Pigouvian Tax

In previous videos, we've emphasized that a price is a signal wrapped up in an incentive, and that prices coming out of free markets coordinate individual actions in just such a way that the outcome looks as if it were created by a benevolent invisible hand. We've shown how price controls can impede this process. And what we want to show now is that even with the free market, sometimes the price isn't right. In particular, when we have externalities -- external costs, and external benefits, which I'll define more in just a few minutes -- then the price isn't right. So what we want to do in this video is show both the causes and the consequences of external costs and external benefits. Let's get going.

Let's begin with the rise of the super bugs. These are bacteria which are now resistant to our antibiotics. Before the age of the antibiotic, even a simple skin cut or a bruise or scrape could kill people due to the infection. And people who were more seriously injured, for example in battle, most of them died not because of their battle wounds, but because of infection which took place after the wound, because of the wound. In the 20th century, the miracle of antibiotics meant that far, far fewer people died from these infections. But that miracle is now coming to an end, as our antibiotics are no longer as effective as they once were.

Why is this happening? Well, part of the problem is that no antibiotic is always 100% effective. And bacteria, like people, are diverse. They have different strengths and different weaknesses. The bacteria which are not killed by an antibiotic -- which happen to have certain characteristics which make them strong against that antibiotic -- those bacteria propagate and survive and become more dominant. So, the evolutionary process has led to resistance. We, however, are not entirely innocent in this process. Resistance has been helped by the overuse of antibiotics.

So why are antibiotics overused? The fundamental reason is that users get all the benefits but do not bear all of the costs of antibiotic use. Each use of an antibiotic creates a small increase in bacterial resistance, at least in a probabilistic sense. But bacteria don't stay in one place or one body. They spread throughout the environment and indeed throughout that world. So an increase, that cost, that increase in bacterial resistance is a cost borne by everyone, not just the user of the antibiotic. We can think of using an antibiotic as creating a little bit of pollution, of polluting the environment with more resistant and stronger bacteria.

This is true when somebody, for example, uses an antibiotic when they have a virus which the antibiotic doesn't help with, rather than when they have bacteria. That's a cost. It's a cost because that use of the antibiotic then generates more resistance, and that resistance spreads around the world. Farmers who use antibiotics, not to combat disease in their livestock, but to help the livestock grow faster, also create more bacterial resistance. But that resistance is something they don't include in their calculus of costs. They don't pay attention to those costs which are borne by other people. When antibiotic users ignore the external costs of their choices, we get overuse. Since some costs are ignored by the decision makers, we get overuse of antibiotics.

Okay, well, with that as an introduction, let's define some terms. Private cost -- this is the cost paid by the consumer or the producer. External cost -- this is a cost paid by bystanders, by people other than the consumer or the producer. It's a cost paid by people other than those who are buying or selling in this particular market. The social cost is the cost to everyone -- the cost when we take into account consumers, producers and bystanders. In other words, it's the private cost plus the external cost.

Externalities -- this is simply another word for external costs or external benefits. We'll talk more about external benefits in a future talk. In other words, externalities is just another word for costs or benefits that fall on bystanders. When there are significant external costs or external benefits, a market will not maximize social surplus. Now, remember we showed earlier that a market maximizes consumer surplus plus producer surplus. That's always true for a free market. However, what we've just learned is that an external cost is a cost that falls on bystanders, not on consumers or producers.

So social surplus, which is consumer surplus plus producer surplus plus bystander surplus -- that's ultimately really what we care about. We care about not just about consumers and producers, we care about everyone including bystanders. So we want to maximize social surplus. However, when there are significant external costs or benefits, the market is not going to maximize social surplus. It's going to maximize consumer surplus plus producer surplus. But that's not everything. When the costs and the benefits to bystanders are not counted, then we're not going to maximize social surplus. In fact, we can say things a little bit more precisely, and we'll do that next with a supply and demand diagram.

Okay, here's our standard diagram with the quantity of antibiotics on the horizontal axis and prices and costs on the vertical axis. As usual, the equilibrium is found where demand intersects supply, or where quantity demanded is equal to quantity supplied. Now the key point here is that the supply curve is based on private cost -- basically the cost of producing the antibiotic. But there's another cost. Every time an antibiotic is produced and consumed there's a cost of bacterial resistance, a cost borne by all of us, by bystanders. There's an external cost and that is not taken into account by the suppliers. So this external cost doesn't go into the price.

Nevertheless, what we really care about is the social cost of antibiotic use, not just the cost of producing the antibiotic, but also the cost of actually using it, including the external cost. So, the market equilibrium, the market quantity, is found where the market demand and supply curves intersect. But the true efficient equilibrium, the equilibrium we would like to be at, is where the demand curve intersects the social cost curve. So, the efficient quantity is less than the market quantity, thus we have overuse. The market doesn't take into account all of the costs of antibiotic use so we get overuse relative to the efficient equilibrium. Now we can actually show this in another way.

Let's look at the value of the marginal unit, the value of the unit, the market unit, the last unit the market produces. What's the private value, what's the value of this unit? Well, it's given by the height of the demand curve. Now, what is the cost of that marginal unit, of that last unit consumed? Well, the private cost is given by the private supply curve, but the social cost is given by the much higher social cost curve.

So notice on that last unit, the cost of that last unit is much larger than the value. That's the sense in which we have overuse. We don't really want to produce this last unit because the cost is greater than the value. Indeed, if we don't want to produce this unit, we don't to produce any unit where the social cost is greater than the value. So in other words, this area right here is a deadweight loss. These are the units for which the social cost is greater than the private value. Therefore, these are the units we don't want to produce -- this is the deadweight loss and this is the overuse of the antibiotic. What conclusions can we make? When there are external costs, output should be reduced to maximize social surplus.

Another way of thinking about this is for determining the efficient level of output, who bears the cost is irrelevant. The fact that these costs are borne by bystanders is irrelevant -- we want to take into account all costs, not just the cost to the suppliers. The problem is, is that when other people bear some of the cost of production, the price is too low. Not all of the costs are reflected in the price. As a result, the price is sending the wrong signal. It's incentivizing too much production. Because the price is too low, antibiotic users purchase too many antibiotics and we get overuse. The solution to this, or one solution to this, is in what's called a Pigouvian tax -- a tax on a good with external costs. Let's take a look at how that works.

The idea of a Pigouvian tax, after the economist Arthur Pigou first talked about these ideas, is pretty simple. The market equilibrium is down here. The efficient equilibrium is here. The problem is that the suppliers aren't taking into account all the costs of their production. They're not taking into account these external costs.

So how could we get these suppliers to take into account all of the costs of their production? Well, one way of doing it is to tax them. A Pigouvian tax equal to the external cost makes the private cost plus the tax, the total private cost, equal to the social cost. Let's remember how we can analyze a tax. Remember that one of the ways to analyze a tax is to shift the supply curve up by the amount of the tax. So, if we impose a tax on the suppliers equal to the external cost the supply curve will shift up until the private cost plus the tax is equal to the social cost.

In this case, we will now have the efficient equilibrium will be the same as the market equilibrium. The market will internalize the externality. All of the costs, private cost plus the tax equal to the external cost, will come to be reflected in the price. And because all of the costs are reflected in the price, consumers will buy the efficient quantity of the good. So, that's one way to handle an external cost problem.

In the next couple of lectures we'll be talking about external benefits, and we'll also illustrate some other ways in which externalities can be handled.