Chapter 32: Externalities

32.1: Introduction This chapter considers situations in which the actions of one individual affect the utility of some other individual – but without the individual being affected deciding to be so affected, in the sense of entering some market and either buying or selling some good. In fact, the basic problem in this chapter is the involuntary consumption of some good without any market being involved. We consider in this chapter externalities in consumption and externalities in production. Externalities in consumption occur when some person’s consumption of some good affects directly the utility of some other person; such externalities can be positive or negative – positive when the utility is increased, negative when it is decreased. Externalities in production occur when some person’s production of some good affects directly the utility of some other person; such externalities can be positive or negative – positive when the utility is increased, negative when it is decreased. Examples are easier to come by than general definitions. Let us start with negative consumption externalities. These occur when one person’s consumption of some good has a harmful effect on someone else: examples include (1) that irritating business-man on the train whose mobile telephone calls annoy others on the train; (2) that youngster with his scooter with the deliberately sabotaged silencer so that every time he or she revs up the whole neighbourhood shakes; (3) the students in the flat opposite who have loud parties at 3 in the morning and wake up all the little old ladies; (4) those tourists who will insist on eating food in pubs when you are trying to have a peaceful cigarette; (5) the Minster bells at 11 o’clock on a Sunday morning after you have had a tiring and emotional Saturday night; (6) the football fans who think that everyone else should celebrate their teams victory (or defeat); etc. In each of these cases someone is getting pleasure out of something but there is someone else who is suffering because of this something. And the key thing is that there is no market for this ‘something’. I should note that these things are obviously personal – what may be a negative consumption externality to one person may not be so to another. Positive consumption externalities are also very common, though for obvious reasons we are less likely to complain about them: examples include (1) that extremely pretty young man or woman who gives immense pleasure to everyone just walking down the street; (2) that beautiful garden in that council flat; (3) that wonderful opera that those really cultivated students across the street play at just the right volume on Sunday afternoons; (4) that really stupid businessman with his mobile phone on the train about whom you can laugh with your friends later that night; (5) an Italian beach on a weekday not in August; (6) the smells from your local Indian restaurant which is right next to your flat; etc. Note again that these may be personal – what may be a positive externality to one person could be negative to another. (“That extremely pretty young man makes me so jealous because he is so pretty.”) Production externalities are when the production of something affects someone else. They could be positive or negative. It could be utility that is affected or the production of some other good. An example of a negative production externality that affects utiltity (have you ever been to Stockton-on-Tees?) is pollution from some factory which pollutes the air breathed by the people who live nearby. An example of a negative production externality that affects production is pollution which damages the crops on nearby farms. Positive production externalities are also possible – like the warm water that a firm produces and in which people can swim - but rarer.

This chapter can only briefly look at the problems caused by externalities, but by the time that you finish the chapter you should be aware: (1) of what an externality is; (2) why it creates a problem for the operation and efficiency of markets; (3) what might be done about it; (4) why it might be difficult to do anything about it.

32.2: Consumption Externalities It might make our life simpler – and it will certainly make the issues we want to discuss clearer – if we work throughout this section with a particular example of a negative consumption externality – that of loud music. Right at the beginning I should point out that I really dislike music played too loud – and I particularly dislike other people playing their music too loud. I rent a flat in the centre of Bari; one year, one of my neighbours (who now seems to have moved on, thank goodness) thought that it would be great fun if he or she played the same pieces of easy-listening Italian music over and over again at high volume all afternoon and every afternoon. It was so loud that it was impossible to think or to work or to sleep or to eat or to watch telly or even to drink lots of beer. And I wanted to do all of these. I tried everything to get them to stop – I appealed to them in my impeccable Italian to turn down the music just a little please (I had to do this in the gaps in the music as I could not even hear myself shouting at them when the music was on); I appealed to the locals to help me; I went to the carabinieri (who went with me to the people concerned who told the comandante from the carabinieri where to go to and who told me to go back to Naples – ‘you foreigner’). Now while I am tempted to think that the ‘easy-music-lovers’ turned on their music and then went to the beach, I suspect that the truth is that they belonged to a frighteningly large set of people who simply like loud music – the louder the better, up to a point (even they have some limit). They got utility out of loud music. (Perhaps it helped them escape from something, perhaps themselves?) In contrast I get disutility out of loud music, the louder the worse. The problem is that, despite the fact that they closed their windows (and the mind boggles as to how loud the music must have been inside their flat) their consumption of loud music imposed an externality on me. And note – there was no market for this music. You will note that one of the things that I did was to go the carabinieri. I thought that they would know the law. John Hey: “Surely they are not allowed to play music this loud at this time of the day?”. Comandante: “Well…”. Clearly this is one solution – that the law says what is permissible and what is not. There are problems though with this. Can the law specify for every possible externality what is allowable and what is not? Can the law specify this sufficiently precisely so as to pre-empt endless disputes about the interpretation? Is the law enforceable in the sense that it is worth bringing cases to court for every possible externality? Is this kind of law efficient? These questions open an enormous Pandora’s box and we cannot hope to begin to answer most of the questions. But perhaps we ought to consider the final question – after all we are economists. Would it be efficient to simply ban the playing of any music, however loud, just because one bad-tempered foreign academic does not like it? Would it be efficient to do the contrary – let anyone who likes loud music play it whenever they want and at whatever volume? Note the problem – that some people like loud music while others dislike it. Is that any different from the fact that some people want to sell some good while other people want to buy the same good? After all, people are different.

