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Copyright ©2011 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458

All rights reserved.

Chapter

Cost-Benefit Analysis Concepts and Practice

Cost-Benefit Analysis: Concepts and Practice, Fourth Edition Boardman • Greenberg • Vining • Weimer

FOURTH EDITION

Valuing Impacts from Observed Behavior: Indirect Market Methods

Fourteen

Valuing Impacts from Observed Behavior: Indirect Market Methods

Using Revealed Preferences

Chapter 14

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Shadow Pricing

One of the key requirements of performing a CBA is quantification of costs and benefits.

However, there are a range of costs and benefits for which a value cannot be easily obtained.

Shadow pricing is suitable when there is no market value, or a market value is not representative of the true value of a good.

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Shadow Pricing

The methods can be broadly categorized into two:

1. Stated Preference Methods

a. Willingness to Pay – asking individuals how much they would be willing to pay to continue to enjoy a particular asset e.g. a park.

b. Willingness to Accept – asking individuals how much they would be willing to accept in compensation for continuing negative impacts e.g. pollution from a road.

2. Revealed Preference Methods

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Valuing Impacts from Observed Behavior: Indirect Market Methods

Purpose: This chapter presents various methods for estimating shadow prices based on observed behavior when markets for the (primary) good, such as human life, do not exist.

• Considerable progress has been made during the past 30 years to value goods that were previously treated as “intangible”.

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Valuing Impacts from Observed Behavior: Indirect Market Methods

• Estimation of changes in social surplus requires knowledge of entire demand and supply schedules.

• We have assumed that there is a market demand curve for the good in question, where we can observe a least one point on the demand curve.

• However, in many applications of CBA, the markets for certain goods such as human life and pollution do not exist or are imperfect.

• Economists have devised methods to value these goods or their impacts enabling to have a comprehensive CBA.

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• In contrast to “stated” or “expressed” preferences (Chapter 15), revealed preferences are not collected by asking individuals for their views.

• They are, instead, collected through direct observation of actual responses to complement or substitute goods.

• They provide indirect estimates of the value of a cost or benefit using surrogate market goods.

Valuing Impacts from Observed Behavior: Indirect Market Methods (Revealed

Preferences)

Simple Valuation Methods

Valuing the impacts of projects using revealed preferences can be conducted using the following methods:

1. MARKET ANALOGY METHOD

2. THE TRADE-OFF METHOD

3. INTERMEDIATE GOOD METHOD

4. ASSET VALUATION METHOD

5. PREVENTATIVE OR DEFENSIVE EXPENDITURES APPROACH

6. HEDONIC PRICE METHOD

7. TRAVEL COST METHOD

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MARKET ANALOGY METHOD

• This method uses data on similar goods in the private market to estimate the implicit “price” or the demand curve for publicly provided goods.

• Governments supply many goods that are also provided by the private sector. Examples: housing, campsites, university education, home care, etc.

• The government usually provide these services free or at significantly below market prices. Thus, the actual price paid may not be on the demand curve. However, it may be possible to obtain an estimate of the entire demand curve using data from a similar good produced by the private sector.

A. Using the Market Price of or Expenditures on an Analogous Good

B. Using Information about an Analogous Private-Sector Good to Estimate the Demand Curve for a Publicly Provided Good

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MARKET ANALOGY METHOD A. Using the Market Price of or Expenditures on an Analogous Good

Example: A local government project provides housing for 50 families and charging a rent of $200 per month so that government revenue is $10,000 a month. This expenditure underestimates benefits because all families would be willing to pay $200 per month or more.

Suppose that comparable units in the private sector charge rent of $500 a month, then the estimated total monthly benefits of publicly provided housing would be $25,000 per month.

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MARKET ANALOGY METHOD

• The market price of a comparable good in the private sector provides a good estimate of the value of a publicly provided good if it equals the average amount that users of the publicly provided good would be willing to pay (WTP).

Where the government provides a good or service at a lower than market price, the price paid by occupants would generally underestimate the benefit of this service because users would be WTP at least this amount; some might pay more.

MARKET ANALOGY METHOD B. Using Information about an Analogous Private-Sector Good to Estimate the Demand Curve for a Publicly Provided Good

• Rather than focusing on the average amount that users of a publicly provided good are willing to pay, it is conceptually better and easier to think about the demand curve for the good.

• We can use private-sector data to help map out the demand curve for a publicly-provided good if the goods and their markets are similar.

