Negative Externalities Manual

Purpose of the Module

This part of the externalities module deals with markets in which, without government intervention, the actions of some create costs for others, without the others sharing in the benefits. The example used is the market for steel, since the production of steel creates air and water pollution that can affect the well-being of people in the communities near production facilities (and possibly even people far away). As a result a purely private market will produce more steel than would be socially best. This module allows you to see the workings of a purely competitive market in steel, and how it compares with the social optimum in the absence of government intervention.

The module allows you to use one of two types of government intervention -- which can affect steel production, the price of steel, employment and wages in the steel industry, and the impact on society of steel production. One type of intervention is a tax on steel production; the other is the issuance (sale) of permits that steel companies would need in order to be allowed to produce. Use of these two tools allow similar effects on steel production, but differ in other effects.

The Model

This module involves the market for a good that creates a negative externality. To understand the workings of the module it is necessary to understand what a negative externality is and why one is present in this case.

Negative Externality

There are a number of kinds of negative externality; this module features a negative externality in production. In steel production there are byproducts that can create costs that will not be taken into account by private profit maximizing firms that decide on how much steel should be produced. Such costs include respiratory damage done to people exposed to air pollution caused by burning coke (a processed form of coal used for steel production), loss of forestation due to “acid rain” arising from the same air pollution, ground water and other land pollution due to the mining of coal and iron ore for steel production. Even some “global warming” and its associated costs can be ascribed to the impact of steel production. (Air pollution includes carbon compounds -- carbon dioxide in particular -- that add to the greenhouse effect that warms the planet, it also includes sulpher compounds, particulates and other sources of individual, population, and planetary problems.)

These negative externalities are also referred to as external costs. For example, the people work in, own, and manage steel companies, and use products made with steel, bear some of these costs just like everyone else. How much cost an individual bears has nothing to do with how much they benefit from steel production. In addition, a decision by one person not to make steel, or not to use steel, would have almost no effect on the amount of these kinds of cost that that person bears. For example, let’s assume that 100 tons of steel are produced in competitive market, with a population of 1000 firms, each owned by one person in a population of 1000, creating a total external cost of $100. If a single firm decides not to produce steel, this cuts production by 1 ton and cuts total external cost by $1. The firm making this choice cuts its own cost by $1/1000 or $0.001, with a corresponding benefit its owner, and the rest of the cost reduction benefits other people. Suppose the production of the ton of steel gave the firm $0.50 in benefits (after the private costs of production are accounted for). That firm (and its owner) is better off producing the steel. Not producing cuts benefits by $0.50 and cuts cost to the firm $0.001, with a net result that the firm (and its owner) is worse off by $0.499. On the other hand, since the total external cost to everyone put together is $1, cutting back production cuts benefits by $0.50, but cuts cost by $1, cutting production represents a net social gain of the difference, $0.50.

Marginal Private Costs and Benefits

In a market people compare the extra benefits they get from consuming a unit of a good with the extra explicit costs (e.g. wages, rent, materials, and other unavoidable costs) they pay to buy the good. It is that comparison that underlies the demand for goods. Economists presume that people deciding whether or not to buy another unit (or any) they take into account only the extra benefits to themselves, not the benefits that might accrue to anybody else. (Family members or close friends may take benefits for each other into account, but if everyone does not do the same with respect to everyone else the results discussed in this module remain correct.) The same comparison determines supply, potential producers compare their private costs with their private benefits and if the extra benefits (e.g., marginal revenue) exceeds the extra cost (private marginal cost) then they will expand production, if the comparison is unfavorable they will cut production.

Marginal and Total Social Costs

When a good creates a negative externality, in addition to the private costs of production paid by the producers, there may be costs that spillover to other members of society. Thus the extra costs associated with additional production can include both explicit and external costs (a.k.a. spillover costs, pollution costs), so marginal social costs are larger than marginal private costs. The same is true for the total costs -- total costs to society are greater than the total costs to those deciding on what to produce. In the case of steel, the ones making the steel get income (benefits) that more than compensate them for their private costs, while other members of society may receive costs that outweigh their benefits.

