Diminishing returns to cigarette tax?

   I've recently read a newspaper commentary on cigarette tax, using some economics concepts for analysis. You may notice that I have already written an article on cigarette tax, which is exactly a response to an article that uses economics to analyze the issue. In other words, now I encounter another article -- both uses economics and both cast doubts on the usefulness of cigarette tax!
   I do not know whether this is a coincidence or not. I simply wonder: Are there really so many people wanting to use economics to support their arguments? Is it really so indisputable that economics will cast doubts on cigarette tax?
   Anyway, as an economics teacher, I am not really interested in why the coincidence will happen. But I am interested in the economics argument used. As mentioned, the recent article uses some economics concepts to downgrade the use of cigarette tax. Does the article use the economics in a valid way? This is what I am concerned with.
   What the article says? Basically it uses two concepts -- the law of demand and the law of diminishing marginal returns -- to explain what has happened for cigarette consumption in the recent decade. What has happened? The article presents us the data: Cigarette tax has been raised substantially three times in the past 10 years -- 50% in 2009; 41.5% in 2011; and 11.8% in 2014. Meanwhile, the share of cigarette smokers in the entire population declined by only 2 percentage points, in a sharp contrast to the reduction of the share from 23% to 15% attained from 1980s to 1990s.
   The article says that the sharp reduction of smoking rate during 1980s and 1990s can be explained by the law of demand. When price increases, quantity demanded decreases.
    Then, the article says that the market of cigarette can be indeed divided into two blocks: price-sensitive smokers (including new and young smokers, and non-addictive smokers), and price-insensitive smokers (including addictive and long-time smokers). It continues to say that the tax hikes have scared off most price-sensitive smokers, and the effects will be small on the price-insensitive smokers if tax rate is to be raised again. Then, the article says that this is also what is predicted by another economics law -- the law of diminishing marginal returns. What this law means? Using the article's own explanation, the law means this: If the same action is taken, the new action will bring about smaller and smaller extra effect.
   In my view, the article does not explain the meaning of the law of diminishing precisely. But this is not my main point. My point is: can we use this law to explain why smoking rate drops slowly in the recent decade? If you understand what the law means, you cannot but conclude that the law is completely irrelevant to the phenomenon.
   Firstly, the law is about production, not consumption. For the law to be valid, the production activity needs to involve two inputs or more. If two inputs are required to produce a good but only one input increases, eventually the marginal product will decrease. That's what the law means. From this perspective. we can't see how it is relevant to the fact that cigarette consumption decreases slowly.
   Secondly, we have to understand why the law is valid. If we don't understand, then we may be moved by someone's saying like this: although cigarette is about consumption, the same logic may still be applied to consumption, and we should not be so rigid in applying an economic law. However, if we understand why the law is valid, we can clearly get that the law is not applicable in the case of cigarette consumption.
   Then, why? The key point is, again, two inputs or more are involved in producing a good. Since two inputs are required, using one input is not an option. Otherwise, why don't we use only one input? If two inputs are required, this also implies one input cannot perfectly replace another. The difficulty of replacing one input by another also increases when the ratio of one input to another is increased. This is because one input is too few relative to the increasing amount of another input. This is a congestion effect. A typical example is this. Workers and factory workshop are needed for producing a good. If we simply increase the workers, with only the same size of the workshop, sooner or later the workshop gets crowded. Workers find it difficult to move inside the workshop. The additional output by employing more workers is smaller due to the congestion effect.
   Now, is cigarette consumption tax subject to the same congestion effect? The issue is not a two-input or two-factor issue. The issue is not increasing one input or one factor but keeping another unchanged. How can we say diminishing marginal returns applicable to cigarette tax?
   Well, let me be more sympathetic to the article writer. Perhaps the writer means the law of marginal utility (or marginal benefit) instead of marginal return. The former is exactly about consumption while the latter is about production. Perhaps the writer intends to attribute the slowly declining cigarette consumption to the law of diminishing marginal utility (or marginal benefit) but he cited another law by mistakes.
   If this is the case, my first response is: don't try to show off your economics knowledge if you are not really familiar with it. My second response is: this is still not valid. The law about marginal utility or benefit can't help explain why consumption is declining slowly. If we derive smaller and smaller utility or benefit from a good when the quantity consumed of the good increases, other things being equal, we are willing to pay a lower and lower price for the new quantity. This is reflected by the downward sloping demand curve already (but there are some complications involved and we set aside this problem here; interested readers may read my earlier post). But it has nothing to do with the demand curve being steep or flat.
   In fact, in terms of the shape of demand curve, you need a convex demand curve to reflect that situation that the cigarette consumption declines slowly when tax is very high. What is a convex curve? A convex demand curve looks like what you will have if you turn the symbol  (  anti-clockwise by 15 degree -- it is steep when price is high and flat when price is low. While this is a possible shape of the demand curve for cigarette, diminishing marginal utility (or marginal benefit) cannot explain it as mentioned.
   In conclusion, I think the article writer is simply wrong in applying the law of diminishing marginal returns or utility to the case of cigarette tax. The writer is obviously not very familiar with the precise meaning of some economics concepts but still try use it to support his own arguments. On the one hand, I am glad that people try to apply economics to argue as this shows that people think that economics is useful and using economics will enhance the persuasiveness of arguments. On the other hand, I am sad that even elementary economics concepts like the above laws are not well mastered. The road for economics education and popularization is long.

