 I thought what I'd do is talk about corrective taxes. Largely, it's gonna be environmental taxes, taxes related to health. And a couple of reasons for that. One is that while I'm doing some, think about this at the moment, think about some of these issues. And so they're in my mind, but also as I think about them, they're kind of a little bit less straightforward, maybe than I used to think they are. So, and I saw too that this wasn't, I think covered elsewhere in your work. So I thought maybe let's spend some time thinking about corrective taxes. So what do I mean by corrective tax? So what I mean is just a tax or a subsidy, could be a subsidy that's motivated not by the usual kind of revenue concerns that we have in mind when we think about taxism, but actually is motivated to try and correct some kind of market failures. And so we see there's something wrong in the outcome without government intervention. And the corrective taxes when we think the best way to address that problem, or at least a way to address the problem is by some form of taxation. So that's all I mean by a corrective tax. And as I say, I think one reason, maybe you step back a bit. Suppose you were, if you were designing a tax system from scratch, there was no taxism at all. And you were to think, well, how would I want to raise whatever revenue I need? Well, you might think, first of all, you might think of rent taxes which as we talked a bit about yesterday, rent taxes are non-distorting. So we can raise some money through them without creating excess burden. That sounds a good thing. So they might be high up on your list. And probably not far down the list, maybe even second on the list would be corrective taxes of various kinds. So those are taxes, as we say, that basically make the markets system work better, but as a side product, produce some revenue. So you might think, well, environmental taxes really should be much higher up the list of tax instruments that governments use than actually they are. So in a way, there's kind of a bit of a puzzle there. Why corrective taxes aren't an environmental taxes aren't more of a mainstay of government revenue systems. And in what happens, I think, in terms of the policy debate is that every so often when people think about a good tax system design, the idea that environmental taxes can be a big part of the answer that the corrective taxes, in particular environmental taxes can be a big part of the answer, tends to become slightly rather popular among sort of civil society and elsewhere. The case gets pushed rather heavily for these kinds of taxes. So the question is kind of, well, okay, is that really true? How should we think about the role of corrective taxes? And ultimately, do we think they have a big part to play in the national tax systems, including I think not least developing countries where again, these are often particularly advocated on the grounds that many developing countries are really serious environmental problems. So maybe taxation is a way of addressing those raising revenue at the same time. So that's the kind of broad context of why I think it's worth spending time on corrective taxes. And there are gonna be two broad forms of corrective tax I'll talk about. The first are addressed to what I'm sure you've come across the idea of externalities. The idea that when one agent, a firm or an individual takes some kind of decision, that may have some effect on people who are not part of the decision. So they're kind of innocent bystanders may get affected by the decisions that a firm or an individual takes, may be affected badly. And that's typically what we'll have in mind, may be affected for the good, for the better as well. But nonetheless, the idea is that somebody, you take an individual firm, takes an action decision and that affects people not party to the decision. So that's what I mean by an externality. I should say a slight footnote. Typically we would set aside externalities that operate through the price system. Oh, I see the power's gone off. Are you still there? Or am I still there? Should I wait? Can you hear me? Tell me when you hear me again. Are we back? We are. It's the electricity class, yes. So, do you know, do you remember where you lost me? You can still see me, right? I can't see myself anymore, but you can still see me, right? What's the slides? You are your slides, and we're starting off to explain externalities. Okay. So externality, as many, I'm sure many of you know, is something that happens when the decision that's taken by some individual or firm has effects on other individuals or firms who weren't party to that decision. So, for example, I lost the examples. Of course, I like being a smoker. I use smoking examples a lot. So I smoke and that irritates other people who weren't involved in the decision for me of my decision of whether to light up. So, and of course we set aside externalities that may operate through the price system. It could be that, you know, if, because I decide I want to pay more for some artwork that increases the price paid by somebody else, so in a way it's an externality, but it's what's called a pecuniary externality, a pecuniary externality, and doesn't in itself cause any inefficiency. So it's inefficiency. So we're really talking about effects that don't go through the price system. And these things arise in many contexts, externalities rise in many contexts. For example, in the financial sector, too big to fail banks can take on more risk than they should with the implication that other people are going to bear the costs if they go bust. But I'm going to be focused particularly on, as given what are my earlier remarks on environmental issues, environmental externalities, which often turn out to be health related. So most of what I'm going to talk about is really dealing with externalities. We'll also talk about the kind of second target, potentially of corrective taxes, which is what's called internalities. And those are related to problems of self-control. So they're not kind of operating between people. The idea is they're operating within a person in terms of their own character, motivations, strengths and weaknesses and so on. So what I'm going to do is talk about externalities a bit more, talk about the externality problem, instruments one might use to address externality problems. Then I'll focus on tax-based approaches to deal with the externalities, take up some further issues and then I have a bunch of applications we might talk about at the end if there's time. So externalities, so I wanted to go through the basic problem of externalities, partly because I think it's actually a little bit more subtle than is often recognized. It's basically, I think the point, large part of the point, a large element order, what to say is apart from there being several instruments by which you can deal with externalities and taxation is only one, we often think of taxation as being an efficiency issue, but it's also a distributional issue and I'll come back to that. So there are equity and distributional issues involved in dealing with externalities, which I think often get left aside. So here's the basic framework. I'm sure you've come across something like this to think about externalities and I apologize for the quality of my diagrams which involve more use of an iPhone than I would have liked, but that's how it worked out. So here's the basic structure. We have some on the kind of horizontal axis, going from left to right is something good, is clean air, Q, going from left to right, could be clean water, whatever it is, but the point is that's a good one. Going from left to right is a good thing. And essentially there is some benefit derived from clean air in amounts, big B of Q, that's the social benefit of the clean air in amount Q, but there's some cost of providing clean air. That is to provide clean air, for example, firms may have to incur some abatement costs to reduce the damage that they do to air quality. So C of Q is the level, sorry, C of Q, I shouldn't say marginal, their C of Q itself is just the cost of providing clean air. And then what we have in the picture are the marginals, the marginal benefit B prime. So essentially as clean air, as the air gets cleaner, benefit goes up, social