Social Optimum

It is usual for economists to say that an outcome is a social optimum when social marginal benefits equal social marginal costs. Actually what this condition describes is efficiency and that is related to an optimum -- other things being equal it is always better to be efficient that to be inefficient. However, this economic definition of Social Optimum should not be confused with a “just” or morally good outcome -- that is another matter altogether.

Marginal Cost

The private marginal cost of producing steel is assumed to be increasing: the more steel that is produced, the higher the extra cost of producing one more unit. The social marginal cost is

2 assumed to equal the marginal private cost up to a minimum, or threshold, level of production. This minimum level of production is considered to be a level of production at which emissions have exceeded the assimilative capacity of the environment and pollution begins to cause environmental damages. After this threshold level of production has been reached, marginal social cost exceeds private marginal cost and grows more quickly. As a result, the more steel is produced the greater the gap between social and private costs and the greater the external costs.

The Market for Steel

A description of the market for steel and the various possible outcomes can be presented numerically or graphically. The module presents both, of course. The graphical presentation of the market is shown in Figure 1. That figure assumes no government intervention -- no tax on steel production and no permits required for firms that want to produce steel.

Figure 1 Supply, Marginal Social Cost, and the Demand for Steel

MSC = S´ MPC = S

D = MPB = MSB

Steel (in tons) QT QS QP

In Figure 1, MSC is the marginal social cost of producing steel, whereas supply -- marginal private cost (MPC) -- represents only the costs firms in a competitive industry will take into consideration when deciding on output. The point (PP, QP) represents the competitive market equilibrium, where supply equals demand, or the private optimum. The point (PS, QS) is where marginal social cost equals marginal social benefit (assuming social and private benefits from steel production are the same (MPB = MSB). In the module the area between marginal private and marginal social costs (up to a given output) indicates the total external costs (costs to society that are not direct costs to firms) generated at that level of production. The initial conditions graph in the module shows the external cost as a yellow area between the two cost lines.

The other side of the coin from the production of steel is the production of pollutants. Figure 2 illustrates the same results as Figure 1, but shows the production and effects of pollution. In Figure 2, the horizontal axis measures the amount of pollution created, not the amount of steel produced, the line labeled MD represents the extra, or marginal, damages caused by producing more units of steel and pollution, and the MAC line represents the marginal abatement costs -- the extra costs incurred by reducing pollution. Since no firm will pay more for a permit than it

3 would cost to abate the pollution, but would pay up to that amount, the MAC line can be considered as a demand curve for permits. The supply of permits will be whatever the government decides on (on the graph it would be a vertical line at the quantity selected). Note the MD line begins to rise from the horizontal axis only after a certain amount of pollutants (Q T) been produced. Technically QT is the quantity of emission, but up to QT the emissions cause no damage to the environment. At larger production levels MD begins to rise, and this corresponds to the point in Figure 1 where MSC begins to diverge from MPC. The amounts QP and QS in Figure 2 are the amounts of pollution corresponding to the steel production amounts with similar designations in Figure 1. Since the private and social costs diverge more and more as output increases, this is a market in which external costs per unit get larger and larger as output rises.

Figure 2 Marginal Damages and Marginal Abatement Costs

MAC Quantity of Emissions 0 QT QS QP

In Figure 2 the social optimum, QS , is a level of production where the extra cost to society of reducing pollution is equal to the extra damages done to society by an extra bit of pollution. The market result (with no government intervention) is at QP.

Private Market Equilibrium

In a market where there is no government intervention the outcome is the result of optimizing behavior by market participants. Buyers match the market price against their marginal benefits; sellers compare the marginal revenue from selling another unit with the marginal cost of producing it. In a perfectly competitive market there are (infinitely) many suppliers. Though each seeks to maximize profit, none are able to affect the market price by their decisions. As a result when they set their marginal cost equal to their marginal revenues they are also setting marginal cost equal to the price of the product. The competitive market will therefore not take into account external costs that are not reflected in the private supply for their product.

