Download what is externalities and types and more Lecture notes Microeconomics in PDF only on Docsity!
Externalities, the Coase Theorem and Market Remedies
David Autor
14.03 Spring 2004
1 Introduction
You were introduced to the topic of externalities in 14.01. An externality arises when an economic actor does not face the ëcorrect priceí for taking a speciÖc action. The correct price of an action is the marginal social cost of that action. As we discussed during the section on General Equilibrium, when markets work properly, they align private costs and beneÖts with social costs and beneÖts. When private beneÖts di§er from social beneÖts (either higher or lower), externalities result. Some classic externalities include:
ñ Tra¢ c: When I take the highway, I increase congestion for other drivers, a negative exter- nality. Since the toll on the Mass Turnpike does not vary with tra¢ c conditions, I probably face the wrong price of driving on the highway (too high at non-peak hours, too low at peak hours). As a result, I use the Pike ëtoo muchí during peak hours and not enough during non-peak hours. ñ Disease transmission: When I decide whether to have my children receive áu shots, I con- sider whether the cost of the inoculation in time, money, discomfort is worth the reduced risk. I probably do not consider that by protecting my children from the áu, I also protect the children at their school. Because my private beneÖt of the shot does not incorporate the external social beneÖt of the shot, I am less motivated than I ìshould beî to get my children inoculated. It is therefore likely that too few children receive small pox vaccines.
Ironically, there are other parents who recognize that, because most parents do get their children inoculated, other kids may be reasonably protected even without receiving an inoculation. Hence, these parents free-ride on the positive externality, and are even less
motivated to get a shot than the parents who do not consider the positive externality they are generating. This exacerbates the problem.
Pollution: Because clean air is not priced, I pay essentially no cost to pollute the air. When I decide whether to drive to work or take the train, my marginal cost of driving (fuel plus wear and tear on my car) probably does not incorporate the social cost of additional pollution. Because my private cost is lower than the social cost, I will likely drive ëtoo muchírelative to a case where I faced the full marginal social cost.
Are these externalities never ëinternalizedíby the market?
2 The Coase Theorem
Until the publication of Ronald Coaseí1960 paper, ìThe Problem of Social Cost,î most econo- mists would have answered yes. Coase made them reconsider that view. Coase gave the example of a doctor and a baker who share an o¢ ce building. The problem: the bakerís loud machinery disturbed the doctorís medical practice. The doctor could not treat patients while the bakerís machinery was running. The standard economic reasoning (at the time) was that the baker should have to compensate the doctor for the harm he was causing since he was ëcausingíthe externality. Having the baker provide compensation would correct the externality imposed on the doctor. But is this reasoning complete? Coase pointed out that one could re-frame this problem as follows: a doctor sets up his o¢ ce in a new building and after moving in notices that the bakerís machinery is too loud for him to conduct his practice. He demands that the baker shut down his operation due to the disturbance. Who is responsible for the externality in this case? One can legitimately argue that the doctor is creating an externality by requiring the baker to bake in silence. The bakerís noise can be viewed as an ëinputíinto his production of baked goods. Without it, the baker could not perform his work. So perhaps the doctor should accommodate the baker, either by moving his practice or by installing soundprooÖng. If this reasoning is valid, then who should compensate whom? From a legal point of view, the answer may be clear. From an economic point of view, the answer is indeterminate based only on the information provided.
Rather, the Coase theorem suggests that the market can potentially solve externalities if prop- erty rights are clearly assigned and negotiation is feasible. In some cases, this is clearly infeasible.
ñ Airlines cannot realistically negotiate with individual homeowners for overáight rights to their houses, even though these overáights do create externalities. ñ I cannot negotiate with all handicapped drivers for the use of an empty handicap space in an emergency, even though Iíd be glad to pay these drivers handsomely to rent the parking space.
A key inference that follows from the Coase Theorem is that the best solution to resolving an externality may not be to regulate the externality out of existence but rather to assign property rights or facilitate bargaining so that the relevant parties can Önd an economically e¢ cient solution.