benefit goes up, but it goes up at a decreasing rate, so the B prime is slipping down. Conversely, to create clean air, the cost of creating clean air essentially goes up at the margin as the initial quality of clean air increases. So the more clean air you have to begin with, the more costly it is to increase, improve air quality. So it's helpful, I've set up that diagram in terms of clean air going from left to right. It's helpful, I think, to think of emissions, some kind of pollutant going from right to left, which is essentially damaging air quality. So E is some emission of some pollutant that reduces air quality. And so the link between emissions and clean air is given by that equation at the bottom on the left, that emissions are equal to big Q, and big Q is like the most clean, the most clean that air could possibly be, maybe it's 100% or something. So emissions are simply the maximum quality of air, less the actual quality, just to make it simple. So it's good to keep in mind in both the Q going from left to right, and the E emissions going from right to left. So that's the basic structure. And as I'm sure you know when we think about, or what's the efficient outcome here? Well, the collectively efficient outcome, the one that maximizes benefits less costs to society as a whole, is gonna be where marginal benefit equals marginal cost. And that's at the level of air quality Q style in the picture. So that's all very straightforward. But just to keep track of what's going on, I'm imagining here that we start in a world where the polluter in this story can emit as much as they want. So let's imagine that the allocation of property rights is that there's no restriction on how much the polluter can emit. So in the absence of any intervention, they're gonna emit as much as they want. They're gonna drive their costs as low as possible. So we're gonna start at that point O in the picture, down the left, the origin. That's kind of where we start. So what happens now when we move to the collectively efficient point Q style? Well, relative to O, there's an increase in the benefits, which is gonna be the area under the marginal benefit curve. So the social benefit goes up by that little triangle, by the triangle A plus the triangle on top of it B, that's the total increase in the social benefit. But there's an increase in social costs of this amount alpha, just that red triangle. So the collective gain from doing this is beta. So what have we shown? We've shown moving to the efficient, the collectively efficient outcome. We have a basis, a net social gain of beta. But the point to emphasize, I think, is that this doesn't mean that both sides have gained. Doesn't mean that both the polluter and the pollutee have gained in moving from O to Q style. That is importantly, Q style is Pareto efficient. That is, if we were to start at Q style, there's no way we could change the level of Q and make both parties better off, because we're already maximizing the net social benefit. However, it may not be a Pareto improvement over where we started off A, 0.0, sorry. So it's not necessarily Pareto improvement. I haven't told you yet how we get from O to Q style. And how we do that is going to matter quite a lot for who gains and who loses from doing this. So going back to the point I was making, this was why I think we have to think that dealing with externalities is a distributional issue as well as an efficiency issue. And it's going to mean, for example, that when you impose a corrective tax, there's going to be an issue of, well, okay, clearly the person suffering from the externalities is going to benefit. But what about the person who's being required to emit less? They're presumably worse off. So if we really want to bring about a Pareto improvement, we're going to have to think about compensating the people who are essentially being required to emit less than they otherwise would have done. So that then brings us on, oh, how did I do that? Oh, hang on, managed to go right to the end. Okay, okay, okay, okay, okay. So now we come on to the instrument choice issue that is how do we deal with an externality? And one way of thinking about this problem is, well, okay, so COVID, we've had COVID. Clearly there was an externality and I just got COVID. So I was stuck in my room for 10 days. So you could ask yourself, well, okay, there would be an externality. If I were to go out on the street, I might make other people sick. But well, okay, why didn't we have a tax-based approach? Why wasn't it that I, instead of being stuck in my room for 10 days, I wasn't presented with the option of paying a charge and being free to go wherever I want. So just to put in your mind that there is an issue of instrument choice here and we should really try to articulate, well, why is that? What exactly was the feature of the COVID problem that meant we thought taxation wasn't the way to go? So how do we, how are we going to address externality? So one approach is known as the Cosian bargaining after Ronald Coase, which basically says, well, let's just leave the two parties to get on with it. Essentially the polluter would be willing to pay, sorry, the pollutee, the person suffering would be willing to pay the polluter an amount bigger than alpha, but less than alpha plus beta to induce them to move to Q star. So basically, if you look at that picture again, we're saying the person who's suffering could pay an amount to pay the polluter, could pay the polluter an amount bigger than alpha, but yet still leave themselves a net gain from doing so. So the Coasean solution basically one side bribes the other into doing, to arrive at efficient solution. Question then is, well, who gets, how does the net gain, net gain from doing, let's remember it's beta, how does that get shared out? Who gets it? Well, that's going to depend on the bargaining power. But notice that one feature of the Coasean solution is at both sides of gains because one has been happy with the bribe they're paying, the other one's been happy with the bribe they've received. So it's quite a nice solution in that sense. It really does generate a prato-improvement relative to O. Of course, practical importance of the solution is often said to be limited because with many externalities, there are going to just so many people affected, we can't realistically match them getting together to negotiate. Well, you might think, well, okay, that's fair, but well, maybe that works in international context. Maybe when you have a bunch of countries negotiating over climate issues, say, maybe then you could think of some kind of Coasean solution. And to some extent, maybe it's surprising that we don't see more kind of side payments, bribes of various kinds being paid, for example, in climate negotiations, we do have climate finance and so on, but you might think that might expect to see more of it. And I think part of the reason we don't is that even with relatively small numbers, you still have this kind of a free-riding problem. That is that the people who might be called on to reduce their emissions, their pollution would prefer that other people reduce their pollution emissions instead. So anyway, that's one solution, Coasean bargaining, may have slightly more applicability than as often said. Another is the one that lawyers like and that we don't often talk about as economists. This is basically a liability approach. So this basically says, well, look, if some damage occurs, then what we do is we require the polluter to actually compensate the pollutee. What does that mean? Well, it doesn't fit very neatly into the framework above because this is all this liability is really for a world where damage might or might not occur. But basically the idea in the language above is that the polluter is gonna basically incur two costs. They're gonna incur the costs of abatement, C of Q, but they're also gonna require, pay some damage to the pollutee. What's the damage going to be? Well, the damage in the set its framework above is the benefit at BQ. So that's the benefit with perfectly clean air, less the benefit from the actual clear air quality. So that's kind of the damage that the pollutee suffers. And so the polluter is gonna minimize the sum of that damage payment and the costs