Chapter 7 Benefit–Cost Analysis: Benefits

As noted above, a marginal damage function shows the changes in damages suffered by people or other elements of the ecosystem when exposed to pollution or environmental alteration. Damages can occur in many forms, ranging from direct physical damage, such as health impacts, to degradation of the aesthetic quality of the environment (e.g., lowered visibility or psychic damage). In other words, “damages” include all the negative effects of the emissions. Looked at from a different perspective, the marginal damage function for increases in emissions is the same as the demand/willingness-to-pay function for decreases in emissions. If a small increase in emissions causes a person $10 in increased damages, the maximum he would be willing to pay to decrease emissions by that small amount would presumably be $10. We want to focus, therefore, on willingness to pay for environmental improvements.⁹

Our focus in benefit–cost analysis is on net benefits. A key concept economists use is called consumer surplus.

Consumer surplus is illustrated first for a private good where market prices reflect WTP, then for a public good, like environmental quality, where “price” in the form of WTP must be imputed.

In the case of private goods, consumer surplus is the difference between what a consumer is willing to pay for a particular amount of the good and the market price he or she actually has to pay.¹⁰ Figure 7-2 shows a person’s demand for organic apples (and is the same as the demand curve of Figure 3-1). Suppose the market price of apples is $3 per kilogram. Reading off the demand curve, the consumer wishes to buy 4 kg at this price. Now consider the consumer’s net benefits for his purchase of 4 kg. He would be willing to pay $4.50 for the first kilogram of apples. We can read this off the demand curve in Figure 7-2 or use the inverse demand function from Chapter 3 (P = 5 – .5Q^D) to derive that WTP price. This means his net benefit from purchasing the first kilogram is $4.50 minus the $3 per kilogram he has to pay, or $1.50. The second kilogram yields a net benefit of $1 and the third, $.50; the fourth, of course, yields no additional net benefit because price equals the consumer’s WTP. Consumer surplus is then calculated as the sum of all these net benefits from zero to the quantity purchased. It is the area under the demand curve above the price of the good from 0 consumption to the 4 kg of apples the person chooses to buy (area a). We can readily calculate this area—it is the triangle with base of 4 and height of $2, which equals $4. These are this consumer’s net benefits from purchasing 4 kg of apples at a price of $3 per kilogram. The principle is the same whether we are dealing with individual or market demand curves. To recap,

Consumer surplus is the difference between the consumer’s WTP for a good as represented by his demand curve and the market price of the good summed over all units of the good purchased. If the market price of apples is $3 per kilogram, the consumer buys 4 kg and his consumer surplus is area a, which equals $4. If the market price of apples falls to $2 per kilogram the consumer will buy more apples and get a greater benefit due to the fall in the price. The net gain from the fall in the price is measured by change in consumer surplus – the shaded area, which equals the difference in consumer surplus from the equilibrium at a price of $3 per kilogram and 4 kg purchased to that at $2 per kilogram and 6 kg purchased. The net benefit/change in consumer surplus is $5.

How is consumer surplus used to measure WTP? The following example illustrates.

Benefit–cost analysis of public projects and policies involves changes in situations. Consumers may initially be at one equilibrium, then move to another as a result of the policy or project. Their net benefits are then found by looking at the change in consumer surplus with and without the project. For example, suppose the public program is a subsidy to organic apple growers as part of a sustainable agriculture program. The subsidy lowers the equilibrium price of apples from $3 to $2 per kilogram. Look again at Figure 7-2. At $2 per kilogram, the consumer wishes to buy 6 kg. He also has higher net benefits for each kilogram purchased up to 6 kg, because the price per kilogram is $1 cheaper. Total consumer surplus in the new situation is ¹/₂($3 times 6) = $9. The change in consumer surplus is thus the difference between total consumer surplus with and without the policy ($9 – $4) = $5. This is shown as the shaded area in Figure 7-2. The change in consumer surplus represents the net benefits accruing to this consumer from the government policy and, hence, his WTP for the policy.

In the case of a public good, there is no market price for the good but the principle behind consumer surplus is still appropriate. The difference is that the analyst must infer people’s WTP rather than use market prices. With a public good, such as environmental quality, what is being offered is a specific quantity of the good. The person is then asked for her WTP for that quantity. Figure 7-3 illustrates: we use exactly the same equation for demand curve as in Figure 7-2 to facilitate comparison, but interpret the quantity axis as some measurable indicator of environmental quality (EQ).

Suppose the initial level of EQ is 4 units. The consumer is then asked what she is WTP for 4 units. Her answer (reading off her demand curve): $3. Consider a public project that increases EQ to 6 units. Ask again—what are you WTP for 6 units of EQ? Answer: $2. It then makes intuitive sense to measure the total benefits from the public good as argued in Chapter 3 (see Figure 3-2) as the area under the demand curve between these two quantities, because there is no market price she has to pay. The area under the demand curve between the old and the new quantity represents her WTP for the increase in EQ. The change in consumer surplus can be calculated numerically from Figure 7-3 as the area of the rectangle marked a plus the area of the triangle marked b. Area (a + b) = $5. This number should be familiar to you. It is exactly the same as the change in consumer surplus measured for the private market (using the same demand curve), and shown by the shaded area in Figure 7-2.