Part of the problem is that there is no market for loud music. But it might be interesting to consider what would happen if there was – or at least consider the background to such a market. Participants in it would be me and my neighbours in Bari. Let us assume that we would be the only participants. (I should note that when I asked my other neighbours whether they liked the loud music or not, they used to reply (after my asking several times as they were having trouble hearing what I was saying) “what loud music?”.) We would be involved in a process of exchange. In analysing such a process we can use the apparatus of chapter 8, and can construct an Edgeworth box. I begin with my neighbours and shall refer to then from now on as “the young person”. I shall refer to myself as the “older person”. The key components of the story are loud music and money (which I would have been willing to pay to get the noise reduced if it was indeed the case that they had the right to play such loud music). I shall make the assumption that the young person has preferences over loud music and money – preferences of the usual kind. To the young person money is a good and so is loud music – indeed one could measure the quantity of the good ‘loud music’ by the loudness of it. The young person is happier the louder is the music – up to a certain level, I suppose, which is, I suppose, the level at which he or she played it (except when shouting at the comandante from the carabinieri). Obviously I did not have the opportunity to measure precisely the utility function of the young person over money and loud music, but we can do our analysis in principle with some general specification. Let us assume that these preferences have the usual form – as pictured in figure 32.1.

In this figure the quantity of money that the young person has is measured along the horizontal axis and the volume of the music to which he or she is listening is measured up the vertical axis. The higher up the louder the music and the happier the young person. I am assuming the usual situation in which the indifference curves are convex: the less money the individual has the less he or she is willing to pay to have an increase in the volume of noise. You will notice one rather special feature of this indifference map – the indifference curves become vertical when the volume of noise reaches 100. This means that even the young person has had enough noise when the volume has got that high – this is his or her limit. What about me? Well I consider loud music a bad – the louder it is the less happy I am. What I regard as a good is the opposite. I will call this opposite ‘peace and quiet’ but this is not a particularly good description as it sounds like an all or nothing thing. What I mean by this is the following: as ‘peace and quiet’ increases then the volume of music played by the neighbours decreases. What would be bliss to me is total silence – which is measured 100 on the peace and quiet scale. The other extreme – when the neighbour’s music is blasting out at their limit – gives me 0 on the peace and quiet scale. In between as the amount of peace and quiet increases I get happier and happier. My preferences between the two goods ‘peace and quiet’ and money are as illustrated in figure 32.2.

Note that my indifference curves become vertical when ‘peace and quiet’ gets to 100 – as I have already explained this is when there is total silence and I am 100% happy (as far as noise is concerned). My preferences between the two goods, ‘peace and quiet’ and money have the usual convex shape. Now put us together – after first turning me upside down – to form an Edgeworth box. Notice that we can do this as ‘peace and quiet’ is the opposite of the volume of the loud music. You might want to know what the initial endowments are – so let us assume that both me and the young person have 100 in money. As far as the initial endowment of the variable on the vertical axis, this is something we will have to discuss, but we can leave the height of the box equal to the joint limits of 100. If the young person has a certain volume of loud music then I have 100 minus that as far as my ‘peace and quiet’ variable is concerned. We get the Edgeworth box pictured in figure 32.4.