they incur. And if you just look at that equation long enough, you'll see that B of Q is just fixed. That's just whatever the benefit from perfectly clean air is. And then minimizing minus B plus C is the same as maximizing B minus C. So again, you have, this would lead us to the efficient solution that we saw of Q-star earlier. What are the gainers and losers? Well, a polluter is losing alpha, which is those costs of the air in the diagram representing the costs incurred of air quality C plus this damage payment B of Q. So the polluter loses more than alpha. When is so, again, so the distribution is quite different from the Cosian solution, for example, even though the outcome is the same. So distribution quite different outcome in terms of air quality is exactly the same. So when is this approach most likely to be suitable? Well, clearly arguably that's gonna be most suitable when damage may not occur, when it's hard to assess a priori what the damage will be. So for example, this is the sort of thing you might be suitable for oil spills or for, designed for kind of, you know, emergencies, catastrophes of some sort like that, that occur rarely, it's hard to know how much they will cost. And but afterwards, after the effect, we can assess what the damage was. But of course, it also requires a strong judicial system because all this stuff is going through the courts. It's the courts that are determining what the damage is and so on, what the culpability is. So again, so apart from the rare damage, hard to assess in advance, there's a requirement of a strong judicial system. A third approach straightforward is regulation, which in this model simply says, well, we would just dictate that air quality must be at least Q star. We wouldn't necessarily ban any emissions because that wouldn't get us to the efficient solution. But we simply dictate, well, okay, air quality has to be at least Q star. The polluter again loses from this. The polluter incurs the cost alpha or the benefit goes to the polluty. When is this kind of approach most likely to be suitable? Well, this may make sense when damage is sure to happen. And maybe when there are relatively few polluters that the regulators can look at or Q star, the optimal quality varies relatively little and is readily observed. Sorry, did I? Okay, sorry, I thought I heard a question. So we've already been through three solutions, three approaches before we even come to taxation. And I think that's important in itself. Taxation's not necessarily gonna be the top of anyone's list when it comes to deal with externalities. So the Pagovian solution, as I'm sure you know, what we do is we basically decentralize a solution at Q star by setting a tax T star equal to the marginal cost of abatement at that point, C prime of Q star. How does, why does that? Well, what the producer is now going to minimize T star times the level of emissions. T star is a tax on emissions. Emissions remember a big Q minus little Q. And so the producer's gonna minimize the tax payment plus the cost incurred C of Q. And that you can see results in setting marginal cost equal to T star, which implies that output is gonna be a Q star. So that's basically how it works. Point to note again, consistent with my earlier theme is that the polluter, who's benefited, who's gained? Well, clearly the pollutee, the one suffering has gained that whole area beta plus alpha. On the other hand, the polluter has not only lost alpha, that those abatement costs, but now also that whole triangle, that yellow triangle of tax payments, T star times Q, T star times big Q minus little Q star. That's all tax payments. So a couple of things to notice there. Well, when do we think this is gonna be most suitable the tax approach? Well, maybe not too difficult to believe that it's gonna be most suitable when we think the source of pollution, the pollutant is just a simple, single, well-defined commodity. If you think about an oil slip, what exactly would you, oil slip, what exactly would you tax? Maybe hard to decide. So the tax works well as all taxes do, I guess, when the base can be very simple, when the appropriate base is very simple. And also really when you can impose the tax on a relatively few number of firms, again, consistent with standard tax principles, you'd like not to have to tax every little retailer, but to be able to tax a few kind of upstream users and reach the whole economy that way. One might come back to some of those points, but there's the other thing to notice about taxation is there's now a new question that didn't arise when we talked about any of those other methods, which is what do we do with the revenue? And we have to do something with it. If the revenue is wasted, if that little triangle just gets completely wasted, then the whole thing may be a bad idea. That area gamma may be bigger than beta, you could draw it that way, in which case if we throw the revenue away, this whole idea was a bad idea. So that's again, again, this whole distributional issue coming in. And it's worth noting that the Pigovian tax really has two elements, the argument Pigovian tax as a root two, excuse me. If you talk about a Pigovian tax, and you simply point out that the Pigovian tax gets us to the right level of the externality, that's only part of the story. Because if that's all you've done and you haven't done anything with the revenue, you may have made things worse off. So the question, what you do with the revenue, do you try to compensate the polluter? Is there actually enough money? Is gamma large enough to compensate the polluter? All these questions I think are often overlooked when we simply talk about Pigovian tax as we say, oh yes, set T star, we get Q star, end of story. That really shouldn't be the end of the story. And I think that matters in important ways for policy as we'll see later. Excuse me, think about having something to drink. So just to note, oh, excuse me, one moment. So just to note the, that's the tax base, that's the Pigovian tax. Very similar results come about if you use what's called cap and trade or emissions trading. So based on the story here is instead of setting a tax, what we do is we create permits to emit in an amount, big Q minus Q star. And then we essentially auction these permits so that firms can essentially bid against each other to acquire the permits allowing them to emit. Not too difficult to believe that that C prime curve really becomes a demand for permits in that sense. And the market for those Q star, the right to emit big Q minus Q star pollutants will clear at a price of T star. So essentially the cap and trade in this simple framework is gonna be the same as a tax-based approach. You're gonna end up with the same, can end up with the same air quality and also the same revenue, but now the revenue is the form of, is in the form of sales of licenses to emit. There are some differences in practice. Rights are often allocated for free, which rather dissipates the revenue effect. It's actually more, slightly more common that the proceeds of emissions trading are earmarked, slightly more to particular purposes than the tax revenues from corrective taxes, but we'll come back to that later. But I'm not gonna say much more about cap and trade because to the kind of, to the first order, it's much the same as the tax-based solutions that I'll be focusing on. Well, so let me just focus a little bit on what are often the two leading contenders for dealing with externalities, taxes and regulation. How do we, how do we compare them? When is taxation going to be important, and when is regulation going to be appropriate? So we're basically focusing on what are the differences between the two, which again, you can have at the back of your mind, why was regulation rather taxation better to deal with COVID? Well, one issue is compensation is a more fundamental issue with taxation because remember taxation imposes additional rectangle of loss on the polluter. So the question of, well, you're making the polluter much worse off with taxation than regulation. What are you gonna do about that? Do you think it's appropriate instead to try to compensate the polluter? There are also differences that arise in the second bullet when you have many polluters and the