Government Intervention

Governments often intervene in markets like this and such intervention is present in this module. To simplify the government’s role it is assumed that the government has perfect information

4 about the market and the externalities. Of course that is not true in the real world, so results in this module may be better than they would be in practice. They sometimes do so by creating directives that order firms to do things, e.g., install certain anti-pollution equipment, but those types of policies are not covered in this module. Governments also put taxes on products in order to cause reductions in their production (an extreme case is a type of match that was prone to ignite in people’s pockets -- it was taxed so heavily by the US government, in an era when an outright ban was not possible, that production ceased). That is one of the options in this module.

A less common policy option is to create a market for permits. First the government requires a permit that allows the holder to emit pollutants (with technology fixed this is equivalent to a permit allowing production of the product). Anyone without a permit cannot create pollution and therefore cannot produce the product. If, at the current market price, firms want to produce more of the product than the stock of permits allows, there is an excess demand for permits. In this case, the question is: who should get the permits and the potential profits they represent.

The government could simply give the permits to those first in line to apply, or give them at random to some of those who applied. If they did either of those things, and the permits could be transferred among private parties, the most efficient firms would have an incentive to buy permits from less efficient ones. An efficient firm might expect a profit (over production costs) of $10 per ton of steel produced. A less efficient firm (selling steel at the same price but having higher costs) might expect a profit of $6 per ton. If the less efficient firm has a permit and the more efficient firm does not, the more efficient firm could offer $7 in exchange for the permit. If the permit trade occurs, the more efficient firm gets the permit, produces the steel, makes $10 over the cost of production, pays $7 of that to the original permit holder, and gets to keep $3 in profit (which is better than nothing because it would not have been able to produce this unit without the permit). The less efficient firm does not produce the steel, loses both revenue and cost -- and $6 in profit. However, the less efficient firm gets $7 for its permit and is better off selling the permit than selling steel ($7 is better than $6).

If the government does not give away the permits but sells them to the highest bidder the basic results are the same. The less efficient firm would not bid more than $6 to get the permit, the more efficient firm would outbid it, get the permit, and produce the steel. If the government gives away the permits, the recipients get the revenues (either by producing -- if they are efficient -- or by selling their permits if they are not). If the government sell the permits, the government gets the revenue. This module does not deal with the question of who gets the revenue collected by the government. For both types of policies the module assumes that the changes in private costs caused by the government do not cause firms to develop and implement any new technology that affects the results.

Tax Policy

If the government levies a tax on pollution, which is in effect a tax on steel production, the results can be seen in Figure 3. The imposition of the tax raises the marginal cost to the firms of producing steel, so the supply curve shifts upward by the amount of the tax. The module assumes a tax set as a fixed number of dollars per ton of steel produced rather than as some percentage of, say, the current market price of steel. The size of the tax increase determines the new market equilibrium price and output. If the amount of the tax is set exactly right it is

5 possible for this policy to shift the market equilibrium so that the market equilibrium output and the socially optimum output are the same. It is equally valid to say that the perfect tax makes would internalize the external cost causing the MPC to shift up and be equal to the MSC.

Figure 3 Supply, Marginal Cost, and Demand for Steel with A Tax

$/ton MSC

MPC with Tax

MPC PS PP

Steel (in tons) 0 QT QS QP

The equivalent of the results in Figure 3 can be seen in Figure 4, which features the marginal damage and abatement costs of pollution.

Figure 4 Marginal Damages and Marginal Abatement Costs

$/ton MD

MAC Quantity of Emissions 0 QT QS QP

In Figure 4 the amount of the tax, set on the vertical axis, determines production. Properly set, it causes production to be at the intersection of marginal abatement cost and marginal damage done by pollution.

6 Permit Policy

If the government issues permits the results are shown in Figure 5. The limited number of permits limits the production of steel and, if the limit is set perfectly, the permitted output will be the socially optimum level or emissions as well. Note that the value of the permit to a firm in the market would be the difference between the market price of the product (set on the demand curve) and the marginal cost of producing the product (on the supply curve). If there is a competitive market in permits as well as in steel, in equilibrium the price of a permit will equal that value. (To see this, assume that the price of a permit was less than this value, then some firm would be willing to bid higher to get the permit, get to produce the product, and get the profit represented by the difference between the value and the current permit price. This would keep happening until the bidding matched the price of a permit -- not the price of steel -- to the vertical gap between demand and supply at the given permit quantity.)