3 Remedying pollution: Three approaches
Consider two oil reÖneries that both produce fuel, which has a market price of $3 per gallon (assume demand is inÖnitely elastic so that this price is Öxed regardless of the quantity produced). Assume that each reÖnery uses $2 in raw inputs (crude oil, electricity, labor) to produce 1 gallon of fuel. In addition, each plant produces smog, which creates $0: 01 of environmental damage per cubic foot. The amount of smog per gallon of fuel produced di§ers at the two plants:
s 1 = y 12 ; s 2 = 12 y 22 ;
where y 1 ; y 2 denote the number of gallons of fuel produced at each plant. So, plant 2 pollutes only 12 as much for given production. Assuming initially that there are no pollution laws. In this case, each plant will produce as many gallons as it can until it runs out of capacity (since it makes $1 proÖt per gallon). Assume each plant can produce 200 gallons.
3.1 Competitive outcome
What will Örms optimally do in the absence of any legal framework for resolving the externality? The problems for the respective Örms are:
max y 1 1 = y 1 (3 2) s:t: y 1 200 ; max y 2 2 = y 2 (3 2) s:t: y 2 200 ; y 1 = y 2 = 200:
Each Örm ignores the social damage from its smog production (notice that s 1 ; s 2 do not enter into the Örmsí proÖt maximization problems). Hence, pollution is s 1 = 40; 000 ; s 2 = 20; 000. The negative pollution externality is $400 and 200 from plants 1 and 2 respectively.
3.2 Welfare maximizing case
Before analyzing how to correct this externality, we need to determine the ëoptimalí level of pollution. In this case, optimal pollution is non-zero. More generally, not all activities that generate externalities should be stopped. But if these activities generate negative (positive) externalities, then social e¢ ciency generally suggests that we want to do less (more) of them than would occur in the free market equilibrium. To get the socially e¢ cient level of fuel production, we want to equate the marginal social beneÖt of the last gallon of fuel to the marginal social cost. What is the social beneÖt? It is $3. This comes from the inÖnitely elastic demand curve. The marginal social cost of production is $2 in raw inputs plus whatever pollution is produced. The e¢ ciency condition is M Bs = M Cs; marginal social beneÖt equals marginal social cost. We therefore want it to be the case that at the margin, that no more than $1 of environmental damage is done per gallon of fuel produced. Consequently, no plant should produce more than 100 cubic feet of smog per gallon of fuel. (Note: no plant should produce less than this amount either since the pollution is indirectly beneÖcial: it is an ëinputíinto the production process; less pollution means less fuel production).
ñ Once passed, such laws are di¢ cult to modify as technology or pollution costs change. ñ If the law cannot be written to regulate each plantís output di§erentially, further ine¢ cien- cies will result. ñ [For example, calculate as an exercise the optimal amount of fuel production to permit these two plants to produce if the regulator must apply the same numerical production cap (in fuel) for each plant. (Hint: the answer is not 75 gallons.) This is actually a commonplace case: regulators can set average output at the industry level but cannot further regulate the behavior of individual plants. As your calculation shows, this leads to ine¢ ciencies where some regulated plants pollute ëtoo muchí and other regulated plants pollute ëtoo littleírelative to the e¢ ciency condition that M Bs = M Cs.]
Despite these weaknesses, command and control regulation is the most common approach taken for regulating externalities.
3.4 Pigouvian tax (ëprice regulationí)
An alternative approach is to use the price system to ëinternalizeíthe externality. We know from above that the marginal social cost of pollution is $0: 01 per cubic foot of smog. If we charged Örms for polluting, the social cost would be incorporated in the private cost. Done correctly, Örms will make optimal choices. This type of tax is known as a Pigouvian tax after the economist Pigou who suggested it. SpeciÖcally, it we set the pollution tax at t = $0: 01 per cubic foot of smog, then each plant would choose the optimal quantities due to its proÖt maximization. In other words
max y 1 = y 1 (3 2) t y 12 ; where t = 0: 01! yp 1 = 50 max y 2 = y 2 (3 2) t 12 y^21 ; where t = 0: 01! y 2 p = 100
This solution achieves the desired result with arguably less complexity. Facing this tax, plants will choose the e¢ cient amount of production. We do not have to write a separate law for each plant. Note that this problem is made especially simple by the assumption that the marginal damage of pollution is always $0: 01 per cubic foot. If the marginal damage varied with the amount of pollution (plausible), then setting the right tax schedule would be much harder. For example,
if pollution above a certain threshold caused mass extinction but pollution below this level did little harm, this Pigouvian taxation scheme would be quite risky. Setting the tax slightly too low would result in calamity.