damage depends on total emissions. So for example, one might have in mind climate, for example, climate change, where the impact on global emissions simply depends on the total of emissions over all sources of emissions, all firms. So suppose in this picture differs only from the previous one, only in that I've added, imagine that there are two firms. Now C1, a C2, they have different marginal cost structures and C prime is now the horizontal addition of those two cost curves. And C prime, I think you'll easily convince yourself, gives you essentially the cost of a total amount of emissions when those emissions are allocated efficiently between the two emission sources. But anyway, suppose we look at this world and again, the optimum is we want total emissions of Q star, how can we achieve that? Well, one way is we can go around all these firms, we can go to a firm too and say, okay, your optimal emissions are Q star too. And then we go to, your optimal emissions are kind of the opposite of that, rather reading from big Q. So we could say to firm two, your optimal emissions of big Q minus Q star two. Then we go to firm one, we look at their cost curve and we say, oh, no, you have rather heavy costs. So your emissions are going to be, we allow you somewhat heavier emissions of big Q minus Q star one. So you'd have to go around these firms, figure out individually what their optimal emissions are. But on the other hand, if you figure out, if you look at this picture and you instead simply set a price of T star at the same level where C prime intersects B prime, you can see that those two firms will automatically by equating their marginal costs to the tax, they'll automatically choose the efficient levels Q star one, Q star two. So the tax achieves the minimum, achieves the essentially goal of output of the... Sorry. Achieves the goal of overall emissions reduction in the most efficient way. It does it automatically through the price system. Regulation of course doesn't, you have to have much more information to make the regulatory approach work. And that I think just to anticipate a bit is one reason why most economists think that carbon taxation is going to be able to mitigate, to reduce emissions than regulatory measures because essentially this is a climate change fits this kind of situation very directly. Many different emitters with different cost structures. Let's have a single price and allow that to automatically determine who should mitigate most and who should mitigate least. One other, oops, why do I keep doing that? So one other difference between taxes and regulation that I think gets a lot of attention and I think is quite interesting is well the model I had above, everything was perfectly certain. Suppose though that we don't really know what the cost structures, and I'm going back now to world with basically just one firm as it were. We don't know what cost structures will turn out to be. So there's some uncertainty. Suppose there's uncertainty. Well, how can we compare price and tax and regulatory measures then? Well, this is a kind of very nice analysis, classic analysis due to Weizmann back a long time ago, but still I think a classic. So, okay, so we look at this picture again. So suppose we know that the benefits, the marginal benefit curve is B prime. Actually, if we doesn't really matter as we'll see if we're uncertain about P prime, but let's assume for simplicity. We know the marginal benefits, the marginal social benefits there. We think on average, the marginal cost is going to be given by that unbroken C prime line, but there's some chance marginal cost will turn out to be either lower C L prime or higher C H prime. And we think, well, okay, in this world, should we go for taxation or should we go for regulation? Well, let's think first about regulation. And let's imagine that the costs have turned out to be low. So we're working in that C L prime world. So then the real optimum is that L is at that point L where the B prime intersects C L one. However, with regulation, we're stuck. We've fixed the quantity at Q star. And Q star is clearly too low because if we look at when we're at Q star, you can see that, well, given B prime and given C L prime, the marginal benefit exceeds marginal cost. So we should be emitting more and the dead weight loss from our output being stuck at Q star is that red area. So that's the red area between the B prime and the C L prime. That's the kind of inefficiency we've got from using regulatory measures. But well, suppose instead that we had used taxation and we'd set the tax T star according to where we think correctly that C prime and B prime intersect. But now again, suppose that in fact what's happened is that the costs have turned out to be very low. Well, what's gonna happen is that the, I should have marked this on the diagram, but at the tax of T star prime, the level of air quality is going to be where that red, where that kind of vertical red line intersects the C L prime line. That's where the firm is going to choose to abate. And you can see that so relative to that point well at that point, the marginal cost of abatement, the C L prime exceeds B prime. So we've actually abated rather too little or the air quality is kind of rather too high. And so now the dead weight loss, we look to compare the, that we sent you look at the area above the B prime curve but below the C L prime curve. And that's that yellow shaded area. So what this is saying is the dead weight loss from choosing regulation if things turn out, if costs abatement costs down to be lower than expected at C L prime, dead weight loss using regulation is that kind of red area but the dead weight loss from using taxation is that big yellow area. So in this context, regulation is clearly better. And you can do a similar exercise with the C H prime curve if costs turn out to be higher than expected. And you get a similar conclusion. You get a big yellow area and you get a small red area. So what is that saying? That saying in this situation, regulation is better than taxation. Why is that? Well, if you just look at the diagram, what have I fixed up to make the diagram look like that? Or what I've done is make the benefit curve very steep relative to the to the marginal cost curve. And that turns out to be the kind of critical thing that regulations preferred, whenever the marginal benefit is steeper than marginal cost. And essentially the intuition is there because getting the tax wrong has a big quantity effect when the cost curve is very flat. And that has a big damage impact. The lesson from that, I think, is that regulations like to matter more when there's an externality that has a real kind of tipping point property. That is, if there is some level of the, in this example, air quality, but more generally, whatever environmental index you have in mind, if there is some quantity such as really, really costly to go beyond that, then that suggests that regulation is going to be the way to go. And that's something that I think people have drawn discussed a lot in the context of climate change, given that in the climate context, we know there are these real tipping point problems when the kind of West Star tank shield begins to melt and methane gets released from permafrost and all that sort of stuff. So there are potentially significant lessons there for climate issues that we may come back to. So I'm not gonna go through this. This is just gonna have a little bit of a heat map trying to identify which of the various instruments we've talked about is most suitable in different circumstances. But as I said, I won't go through this, but the two points to bear in mind, I think, are just this one that, well, yes, taxation isn't the only response to extra analysis. It often will not be the best response. And in many contexts, something I've already talked about, you may want to combine appropriate instruments. You may want an element of regulation and an element of taxation. And we'll see some examples of that later on. So again, the other takeaway from all this is just this whole point that there are all these distributional effects that we might want to worry about or think about at least when we ponder alternative ways of addressing environmental problems or corrected