The threat of carbon taxes and other political means of protecting the environment has sparked a lot of debate over the years on whether these types of regulations and interventions promote economic efficiency. Depending on the case, the arguments in defense of these interventions can go two ways: (1) economic efficiency should not be prioritized (philosophical defense) or (2) prices should be changed to reveal true costs (economic defense). I want to comment on the second defense.

My argument here is inspired by Daniel Kuehn’s recent post on free market economics and carbon taxes. Daniel’s point is simple: a carbon tax is an alternative means of nudging the allocation of production (relevant to the creation of pollutant waste) in the right direction. Prices are still the main tool deciding the allocation of goods, but the new price better reflects relevant information (originally not present, and difficult to present because the Coase theorem is inapplicable). This is basic negative externality logic and, I admit, usually, the logic is good.

So, the purpose of this post becomes two-fold: (1) show how externality logic is sound and (2) show why externality logic is not applicable to pollutant output.

The Logic of Externalities

As a means of literally illustrating the problem, I quickly put together the following graph which basically summarizes the problems associated with externalities. Unfortunately, I do not known any type of drawing program other than Paint, which is horrible, and so I am stuck with Excel as my main graphing tool. So, there is no fancy deadweight loss triangle; written instruction will have to suffice. Most readers can probably skip to the two examples.

In the above graph, you see three curves.

The downward sloping curve, labeled “private marginal benefit” (PMB), is the benefit of production that is internalized to the firm/agent (and, by extension, to anybody who transacts with the firm/agent for the product produced); we assume that all the benefits are internalized, or that PMB is equal to the social marginal benefit (SMC).

There are two upward sloping curves, one being dotted so that it is easier to distinguish. The solid line, labeled “private marginal cost” (PMC), represents the costs of production that are internalized. These are costs that are borne fully by the firm/agent and transacting parties. The dotted lined, labeled “social marginal cost” (SMC), are additional (relative to the PMC curve) costs that are externalized to third parties, or parties not directly related to any private transacting occurring. Thus, the SMC curve represents the true costs of production (PMC + externalized costs).

For simplicity’s sake, let us assume that we can objectively define where all these curves lie — in other words, these represent the actual costs and benefits. Under this assumption, we can say externalities represent a loss in efficiency. We can put this in a way that is perhaps more acceptable to stricter free market economists: the costs of production are subsidized by “society” (or, other people), and thus the intensity of production of the product is higher than it would be otherwise (overproduction).

To give you an example of externalities well applied, we will first go through the example of the railroad track and the farmer. Using this as a starting point, I will then show you why the logic may not apply to pollutant waste production.

The Railroad and the Farmer

This is a great example, because it allows us to see why externalities need to be assuaged. Unfortunately, a great example comes with a little bit of math; you will just have to trust that I know what I am doing.

There is a railroad, and this railroad passes by a farm. The railroad makes a certain profit, which is defined by the function R(X) = 4x – .5x2 (the function is parabolic, because we assume that marginal costs begin to outstrip marginal revenue). The farmer makes a constant profit of $10 (let us keep the numbers small), which represents the yield of his crops. However, this farmer suffers some damage with each passing train on the adjacent railroad. The amount of damage is known and is defined by the function D(X) = .5x2. Here are the two functions illustrated (remember D(X) is the amount of damage sustained by the farmer per run, while R(X) is the railroad’s profit),

We can see that some of the railroad’s profits must have the damages on the farmer discounted, because some profit comes at a cost borne by another person (the farmer). Thus, total profit for both (more accurately, aggregate surplus) is defined by π = R(X) + 10 – D(X); or, total profit is equal to the railroad’s profit, plus the farmer’s profit (without the externality), minus the damages borne by the farmer.

How do we decide what the most economically efficient outcome is? You have to see where total profit (aggregate surplus) is highest.

Since the answer we are looking for is related to the rate of change of the total profit function, you have to take the derivative of the total profit function, and you set that equal to zero. That is, the derivative of π = 4x – .5x2 + 10 – .5x2 is taken and it turns out that the most efficient number of train runs is equal to 2. You can even make a table with different number of runs, and you can see the relation that the process of taking the derivative might hide.

You can see the relationship better on the table above. Where economic efficiency lies — according to our hypothetical example — is at 2 runs.

There are two ways that efficiency can be achieved: regulation or the free market. I am not going to go through all the possible regulatory options, because some involve the distribution of wealth (which does not have much to do with economic efficiency, per sé — at least, not when looking only at total profit). Just know that government can regulate to achieve economic efficiency, and right now the government includes the court system. Just an example: the courts can rule in favor of a law that forces the railroad firm to pay the farmer the entirety of the damages suffered.

The market might achieve economic efficiency, as well. This would be the result of the market process, including attempts by the farmer to better protect her property. Alternatively, a court system on the free market would help the farmer protect her property by calling on the railroad company to completely subsidize her costs.

