Environmental Economics, Econ 4545

University of Colorado, Spring 2001

Instructor: Vijaya Sharma, Ph.D.

1. Trade-off between Market Goods and Environmental Quality

• Production possibility frontier of two goods: market goods and environmental quality (draw a PPF)
• The more the production of market goods, the lower the environmental quality, given a state of technical know-how
• Values placed by a society on environmental quality and on market goods (the social indifference curve, derived from social welfare function) determine the choice of the society where to locate on the PPF
• Value of environmental quality vis-a-vis market goods may differ among societies according to educational level, income, and information.
• A short-run choice can affect long-run choices between environmental quality and market goods
• Excessive emphasis to market goods in the short run may damage the assimilative capacity of the environment and thus future productive capability of an economy (this shifts the PPF inwards).

1. Linkage Between Economy and Environment

• Draw a box diagram to show linkages between Nature and economy.
• Nature provides raw materials and energy to the economy. Economy uses the resources to produce goods that are then consumed. During production and consumption processes, residuals are emitted to Nature.
• Environmental economics is the study of the flow of residuals (see the box diagram) and its impact in the natural world.
• According to the First Law of Thermodynamics (also known as the Law of Conservation of Matters), matters only change in shape, size, or phases, the total weight is conserved. What goes in must come out. Thus, the total weight of raw material and energy inputs to economy must be balanced by the total amount of residuals flowing to the environment.

1. Simple Model of Pollution Control

• Pollution causes many types of damages. The benefit of pollution control is a reduction in damages of lives and properties.
• Let us define marginal damage. Marginal damage is the additional damage caused by an additional unit of emission.
• Example:
• If total damages increase from $30,000 to $35,000 when emissions increase from 10 tons per week to 12 tons per week, marginal damage is $2,500 per ton. [($35,000-$30,000)/(12 tons-10 tons)]=$2,500 per ton.
• Marginal damage function is a relationship between quantity of emissions and the damage caused by emissions. Draw an upward-sloping marginal damage curve.
• The curve assumes that marginal damage increases with increasing emissions.
• There is a threshold below which marginal damage is zero.
• The area below the function measures total damage.
• Marginal damage is a time-specific function; it may shift with time because of changes in natural environment.
• Let us focus on marginal damage from a non-cumulative pollutant (a pollutant which does not accumulate over time).
• The marginal damage function is a population-specific function; it may shift with an increase in the number of people exposed to the pollutants.

• This function denotes the additional cost of achieving one more unit decrease in level of emissions.
• It is sloping upward to the left. Draw a marginal abatement cost curve.
• The higher the emission reduction, the greater the marginal abatement cost.
• At its right end, the curve starts from the maximum level of emissions with no abatement efforts, i.e., from the uncontrolled level of emissions.
• This function reflects the minimum costs of achieving different levels of emission reduction. In other words, pollution abatement is being carried out in a cost-effective manner. We will later discuss in more length the equimarginal principle of achieving a target in the least cost, or cost effective, manner.
• Note that there is always an upper limit on abatement costs, which is the cost of stopping operations of the polluting plant (zero emission).
• Area below the curve measures total abatement costs of achieving a reduction in emissions.
• Different sources, i.e., polluters, may have different MAC functions because of different technology of abatement available to them.
• For the same source, its MAC function may shift with time periods because of improvement in technology of pollution control.
• Aggregate marginal abatement function of the industry is the horizontal summation of the MACs of individual firms (just as is the industry supply, or the marginal cost of production).