taxation more generally. So maybe just a touch on a couple of further issues on, so now I'm putting aside that this whole range of instrument choice, focusing particularly on taxation. What are some of the issues we come across then? Well, there's a lot of talk, as you probably know in the literature about the idea of there being a double dividend from environmental taxes in the sense that, well, maybe with environmental taxes, we can actually reduce excess burden, make the tax system more efficient, and address environmental issues at the same time. I think that literature has been extraordinarily uninformative. It's very difficult to see how that can happen unless the initial tax system isn't in some sense optimal to begin with. And if it's not optimal to begin with then, why and when you're reforming it to start from the outset. So I kind of mentioned double dividend rather dutifully. I don't think the literature on that has been terribly instructive. What has been, I think, an instructive insight is to say, well, okay, suppose that we want revenue, so let's now introduce a revenue motive. And so suppose we just have a single kind of indirect tax, we're in a kind of a Ramsey rule world where we're just setting one tax on some commodity. But now suppose that commodity generates some adverse externality. What does the tax rule look like in that case? Well, so now our problem is going to be to maximize, and I'll just try and briefly explain the notation. V of P plus T is the kind of the indirect utility that is gives how well off the consumer is, given that they face a price of P the producer price, T the tax. On the other hand, so that the V is indicating how well off they are. We know against this, however, we weigh some damage at a rate of D that is associated with consumption X of this good. And the consumption X of this good depends on the consumer price plus the tax. And so the first two terms really consumer welfare, given there's some damaging consequence of the consumption of the tax good. And then the final term is to indicate that we care about revenue. So revenue is big T times X, the tax times quantity consumed. And Lambda is then just the weight, the social weight we attached to raising revenue. So Lambda's got to be bigger than one, otherwise we wouldn't bother to raise revenue at all. So if you then grind through that exercise and maximize that with respect to T, you do the optimal tax exercise now with the personality. What do you get? You get the result in that T over P equation there. And with so on the right hand side, we have two terms. The first term, the Lambda minus one over Lambda times one over E, E being the elasticity of demand. That's really just the standard Ramsey rule in this context. So you have the Ramsey, so the optimal tax has this Ramsey component. And then the second term is relates to D which is the damage. So that's where the externality comes in. So you're charging something higher than the Ramsey tax to reflect the damage that consumptive this good does. Couple of points to note there, this is a kind of a simplified form of the kind of, an edit, what's called an additivity principle associated with SAMO that when you have environmental damage of this sort, you basically end up with an additional kind of additive term in your various optimal tax expressions. But the other point to note is that, remember I said that Lambda has to be bigger than one for this problem to make sense. Well, if Lambda is bigger than one, then that final term is less than D. So what does that mean? That means that the add-on, the kind of the add-on tax to the Ramsey component is less than the kind of first best Pigovian rate. That is, you don't simply take the Ramsey tax and then add the Pigovian tax calculated is equal to marginal social damage, you add less than that. Essentially because it's sort of the creative component is smaller than the first best Pigovian term. And that's intuitive because one of the effects of the tax is going to be essentially to amplify initial distortions. Typically, if the initial system is optimal, you can only through by adding another tax increase excess burden. And because you're increasing excess burden, that makes environmental taxation less attractive than the first best calculation I would suggest. So that's, I think, an important lesson. There are some qualifications to it that I think are quite important in practice. But it's again, worth bearing in mind that actually, when we're thinking about, when you're concerned about revenue, that doesn't kind of amplify the environmental tax add-on. It actually, if anything reduces it if the initial tax system is set well to begin with. So this, I think, is an important slide. So let me spend a little bit of time on it. What to do with the money? You've imposed your perfectly calibrated Pigovian tax. Let's go back to the first best world. You've imposed that tax, you've raised some money. What are you gonna do with it? And we know that if you throw it away, that may mean that the whole process has actually reduced social welfare. So what are you gonna do with it? Well, one thing, of course, you can do is simply add it to general revenues and in the sense of financial additional spending through that route. And that's the route I think many people hope, for example, that environmental taxes are going to have untapped potential to meet strong revenue needs in developing countries and elsewhere, particularly with the SDGs in mind. And I guess something like that may be what many kind of public finance people would argue for. Well, they'd say, well, look, it's a tax like anything else. Let's use it with spending as a priority. Let's use it to increase spending. An alternative use that some people advocate is, well, why don't we reduce other distorting taxes? Why don't we, for example, and this is something often heard is to say, well, look, we know the corporate tax is very distorting. So why don't we reduce the, why don't we use the money to reduce the corporate tax? You could think of other taxes as well, the one might reduce. Alternatively, we could actually try to compensate the losers. We could recognize that in this process we have made some firms, some individuals better off. Should we compensate them? So again, for example, if you think about climate issues where we might be raising gas prices and energy prices more generally, should we be actually compensating the people who are now facing higher energy prices? In some sense, in some deeper sense, they are the polluters, but nonetheless, we may think it appropriate to compensate them. Are there actually adequate tools in practice to do that? So, for example, we might think of some developing country. We might think about using biometric identifiers to pay poll subsidies to compensate people. But there's a whole kind of question that we use the money to compensate the losers, which in a way I think would be consistent with the spirit of the initial Pagodian rationale for these taxes, or do we earmark? That is, do we allocate this spending or this revenue that we get from environmental taxes? Do we allocate that to particular purposes? Maybe to environment-related spending. Now, it has to be said, most public finance people don't like earmarking taxes, particular spending in that way, because it kind of makes, you know, it's either meaningless if the earmarking doesn't really constrain how much you spend on a particular item. Or if it does constrain what you spend, well, you might not want to be constrained in that way when some other spending needs turn up. So people tend not to like earmarking in public finance terms. Maybe it can be used on the other, and maybe earmarking can be used as some kind of compensation, either to firms or to individuals, something I remember Yuka's written about. And maybe by earmarking, you know, maybe it's a way of overcoming people's natural suspicion when governments introduce new taxes, that somehow the money is gonna be wasted. So there's a kind of a full menu for you there, of things that you might want to do with the revenue from environmental taxes. And I think that the point I'm making is that this issue here is not just a kind of, a minor add-on when you think about environmental taxes, it's, I think, a