Figure 7-3: Deriving Consumer Surplus for a Public Good

The change in consumer surplus for an improvement in environmental quality from 4 to 6 units is the area under the demand curve between these quantities. This is area (a + b) and equals $5.

There are essentially four ways of trying to find out how much people are willing to pay for improvements in environmental quality. All derive measures of changes in consumer surplus associated with the change in environmental quality. These are as listed in Table 7-1:

 Preventive or mitigating expenditures

 Hedonic estimation

 Surrogate markets

 Contingent valuation

Noise pollution can be used as an illustration.

Example: How to value reductions in traffic noise

One feature of the modern world is high-speed roadways (highways, expressways, freeways, and turnpikes), and a major characteristic of these roads is that the traffic on them creates noise. Thus, the people who live nearby suffer damages from this traffic noise. Suppose we would like to estimate the willingness to pay of people living near highways to reduce traffic noise. How might we do this? Three of our four approaches could be used.¹¹

The homeowners themselves may have made expenditures to reduce the noise levels inside their homes. For example, they may have installed additional insulation in the walls of their homes, put double-thick glass in the windows, or planted shrubs or installed other outside noise barriers to dampen the noise. When people make expenditures like this, they reveal something about their willingness to pay for a quieter environment. In general, then, if we can find cases where market goods are purchased in order to affect a consumer’s exposure to the ambient environment, we may be able to analyze these purchases and use market prices to infer one component of the value people place on changes in the ambient environment.

The noise in the vicinity of the road may have affected the prices that people have paid for the houses there. If two houses have exactly the same characteristics in all respects but the level of exterior noise, we would expect the one in the noisier environment to be less valuable to prospective buyers than the one in the quieter environment. If the housing market is competitive, the price of the noisier house would be lower than the other one. Thus, by looking at the difference in house prices due to the presence of noise we can estimate the value people place on reduced noise pollution. Any time the price of some good or service varies in accordance with its environmental characteristics, we may be able to analyze these price variations to determine people’s willingness to pay for these characteristics.

Both of the foregoing techniques are proxies for WTP in the sense that they look for ways of analyzing market data to find out what they imply about the willingness to pay of people for closely associated environmental characteristics. The third way is deceptively direct. We could conduct a survey among homeowners and ask them how much they would be willing to pay for reductions in noise levels around and inside their homes. This direct survey approach has received a lot of attention from environmental economists in recent years, primarily because of its flexibility. Virtually any feature of the natural environment that can be described accurately to people can be studied by this method.

In the remainder of the chapter we illustrate, using more detailed examples, how these techniques have been used to estimate the benefits of improvements in environmental quality, highlighting problems and pitfalls the benefit–cost analyst encounters.

Preventive or Mitigating Expenditures

Air and water pollution can produce a variety of adverse health conditions, ranging from slight chest discomfort or headaches all the way to acute episodes requiring hospital care. People often make preventive or mitigating expenditures to try to avoid, or avert, these conditions, and these mitigation costs are an expression of their willingness to pay to avoid them. Consider the following example.

Urban smog is formed from a combination of air pollutants (sulphur dioxide, particulate matter, nitrogen oxides) during days when temperatures are high, there is little wind to disperse pollutants, or a temperature inversion exists where cold air is trapped in a region by a mass of hot air above it. Certain Canadian cities (e.g., Vancouver, Toronto, Montreal) are more prone to smog because they have high emissions of air pollutants and conditions favourable to the creation of smog. The components of smog (the above pollutants plus the ground-level ozone produced by the interaction of the pollutants with sunshine) contribute to asthma attacks and other respiratory problems.

Suppose you have asthma and want to reduce your exposure to smog. A defensive expenditure would be the purchase of an air purifier. Your costs involve the initial purchase of the purifier (a capital cost) plus the operating costs of running the purifier during high-smog days (electricity, air filters for the purifier). We assume you would not buy the purifier if smog were not a problem in your city. However, other people (e.g., smokers) might purchase air purifiers for reasons unconnected to urban smog.

The economic analyst could calculate defensive expenditures by looking at market data for air purifiers. The steps the analyst could take are as follows.

1. Collect data on air purifier purchases in two cities—one with a large number of smog days, and one without.

2. Estimate market demand curves from this data.

3. Use the demand curves to calculate the benefits of reducing urban smog by measuring the difference between willingness to pay for air purifiers with and without smog.

We assume the analyst has completed steps 1 and 2. The estimated market demand curves from step 2 are shown in Figure 7-4.¹² Hamilton, Ontario, is in a “smog belt” in eastern Canada with a number of summer days where smog is a problem. Winnipeg, Manitoba, has very few, if any, smog days per year due to its location away from smog-generating activities and a favourable topography and weather (no mountains, lots of wind). The demand curve for air purifiers in Winnipeg lies wholly inside that of Hamilton.