Wait, is not that last free market option almost exactly the same as one of the government solutions? Yes, yes it is. This is the basis for Daniel’s argument that what the regulations he supports are meant for are to protect property rights and promote a more efficient allocation of resources. This is what leads him, and other economists (such as Krugman), to conclude that their solution is essentially a free market one.

There are nuances to the topic of externalities that have not been discussed, are not widely recognized as relevant, and are not even all that clear. For example, the costs of enforcement — if this task is delegated to government — is externalized to the taxpayer. Whatever rule is decided on ought to be dynamic, in the sense that the data might change. For instance, if either the railroad or the farmer install a firewall between the railroad and the farm, the externalized costs will fall (a rule that forces the railroad firm to pay all damages, by the way, would lead to the construction of a firewall, if the cost of the firewall is less than profit earned — but neat rules like these are not always possible). The unnamed nuances will change depending on what type of rule has been implemented and legislation, and what particular institution did the implementing and legislating. This is not to say that the market solution (the market process) does not have nuances of its own.

It is also worth mentioning that simple models like the one I went through are highly idealized. I am not sure that more complex models are much better. Even if more complex models are better, the fact remains that perfection will not be attained. This is true both of government and market solutions. The objective, therefore, is to attain the best solution possible.

Overall, though, this example illustrates Daniel’s point. Externalities cause economic inefficiencies (not just changes in distribution) — they are, in some sense, price distortions —, and it makes sense to help solve these problems.

Pollution

I should start with a caveat: while in this section of the post I question the need for a solution, if a solution is needed then some solutions are better than others. For instance, I think a carbon tax is a better solution than subsidizing wind power.

I think there are several issues at stake. It is worth mentioning that I am just putting my thoughts on paper now (although, I have written about this in the past), and so this post is not meant to be comprehensive in any way. I hope I can just raise interesting objections to government intervention in an effort to internalize all costs related to the production of output that leads to the production of pollutant byproduct.

I. More than an economic one, this is a scientific question. An idealized economic solution can only be found in a situation in which the economists have complete knowledge of the issue at hand. That is, an idealized solution to pollution could be found if we knew the exact data, with absolute precision — in lieu of perfect information, we have to rely on the data we can collect and hope that it is good enough to come up with the best possible solution. But, the data we do have is extremely suspect, and it is become more suspect as it becomes more and more evident that the scientific debate has been negatively skewed (either because of data falsification, or lack of scientific debate, or for whatever other reason might exist). If there is reason to doubt the data, then I do not think that it should be used to quantify the values necessary to search for a solution. On this topic, though, I withhold my opinion, because I am not qualified to give it (even though I am a skeptic).

II. Depending on the cost being discussed, the cost will manifest itself sometime in the future. There is a degree of uncertainty to the values being considered. If there is causality between production of pollution and some type of cost, then you have to know how much pollution will be produced between the range of relevant years. So, if you expect the temperature of the world to rise by 5 degrees Celsius as a result of production of pollution, then it must be because you expect there to be a specific volume of production of pollution. Production that cannot be sold for profit, though, is an important cost to producers, though — they are interested in reducing waste (productive efficiency), if they can find cost-effective ways of doing it. It could be that within three years a new technology is implemented that cuts the production of pollution by half. This would completely change the model. Forcing firms to bear future costs in the present might undermine dynamism which would have lessened the costs, regardless (lessened them to a point, even, that would make them non-existent).

III. More than a criticism, this is a point I want to bring up. These topics, unlike the idealized railroad and farmer example, are highly complex. There are a myriad of relevant factors, and some are completely unrelated to the main subjects at hand. For example, pollution may lead to some outcome all else being equal, but all else will not remain equal. This point, of course, goes both ways; it applies to all arguments.

IV. Like I said in the caveat above, some solutions are better than others. I think, for instance, that if we can find the true social marginal cost (SMC) curve a tax on pollution or something similar is superior than, say, investment into wind and solar power. These types of investments are effectively direct allocation of goods by the government — the government is pouring funds into some industries over others. Instead, the price of carbon production should be increased to reflect true costs, and then entrepreneurs can decide how to invest their money into energy production based on the new constellation of prices.

Going back to externality logic, the crux of my argument is that the true social SMC curve is completely unknown. In fact, one could make the case that where the SMC curve is postulated to be is completely off. A global warming skeptic, for instance, might say that SMC is equal to PMC — of course, evidence must be presented either way. Alternatively, true SMC could be greater than PMC, but the postulated SMC might be so high that any legislation based on it may create greater inefficiencies than inaction would have. Thus, a large part of my resistance is scientific in nature (a topic I cannot really comment on), but the more crucial argument is: we have no way of knowing what the SMC will actually be, since we are talking about a cost that will materialize sometime in the future.

There are grounds to grant Daniel his point about market allocation, as I show above in the railroad and farmer example. I do not think these grounds extend to the world of pollution. As a final caveat, my criticisms refer to some cases of pollution, such as global warming and pollution which may or may not have an effect on your health down the road (this is where point III comes in). In cases where the externalized costs of pollution are well documented and are present costs, then it is legitimate to search for a solution and a solution might be found.