large part of the issue. Let me then, in a few minutes, let's say a little bit about some of the applications. And maybe I'll try and speed up a little bit near the end, applications of this idea. Well, of course, the main application, the leading application these days, is in thinking about dealing with climate change, which, you know, next turn calls the mother of all externalities. We know there was a big externality from the emission of global greenhouse gases. Of course, there's a problem, a free rider problem in dealing with this global problem from greenhouse gases that everybody would rather that somebody else did the reduction of emissions. The point I wanted to make when we think about climate change is that, well, if you all say a small developing country, you may well think, look, what I do, and you'd be right to think, what I do makes little difference to climate change. I'm a small country. I didn't cause the problem anyway. So really, why should I do anything? Those are all kind of perfectly reasonable concerns. However, it turns out that burning fossil fuels in particular has caused significant local externalities in the form particularly of air pollution. That is, there are substantial local co-benefits from reducing the burning of fossil fuels. That is, but reducing burning of fossil fuels is not simply good for the global environment. In many countries, it's good for the local environment too. And I think that's possibly the more persuasive case for many such countries as to why they ought to be taxing fossil fuels more heavily than they are. The chart on the right simply illustrates that. It basically illustrates that even if you take account of just the domestic environmental benefits, nothing to do with climate change, even leaving aside climate change, you get very large, potentially very large domestic benefits from effective carbon taxation. You can see in some in China, we're talking about over 3% of GDP in other countries. We're certainly in the sort of significant parts of significant fractions of 1% of GDP. So that's a key lesson. Substantial co-benefits make a difference to the case for fossil fuel mitigation. There's a whole set of issues to talk about as between tax and cap and trade. We might want to think, for example, well, maybe cap and trade is better for climate because of those tipping points that as we can kind of fix with cap and trade, you're fixing the total quantity of emissions. Maybe that's a good plus given these kind of tipping points, given what we were saying earlier on about the importance of those. Well, that's not completely persuasive because some of these things happen quite slowly and you can adjust tax rates over time. Tax can be less prone to exemptions. So the case for carbon taxes in particular, I think still remains strong. People always worry, of course, about the distributional impact of carbon taxes, carbon prices to deal with burning of fossil fuels. It turns out actually, maybe not surprisingly, that the distributional impact of taxing carbon is not necessarily regressive in many low-income countries. You can see that on the picture on the left basically shows is indicating the distributional impact of carbon taxation. And you can see that in the US and China, it's pretty regressive because of a large proportional burden that's borne by the lowest core, the core to quintile. But that's not true in India. In fact, the opposite is true. And that may be true more generally in low-income countries where people are off the grid. So to some extent, they're protected from the increases in fossil fuel prices. So that's all I wanted to say about climate change except that what I've been focusing on has been basically related to fossil fuels, CO2. But that's fossil fuels, but that's not the only source of greenhouse gases. Many others are no less important in many low-income countries. Land use change, agriculture, and there's a whole set of unresolved issues, I think, as to what scope there is for tax measures in those sectors as opposed to regulatory sectors. And that's where I think thinking through some of the issues we were talking about before on instrument choice can be important. So let me maybe just, I'd like to get to the end of this slide because it introduces the, well, I'm gonna introduce the internality idea. So tobacco taxation, close to my heart. Tobacco tax, we know that smoking has many adverse externalities, passive smoking, health risks, unpleasantness, undeniable, all kinds of externalities that are bad. On the other hand, there are some positive fiscal externalities. For example, if smokers die early, then that lowers the pension payments for them and that increases the pool available for everybody else's pensions. So there's a beneficial effect of smoking in fiscal terms. And in some, some writers claim that actually, some of these positive benefits actually outweigh the adverse ones. Again, smokers, we have smokers have, oh, and go into the gory details, but you can see where I'm going. But in any case, some of that is controversial, but I think what is not so controversial is that it's hard to explain why cigarette taxes are so high in many countries, purely on the basis of externality arguments, in a way it doesn't, it tends really not to add up. So why are cigarette taxes so high? And let me make an aside here. Remember that this is supposed to be a corrective tax and we talked earlier about corrective taxes and maybe you want to compensate the losers. And it's not completely jerky, but how come no one feels a need to compensate smokers for the tax they suffer? And I think that's maybe where this idea of sin comes into it. I don't like talking about sin taxes, but there's some notion that it's inherently, inherently a bad thing. Otherwise, I think, you know, I don't know why in some intellectual sense, compensation arguments don't come into it rather, rather more. But so the answer to the question, why are cigarette taxes as high as they are seems to be the rationale now given most commonly is this problem of internalities. What is an internality as opposed to an externality? It's basically the idea of a time consistency problem. That is that when you're young, you might want to say, well, I'd like to smoke for a few years, but then I want to quit. I would like to quit in a few years. The trouble is when that time comes to quit, when you're a few years older, it's become too hard to stop. So it's a time consistency problem in the sense that it's very difficult to go through in the future with what seemed to you to be the optimal decisions today. And so the rationale then for the high tax is to kind of essentially deter people from starting and hence to address nothing to do with externalities or passive smoking or anything, but to help people kind of overcome this time consistency problem by not smoking in the first place. And that argument can be used to rationalize much higher taxes. People are already saying that called for a tax of about $10 a pack in the US 20 years ago, and there's certainly taxes kind of above that now in a number of US states. Some people argue that this is actually even progressive because we know that low income groups tend to smoke more at least in the sort of advanced economies. So some say this is actually progressive measure. Others and I'll leave it to you. Others might say it's actually really just paternalism by another label. So I think let me just take for me two more minutes. You okay? Yeah, sure. I just want to say something. I just want to make a couple of other points. Let me say something about alcohol because this is the kind of the others. I'm focusing on these because these are sort of the well-established taxes that partly have a sometimes given a corrective motivation. Alcohol in particular, we know the externalities are huge from abusive alcohol consumption, road accidents, domestic violence, crime, health, all kinds of things, self-damage, all kinds of internality concerns as well. So the question now becomes or why aren't taxes higher on alcohol? Given all these horrendous side effects of abusive alcohol consumption? Well, one reason I think is the damage from alcohol, it doesn't just depend on how much you drink over your lifetime. It's not very linear. Smoking