• Let us assume that MD and MAC have been evaluated from the perspective of society.
• MD can be interpreted as the marginal benefit of reducing emissions (damages saved), and MAC is the marginal cost of reducing emissions.
• That is, they are social marginal benefits and social marginal costs of reducing pollution.
• The efficient level of emissions (the level that maximizes social net benefits) would then be where MD and MAC are equal (MAC=MD), the point of intersection of MAC and MD. Explain graphically.
• Alternatively, we can interpret both MD and MAC as costs.
• No matter which level of emissions a society chooses, it has to incur costs on bringing down emissions to that level, and at that level, there are some damages still remaining. At any level of emissions, therefore, the society incurs abatement costs plus costs of damages.
• The society would be efficient if it chooses that level of emissions which is associated with the minimum possible total of abatement costs and damages.
• The area below the MAC is total abatement costs and the area below the MD is total damages. Show in the graph that only at the intersection of the two curves (MAC and MD), the sum of the two costs is minimum.
• Here, we ignored costs of enforcing emission standards.
• Sources (polluters) may not follow the chosen emission standards voluntarily, and the society may have to incur costs on enforcement. If so, enforcement costs should be included while deciding the efficient level.
• The more emissions polluters are asked to cut back, the more expensive it gets for them to cut back each additional unit of emissions. (This is because of the increasing MAC).
• Therefore, polluters are more likely to cheat on cutbacks when the efficient level involves larger emission reductions.
• Consequently, the marginal cost of enforcing cutbacks is also likely to increase with mandating higher and higher levels of reductions of emissions. That is, marginal enforcement cost would be increasing with increasing abatement.
• Thus, there are two types of costs involved in achieving a reduction in emissions: costs incurred by sources for abatement and costs incurred by the pollution control authority for enforcing the abatement target. In other words, the total marginal cost (TMC) of emission reduction is the sum of MAC and marginal enforcement cost (MEC). TMC=MAC+MEC. Show in a graph.
• Note that the gap between the TMC and MAC increases progressively with additional reductions (as one moves to the left along the MAC), reflecting increase in MEC with increase in emission reductions.
• Efficient emission level is then given by the intersection of the TMC and the MD curves.
• This efficient level would be lower than the previously determined efficient level with no enforcement costs, implying that the society should be willing to accept lower emission reductions for the sake of enforceability of emission standards.

1. Cost Effectiveness and Equimarginal Principle

• Cost Effectiveness
• Distinguish cost effectiveness from efficiency
• Cost effectiveness - achieving a given target at the minimum possible cost
• Efficiency is more than cost effectiveness. Cost effectiveness is necessary, but efficiency has to also balance marginal benefit with marginal cost. In the context of our model of pollution control, the industry MAC must reflect the minimum possible marginal cost at each level of emission reduction, and then efficient level of emissions would be the level that equates MAC=MD. Let us discuss cost effectiveness in this section.
• Suppose a city decides to reduce air pollution by 50%. A number of alternatives exist to achieve this target, like reducing auto emissions, reducing factory emissions, or a combination of the two.
• Benefit of each alternative in this case (benefit of reducing air pollution by 50%) is the same, no matter which alternative is chosen. This allows us to focus on how to minimize the cost of reducing pollution.
• The objective of cost effectiveness is to choose the alternative that achieves the given target at the minimum cost possible.
• The Equimarginal Principle of Cost Effectiveness
• To minimize the total cost of abating pollution by a given level, allocate abatement among multiple sources such that marginal costs of abatement are equalized.
• Discuss an example to show the equimarginal principle: MC_a=MC_b=... across all plants (subscripts a and b denote different plants).

Let a firm have two plants: Plant A and Plant B. The table below shows marginal abatement costs (MACs) of reducing pollution in the two plants.

According to the equimarginal principle,

1. if total targeted reduction of pollution is 10 units, the total cost minimizing allocation of abatement should be 6 units in Plant A and 4 units in Plant B, with MACs of $1.00 in both plants. Verify that any other allocation increases the total cost.
2. If total targeted reduction of pollution is 7 units, the total cost minimizing allocation of abatement should be 4 units in Plant A and 3 units in Plant B, with MACs of $0.80 in both plants.
3. We can tabulate (see below) the cost-effective MAC schedule of this firm, for all levels of emission reduction. If these were the only two plants in the industry that emitted the pollutants, we would use the following schedule as the MAC (instead of MAC of Plant A or that of Plant B) in our MAC-MD model of pollution control discussed earlier.
4. Before we part with this section, let us, therefore, remember that cost effective allocation of a given level of emission reduction is achieved when MACs of all sources (polluters) are equalized for that level of reduction. In other words, remember the equimarginal principle of cost effectiveness.