Step 3 requires calculation of the benefits of reducing smog. If Hamilton could reduce smog to the level of Winnipeg, its inhabitants would presumably reduce their air purifying expenditures to a level similar to that of Winnipeg (other things being equal). The WTP to reduce smog to Winnipeg’s level is then estimated by the difference between the two demand curves in Figure 7-4. This is the difference in total willingness to pay for the air purifier. Quantitatively, we simply measure the area under each city’s demand curve and subtract Winnipeg’s from Hamilton’s. Total willingness to pay of people living in Hamilton to remove all smog would be $150,000; total WTP from Winnipeg is $50,000. The difference is $100,000. This represents the WTP of Hamiltonians to have their air quality improve to that of Winnipeg. Now suppose the average price of air purifiers in both cities is $75. WTP should be measured as the change in consumer surplus due to different air quality. This will be the difference between the two demand curves above the market price of the good, which is shown as the shaded area in Figure 7-4 and equals $55,468.75.¹³ Remember that we use the change in consumer surplus because we need to net out expenditures on the good. If people do not spend money on the good in question, they will spend it on some other good; hence, we measure only the surplus as WTP.

Two demand curves for air purifiers are estimated. Hamilton is a city with many high-smog days; Winnipeg is a city with very few smog days. Hamilton’s demand curve lies above that of Winnipeg because people are engaging in defensive expenditures to mitigate damages from urban smog. The difference in the demand curves shows the willingness to pay of people in Hamilton to protect themselves from smog. Willingness to pay for smog protection is estimated as the shaded area. If smog in Hamilton is reduced to the level of that in Winnipeg, the shaded area would be the benefits of the reduction in smog damage because people in Hamilton would now buy fewer air purifiers.

To use the change in consumer surplus as the WTP for improving air quality in a benefit–cost analysis, it would have to be converted into an annual value. This is because the air purifier is a capital asset that yields services over time, but also depreciates. Suppose air purifiers last 10 years and we assume they depreciate evenly over their life. Then the service value(depreciation) each year is one-tenth of the initial value, or $5,547.¹⁴ This amount is then the benefit per year of reducing Hamilton’s smog to the level of Winnipeg’s and this amount would be discounted in the normal fashion in a benefit–cost analysis.

^14. Other approaches are possible, for example using declining balance depreciation.

The example gives you a flavour of the approach taken in using defensive expenditures as a measure of willingness to pay for higher environmental quality or damages incurred from pollution. It is a proxy approach in that we are inferring from people’s behaviour how they value environmental quality. There are many practical challenges. The approach cannot be used for all environmental problems because we may be unable to measure defensive expenditures linked to the specific environmental problem, or there are no defensive actions people can take. As the example suggests, it may be difficult to discern whether the expenditure is connected to a specific environmental problem. Do differences in demand curves across cities reflect air pollution or some other characteristic? Finally, defensive expenditures will not capture all the disutility people get from environmental degradation, just the part they can address through defensive actions.

Let’s turn to an example—housing markets.

Suppose you had two houses that were exactly the same in terms of all their physical characteristics (number of rooms, floor area, age), as well as in locational factors (distance to neighbours, distance to shopping facilities). But assume one house is located in an area of substantial air pollution, while the other is located in an area with relatively clean air. We would expect the market prices of these two houses to differ because of the air-quality difference. This conclusion generalizes to a large housing market involving many properties. The surrounding air quality is essentially a feature of the location of a house—so, as houses are bought and sold in the housing market, air-quality differences would tend to be capitalized into the market prices of the houses.¹⁶ Of course, homes differ in many respects, not just in terms of air quality. So we must collect large amounts of data on many properties to use the hedonic approach.

The derivation of a hedonic price function is done using statistical techniques. The analyst typically collects data on a sample of housing units sold over a particular time period. The relationship between housing prices and all the possible characteristics that might influence people’s willingness to pay for each house is then estimated statistically. These characteristics can include the size of the house, number of bedrooms, bathrooms, age of the home, its location, neighbourhood characteristics such as proximity to schools and parks, and a measurable environmental variable, such as air quality. The analyst graphs what is called a hedonic price function for the environmental variable (measured by an air quality index, or AQI), holding all other characteristics constant. Panel (a) in Figure 7-5 illustrates this relationship. The hedonic price function is shown as P(AQI; z), where z is all other characteristics that are held constant. The function is not a straight line to show that for most people, their marginal willingness to pay for a characteristic changes as more of the characteristic is supplied. At low levels of air quality, people’s willingness to pay for a small increase in air quality might be quite high. But if the level of air quality is already high, a small increase will not yield a large increase in willingness to pay. If one then measures the slope of this hedonic price function for different levels of air quality she obtains the hedonic demand function for air quality, which depicts the marginal willingness to pay for each increment in air quality, again remembering that all other characteristics of the house and its location are held constant.