damages and sometimes kind of linear over your lifetime. So damage really arises from, or some of the most damaging forms of adverse effects, adverse externalities, arise as you know probably when you drink a lot in a very short period. So it can be hard to essentially implement a tax that depends on the next drink that depends on how recently you had your last drink on what was it. So it's harder to reach, it's harder to kind of control the most damaging consumption through taxation for alcohol than it is through tobacco. Another reason may be that if you have, when you have heavy taxes on alcohol, and I don't know if this may be more topical than I thought it was gonna be, you have heavy taxes on alcohol, that leads to bootlegs that leads to illicit production. And same is true of cigarettes, but illicit cigarettes don't kill you any more quickly as far as I know than regular cigarettes. However, bootleg alcohol can, I think as we know, can be really deadly. So there is a real issue with alcohol of encouraging bootleg consumption. So let me, I'm just gonna briefly give you a flavor of some of the current issues that were fit under this heading. I'm not gonna go through them, we can talk about them if you like. And if there's time, I talked about cigarettes. Well, the big issue now with cigarettes is what to do about electronic cigarettes. In a way it's difficult for governments because we know they're less damaging. So you might say, well, shouldn't they have a low tax? Well, it's not clear yet how policymakers react to that. I think there's certainly, they're worried about revenue if people, if they put a low tax on e-cigarettes. So the addiction to some extent may be more on the part of governments and on the part of smokers. But I think that's an area where policy is not yet sorted out. Marijuana in a number of countries is now becoming a kind of a serious revenue raiser. A lot of issues around soft drinks, question of whether we should have heavy taxes on soft drinks as part of the way to deal with obesity issues. Actually, maybe less of an issue in many developing countries in part because they already have quite often taxes on soft drinks, more as a kind of revenue raising item than as anything else. I haven't talked about research and development, which I just mentioned here because that's an example where there may be beneficial externalities. So the correction becomes an extent to which you want to subsidize basic research that may spill over into other areas. There are issues now about beef and dairy. We know that beef and dairy account for a huge proportion of greenhouse gases, 6% of all greenhouse gases from beef. And that does make the question of tax responses in that area a kind of a real one. Many countries talk about taxes on fatty foods. It's not clear why we should do that when in many countries, many advanced countries we don't tax food properly at all. Maybe we should just tax food, say, in the UK. And so this whole issue becomes, well, there's all kinds of areas now where you could think of externality and internality arguments for corrective taxes. But question becomes, where do you actually draw a line if you need to in the kind of tax differentiation this would imply? So, sorry, that's been a bit of a rush. But I hope I've given a sense of this is, I think a more richer area, I think, than I thought it was a few years ago. So back to you, you could see if there's any questions. And sorry, I've run you right into time. Sorry. No, no need to be sorry. That was excellent. That was an excellent overview. Thank you so much. Any people, questions? Yes, please. Yeah, so only the question of why is figuring taxes are so high. I was thinking about how in some countries they can just do like, how it's expected. And then they will give you like a ticket or something. But when it comes to tobacco or cigarettes, there's no way of doing that. So that could probably explain why they can just pass it. Because if alcohol, if they get there, if they taste it, and they find it actually about that. So maybe that could explain. I see we can be like, so tobacco, I don't know. Yeah, I didn't get all of that. But I think you're getting to the point about how, again, coming back to the instrument choice thing, right? That in many cases, and I should have maybe elaborated, you want to have both taxes and regulatory measures to address a problem. So like smokers, as well as the heavy taxation, there are restrictions on where you can smoke. You have to go outside pubs to smoke, which is kind of regulatory measures supporting the tax measures. And as you say, the easiest way for the driving or for the drinking, maybe direct ways in which you can directly monitor and charge people how much they've drunk are the kind of ways, things you've been thinking about. Obviously it has a productive role. But I hope I got you understood you're right. But I think you're dead right. That it's the mix of tax and regulation that matters and the appropriate mix is going to be different in different contexts. Please. Yeah, thank you for the presentation. I was quite hopeful, I think particularly in the arguments between using a tax or regulatory measures. I think my question is more related to the argument that we need to compensate the producers or the smokers. I think I thought that argument. Could you maybe just elaborate a bit more? Because in my understanding, the benefits that was already there perhaps existed because of the inefficiency in the market, right? So then if we try to correct the market by which you still compensate the producers, yeah, so maybe you could just explain that a bit more. Yes, OK. I just want to feel to go back to the picture. So it's really, how much is it this one? I think there's a distinction. When you think about policy, you're starting from some position. Do you want to arrive at an outcome that's Pareto efficient, that you'd want to arrive somewhere from where you can't make anybody better off without making anybody worse off? And or do you care about what happens on the way to that point? That is, do you want to have a Pareto improvement in moving to the Pareto efficient point? So maybe in some cases you don't. But I think in general, we might say that we might say, if we can bring about a Pareto improvement, that would be something we would like. Rather than have one person benefit, and another person lose, even if the benefit, personally benefits, benefits more than the person who loses, we might in general think it would be fair if we could arrange things so that everybody gains. And the point in the externality context is that, yes, you could, by eliminating the externality, you could, if you wanted to, make both people better off. In this example, you can, you know, in this example, you can, in this example, you can clearly that the person who's suffering benefits, they benefit by this whole area beta plus alpha. The pollutee is certainly going to lose the amount alpha, but you could share some of that surplus with the polluter and make them both better off, just because total benefit's gone up. So you could, total net benefits gone up, so you could make them both better off. So I think step one in the argument, the bit I'm trying to put in your mind, I think, is that, well, in eliminating the externality, you could, in principle, make everybody better off. So why wouldn't, why wouldn't, why do you ever not want to do that? And one argument might be, it has to be some kind of moralistic argument, could be that, well, you take the view that that allocation of property rights is in some sense wrong, that it was not, it was not appropriate that I could smoke as much as I wanted, or that this firm could admit as much as it wanted. You could say, well, that was the allocation of property rights, but I don't think it's the right one. I don't think it's fair. So I'm not going to compensate at the person who I'm going to be making worse off. Okay, so that would be one argument. And okay, I'm happy if that's the argument people want to make. I guess I would just sort of like it to be, I'm arguing that's an argument one would try to make. But then there are other contexts, I think where I've, where if I say you should compensate the losers, you would say, well, yes, of