Cost Effective MAC Schedule

1. Performance of Free Market in the Presence of Negative Environmental Externalities

• A competitive market fails to achieve economic efficiency in certain cases. There are two such cases of interest in environmental economics.
• Production of goods associated with environmental externalities
• Production of public goods (many environmental services are public goods)
• Firms in their production decision consider only private costs and ignore external costs (those costs that are not borne by the firm but are true costs to the society).
• Market S-curve only represents private MC, whereas the social MC would be higher because it includes external costs. Draw a figure to show this, and this is what you have learned in your Principles of Microeconomics.
• To the society, costs are actually higher and therefore fewer quantities of such goods should be produced. But, the market output exceeds the efficient level of output.
• Also, study Professor Phil Graves' note on "The Economic Theory of Environmental Quality," which is available in his web site and which I discussed in the class too.
• This presents a rational for the government to intervene to correct the market failure to produce efficient quantity. We will discuss emission charges and tradable discharge permits as two alternative forms of government intervention to control pollution.

1. Economics of Emission Charges

• A kind of user fee: pay for services of environmental resources
• A kind of compensation fee for damages caused
• Charges offer incentive to conserve environmental resources

• Polluters are charged a fixed $ amount on every unit of effluent emitted
• Polluters free to choose how much emissions they abate and how much they emit by paying applicable emission charges
• Polluters abate if it is cheaper to abate than to pay the charge, but they pay the charge if it is more expensive to abate.
• To minimize cost, polluter abates until MAC balances with the charge.
• Draw MAC curve and a horizontal line from the vertical axis to denote the emission charge ($t per ton).
• Intersection of this horizontal line and the MAC gives the level of pollution emitted by the polluter (say e).
• The difference between e and the uncontrolled level of emissions is the level of emissions abated.
• The area bounded by the MAC and a vertical line at e is the total abatement cost incurred; label this area as a.
• The area of the box to the right of e (bounded by the charge line, e-line, and the two axes) is the amount of total charges paid; label this area as b.
• Total compliance cost to the polluter = (a+b)
• If the polluting industry is not competitive, the competitive pressure of emission charges may be small, as it may be possible to pass on the entire the tax burden of emission charges to consumers (example: a regulated electric power plant).
• If you give a choice to polluters to choose either a charge of $t per ton or an emission standard of e tons, they are likely to prefer emission standards.
• Compliance cost with e emission standard is area a.
• Compliance cost with charge system is (a+b).
• Compliance cost cheaper with emission standard
• Under a charge system, polluter also pays for emitting, besides for abating, whereas environmental services are essentially free under emission standard system.

Level of charge

• The greater the charge, the greater the emission reduction.
• Convince yourself of this by drawing two tax lines in the above graph.
• The level of charge depends on the desired level of emission reduction.
• Charge per ton = MAC at the desired level of emissions (show in a graph)