Herd immunity as a public good

   Most economics students at high-school level should have encountered the concept "public good" already. Usually, they will be given examples like national defense, lighthouse, streetlights, fresh air, etc. I recently read some articles in relation to the current pandemic. They discuss herd immunity as a public good. It's timely that we use this example to explain the concept here.
   The "herd immunity" mentioned by the articles refers to vaccination that prevents widespread infections of a disease. It does not refer to an idea that is now proved to be a disaster -- allow more people to get infected by a disease (covid-19) so that a large part of the people in a community gets immunity and will not infect the rest of the society.
   Herd immunity in relation to vaccination is a much better idea than taking the risk to get infected first. But it is still not free of controversy. Some people (including influential people) believe that vaccination is unnatural, will cause severe side-effects, and does more harms than benefits. These accusations are not completely wrong though may be exaggerated in some aspects. Of course, these arguments were formulated before the covid-19 outbreak. They are more about flu, and covid-19 is more dangerous than flu. But these arguments cannot be simply ignored. We need some arguments for vaccination. The articles I read argue for the moral duty of accepting vaccines. They are not economics articles but try to use some economics concepts like public good.
   If many people have already taken vaccines, they are immune to an infectious disease. The disease cannot be easily spread in such a society. This is said to be a public good by the articles. Why? Recall the definition of public good. The good is non-rivalrous and non-excludable. A good is non-rivalrous if someone's taking it will NOT diminish its availability for others (such as streetlights). A good is non-excludable if there is no (easy) way to prevent one from taking or enjoying it (like fresh air) within a scope (say, in a city) when the good is already there. Now, herd immunity is both non-rivalrous and non-excludable. If most people are immune to the disease already, it is not easy for you to get infected. Your low risk of being infected will not make others more risky. Others still can enjoy the low infection risk. Also, you cannot prevent others from enjoying this low risk.
   If herd immunity is a public good, so what? To these article writers, they argue for the moral duty to take the vaccine so that immunity can be established at the community level. If few people take the vaccine, there is no significant effect at the social level though the few who have taken vaccine can protect themselves. But most people, without taking vaccines, will not run on street with a sense of safety. So, people should take vaccines. They should be told to do something good for the community.
   To economists, perhaps we tend to argue for policy supports. From an economic viewpoint, voluntary contribution to a public good will normally lead to under-supply of the good. If taking vaccines involve bearing a private cost (the side-effect of taking vaccines as well as monetary cost), and if others choose to take vaccines already, you are still safe without taking vaccines yourself. You are said to be a "free-rider" in economics. When many want to free-ride on others' providing the good (waiting for others to take the vaccines), the supply of the good will be too low. Therefore, some policy supports are justified, for example, subsidizing the vaccine costs. Of course, like what the article writers do, moral persuasion may also be done.
   Some public goods may be, or may be turned, excludable. For example, people living near Disneyland may free-ride on the fireworks displays sent from the theme park. They can watch the displays remotely but have never paid the theme park entrance fee. The good is non-excludable. But is it? In fact, before Disney builds a theme park, it will find site farther away from residential area and often requires the local government not to build new houses near the theme park. This effectively "excludes" those free riders from enjoying the good without paying. If a public good is excludable, we have a stronger case for voluntary contribution (like what Disney does). But in the case of herd immunity, it is not. So, voluntary contribution is less likely.