Markets fail to reveal appropriate prices for most benefits of environmental improvement directly.  Sometimes economists can infer values indirectly from analysis of real markets for goods associated with environmental amenities. For example, the water quality in a lake is likely to influence expenditures on fishing trips to the lake: in effect, by supporting more fish, water quality is a complement to tackle, bait and other observable expenditures on fishing trips. A decline in water quality shifts the demand schedule for these market goods downward. The resulting decrease in consumer surplus in these markets represents a partial measure of the economic damage of reduced water quality.

Other market goods may substitute for environmental quality. For example, the decline in water quality may also cause an upward shift in household demand for water filtration systems. The increase in defensive expenditures is another partial measure of the economic damages.

In many cases, however, changes in environmental quality leave no significant market trace. Economists can still evaluate such changes directly from surveys using hypothetical markets for the environmental amenity. These are known as "contingent valuation" methods.

We can distinguish two categories of environmental amenity benefits: use values and non-use or existence values. Use values may be inferred from markets for goods which are complements to the environmental amenity, or are substitutes for it, as in the lake example.  Recreation expenditures by bird-watchers or wildnerness recreationists express partial economic values for non-game birds or wilderness areas.  But these amenities often have significant existence values beyond any discernible use value.  For example, most people will never see a whooping crane, but still have some positive willingness-to-pay for prserving the species.  The majority of Americans don't want the Arctic National Wildlife Refuge opened to oil drilling, even though they will never visit there.  The valuation of such non-use values is one of the biggest challenges in environmental economics.

Welfare Measures

Suppose we are trying to evaluate an environmental improvement from Q₀ to Q₁. We might describe the change to a survey respondent with income M and ask her "What is the largest amount of money you would be willing to pay" for this improvement.  This implies that the respondent is entitled to Q₀, and the level of utility U₀(Q₀,M) associated with it, where M is her money income.  If she responds truthfully, her stated $WTP represents the income adjustment that would exactly offset the utility gain from the environmental improvement.  Formally, U₀(Q₀,M) = U₀(Q₁,M-WTP).  WTP is a welfare measure associated with an income-compensated, utility-neutral demand for Q.

We laid out the demand theory foundations for this several lectures back.  Conventional (Marshallian) demand schedules Q(P,M) include both substitution and income effects. If the price of a normal good X declines from P₀ to P₁, consumers buy more of it for two reasons: first, they substitute it for other goods which are now relatively more expensive; second, since the decline in price increases the effective purchasing power of their budgets, they can afford a little bit more of everything. The substitution effect is "utility-neutral" since it implies a movement along the same indifference curve; the income effect implies a jump to a higher level of utility, and thus quantifies the welfare gain resulting from the price decline.

Income-compensated (Hicksian) demand schedules Q(P,U) reflect  just the substitution effect.  The income effect is removed by adjusting the consumer's budget so that the ex ante and ex post utility levels are the same.  In the context of a price decline, the compensating variation is the income adjustment that leaves the consumer at the old utility level under the new price:  U₀(P₀,M) = U₀(P₁, M-CV).  Graphically, this is the area behind the compensated demand schedule associated with U₀.

Alternately, you might ask a survey respondent "What's the minimum amount of compensation you would be willing to accept" (WTAC) to forego the same improvement from Q₀ to Q₁.  Now we are implying the respondent is entitled to Q₁ and the higher level of utility U₁(Q₁,M) associated with it.  Assuming he responds truthfully, his stated $WTAC represents the income adjustment that exactly offsets the utility loss from the environmental improvement.  Formally, U₁(Q₁,M) = U₁(Q₀,M+WTAC).  This utility-neutral measure is based on the consumer's ex post level of utility U₁. Graphically, this is represented as the increase in the area behind the compensated demand schedule associated with U₁.

At least in theory, these measures should be directly quantifiable via survey methods.  The income-neutral consumer surplus, which is the area behind the conventional Marshallian demand schedule Q(P,M), and is intermediate between CV and EV, is not based on a consistent utility level.

Note that the welfare measure we obtain depends on how we frame the question and how respondents perceive their entitlements (which determines their reference level of utility).  For a price decline or quality improvement, CV < EV: people will pay less for an improvement they are not already entitled to than the compensation they would require to forego the same improvement if they were already entitled to it.  Conversely, for a price increase or quality reduction, CV > EV.  In either case, CV and EV bound the Marshallian consumer surplus measure.

Conventional demand theory suggests that since the difference between CV and EV is due solely to the income effect, it should be small.  However, a number of empirical studies indicate very large (three- to ten-fold) differences between WTP and WTAC.  Hanemann demonstrates that the size of the discrepancy between WTP and WTA increases with the income elasticity of demand for Q and decreases with the elasticity of substitution between Q and market goods.  So as the elasticity of substitution between Q and market goods approaches zero (Q has no substitutability with any market good), the discrepancy between WTP and WTA approaches infinity.

Psychologists Kahneman and Tversky offer another reason why WTP and WTA may diverge: people view gains and losses very differently, so that the magnitude of the utility gain from winning $10 can be substantially  less than the magnitude of the utility loss from losing $10.  The implication is that respondents to contingent valuation surveys base their responses on a reference set of entitlements at which their demands for Q are discontinuous.  This is sometimes termed an "endowment effect."

Some CVM studies

The first CVM studies were conducted in the early 1960's by Robert Davis and Jack Knetsch, who validated recreationists' stated willingness-to-pay for wilderness recreation in Maine against actual travel expenditures.  

A series of studies by Bishop and Heberlein tested the consistency of CVM with experimental markets for hunting licenses in Wisconsin. While their CVM results were broadly consistent with their experimental market results, both sets of results demonstrated much larger empirical differences between WTP and WTAC than conventional demand theory would predict, given that recreational hunting does not typically take a very large share of consumer budgets. These large discrepancies between WTP and WTAC imply low substitutability between hunting and other forms of outdoor recreation.