• If information on MAC and MD are known, set charge = MAC at the efficient level of emissions (e*). Let this charge be t* per ton.
• This would ensure efficiency.
• Draw MAC and MD.
• Label the area below the MAC to the right of e* as a.
• Label the area below the MD to the left of e* as b.
• Label the area above the MD but below the t* line as c.
• Polluter=s abatement cost = a and charges paid = (b+c) at e* level of emissions
• Actual damages inflicted by polluter at e* = b
• Polluter pays charges (b+c) in excess of damages (b); note: c is a transfer payment.
• If charge is seen as a user fee, it is okay.
• If charge is seen as compensation fee, polluter may consider unfair to pay charges in excess of damages.
• To make this fairer, can implement a Atwo-part charge system.@
• Polluters are waved charges up to a certain level and required to pay only for emissions in excess of that level, such that total charges paid = total damages.
• Uniform t* charge for all polluters can lead to e* only when emissions from all sources of pollution cause uniform or equal MD
• If this is not true (for example, MD different in rural and urban areas from the same level of pollution), uniform emission charge cannot be efficient.
• May have to implement zoned emission charges - different charges for different zones; but the same charge for all firms within a zone
• Explain graphically.
• If information on MAC or MD not known, e* and t* cannot be determined.
• If information on MD is lacking, the government first decides the desired level of emission reduction from some technical/scientific criteria and then determines the appropriate charge (graph).
• Note: the emission charge so determined would be cost effective in achieving the desired level of emissions e.
• Draw MAC1 of Firm 1 and MAC2 (above MAC1) of Firm 2.
• It is relatively cheaper for Firm 1 to abate emissions.
• Draw a horizontal charge line ($t per unit) from the vertical axis.
• Intersection of charge line with MAC1 gives e1 on the horizontal axis and with MAC2 gives e2 on the horizontal axis; note e2>e1.
• Firm 1 reduces emission by larger amount (because cheaper) than Firm 2.
• At the individual levels of emissions firms choose under emission charge system, MAC1=MAC2=t.
• Satisfies the equimarginal principle; therefore, cost effective
• Even if information on both MAC and MD are not known, charge system would be cost effective for whatever level of emission reduction is achieved.
• At the time of setting charge, no knowledge of how much emission would be reduced.
• But, by whatever level emission is reduced, it is reduced at the least cost
• because, each polluter equalizes its MAC to the level of charge
• therefore, MACs equalized across all firms (equimarginal principle)
• explain graphically

• The same charge per ton for each firm
• One who pollutes more pays more.
• Distributional impacts depend on changes in price and quantity of outputs of taxed firms.
• If charges do not affect prices of outputs, and the full tax burden falls on the owners of the firm.
• If charges increase prices of outputs, the tax burden partly falls on consumers too.
• Distribution depends on who mostly consumes outputs: poor or rich.
• With prices up, output declines. Displaced labor may have to incur costs on finding new jobs.
• Distributional impact also depends on whether tax revenues from emission charges are directed mostly to poor or rich.

• Stronger incentive, compared to emission standards
• Reduction in emissions also greater when improved methods are developed.
• Explain graphically
• Draw MAC1 (the current abatement technology) and charge line ($t per unit), resulting into e1 level of emissions.
• Draw potential technology MAC2 (lower than MAC1) and level of emissions e2 (intersection of MAC2 and charge line) with this technology. Note e2<e1.
• Label area between MAC1 and MAC2 to the right of e1 as a.
• Label area below MAC2 to the right of e1 as b.
• Label area bounded by the charge line, MAC2, and e1 line as d.
• Label area bounded by MAC2, e1 line, and e2 line as c.
• Label area bounded by the charge line, e2 line, and the two axes as f.
• Compliance cost with MAC1 technology = (a+b+c+d+f)
• Compliance cost with MAC2 technology = (b+c+f)
• Potential cost saving (incentive to innovate MAC2) = (a+d)
• Potential cost saving with emission standards of e1 = a
• With emission standard, emissions remain at e1 even with MAC2.
• With charges, emissions reduce to e2 with MAC2.

• Enforcement more expensive than standard system
• Measure cumulative discharge over the billing period, bill the polluter, and collect charges.
• Enforceable in point-source emissions, but difficult to measure actual emissions from nonpoint sources.
• Nonpoint sources require a Asecond-best@ approach of taxing inputs that are associated with emissions.
• Examples: taxes on chemical fertilizers, agricultural pesticides, gasoline, etc.