We should be careful about the interpretation of this. Along the horizontal axis is money – measured from the left the amount that the young person has and measured from the right the amount that I have. Initially we each have 100 so we start in the middle horizontally. Along the vertical axis is the volume of the music, as measured from the bottom, or the amount of peace and quiet, as measured from the top. Any point in the box indicates how the 200 in money is divided between us and how high is the volume of the music being played. If we are 50 vertically then the volume is halfway to the limit while I regard the amount of peace and quiet as halfway between heaven and hell. If we are at 0 vertically then the young person has turned off the music and I have 100% peace and quiet. If we are at 100 vertically then the younger person has the music as loud as they can bear it and I have zero peace and quiet. You should note that the variable along the horizontal axis is to be shared (initially equally); the variable on the vertical axis is not to be shared in the usual sense, but to be experienced equally. (That, of course, is the problem.) An economist looking at the above figure would conclude that any sensible arrangement would be along the contract curve – whose position is obvious from the figure. Indeed a point off the contract

curve is inefficient is the sense that we could both be better off by moving away from that point towards the contract curve. But where do we start? This is part of the problem and takes us back to the law and the carabinieri. My young neighbour clearly thought that he or she was entitled to as much noise as he or she cared to make – so I presume that he or she felt that the initial endowment point was that labelled E in figure 32.7.

The economist would then say that with competitive trading we would end up at an efficient point – namely that labelled X in figure 32.7. Given the endowment point (which I obviously do not like but have to accept if that is indeed the law) I pay some money to the younger person and he or she turns down the volume a bit. He or she does not have it as loud as he or she would unconstrainedly have it – but he or she is compensated with a little extra money to buy some more CDs. I am happier than I would be if the volume was not turned down. However, I obviously think differently about the endowment point – I think I am entitled to complete peace and quiet. I think we should start from the point labelled F in figure 32.9,

The economist would then say that with competitive trading we would end up at an efficient point – namely that labelled Y in figure 32.9. I would accept a little bit of noise in return for a bit of money (with which I buy earplugs) and the younger person is happy to pay a little money in return for being allowed to play his music loud. Notice what would happen if trading was not allowed and there was a clear statement of the law – which was enforced perfectly. We would end up at either the point E (if the younger person had the right to noise) or at point F (if I had the right to silence). Neither of these points are efficient – they are both off the contract curve. The economist’s contribution is that competitive trading would take us to a point on the contract curve – and the inefficiency caused by the externality would be

eliminated. We should note that the externality itself can not be eliminated – that exists because I and the young person have different tastes. The problem of course is the ‘competitive trading’ part of this story. There was a problem in the first place because there was no market for noise. To implement the economist’s story we need somehow to create a market in which competitive trading can take place. You can probably see other problems – even if my neighbour understood and accepted all of the above story he or she might think that there should be some relationship between the assignment of property rights (do I have the right to silence or does my neighbour have the right to noise) and the operation of the market. He or she might well think that if he or she has the property right (the right to noise) then he or she also has the right to set the price in the market. And we already know that this institution leads to a point off the contract curve and hence is inefficient. Indeed I might well prefer the point E to the point that would be chosen by my neighbour. Similarly he or she might prefer point F to the point that I would choose if I had the property right (the right to silence) and could set the price. More generally it is not clear how competitive trading could be enforced if the law relating to the original problem was itself not enforceable. Anyhow the economist’s way of looking at the problem does enable us to see where efficient outcomes may lie. An alternative way to get to one of these outcomes is for the government to impose a tax on the imposer of the externality. But again this requires us to define the imposer. If it is the young person then he or she could be taxed proportionately to the volume of the music. This would imply a budget line for the young person through the endowment point – and could force the young person to choose a point on the contract curve – if the level of the tax was chosen correctly. The proceeds of the tax could be paid to me (but not necessarily to me if we were only interested in the efficiency of the market) – and this would create the market. But there remain problems – not least the enforcement of the tax. In practice this would prove difficult and complicated. Indeed such complications lead to simpler practical solutions – such as the banning of loud music at certain times of the day (coupled with legal enforcement through the paying of fines for those caught violating the ban). In fact, if you think of the myriad externalities that we are subjected to in everyday life, when the law intervenes it is usually in such a form. Examples include: (1) the banning of smoking in public places; (2) limits on emissions of carbon dioxide from car exhausts; (3) offences such as ‘drunk and disorderly’. When the externalities are too minor to make legal intervention worthwhile there are usually appeals to ‘public spirit’: “please use your mobile phones with consideration to others…”.