• However, using expenditures alone underestimates total benefits because it ignores consumer surplus.

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MARKET ANALOGY METHOD

B. Using Information about an Analogous Private-Sector Good to Estimate the Demand Curve for a Publicly Provided Good

Example: Suppose a municipal government wants to measure the gross benefits of a swimming pool that it owns and operates. It doesn’t charge an admission fee and the pool receives 300,000 visitors per year. (point a in Figure 14-1).

In a comparable municipality, a privately operated swimming pool charges $5 for admission and receives 100,000 visitors per year (point b). If these two municipalities and pools were comparable, it would be reasonable to assume that points a and b are both on the demand curve.

Using revenues at the private pool ($500,000) would underestimate the benefits of the public pool because it omits the consumer surplus of those willing to pay more than $5, the area of triangle cbd, and those willing to pay something less than $5, but more than $0, the area of triangle bae.

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Figure 14-1 Demand Curve for Visits to a Municipal Swimming Pool

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THE TRADE-OFF METHOD

• Economists may use the opportunity cost as a measure of its value.

• To measure the value of a good or commodity using opportunity cost – i.e. the value of what an individual would have to give up to obtain something – as a proxy for a good or commodity which has no market value.

For example, time saved could be valued using the after-tax wage rate. People make trade-offs between time and money wages and we can use the rate at which they make this trade-off to value time.

Similarly, the trade-off that people make between changes in fatality risk and wages can be used to value a statistical life.

A. The Value of Time Saved, VTTS B. The Value of a Statistical Life, VSL

Forgone Earnings Method Simple Consumer Purchase Studies Simple Labor Market Studies

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THE TRADE-OFF METHOD

A. The Value of Time Saved, VTTS

• The obvious analogous market for time saved is the labor market.

• In the absence of market imperfections (i.e., people can choose the number of hours they work and there is no unemployment), the wage rate equals the marginal value of time.

However, using the wage rate is only a first approximation.

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THE TRADE-OFF METHOD

B. The Value a Statistical Life, VSL

1. Forgone earnings method - This method is an inappropriate method. It suggests the value of a life saved equals the person’s discounted future earnings.

• It generates higher values for young, high-income males than old, low-income females. For retired people, the resultant value of life may be negative.

• Conceptually most problematically, this method does not reflect what people are WTP for a small reduction in risk of their death.

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THE TRADE-OFF METHOD

B. The Value of a Statistical Life, VSL

2. Simple Consumer Purchase Studies - This method estimates the value of life by observing how much people pay for life-saving devices, such as safety belts.

• Example: If people are indifferent between paying an extra $300 to reduce the probability that they will die by 1/10,000, then they value their life at $3 million.

3. Simple Labor Market Studies - Similarly, if a person is willing to forgo an extra $3,500/yr to increase the probability that he will not have a fatal on-the-job accident by 1/1,000, then he values his life at $3.5 million (or more).

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INTERMEDIATE GOOD METHOD

Intermediate goods – goods that are used as inputs to some other downstream business.

If a project produces an intermediate good that is not sold in a well functioning market, then its value can be imputed by determining the value added to the “downstream activity”:

Annual Benefit = NI(with project) – NI(without project)

where, NI = net income of downstream business. The total benefit of a project can be computed by discounting these annual benefits over the project’s life.

Example: This method can be used to value improvements in human capital, such as training programs, by comparing the average incomes of those in the program to those who are not.

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INTERMEDIATE GOOD METHOD

Example: Valuing the benefits of education and training programs.

The intermediate good method measures the annual benefit of human capital programs by comparing the average incomes of those who have been enrolled in them and the average incomes of those who have not.

The total benefits is found by discounting the annual benefits over the years people work after graduation and multiplying by the number of participants.

Some problems with this method are:

1) It assumes the difference in income captures all of the benefits (there may be consumption benefits as well as investment benefits)

2) It assumes all other variables are held constant (e.g., educational ability).

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ASSET VALUATION METHOD

Government projects often affect the prices of assets such as land and housing. The impacts are said to be capitalized into the market value of assets.

The impacts of a project or policy can be imputed from changes in the price for certain capital goods.

Observed increases or decreases in asset values can be used to estimate the benefits or costs of projects.

This method is often used to value differences in housing. For example, data can be collected on average prices of houses with a large garden, or close access to a country park. These can be compared against houses without those attributes, to obtain an estimate of the value of having a large garden or local access to a country park.