3.5 Assigning property rights: The Coasean approach
The Pigouvian tax idea does not really use the Coase theorem. It aligns private and social costs by pricing the social costs, thereby causing Örms to internalize these costs. The tax arguably does use property rights ñthe state is now selling Örms the right to pollution at price $0: 01 per cubic foot. But the Pigouvian solution does not create conditions for negotiation among Örms. The state sets the price and collects the tax. The Coase theorem suggests that we may be able to do even better. If property rights are fully assigned, then the regulatory body should not, in theory, have to be involved. Instead, parties will negotiate among themselves to Önd the lowest cost solution to correcting the externality. How can this insight be applied? Because Örms do not own pollution rights, there is not an e¢ cient negotiation over the how much pollution is generated. This motivates the idea of selling pollution rights. Using the algebra above, we can calculate that the ëoptimal amount of pollutioní is 502 + 12 1002 ^ = 7; 500 cubic feet of smog. This is the socially e¢ cient quantity of pollution that that results from producing the optimal quantity of fuel. In this example, the government could issue 7 ; 500 ìpermits to polluteî 1 cubic foot of smog. These permits could be used by the permit holder to pollute, or could be sold by the permit holder to another reÖnery so it could pollute instead. How would this work? Consider two cases. First, the permits are all given to Plant 2 , the more e¢ cient reÖnery. It could do the following:
- Produce 122 : 4 gallons of fuel (pollution is 12 122 : 42 ' 7 ; 500). Its proÖts would be $122: 40.
- Produce 100 gallons of fuel (pollution is 12 1002 = 5000) and sell its 2 ; 500 remaining permits to Plant 1 (assuming that this transaction is next to cost-less). With these 2 ; 500 permits, Plant 1 could produce 50 gallons of fuel (pollution will be 502 = 2; 500). Since its proÖts are $1 per gallon, it would pay up to $50 for these permits. Plant 2 would therefore make $150 in proÖts by using 5 ; 000 permits and selling 2 ; 500 others.
What di§ers between the two allocations is: which plant makes the proÖts (a transfer among plant owners). This cap and trade example demonstrates the power of the Coase theorem. By assigning property rights to pollution, the government allows the market to correct the externality. And as the Coase theorem indicates, the exact distribution of property rights to interested parties (Plant 1 or Plant 2) has no e§ect on economic e¢ ciency. But it does greatly a§ect the distribution of proÖts across the two plants (or their owners). This allocation problem is a major political stumbling block to implementing cap and trade regulations generally: how do lawmakers assign the initial ownership rights to pollution (or other negative externalities)?
4 Comparison of the three methods of abating an externality
These three methods ñ command and control, Pigouvian taxation, and cap and trade ñ have identical economic consequences. But they are not identical from a regulatory perspective. Command and control regulation requires intimate knowledge of the production structure of each plant. It is cumbersome to implement and to get right. Sometimes it is not feasible or legal to regulate Örmís behavior at the plant level. The Pigouvian taxation has the advantage that plants will optimal choose the level of pollution that maximizes their proÖts, including the cost of the Pigouvian tax. But Pigouvian taxes are risky when the marginal social cost of pollution varies with the quantity ñ for example, above a certain threshold everyone dies. In these cases, it is di¢ cult and possibly risky to attempt to set the tax exactly right. Cap and trade regulation has several special virtues:
- Like command and control, it allows the regulator to set the amount of pollution to whatever level is desirable (the Pigouvian tax will not do this unless the regulator knows the cost structure exactly).
- Like the Pigouvian tax, cap and trade is comparatively simple to implement since the regulator does not need to write a separate law for each plant.
- Unlike the other means of regulation, it causes Örms to optimally reallocate pollution among themselves through trade (as the Coase theorem predicts). Even if the regulator does not
know Örmsícost structures, the cap and trade system will cause the least polluting Örms to do the majority of the production since its social cost of production is lowest.
- If the regulator cares speciÖcally about which plant does the polluting, however, cap and trade will not generally achieve the desired result. This case might be relevant if introduc- tion of a cap and trade rule caused substantial geographic concentration of pollution (letís say all the low-cost polluters in the U.S. just happen to be located in Harvard Square). There is an article by Schmalensee et al. on your syllabus that discusses the creation of the market for Sulfur Dioxide emissions in the United States. This policy experiment is a triumph of economic reasoning applied to environmental regulation. You may be interested.