1. Economics of Tradable Discharge Permits

• Permit system offers economic incentives similar to emission charges, but it develops and works through a permit market.

• The pollution-control authority initially distributes permits to polluters.
• A permit entitles the permit holder to emit one unit of a specific pollutant.
• Permits are transferable; they can be sold and bought in the permit market at a price mutually agreed by the parties.
• A polluter has three options
• Either emit only the amount of pollutants that is covered by the initial holding of permits.
• Or, purchase additional permits from another permit holder and accordingly emit more.
• Or, emit fewer amount of pollutants and sell surplus permits to interested buyers.
• Obviously, the choice among three options depends on abatement cost and price of permits.

• Assume two polluters and equal initial allocation of permits to each of them.
• Assume polluters differ in MAC: MAC1 and MAC2 (below MAC1) in a graph.
• At the initial level of allocation of permits, marginal cost of abatement is lower for Firm 2.
• Difference in MAC offers the two firms an opportunity of gains from trade of permits.
• Firm 2 can sell some permits to Firm 1 at a mutually agreed price.
• Price would lie somewhere between the two MACs at the initial levels of allocation of permits.
• Trade of permits would continue until MACs of both firms are equal (graph).
• If we extend this trading possibility among many firms in the industry, it is easy to see that there would develop a market of permits.
• Draw a graph with number of permits (Q) in the horizontal axis and price of permit (P) in the vertical axis.
• Like any other good, demand for permits would be a downward-sloping demand curve (D).
• Supply of permits is decided by the pollution-control authority, according to the total targeted amount of pollutants that can be emitted in aggregate.
• Draw a vertical supply curve (S) to show the number of permits issued by the pollution-control authority.
• Intersection of demand and supply gives the equilibrium price of permits in the market.
• Each polluter would emit at the level where price of permit is equal to its MAC (the point of intersection of price of permit and MAC curve).

• Each firm emits at the level where P (the price of permit) is equal to its MAC.
• P is fixed for each polluter; therefore, MACs are equalized to P across all polluters in the industry.
• Permits are cost effective in reducing pollution to the targeted level.
• If the number of permits issued is equal to the efficient level of emissions (MAC=MD), the system would as well be efficient.
• Determination of the efficient level, however, depends on availability of information.

• By reducing MACs, polluters can save abatement costs and earn revenue from sale of surplus permits. Draw a graph to explain this.
• Let the current abatement technology be MAC1, so that price of permit (P) results into e1 level of emissions (the intersection of P-line and MAC1).
• Let the potential technology be MAC2 (lower than MAC1).
• when MAC2 is developed, the polluter would actually emit only e2 (the point of intersection of MAC2 and P-line).
• Note that e2<e1, requiring only e2 permits instead of e1.
• Label
• area between MAC1 and MAC2 to the right of e1 as a
• area below MAC2 to the right of e1 as b
• area below MAC2 between e1 and e2 as c
• area below P-line and between the two MAC curves and between e1 and e2 as d
• area below P-line to the left of e2 as f.
• With innovation of MAC2 technology,
• saving of abatement costs equal to (a-c)
• firm needs only e2 number of permits
• (e1-e2) number of permits is now surplus
• surplus permits can be sold at price P, generating a revenue equal to (c+d)
• total incentives to innovation is the amount of abatement cost saved plus the amount of revenue from sales of surplus permits, i.e., (a+d)
• Compare this incentive with the incentive available in case of emission charges
• they would be equal

• Compared to emission charges, enforcement is likely to be less intense with permits, because it primarily relies on market.
• The pollution-control authority, however, must monitor each polluter frequently to ascertain that emissions of the polluter are within limits of its holding of permits.
• The authority would know the initial allocation of permits, but actual holding of permits may be different because they can be bought or sold in the market.