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ASSET VALUATION METHOD

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More Examples:

• The “value” of noise can be inferred from comparing the price of a house in a noisy neighborhood to the price of a similar house in a quiet neighborhood.

• The difference in the market prices between houses with a view and houses with no view provides an estimate of how much households are willing to pay fro a view (assuming that these houses are similar in all other respects).

An advantage of using market prices is that information is quickly and efficiently capitalized into prices so that price changes or price differences provide a good estimate of the value of the policy change. Also, appropriate data are often available.

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PREVENTATIVE OR DEFENSIVE EXPENDITURES APPROACH

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• The preventative or defensive expenditure method estimates the value of a cost by observing the value of the costs incurred in attempting to mitigate or prevent the effects of a negative externality (something undesirable) such as pollution.

• If you hire someone to clean your windows periodically, the cost of this action in response to the smog is termed a defensive expenditure – it is the amount spent to mitigate or even eliminate the effect of a negative externality.

DEFENSIVE EXPENDITURES METHOD

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The level of a public good or externality (e.g. smog) and other goods (window cleaners) are inputs to some production process (window cleaning).

For example, when the negative externality of smog is reduced, less labor is required to produce the same number of clean windows. The change in expenditures on the substitute input (window cleaners) is used as a measure of the benefit of reduction of the public good or externality.

The change in expenditures can be used as a measure of the cost of the change in pollution.

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PREVENTATIVE OR DEFENSIVE EXPENDITURES APPROACH

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Another Example:

• Using this measure could estimate the cost of noise pollution from a road by observing the expenditure of individuals living close to the road on double-glazing to block out noise pollution.

• If we wish to estimate the benefits of introducing boarding on the sides of the road to block out the noise, we could do so by looking at the changes in expenditure on double-glazing by households located close to the road over time.

• The limitation of this method is that some actions may be taken for a number of reasons, and not solely in order to mitigate a negative externality. For example, individuals may invest in double-glazing to reduce energy bills, or in order to make their home more attractive to potential buyers.

PROBLEMS WITH SIMPLE VALUATION METHODS

1. Omitted Variable Problem

If a relevant explanatory variable is omitted from the model and if it is correlated with the included variables of interest, then the estimated coefficients will be biased.

Examples: • The price of a house typically depends on factors such as its distance

from the central business district and size, as well as whether it has a view.

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PROBLEMS WITH SIMPLE VALUATION METHODS

2. Self-Selection Bias

The self-selection problem arises whenever different people attach different values to particular attributes.

Example: Suppose we want to use differences in house prices to estimate a shadow price for noise.

People who are not bothered much by noise, possibly because of hearing disabilities, naturally tend to move into noisy neighborhoods. As a result, the price differential between quiet houses and noisy houses may be quite small, which would lead to an underestimation of the shadow price of noise for the “average” person.

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THE HEDONIC PRICE METHOD

The hedonic price method (sometimes called the hedonic regression method) can be used to value an attribute, or a change in an attribute, whenever its value is capitalized into the price of an asset, such as houses or salaries.

This method offers a way to overcome problems from omitted variables and self-selection bias.

It consists of two steps: 1. The first step estimates the relationship between the price of an

asset and all of the attributes (characteristics) that affect its value. From this it derives the marginal effect of an attribute (e.g., a better scenic view) on the value of the asset, while controlling for other variables that affect the value of the asset.

2. The second step estimates the WTP for the attribute, after controlling for “tastes,” which are usually proxied by socioeconomic factors.

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THE HEDONIC PRICE METHOD

Example: Suppose one wants to estimate the value of a scenic view.

The first step estimates the effect of a marginally better scenic view on the value (price) of houses (a slope parameter in a regression model), while controlling for other variables that affect house prices.

House and other property prices are not simply determined by one variable. They are a product of a number of factors.

The hedonic price method is used to measure the relative importance – through use of regression analyses – of these independent ‘explanatory’ variables on house and property prices.

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THE HEDONIC PRICE METHOD

For example, we may postulate the following multiplicative model showing the relationship between the price of a house (P) and all of its attributes, such as quality of its scenic view (VIEW), its distance from the central business district (CBD), its lot size (SIZE), and various characteristics of its neighborhood, NBHD:

(14.3)

Equation 14.3 is called a hedonic price function or implicit price function. The change in the price of a house that results from a unit change in a particular attribute (i.e., the slope) is called the hedonic price, implicit price, or rent differential of the attribute.