5 Summary
Externalities are a source of economic ine¢ ciency. But they are also potentially correctable through the market. The Coase theorem identiÖes the two conditions needed for an e¢ cient market solution: complete property rights and zero (or low) transaction costs. Sometimes these conditions can be approximated by assigning property rights, thereby creating a market for the externality. Understanding why externalities persist in equilibrium comes down to identifying why the Coase theorem does not hold in a speciÖc circumstance. Rectifying the externality often means Önding a way to restore market conditions so the Coase theorem will hold. When that isnít feasible, external quantity regulation (like command and control regulation) may be needed.
6 An example: The market for real estate brokers
As weíve discussed this semester, the price system solves an informational problem: determining how much of a good should be produced and how much should be consumed. Production should occur until the marginal willingness to pay is equated with the marginal cost of production. When prices rise, more should be produced and/or less consumed. When prices fall, less, more should be consumed and/or less produced. Prices provide signals to consumers and producers about how to adjust production and consumption. These signals continually push the market back towards equilibrium.
dollar (for example, by waiting in line) seeking $100 in rents, then $900 is lost on rent-seeking.)
Could this case be relevant in the real estate market? Consider the following simple conceptual model:
- There is a supply of houses on the market that depends on the transaction price of a real estate deal. Denote H (P ) as the number of houses for sale at price P , with H^0 (P ) < 0 :
- There is a supply of real estate agents, R (P ) ; willing to provide services at price P; with R^0 (P ) > 0 :
- In free market equilibrium, P ^ solves H (P ) = R (P ): the supply of brokers is equated with the demand from sellers to sell their houses.
DeÖne the following quantities:
- The sum of sales commissions is the number of houses times the transaction price. Notice that this is also the sum of wages paid to brokers. ln (C) = ln (P H (P )) = ln P + ln H (P ) :
- The average realtor wage is the sum of commissions divided by the number of brokers. ln (w) = ln [P H (P ) =R (P )] = ln P + ln H (P ) ln R (P )
In free market equilibrium, the realtor average wage is:
ln (w) = ln
P H (P )
R (P )
= ln P ^ + ln H (P ) ln R (P ) :
But we wonít reach this free market equilibrium because P is not set by supply and demand. It is set by the price of housing itself.
Index the price of housing by HP I, for Housing Price Index. HP I measures changes in the real cost of housing; a 1 percent rise in the HP I means a 1 percent rise in the cost of housing: @ ln P=@ ln HP I = 1.
How does an exogenous rise in HP I a§ect the wages of real estate brokers? Your Örst instinct might be that @ ln w=@ ln HP I = 1: But this is not quite right. The reason is that an exogenous increase in the transaction price will reduce the number of houses for sale and increase the supply of realtors.
In particular: @ ln C @ ln P = 1 +^
@ ln H (P ) @ ln P <^1 ; so commissions will rise less than one for one with prices.
In addition, new brokers will enter the market.
@ ln R @ ln P >^0 :
Putting these together:
@ ln w @ ln P = 1 +^
@ ln H (P ) @ ln P ^
@ ln R @ ln P <^1 and^?^0.
In words, broker wages must rise less than one for one with house prices. Moreover, itís possible for broker wages to stay the same or fall when prices are artiÖcially increased by a change in housing prices. If a su¢ cient number of new brokers crowds into the market when HP I rises, broker income per capita may remain unchanged (or fall).
If this occurs, it has a second direct implication. DeÖne Realtor productivity as
= H R^ ((PP )) ;
equal to sales per realtor. What is @ =@ (ln P )? @ @ ln P =
ln H (P ) @ ln P ^
ln H (R) @ ln P <^0 : Sales per broker fall as housing prices rise. More brokers chase a Öxed amount of business, which reduces productivity per broker.
In what sense does this set of outcomes reáect an externality? The problem is pure business stealing. Increased Broker supply in response to an HP I-induced price rise does not increase the number of houses sold nor (to a Örst approximation) raise the well-being of sellers. It simply sends more realtors into the market to chase a Öxed quantity of deals. Output in the realty sector is unchanged by the rise in realtors. But the opportunity cost of realtorís labor in other sectors is lost.
This scenario is a purely dissipative externality. Society is made worse o§ by the entry of new real estate brokers into the sector (due to their opportunity costs). But neither incumbent nor entrant brokers nor homeowners beneÖt from rising prices (at least in the case where @@^ lnln wP 0 ).
