One of the greatest threats facing society is the rise of inequality. I think that many people, however, don't quite have a good grasp on
why inequality is a serious problem for society. Many arguments against inequality seem to be made on a moral basis, not an economical one, which while important, is only half the story. I think that it is important to recognize both.
It is important to note that some degree of inequality isn't always a bad thing. There are many times that equality is also inefficient. As I make the case for the inefficiency of excessive inequality, I will also make the case for the inefficiency of perfect equality. This may sound counterintuitive, so I want to make my position clear: there is an "ideal" amount of inequality, but the US is likely far beyond it.
An analogy from chemistry will help to illustrate this idea. In physical chemistry, we learned about a phenomenon known as the Boltzmann distribution. For those who are not familiar with it, a quick introduction is in order. The Boltzmann distribution shows the proportion of gas molecules which carry a certain energy at a certain temperature. On the x-axis is the energy carried by an individual atom, while the y-axis shows the number of molecules at that energy level. As can be seen from the example diagram, to some extent the Boltzmann distribution is similar to the normal distribution, but it has a long right-sided tail.
The Boltzmann distribution explains many aspects of chemistry which I find incredibly interesting, but the important note is that for a gas at a given temperature, even though the average temperature of all the atoms may be 100K, or 200K, or 300K, the natural state will have many molecules above or below that. It may seem counterintuitive that some molecules of a gas at 100K will be moving faster than the average speed of the molecules of a gas at 300K, but the Boltzmann distribution shows us that although they may be few, they are present.
The Boltzmann distribution can be explained (at least partly) using entropy and probability. Suppose that there are 10 atoms, and 20 units of energy to be divided among them. The average value, regardless of the distribution, will be 2 units of energy per atom. However, if the energy is randomly distributed, the odds or this occurring is quite low.
To understand why, let's imagine a system which contains exactly 3 atoms, and has 3 units of energy. If we randomly distribute the energy throughout the system, it is easy to see that the average is 1 unit of energy per atom. However, the most equal situation, where each atom gets exactly 1 unit of energy, is not the most common. To demonstrate, let us randomly assign the first unit of energy to one of the 3 atoms. It doesn't matter which one we assign it to, so in this case it will go to atom A, but in reality, at this point which atom gets it does not actually change the distribution, since all the atoms are equal. When we assign the 2nd unit of energy, we have a 1/3 chance of assigning it to atom A again, and a 2/3 chance that it goes to an atom which doesn't already have a unit. From there, we can assign the third unit, which gives us 9 possible states, some of which are actually "degenerate," or equal, to each other.
| Atom | I | II | III |
| A | | 2 | 3 | 2 | 2 |
| B | | 0 | 0 | 1 | 0 |
| C | | 0 | 0 | 0 | 1 |
| A | 1 | 1 | 2 | 1 | 1 |
| B | 0 | 1 | 1 | 2 | 1 |
| C | 0 | 0 | 0 | 0 | 1 |
| A | | 1 | 2 | 1 | 1 |
| B | | 0 | 0 | 1 | 0 |
| C | | 1 | 1 | 1 | 2 |
If we consider every possible state of the system, we can see that there are really 3 possible distinct distributions: the first state is where each atom is equal, the second is where one atom each has 0, 1, or 2 units, and the final is where one atom has all 3 units. The table shows that during the distribution, 2 in 9 systems will have an equal distribution, 1 in 9 systems will have all the units allocated to one atom, and the remaining 6 in 9 will distribute the units in a 0, 1, 2 fashion.
As you can see, only in about 20% of the hypothetical systems do we see an "equal" distribution. The majority of the cases have a some degree of inequality. Indeed, 10% of the total will have the maximum amount of inequality possible in this system. While it is possible to rearrange the system such that equality is achieved, this takes energy. This energy needed to arrange the system is related to the concept of entropy. If we now take the total number of atoms with each level of energy, we can see that the Boltzmann distribution is beginning to form - fewer than half of the atoms which actually have the average energy value, despite it being overall the most common value.
This distribution is not some fluke due to the small size of the demonstration. In fact, the distribution becomes more and more pronounced as the number of atoms becomes larger. For a system like ours, with only 3 components, there is a 33% chance that you observe something "unexpected." But if you have even just a gram or two of gas, with its trillions of atoms, any significant deviation from the Boltzmann distribution, even as little as 1 or 2%, is unlikely due to the sheer quantity of atoms.
The Boltzmann distribution is not static, either. At higher temperatures, when more energy is allocated to the system, the average energy will increase, but the inequalities will be magnified exponentially.
Now let's bring this conversation back to the discussion of economic inequality. I postulate that the principles which guided the organization of those atomic microstates are also relevant to the real world economic state. If this is true, there are several important corollaries. First, that inequality is not a sign that the system is broken, but rather an expected result of resource distribution. Second, that to eliminate the inequality entirely would take work, which could be an inefficiency for the system.
But instead of focusing on inefficiency of equality, which is not as pertinent to the current state of our society, I want to hone in on the inefficiency of inequality. Let's look at that distribution again, but now let's replace the atoms with people, and the energy with wealth.
We can see that in most societies there will be some degree of inequality, yes, but that the most unequal societies are also not the norm - the society which gives all of its wealth to just one individual, in this case, makes up just 10% of the total possibilities. Conversely the perfectly equal society is also fairly rare, with just 20%. Overall, the majority will feature some degree of inequality, but not to an exaggerated degree. Just as it takes energy to rearrange a state to be perfectly equal, it also takes energy to rearrange a state to be unequal - what's important isn't the direction of the movement, but rather the deviation from the expected state.
In real world terms, what that means is that we need to determine if the degree of inequality that we are currently experiencing in the United States is due to the natural distribution of wealth and resources. If that is not the case, then something must be keeping the distribution from its natural state, resulting in inefficiencies - or in other words, the system needs correcting.
What might these inefficiencies look like? Anticompetitive behavior, fraud, criminal activities, overworked sectors of society, corruption, political favors and excessive lobbying. Anything that serves to concentrate further wealth and resources in the hands of those who already have it, at the expense of the whole, would lead to inequality and could distort the distribution.
More importantly, these activities also effectively weaken the economic base of the nation by wasting time, energy and capital on detrimental activities, while also enabling further such behaviors in the future.
To be clear, an individual who becomes fantastically wealthy, and in doing so increases the GDP of the nation as a whole, is not a sign of distortion. The problem is if an individual accumulates wealth by concentrating it via redistribution from the lower end of the distribution and not through wealth creation.
Clearly humans are much more complex than atoms, and so it is difficult to know what the ideal distribution is. Wealth inequality has increased dramatically over past 50 years, but is that because there has been an overall increase in wealth to be redistributed, concentrating practices, or some combination of both?
Comments
Post a Comment