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THE HEDONIC PRICE METHOD

• In a well-functioning market, the hedonic price can naturally be interpreted as the additional cost of purchasing a house that is marginally better in terms of a particular attribute.

• Usually researchers estimating hedonic prices assume the hedonic price function has a multiplicative functional form like Equation 14.3. This means that as a characteristic increases (or improves) the house prices increase but at a decreasing rate.

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THE HEDONIC PRICE METHOD

• The hedonic price of a particular characteristic is therefore the slope of this equation with respect to that particular characteristic. For example, the hedonic price of scenic views, rv is expressed as:

rv measures the additional cost of buying a house with a slightly better (higher-level) scenic view.

In the model, the hedonic price of scenic views depends on the value of the parameter β3, the price of the house and the view from the house.

The hedonic price of a characteristic can be interpreted as the willingness to pay of households for a marginal increase in that particular characteristic.

(14.4)

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THE HEDONIC PRICE METHOD

Households differ in their incomes and taste. Some are willing to pay a considerable amount of money for a scenic view, others are not.

The second step of the hedonic regression analysis estimates the willingness to pay of households but additionally accounts for households having different incomes and tastes. To account for different incomes and tastes, analysts should estimate the following WTP function (inverse demand function) for scenic views:

rv = W(VIEW, Y, Z) (14.5)

where, rv is estimated from equation (14.3), Y is household income, and Z is a vector of household characteristics that reflects tastes (e.g., socioeconomic background, race, age, and family size).

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THE HEDONIC PRICE METHOD

Using the methods described in Chapter 4, it is straightforward to use equation (14.5) to calculate the change in consumer surplus to a household due to a change in the level of scenic view. These changes in individual household consumer surplus can be aggregated across all households to obtain the total change in consumer surplus.

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Problems with Hedonic Models

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There are several potential problems with hedonic models.

1. People must know and understand the implications of the attribute that is being valued. For example, people should know the level of pollution at the property they buy and know the expected effect of this level of pollution on their health.

2. Variables should be measured without error (the errors in variables problem).

3. The functional forms should be correct (specification error problem).

4. The market should have enough alternatives so that people can locate at their optimum point on the curve.

5. There may be multicollinearity problems, e.g., fatality risk and non-fatality risk might be highly correlated. Dropping one variable would lead to an omitted variable problem.

6. Markets are assumed to adjust immediately to changes in the attributes of interest and to all other factors.

TRAVEL COST METHOD

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• Most applications of the travel cost method (TCM) have been to value recreational sites.

Suppose that we want to estimate the value of a particular recreational site. We expect that the quantity of visits demanded by an individual, q, depends on its price, p; the price of substitutes, ps; the person’s income, Y; and variables that reflect the person’s tastes, Z:

q = f(p,ps,Y,Z) (14.7)

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TRAVEL COST METHOD

• TCM recognizes that the full price paid by persons for a visit to a recreational site is more than just the admission fee. It also includes the costs of traveling to and from the site.

Among these travel costs are the opportunity cost of time spent traveling, the operating cost of vehicles used to travel, the cost of accommodations for overnight stays while traveling or visiting, and parking fees at the site.

The sum of all of these costs gives the total cost of a visit to the site. This total cost is used as an explanatory variable in place of the admission price in a model similar to equation (14.7).

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TRAVEL COST METHOD The clever insight of the TCM is that, although admission fees are usually the same for all persons (indeed, they are often zero), the total cost faced by each person varies because of differences in the travel cost component.

Consequently, usage also varies, thereby allowing researchers to make inferences about the demand curve for the site.

The travel cost method involves collecting data on the costs incurred by each individual travelling to the recreational site or amenity. This ‘price’ paid by visitors is unique to each individual, and is calculated by summing the travel costs from each individuals original location to the amenity.

By aggregating the observed travel costs associated with a number of individuals accessing the amenity a demand curve can be estimated, and as such a price can be obtained for the non-price amenity.

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TRAVEL COST METHOD Estimating the demand schedule (equation 14.7) for a particular recreational site is conceptually straightforward.

1. Select a random sample of households within the market area of the site.

2. Survey these households to determine their numbers of visits to the site over some period of time, all of their costs involved in visiting the site, their costs of visiting substitute sites, their incomes, and other characteristics that may affect their demand.