Figure 5 Supply, Marginal Social Cost, and Demand for Steel with Permits

$/ton Allowed Output MSC

MPC = S PS PP

Steel (in tons) 0 QT QS QP

As with the tax tool the results of a permit policy can also be seen in a graph showing pollution directly. In Figure 6 results of failing to limit the number of permits from the default value can be seen in terms of the amount of pollution created as well as the resulting marginal damages and marginal abatement cost.

7 Figure 6 Marginal Damages and Marginal Abatement Costs with Permits

Permits $/ton MD MAC

Quantity of Emissions 0 QT QS QP

Running the Module

As with all other modules this one begins with a display of initial conditions. They show the results in the steel industry when the government has taken no anti-pollution measures at all, no taxes, no required permits. Table 1 below shows the results for the industry and for society under these circumstances.

Table 1 Initial Conditions in the Steel Industry

Production (000s of tons): 150 Current Regulations and Anti-Pollution Taxes: None Pollutants Emitted (tons): 150 MPC: $ 250 Price of Steel (per ton): $ 250 MSC: $ 300 Employment (000s of hours): 1125 MEC = MSC – MPC = $ 50 Average Wage (per hour): $20 Total External Cost = $1250

After observing the tabular description of the initial conditions the user clicks on “Continue” and sees the graphical (though less detailed) equivalent. In particular, the graph does not show that employment and wages in the steel industry depend on the output and prices created in the steel market. (The relationship is not complicated -- any policy that reduces steel production reduces the demand for steel workers. A reduction in demand for steel workers will cut employment and wages in the labor market. These effects of anti pollution measures often causes political resistance to such measures.)

After seeing the graph of the initial conditions the user clicks “Continue” and must choose whether to use tax or permit policy and then select continue again. (It is not possible to select “Continue” before picking one of the policy tools.) If the user picks “Issue Permits” a box will

8 appear and the user will be asked to decide how many permits to issue. There is a default value in the box; if that default value is left there the eventual results will be the same as if there were no permit policy at all. Once the number of permits is entered the user must click “Continue” to see the results.

If, for example, the user has left the default number of permits unchanged the results will look like this:

Table 2 Sample Results Table for Permits

Steel Output (000s tons) 150 Pollutants Emitted (000s of tons) 150 Price of Steel (per ton) $ 250 Employment (000s of hours) 1125 Average Wage (per hour) $ 20 MPC $ 250 MSC $ 300 MEC = MSC - MPC $ 50 Permit Price $ 0

After seeing these numerical results the user can see the graphical representation, similar to those shown in Figures 5 and 6, except that the amounts will differ.

The user can then go back and change policy, using taxes this time. One difference in the results is that when permits are issued the permit price is reported, while when tax policy is used the amount of taxes collected is reported. Again, the results are available in graphic form by clicking on “See Graph.”

Mathematical Model

In this module the demand for the product (steel) is:

Pd = 400 – Q(steel)

The supply of steel is:

Ps = Marginal Private Cost =100 + Q(steel)

If a tax is set then the amount of the tax is added to this equation so its intercept (at Q = 0) is 100 plus the tax.

The equilibrium market output is (setting demand equal to supply and solving):

Q* = (400 - 100) / (1 + 1) = 150

The amount of labor hired is determined by:

9 Employment = 0.2 * (Q* / 2) ^ (1 / .5)

Note that the employment function implies diminishing marginal returns to hiring labor.

The wage associated with employment in this industry is:

Wage = 20 + (12.5 * (Q* - 150) / 150)

The module assumes that every ton of steel produced means another ton of pollutants emitted. This ignores the possibility that differing amounts of pollution would be created as different production facilities are brought on line with changes in output. It also assumes that methods of production will not be changed due to the policies.

The social marginal cost (for output levels above 100 tons) is given by:

MSC = 2 * Q*

For output levels above 100 tons marginal external cost is:

MEC = MPC - MSC - Tax

Below 100, the MPC and MSC are the same and there are no external costs.

If the tax option is selected then the total taxes collected is the product of the tax per unit and the amount produced.

Taxes Collected = Tax * Q*

If the permit option was selected the market price of a permit is:

Permit Price = (400 - Q*) – (100 + Q*)