We review some highly abstracted models of market behaviors with which we can illustrate basic principles of environmental economics. Remember that the assumptions underlying these models don’t have to be very realistic, as long as the models themselves have adequate predictive capabilities.

Derivations of demand schedules

We begin by modeling consumers as miniature utility factories, using consumer goods as "inputs" to produce satisfaction. We assume rational consumers maximize their utility subject to their budget constraints. Graphically, this implies a tangency between the budget line, representing all affordable bundles of consumer goods X₁ and X₂, and the highest attainable utility contour (indifference curve), representing all bundles of goods X₁ and X₂ which yield the same level of utility. This tangency implies the slope of the budget line (which is the marginal rate of transformation or ratio of goods prices P₂/P₁) equals the slope of the indifference curve (which is the marginal rate of substitution or ratio of marginal utilities MU₂/MU₁). The tangency point MU₂/MU₁ = P₂/P₁ defines a unique, just-affordable utility-maximizing bundle of goods (X₁*,X₂*). As income or price changes shift the budget constraint, we can trace out how the just-affordable, utility-maximizing bundle (X₁*,X₂*) changes.

A demand schedule is the schedule of quantities of a good consumers are willing to buy at various prices of the good. In a two-good world, the demand system can be generalized as X₁ = f(P₁,P₂,M), X₂ = g(P₁,P₂,M) and M = P₁X₁ + P₂X₂, where fand g are mathematical functions. Here, demands for X₁ and X₂ each depend on both prices P₁ and P₂ and the budget M. So we distinguish an own-price demand schedule, a cross-price demand schedule, and an income demand schedule (Engel curve) for each good. Each of these demand functions can be represented graphically if the other two arguments are held constant.  You should study these animated figures until you are clear on these basic derivations.

It is important to distinguish between a shift in demand and a change in quantity demanded. Consider the (own-price) demand for X₁ with respect to P₁: a change in P₁ implies a movement along the demand schedule, while a change in P₂ or M (or any other variable besides P₁ which influences demand) implies a shift of the entire demand schedule.

We can calculate elasticities of demand for either good with respect to either price or income. The elasticity of demand for X₁ with respect to P₁ is defined as the percent change in quantity demanded of X₁ resulting from a one percent increase in P₁.

X₁ and X₂ are substitutes if the cross-price demands for X₁ with respect to P₂, and X₂ with respect to P₁, are positively sloped, so that the cross-price elasticities are positive. X₁ and X₂ are complements if the cross price demands are negatively sloped and the cross-price elasticities are negative.

X₁ is an inferior good if its Engel curve is negatively sloped and its income elasticity is negative. X₁ is a normal good if its Engel curve is positively sloped and income elasticity is positive. X₁ is a luxury good (luxury goods are a subset of normal goods) if its income elasticity is greater than one.

Individuals’ demand schedules for market goods can be summed horizontally to define aggregate market demand schedules.

Economists usually model quantity demanded as determined by prices and income. But it is often more useful to model inverse demand, where the price consumers are willing to pay for an extra unit of the good is determined by quantity of the good supplied and income. We call this inverse demand schedule a marginal willingness-to-pay schedule. The demand graph looks the same, but now X determines P (WTP) rather than P determining X.

Consumer and producer surplus

A competitive market is characterized by full information, so everyone knows what price levels are and sellers can’t engage in price discrimination (charge different consumers different prices). A downward-sloping demand schedule implies that the WTP of most consumers is higher than the amount they actually have to pay. The aggregate amount consumers would theoretically be willing to pay for the equilibrium quantity X, above what they do pay, is called consumer surplus (CS). This measures the aggregate economic benefit realized by consumers in the market. Graphically, consumer surplus is the triangular area below the demand (WTP) schedule and above the market price. An increase (rightward shift) in supply implies a movement down the demand schedule: equilibrium price is lower for all consumers, and the area of the consumer surplus triangle is increased.

Similarly, an upward-sloping supply schedule implies that the willingness-to-sell (WTS) of most sellers is less than the market price they receive.  The aggregate amount that all sellers in the market collectively receive (P_eq x X_eq) above the minimum amounts they would be willing to accept is called producer surplus (PS).

Alternative measures of economics welfare

While CS is a commonly-used measure of consumers' economic welfare, it lacks some theoretical precision.  Remember that we derived our demand schedules above by translating price changes into budget line shifts that let the consumer attain different levels of utility with the same income.  

When doing policy analysis, it's often more useful to have a welfare measure that is utility-neutral, i.e., expressed in terms of income changes that keep utility constant.  When we talk about maximum "willingness to pay" for an environmental improvement or minimum "willingness to accept" compensation for environmental damage, we are actually talking about the income adjustment that would keep utility constant.

So we begin by deriving some utility-neutral welfare measures of price changes, and then extend this analysis to welfare measures of environmental quality changes.