3. Specify a functional form for the demand schedule and estimate it using the survey data.

It is worth emphasizing that when total cost replaces price in equation (14.7), this equation is not the usual demand curve that gives visits as a function of the price of admission. However, as shown in the next section, the TCM can be used to estimate the usual market demand curve.

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Zonal Travel Cost Method

• Using this method, researchers survey actual visitors rather than potential ones.

Visitors are allocated to a particular zone, depending on their “travel costs” (usually distance). For each zone, the analyst computes the average number of visits per year and the average total travel cost.

Using these observations it is possible to estimate the relationship between cost/trip and the number of trips per person. The consumer surplus for a visitor from a particular zone is given by the area below this curve and above the cost of a visit from that zone, as shown in Figure 14-4. By repeating this calculation for each zone, it is possible to calculate the total consumer surplus, as shown in Table 14-1.

TRAVEL COST METHOD

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Figure 14-4 “Representative” Individual’s Inverse Demand Curve for Visits to a Recreational Area as a Function of Total Cost per

Visit

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Zonal Travel Cost Method

• The zonal travel cost method requires the analyst to specify the zones from which users of the site originate.

• Zones are easily formed by drawing concentric rings or iso-time lines around the site on a map.

• Ideally, households within a zone should face similar travel costs as well as have similar values of the other variables that would be included in an individual demand function.

TRAVEL COST METHOD

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Zonal Travel Cost Method

Example

Consider an example of valuing a park.

In this example four zones have been designated by the researcher. Zone A has an average travel time of 1 hour, and a distance of 25km. Zone B has an average travel time of 1.5 hours and a distance of 40km. Zone C has an average travel time of approximately 2 hours and a distance of 80km. Finally, zone D has an average travel time of 4 hours and a distance of 120km.

The admission cost for all users is the same, and is equal to $10. The number of visits per year has been observed by the researcher for each zone. Zone A has an average of 10,000 visits per year. Zone B has an average of 12,000 visits per year, zone C has 8,000 visits, and zone D has 4,000 visits

TRAVEL COST METHOD

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Zonal Travel Cost Method

Example

TRAVEL COST METHOD

Zone Travel Time (hours)

Travel Distance (km)

Admission Cost ($)

Visits per year

A 1 25 10 10,000

B 1.5 40 10 12,000

C 2 80 10 8,000

D 4 120 10 4,000

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Zonal Travel Cost Method

Example

To calculate the value of the asset (V) for a single visit the researcher now uses the simple equation as follows:

V = ((T x w) + (D x v) + Ca) x Va Where, T = travel time (in hours) w = average wage rate (£/hour) D = distance (in km) v = marginal vehicle operating costs Ca = cost of Admission to asset Va = average number of visits per year

TRAVEL COST METHOD

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Zonal Travel Cost Method

Example

In the example the average hourly wage rate is $10, and marginal vehicle operating costs are calculated at $0.16p per km. The researcher can now calculate the value of the country park for each zone to get an overall value for the asset.

TRAVEL COST METHOD

Zone Travel Time (hours)

Travel Distance (km)

Admission Cost ($)

Visits per Year

Zone Value ($)

A 1 25 10 10,000 240,000

B 1.5 40 10 12,000 376,800

C 2 80 10 8,000 342,400

D 4 120 10 4,000 276,800

$1,236,000

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Limitations of the TCM

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1. It is restricted to sites where people (in the zones) have different travel costs. Without variation in total cost, it’s hard to estimate a demand curve.

2. There may be analytical problems in measuring the total cost of a visit. How does one measure opportunity cost of travel time? Should multiple purpose trips be included in the data (desirable if costs can be accurately apportioned to the site)? Also, the journey may have value (and hence the trip has multiple purposes).

Individuals may visit an amenity or recreational site in the morning, but then visit another site or enjoy some other activity in the afternoon. The travel endured to access the amenity was also undertaken to enable access to the afternoon activity. In this case the cost incurred in travelling to the amenity does not represent the value the individuals place on the amenity, but that which they place on both the amenity they visited in the morning and the one which they visited in the afternoon.

Limitations of the TCM

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3. The method estimates the WTP for the entire site rather than features of the site. For example, we do not wish to value a whole park, but instead the fishing ponds within it.

It’s possible to value features if people in zones can choose among alternative sites with different attributes – by using the “hedonic travel cost method”, which treats total cost as a function of both distance from zone to the site and the various attributes of the site.

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Homework

On CANVAS

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