truthful or unbiased answers. Researchers should accurately describe whether a decision can actually affect payment or provision.
4. What can observed behavior tell us?
Question 12 · Valuing a Letchworth visit
You want to estimate the recreation benefit to visitors from access to Letchworth State Park using observed behavior. Which approach best fits that goal?
- Multiply the admission fee by the number of visitors and call the result the complete recreation benefit.
- Use only gasoline spending, since travel time has no opportunity cost.
- Estimate visit demand using generalized trip cost, including money and time, and calculate consumer surplus.
- Ask only nonvisitors how much they value the park’s continued existence.
C. The travel-cost method treats the money and time required to visit as part of the price of access. Estimated recreation demand can then provide a consumer-surplus measure. This approach concerns use benefits expressed through visits; it does not automatically measure all nonuse values of the park. Multipurpose trips and substitute sites also need attention.
Question 13 · Recreation benefit beyond travel spending
A visitor’s annual recreation demand is
P=50-5V,
where P is generalized cost in dollars per visit and V is visits per year. At a cost of $10 per visit, the visitor takes eight visits. What is annual consumer surplus?
- $160
- $80
- $400
- $10
A. Consumer surplus is the triangle below demand and above the $10 cost, over the eight visits:
CS=\tfrac12(50-10)\times8=\boxed{\$160\text{ per year}}.
The $80 in generalized access costs (10\times8) includes money and the opportunity cost of time. It is not the visitor’s consumer surplus. The total area under demand includes both that cost and consumer surplus.
Question 14 · What if visitors can go somewhere else?
A lake closes because of pollution. A nearby lake offers a similar experience at a similar travel cost. Compared with having no close substitute, how does this alternative affect the likely recreation loss?
- It guarantees that the closure causes no welfare loss.
- It makes lost travel spending equal to the value of the closed lake.
- It requires visitors to make exactly the same number of trips as before.
- It can reduce the welfare loss because visitors can switch sites.
D. A close substitute provides another way to obtain recreation benefits. People may switch sites, take fewer trips, or stop visiting. The substitute can reduce the loss without necessarily eliminating it, so a site-choice analysis should account for alternatives.
Question 15 · Cleaner water and house prices
Homes beside a cleaner river sell for $15,000 more than homes beside a polluted river. The first group also has larger houses and better schools. What can we conclude from this comparison alone?
- The $15,000 gap is each household’s annual WTP for cleaner water.
- The gap mixes environmental quality with other housing and location characteristics.
- Cleaning the polluted river must raise every nearby home’s price by exactly $15,000.
- Housing choices cannot provide any evidence about environmental preferences.
B. A hedonic property model must account for other determinants of price, such as size, schools, and commuting. Even a regression’s environmental coefficient needs credible assumptions about unmeasured influences. A house price is also an asset price: a price difference should not be added again every year as an annual benefit.
Question 16 · Paying to avoid contaminated water
A household spends $10 on bottled water, $5 on filters, and $5 worth of time each month to reduce exposure to contaminated water. These are separate costs, and some illness remains. Which interpretation is best?
- Its coping cost is $15 because time does not count.
- Its coping cost is zero because some illness was avoided.
- Its coping cost is $20, but this does not necessarily measure its full WTP for safer water.
- Its exact total WTP for safer water must be $20 per month.
C. The monthly averting or coping cost is 10+5+5=\$20, including the opportunity cost of time. Spending uses resources even when it prevents illness, and it may miss remaining harm. Budgets can limit protection, while purchases may also provide taste or convenience benefits. Observed spending is therefore not automatically the complete willingness to pay.
5. How should we use valuation estimates?
Question 17 · Transferring an estimate to a new park
An analyst finds a study reporting annual WTP per household for an improvement at another park. Before applying it to a Letchworth proposal, which check is most important?
- Whether the original estimate is the largest available number.
- Whether converting to current dollars removes every difference between the settings.
- Whether the environmental change, baseline, affected population, substitutes, units, and payment period are comparable.
- Whether multiplying it by annual visits turns it into total household WTP.
C. Benefit transfer uses existing evidence for a new policy setting. It needs a meaningful match between the original study and the proposed change. Inflation adjustment alone cannot repair a poor match, and a per-household annual value cannot be treated as a per-visit or one-time value.
Question 18 · A small change in mortality risk
Suppose each person would pay $100 per year to reduce their annual mortality risk by 1 in 100,000. What value of statistical life does this imply?
- $10 million
- $1 million
- $100,000
- $100
A. Divide the payment by the risk reduction, using the same time period:
VSL=\frac{\$100}{1/100{,}000}=\boxed{\$10{,}000{,}000}.
Equivalently, 100,000 people would collectively pay $10 million for a reduction of one expected death per year. VSL values small mortality-risk reductions; it is not the price of an identified person’s life. These are assumed teaching values, not an agency estimate.
Question 19 · A decision under uncertainty
A conservation policy has a present-value cost of $50,000. Its low, central, and high present-value benefit estimates are $40,000, $60,000, and $80,000. What does this show?
- The policy has positive net benefits under every estimate.
- The three numbers describe benefits for three different income groups.
- The central estimate is guaranteed to be the true benefit.
- Whether measured benefits exceed costs depends on which benefit estimate is used.
D. Net benefits are −$10,000, +$10,000, and +$30,000. These are alternative estimates for the same policy. The sign changes, so the decision is sensitive to the benefit estimate. The three scenarios have no stated probabilities and are not automatically a statistical confidence interval.
Question 20 · Is a positive dollar total enough?
A wetland project has positive estimated aggregate net benefits. Most costs fall on low-income households, and an important habitat effect has not been monetized. Which recommendation best follows Lecture 7?
- Approve the project solely because aggregate measured net benefits are positive.
- Use the valuation evidence alongside distributional analysis, rights, ecological limits, and evidence about unmeasured effects.
- Give the unmeasured habitat effect a value of zero.
- Treat lower WTP among low-income households as proof that nature matters less to them.
B. Valuation makes trade-offs visible, but a dollar total does not settle every decision criterion. WTP depends on ability to pay, totals can hide who gains and loses, and unmeasured benefits or harms are not necessarily zero. Distributional and ecological evidence should inform the decision alongside the benefit–cost comparison.