1. Comparison of Tradable Discharge Permits with Equivalent Emission Charges

• We should compare TDP with Aequivalent@ emission charges, equivalent in the sense that both permits and charges should lead to the same targeted level of emissions.
• Permits and charges both can be made efficient, when the number of permits and the tax rate correspond to the efficient level of emissions.
• Also, both are equally cost effective for the same targeted level of emissions.
• Both provide similar incentives to innovation of improved method of pollution control.
• Incentives are in the forms of saving of abatement costs and payment of lower tax in the emission charges system.
• Incentives are in the form of saving of abatement costs and revenue from sale of surplus permits in the permit system.
• Amount of incentives is the area between the current marginal abatement cost curve and the likely improved marginal abatement curve, bounded by the tax-line in the case of charges and bounded by the P-line in the case of permits.
• Determination of the appropriate tax rate requires knowledge of MAC in an emission charge system.
• Tax rate is the marginal abatement cost at the targeted level of emissions.
• In contrast, permit system requires no knowledge of MAC.
• Number of permits to be issued is simply the targeted level of emissions.
• Actual level of emissions is certain (known beforehand) and equal to the targeted level in the permit system.
• In contrast, the actual level may not equal the targeted level in the emission charge system if the information on MAC is hazy at the time of fixing the tax rate.
• If you suspect that marginal damages are likely to be very large (a steep MD curve), you want to choose permit system over emission charges.
• Because the number of permits lock down actual emissions to the targeted level.
• On the other hand, if you suspect that marginal damages are likely to be low (a relatively flat MD curve) but marginal abatement costs are likely to be very high (steep MAC), you want to choose emission charges over permits.
• Because emission charges lock down the level of MAC (equal to the tax rate).
• If the number of firms in the regulated industry is increasing, permit system ensures that total emissions would remain the same (equal to the number of permits issued). On the other hand, emissions would increase under the emission charge system.
• In the permit system, new firms increase demand for permits, raising the price of permits. This provides incentives to the existing firms to reduce pollution so that they can sell surplus permits to take advantage of higher price of permits. New firms would buy surplus permits. Thus, emissions of existing firms would reduce, but total emissions would remain the same.
• In a charge system, existing firms maintain their current levels of emissions at t=MAC. New firms add to emissions. Thus, total emissions would increase.
• If there is an ongoing inflation in the economy, both abatement costs and price of permits increase in the permit system, and there is likely to be no change in emissions of individual firms and also of the entire industry.
• Draw a graph with initial MAC0 and P0.
• Now draw MAC1 (above MAC0) and P1 (above P0) such that the intersection of MAC1 and P1 lies just above the intersection of MAC0 and P0.
• With emission charge system, emissions of each firm and, thus, of the entire industry would increase. Since abatement costs increased with inflation but charges did not increase, taxes would prove cheaper than abatement.
• Draw the initial MAC0 and the new MAC1 (higher than MAC0).
• Show that the tax-line (which has not changed) intersects MAC1 to the right of MAC0, increasing emissions.
• If the industry is experiencing continuous technological development, permits system would lead to the same level of emissions (equal to the number of permits), whereas emission charges would lead to lower level of emissions.
• Improved technology reduces abatement costs of firms and, thus, number of permits required. Demand for permits decreases, reducing the price of permits. Both price of permits and abatement costs decrease and emissions remain at the same level.
• Draw a graph with initial MAC0 and initial price P0.
• Draw new MAC1 and price P1 such that their intersection lies just below the intersection of MAC0 and P0.
• Compare this graph to the graph of emission charges.
• Draw MAC0 and MAC1 and draw the tax-line.
• Initial emissions were e0 at the intersection of tax-line and MAC0.
• New emissions would be at e1, the intersection of tax-line and MAC1.
• Note that e1<e0.
• Permits offer greater flexibility to the government to change targeted level of emissions.
• Simply buy permits from the permit market and then destroy or tearing them off to reduce emissions.
• Environmental activist organizations can buy and retire permits to reduce total emissions.
• With emission charges however, only raising taxes can reduce emissions, which is a complex legislative and political process.