32.3: Production Externalities Perhaps because production externalities are generally larger, they tend to be taken more seriously. An example which we can analyse using the same apparatus as above is that of two firms, where the production activities of one firm influence the output possibilities of the other. The classic example is that of the steel producer and the fishery – the former located (rather unfortunately but necessarily for an externality to exist) upstream from the latter. The steel producer produces steel but also uses the water in the river that flows downstream to the fishery. This fact, coupled with the steel manufacturing process, means that the steel producer pollutes the water in the river – and this affects the output of the fishery. Let us be more precise. We assume that the output of the steel producer is steel and that its inputs are labour and pollution. This latter may appear a bit strange in the sense that pollution is normally considered an output, but we should think in the following way: at any level of labour input the steel producer can produce steel – the quantity of which is also dependent on the amount of

pollution it produces – the greater the level of pollution the greater the level of output. Alternatively the steel producer can reduce the quantity of pollution produced but only at the expense of a reduction in the level of output. We can therefore think of labour and pollution as the inputs and steel as the output. We can represent all of this in an isoquant map, the shape of which will depend on the firm’s technology, but will have the general shape illustrated in figure 32.12.

Along the horizontal axis is the amount of labour that the firm uses; up the vertical axis is the amount of pollution produced. The curves are isoquants – as we move up and to the right the quantity of steel produced increases. For any given level of labour, output increases as pollution increases. You should note that I have drawn the isoquants becoming vertical at a level of pollution of 100 – this is presumed to be the maximum pollution that the firm is capable of producing. Note, that if the firm does not have to pay for the input pollution it will choose1 some point along the top of this figure – where the level of pollution is equal to 100. Let us now think about the downstream fishery. It produces fish, and uses labour and the river to produce the fish. What it wants is clean water – the cleaner the better in the sense that the cleaner is the river water the larger the crop of fish for any given level of labour employment. We can portray the technology of the fishery using isoquants in the usual way. See figure 32.13.

Note that we have labour input along the horizontal axis. On the vertical axis is the cleanliness of the water: at 0 the water is maximally polluted; at 100 the water is super-clean. In between it is in-between: as we move up the vertical axis the water becomes cleaner. The curves are isoquant curves for the fishery – as we move up and right the quantity of fish caught increases. As is clear from the isoquant map of figure 32.13, for any given quantity of labour employed, the cleaner the water the

1 If the price of pollution is zero then the isocost curves are vertical and hence parallel to an isoquant when the level of pollution is 100 (and when the isoquants are vertical).

larger the harvest of fish. Notice that the isoquants become vertical when the cleanliness of water reaches 100 – its cleanliness limit. We once again form an Edgeworth box – very much like the one we produced in section 32.2. We assume that the total quantity of labour in this mini-society is fixed at 200 and we make the box of that width. The variable on the horizontal axis is pollution – as measured from the bottom – and cleanliness – as measured from the top. These are the same and both the steel producer and the fishery experience the same level of this variable (it is not a variable to be divided between them, but one to be experienced equally). We make the height of the box equal to the distance between super-polluted and super-clean. We get figure 32.192.

For any given division of the labour between the two firms, if it is the steel firm that can choose the level of pollution, it will obviously choose a level of 100. After all it does not have to pay for the pollution (until the government intervenes), as there is no market for pollution. The fishery then has to accept the level of pollution chosen by the steel producer. But this is obviously inefficient – a point along the top of the box lies off the contract curve and could be improved upon. How? Well, the economist would say, by competitive trading. From where? Well, this depends upon the assignment of property rights. If the steel firm has the right to pollute as much as it wants we start at the point E and competitive trading takes us to point X. If the fishery has the right to clean water then we start at the point F and competitive trading takes us to point Y. Clearly the steel firm prefers to be at point X and the fishery at point Y, but both prefer to be at X rather than at E and both prefer to be at Y rather than at F. So – the economist concludes – if we have a clear assignation of the property rights and if we have competitive trading then we can eliminate the inefficiencies caused by the externality – though obviously we cannot eliminate the externality itself3. Notice that the assignment of property rights does not affect the efficiency of the outcome though it does affect the distribution of the surpluses. Note too that the assignment of property rights plus the establishment of a market is bound to be better (more efficient) than either the assignment of property rights to the steel producer (“you can pollute as much as you like”) or to the fishery (“you can not pollute at all”) – since both of these solutions leads to a point off the contract curve. Having got this far it is clear that there are other ways of reaching an efficient point – a point on the contract curve – for example through the imposition of a tax by the government. The tax could be imposed on the steel firm and the proceeds paid to the fishery (but not necessarily so if we are only

