Pigouvian Taxes in Economics. Overview and Explanation

To discuss the concept of a Pigouvian tax in economics you need to remember when you have a negative externality and how that can create a market failure, where you basically have a situation where one person is imposing costs on another person but not reimbursing that person for those costs.
So let's say for example that you had a situation where you have two roommates and one person is a smoker and the other person doesn't like smoke or they're worried about secondhand smoke and so the one person by smoking is imposing costs on the other person, the roommate by their action and they're not if they're not reimbursing or paying the roommate for what they're doing or they don't have some kind of agreement then we have what's called a socially inefficient outcome is otherwise known as a market failure. 

What is a Pigouvian Tax?

What a pigouvian tax is, it's a corrective tax that is set equal to the marginal external cost, and the marginal external costs all that mean is the cost to people other than the smoker, to the marginal private cost. The man is saying "I smoke, this XY and Z may happen to me." but the external costs are the cost to everybody other than the smoker as the roommate. So if you set a corrective tax a per-unit tax on every pack of cigarettes that though the smoker smokes and you basically set it equal to the external cost per unit which is the cost that the roommate incurs for every pack of cigarettes that smoked. By doing that you can actually bring the socially efficient outcome where the smoker is smoking the socially efficient number of packs.

Graphing Pigouvian Tax

So I want to graph this out for you but let's use a different example, let's talk about traffic congestion. It can also lead to a negative externality. So when you have traffic congestion in a city, let's say that there's an additional person who's saying "Should I start driving to work or should I take public transportation." and so they're going to weigh their private costs of doing that. But they're not going to be thinking about "If I start driving that's going to make congestion even worse for other people, that's an additional car and that might make it other people take longer to get to work." People aren't thinking about other people and what their commute times are, you think about your own commute time and your own cost of fuel and so forth. So let me graph how this can lead to a negative externality and how a pigouvian tax can play a role.

So let's say that the marginal social benefit of driving and so instead of thinking of traffic congestion let's actually map this out as miles driven. Let's say we're going to set up a pigouvian tax on miles driven, that'll be the quantity because we're not gonna think of a quantity of traffic congestion. Well, the more miles people drive then the more traffic congestion you're going to have. So we've got the marginal social benefit or demand curve. There's some social benefit from people driving cars and trucks and so forth they need to transport food or there are commercial purposes there are private purposes, people need to go to a hospital there's a social benefit to people driving but the more and more people drive there are less and less social benefits. When you're thinking "I just want to go to the convenience store instead of walking there's less and less social benefit there." Now we can also map out and think about what is the marginal social cost. So let's say we have our upward sloping marginal social cost curve and the marginal social cost is going to equal (the private cost to that person who's weighing whether or not to drive that decision to drive + the external cost the cost to everybody else in terms of increased traffic congestion). There could be other costs to driving a lot of miles to increase vehicle fatalities but let's just focus on traffic congestion to make things easier.

So let's think about these individual people and let's say that we have another upward sloping curve which is marginal private costs. So the marginal private cost to that individual who is deciding whether or not to drive. So they're just going to say what's the cost of fuel if they decide to drive there's going to be a thing about their own private cost. Now you see that there's a difference between the marginal social cost and the marginal private cost. So in equilibrium where we're going to end up is where the actual equilibrium, absent of any pigouvian tax or anything, we're going to be at what we'll call this Q' and this is going to be inefficient, this is the socially inefficient outcome but this is the equilibrium. If free markets reign and we don't do anything, this is going to be the equilibrium. So this is going to be the number of miles driven and let's just say that it's 100 million miles or something like that.

Well, socially optimal is where marginal social cost equals marginal social benefit, from a social standpoint that's where we want to go with the number of miles driven. So we want to be where marginal social benefit equals marginal social cost, that's considering everybody not just that one individual and that is going to be at Q*. So this is going to be the socially efficient quantity, the reason it's you look this is the point E2 where the marginal social benefit intersects with the marginal social cost curve. That's our optimal quantity, so this is efficient. This is the socially efficient equilibrium but that's not where we're at unless we have this pigouvian tax.

Effects Pigouvian Tax

So what the pigouvian tax is going to do is we're going to solve this difference between Marginal social cost (MSC) and Marginal private cost (MPC). Here we've got a way of solving that what we can do is we can actually set a tax. So let's just say for example that we have got the price of $75 at the socially efficient point and we have got another price of $40 at the equilibrium point. The tax would be the difference between these two price, it'd be $35. I'm just throwing numbers out here, I don't know if any of that makes sense in reality but let's throw that out that's this the amount of the pigouvian tax. It's a corrective tax and what you're basically doing is you're forcing that individual to say "I can't just think about my private cost because now this tax got added on." Well, it basically gives you a per unit charge for the cost that you are imposing on other people. So the government is just saying "Look we're going to step in, there's a market failure, we're going to charge individuals for that external cost." So they're not just considering their private costs but they're also considering the external costs and so you can charge them on the number of miles driven. Maybe you tax them if there's $35 per mile driven or something, that sounds ridiculous maybe I should choose a lot lower numbers but you get the idea. So you charge them for the external cost of the activity that generates the negative externality. You have this per unit charge this pigouvian tax and that basically forces the person to internalize this external cost. Now they're not just going to be weighing their own costs and benefits they're also going to be thinking about society.

Double Dividend of Pigouvian Tax

Now here's another thing to think about there's what's called a double dividend with the pigouvian tax. The double dividend or a double benefit what this means is that with the pigouvian tax has been applied to a lot of things right we already talked about cigarettes traffic congestion there are a lot of different people even talk about using it for like capital volatility and so it's a lot of people talking about different ways to use pigouvian taxes to affect to bring about a socially efficient outcome right but there's a second benefit and that's this double dividend is that we're also raising revenue right we're raising tax revenue here and actually this amount and right here and I'm just going to put little stripes there I know I know that's a little maybe I'll just color it in it's a little hard to see I made this a little ugly I apologize but this amount here that's colored in this square is actually tax revenue so this is tax revenue.

So now the government could say "Now that we've got this tax revenue what we could do is we'll use that money to provide wider lanes on the highway." So that'll actually help reduce traffic or they could take the money and they could give it to some kind of issue for early childhood education. They can do whatever they want but the idea is here you're getting two benefits you're bringing about the socially efficient outcome but you're also generating tax revenue that can be used for some other purpose. Now the pigouvian taxes is basically a similar idea to what you might have heard of a carbon tax but with a carbon tax, you're not actually taxing somebody who produces steel. In this process of producing steel, they generate a lot of carbon or greenhouse gases or whatever in that case the pigouvian tax will be directly on the steel output itself but here what carbon tax you're actually you're taxing what's called like an effluent tax. You're actually taxing the emissions and not the actual output. So it's a little bit different but it's a similar thing. Now sometimes people will say hey look you know pigouvian taxes are nice but to know the pigouvian tax we need to know what is the marginal external cost, we need to figure that out and if we don't know that then how can we really set the tax and so forth? Some other people say "Hey look that if we know the external cost then we also know the optimal quantity, we also know the socially efficient quantity and if we know the socially efficient quantity why don't we just set the quantity and say that's the total amount we're going to allow of miles driven or carbon or whatever and that basically leads into the idea of marketable permits otherwise known as cap-and-trade and we'll talk about that in the articles to come.

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