Here is a graphical representation of a price decline from P⁰ to P¹, which shifts the consumer from U⁰ at point A to U¹ at point B.  There are two components to this increase in quantity demanded, as shown in the ordinary demand schedule.  First, since X is now cheaper relative to Z, there is a substitution effect: the consumer substitutes X for Z.  Second, the price decline increases the effective purchasing power of the consumer's income, so this income effect lets the consumer afford slightly more of both X and Z.  A price decline always has a positive substitution effect, but the income effect may be positive or negative, since the good may be normal or inferior.  In the case of a normal good, this income effect augments the substitution effect.  In the case of an inferior good, the income effect partially offsets the substitution effect.  A Giffen good is so inferior that the income effect completely offsets the substitution effect.

The income-compensated demand shows just the substitution effect.  We can isolate the substitution effect by reducing the consumer's income so that he or she is restored to the original level of utility under the new price set.  Graphically, this means shifting the new budget line in parallel back to the original indifference curve and identifying the consumption quantity at point C.  The area behind this income-compensated demand schedule is known as Compensating Variation (CV).  It is the theoretical maximum amount the consumer would be willing to pay in order to have the the new price.  This can be measured in terms of the other good Z as the vertical distance between the parallel budget lines.  It is more often represented as the red shaded area behind the income-compensated demand schedule passing through point A.  This is the maximum amount the consumer would be willing to pay to have the new price set.  It presumes the consumer is entitled to the ex ante utility level U₀

Here is another welfare measure associated with the same decline in P.  Again, the price declines from P⁰ to P¹, which shifts the consumer from U⁰ at point A to U¹ at point B.  Here we calculate the income adjustment that would give the consumer the same new level of utility with the original price set.  As before, we can calculate this in terms of good Z as the vertical distance between the parallel budget lines, or directly in dollar terms as the area behind the income-compensated demand through point B.  This is the minimum amount of compensation the consumer would be willing to accept for foregoing the price change and being stuck with the old price set.  It presumes the consumer is entitled to the ex post utility level U₁

The choice between CV and EV depends on the reference level of utility.  This is sometimes ambiguous.  We might conduct a survey of lakefront property-owners affected by water pollution.  If we asked some people "How much would you be willing to pay to have the lake clean again?" we are implicitly assuming they are not entitled to the clean lake, and the question elicits their CV.  If we asked other people "What is the minimum compensation you would be willing to accept to put up with this level of pollution?" we are implicitly assuming they are entitled to a clean lake, and the question elicits their EV.

Note that in the case of a price decline CV is smaller than consumer surplus, while EV is larger than consumer surplus.  In the case of a price increase, the situation is reversed: CV > CS > EV.  In most cases, economic theory suggests the differences between CV and EV should not be large, since they're just based on income effects.  Indeed, in some cases we might decide to skip the theoretical niceties and just use consumer surplus as a welfare measure.  Empirically, however, the results of both hypothetical valuation questions as well as constructed market experiments indicate that the differences between CV and EV can be quite large.  We will get into some reasons for this later on.


To formalize the concepts of CV and EV associated with environmental quality changes, suppose we define indifference curves for environmental quality Q and bundles of market goods X which have price P. Since Q isn’t a market good, consumers spend all their income on X: M = PX. The budget line is horizontal with intercept M/P, and intersects the vertical line at Q0, representing the given level of Q. This point falls on some indifference curve representing utility level U₀. The slope of this indifference curve is MU_X/MU_Q, since Q has a positive marginal utility, even if it isn’t a market good. MU_X/MU_Q is the marginal rate of substitution or rate at which consumers are willing to trade X for Q. Since X is priced, we can infer WTP for Q from the utility-maximizing point defined by MU_X/MU_Q = P/WTP_Q. The ratio of WTP’s for X and Q equals the ratio of their marginal utilities. Rearranging terms yields WTP_Q= P x MU_Q/MU_X. In other words, the WTP for Q is the market price of X scaled up or down according to the relative marginal utilities of Q and X.

Strategies for valuing environmental amenities

As mentioned above, we might use surveys to simply ask people their hypothetical WTP or WTA for changes in Q; this method is known as contingent valuation.  We will discuss these direct, hypothetical market methods in more detail later on.

Another approach is to infer WTP for Q from the way changes in Q shift the demand for market good X, as shown in the graph above.  For example, suppose pollution in a lake shifts demand for fishing trips to the left (fishing trips are a complement to water quality). We might determine the demand for fishing trips as a function of trip costs and water quality.  Since pollution shifts the demand for fishing trips inward, the decrease in consumer surplus in the market for fishing trips is a (partial) measure of the economic damage from pollution.

Alternately, suppose the pollution also forces lakeside households to buy water filters (filters are a substitute for water quality). If pollution shifts the demand for filters outward, the increase in consumer surplus in the market for water filters is another (partial) measure of the economic damage from pollution.  We will discuss these indirect, related-market valuation methods in more detail later on.