2 You will note that this box – except for the labelling and interpretation – looks exactly like the box in section 32.2. For that reason we do not reproduce all the intermediate figures. 3 You might be tempted to suggest that the government simply bans the pollution. But notice that there is a cost to society of so doing - unless the steel firm can somehow costlessly eliminate the link between pollution and output.

interested in the efficiency of the market we are discussing). But the tax would have to be computed correctly to guarantee that a point on the contract curve is reached. Also the level of pollution would have to be measured correctly. Note that this introduces extra costs into the whole procedure. As indeed does any procedure which involves the law. Alternatively we could leave everything to the market. As long as the two firms remain distinct the sum of their profits can never be higher than if the two firms merged into one (because generally they would be off the contract curve). And what would happen if the two firms merged into one? The combined management would choose a point on the contract curve and increased the combined profits of the combined firm. So, there is a natural incentive for the two firms to merge and hence internalise the externality.

32.4: Markets for Permits One thing that a market appears to be able to do efficiently is to allocate a fixed number of permits for pollution. Suppose that the government is able to measure the amount of pollution that firms emit and desires to restrict the total amount of pollution in a particular industry. Then it can do what is practiced in America and elsewhere – and that is to distribute to the firms in this industry a number of permits equal to the desired level of pollution and then allow the firms in the industry to trade those permits. It can be shown that competitive trading of permits leads to an efficient allocation of those permits. We can use the same kind of analysis as before – with two changes. We consider an industry composed of two firms and we draw, as before, an Edgeworth box in which the variable on the horizontal axis is labour (as before) and the variable on the vertical axis is permits. The height of the box is determined by the total number of permits that the government allocates. One of the two firms in the industry is measured from the bottom left corner and the second from the top right. Figure 32.20 illustrates. A point in the box represents an allocation of labour and of permits between the two firms.

Suppose the firms start with an equal endowment of labour. Then the initial allocation point is somewhere along the vertical line in the centre of the box. We know already, from wherever we start, that competitive trading of permits between the two firms will take us to a point on the contract curve (included in figure 32.20). Clearly the initial allocation of permits affects the distribution of the resulting surpluses, but competitive trading eliminates any inefficiency in the market.

32.5: Over-Fishing

I am not sure whether this is a public goods/bads problem – which we will discuss in chapter 33 – or whether it is an externality problem. I suspect that it is a bit of each – because public goods problems seem to involve a specific type of externality. In any case, let me briefly discuss it now. Cod – a fish caught for hundreds of years around Britain – is in serious danger of disappearing. In fact, the situation is so severe that there has been at times a total ban on the fishing of cod in the North Sea around the UK. And the reason – because it has been over-fished in the past. And the reason for this: that there is some kind of externality imposed when a new fisherman starts fishing for cod. When a potential new cod fisherman is considering whether to take up fishing or not he or she considers solely his or her costs and benefits and fails to take into account the effect of his activities on the fishermen already in the market. His or her entrance into the market inevitably imposes a cost – an externality – on those other fisherman because it makes it more difficult for them to catch fish. But if there is no organisation to control entry, people will make individual decisions based solely in their own interests. The consequence is inevitable – over-entry and over-fishing. To correct this externality requires potential entrants to be charged the costs imposed on the others. But who is to do this?

32.6: Summary We have made a lot of progress in this chapter, though we have also identified some limits on what economists can say. We have identified what is meant by an externality and have shown that, if a market does not exist and if property rights are not defined or enforced, the externality will cause a loss of efficiency. The clear assignment of property rights, coupled with the enforcement of some kind of trading mechanism, can eliminate the inefficiency but there are problems attached. We have seen that in practice, a more legalistic approach is usually adopted – but this does not eliminate the inefficiency. When the externalities are small and badly defined, an economic solution to the problem is often impracticable. However when the externalities are large and there are ways of measuring them accurately, an economic solution is possible. In the case of production externalities they may be eliminated by market forces – operating through profits and the stock market – which lead to the internalisation of the externality.