course we should. And again, go back to the climate issue. So climate, imagine we're going to raise energy prices and imagine, a little bit contrary to that later slide, imagine when we raise energy prices, well, it actually not perfectly consistent with that slide. When we raise energy prices, the poor are going to be worse off, some of the poor are going to be worse off. Even if the thing's progressive, they're still going to be worse off. So we're raising energy prices to do with this externality and some of the poorer are being made worse off. Well, I guess we'd probably say it's perfectly reasonable to compensate them. We'd probably want to do that. But it's equally true that in the, I had a slight throw every mark, they are the polluters. They were doing, they were doing, they were responsible for the pollution in the first place. So I guess what I'm saying is there's a set of issues there that maybe it's good to elaborate a bit more than we usually do. So I hope that makes some sense. Okay, so we are a little bit over time but there are still two questions. Is it okay to take them? Yes? Please, America. And then, and there you are. Right, some of you will do an additional effect on the building reference just now to be able to contribute to it. When he was speaking on the train effect of a, for example, possible energy pattern, he had said that the study should be, he didn't have that much impact in political countries, right? And then one of the examples is the fact that most of the people are outside of the grid already, so that may have impacted. But then looking at some of what we've seen, one of the things that he increased because of already existing efficiencies in energy price, in that case, which would price it across, I never had it in the market. Wouldn't that have an impact? And just like he said in response to this question that the bar was up in that situation. But in some cases, everyone was up. But it was a small resources that they were to get to that. So maybe to balance how the study came about later that he doesn't have any impact. It should not impact his own when we can, I mean, without experience, we see how it's changed on the level that's in the energy price. Did you get that, Mick? No, I had trouble with that one. I know it was energy prices, but I got, I don't know. It was long, so. Can you speak up a little bit, maybe keep it a little bit? The question is, when you were talking about the distributional impacts, you used the example of positive quality. He said, he was upset that it was low in low income countries that impact wasn't that much. But I'm seeing from normal experience, whenever they then open up almost in energy price, that also affects prices across the market because of the electricity efficiency. The example you gave was being outside of the grid for our communities. But there's also been outside of the grid because the producer also sometimes to buy electricity for himself. So any grid impacts prices across the whole market. But in responding to that question, you had mentioned also that the poor people might be worse off in such a division. So the question is how, if you look at the study by another friend about this law, but from some sort of experience, we see how prices move once they're in energy, getting point in nature aware from. Maybe that might help. I think, thanks very much. I think I got maybe 80%. So it's on this distributional impact. I think, okay, I wouldn't say that the impact on the poor, I wasn't claiming the impact on the poor is small. I was claiming that in the India case, for example, as a proportion of, I think in this case, consumption, it's smaller than it is for the best off. So I was saying the tax in that case seems to be progressive. It still can be the case that there is a large that the impact on the poor in kind of absolute terms could still be large. So I wouldn't say the studies show the impact is small. I think I'd say that they suggest, and it hasn't been done for all that many countries. So I shouldn't be too confident in my generalization, but the claim is that it's not necessarily regressive, but it may nonetheless be a significant amount for the poor, which is why I was saying that, if you do these kind of things, you would, I think, want to think about measures to compensate the very poorest. I think you're asking too about kind of the way in which energy prices get embodied in the whole range of prices. I think that was, if I understood correctly, and that's perfectly true. Of course, there's kind of the indirect effect. And in principle, I believe these studies try to take account of that as I understand, as to the best of my belief, these studies do try to take account of the indirect, you know, they work through the kind of the input output to figure out what the price impact is. So people have tried to take account of that. And I think, so that's the only claim I would make, that in a few cases where this has been looked at, it seems to be, progress, the impact seems to be maybe, maybe not regressive, but that may mean that there's still a kind of a large absolute impact. And that I think does reflect the indirect effects that I think you were mentioning as well as the direct ones. Thanks, a final question, sir. Okay, thank you very much for the presentation. Now, on the issue of what to do with the creative taxes revenue, your fourth point, on the year, you said, most public finance experts do not want this option, but I'm looking at it from a local country perspective, where we already have issues of this money metal revenue that I raised in taxes. And also, given the background that we have a lot of environmental issues back home in our country, what do you advise the setting up of special environmental funds, like say a great fund account, so that in the case where a country introduce these taxes, a certain amount of those monies will be put into those funds so that we can monitor expenditures that are made, but I think with respect to corrections about these issues. And then I'm just opening it up and putting it into the general government funds. I'm glad you asked, because back in 1996, when I was in Essex studying under MIG, we discussed the year more, I think a lot. Well, yeah, so maybe you can answer that when you're good, because I'm a bit taller. No, I'm okay. I'm a little bit torn on these issues, I must say. I think my bottom line is that I don't really like earmarking, because I think it's, you risk end up having lots of nuisance taxes. And there are countries that, once you have earmarking for the environment, then soon you're gonna be having earmarking for health, you're gonna be earmarking for education, earmarking for whatever, for the hosting the next World Cup or whatever it is. And I think that does, you know, earmarking either, if it really constrains your spending, then it's kind of not a particularly good thing, because why should your spending on environmental cleanup be related to whatever your environmental tax is? And there's no necessary link between the two. So you don't want to have a very firm link. On the other hand, if there's not a very firm link, then what are you saying when you earmark? You're kind of just being non-transparent, but I think there is a sense in which, you know, sometimes, you know, if you're willing to play not very nice political games, I think probably there are cases where earmarking has helped to persuade people to accept taxes that maybe in other cases they wouldn't have. There is, I should say, I'm gonna take a minute, whether Yucca likes it or not. So I have a recent book with Jill Slamrod on taxation and basically, you know, trying to make taxation interesting by telling stories from history and so on. The best quote about earmarking is from Winston Churchill when he was Chancellor of the Exchequer in about 1926. But I'm not gonna tell you what the quote is, because then you have to buy the book to find the best quote ever on earmarking, even better than Yucca's writing on earmarking. Was that Winston Churchill? That's the one already, that's the one. So I leave it there. Thanks so much, yeah. This was great. All right, so now we have, yeah, we have prepared for coffee here. Thanks once again, Mick. Thank you. Thanks everyone. Bye bye.