Why equal distribution of income is good

We assume that in an economy consisting of n individuals i₁, i₂, ..., i_n there is a finite total income Y to be distributed. This is distributed so that the individual i_k receives income y_k.
Let U(y) be the utility gained by an individual with income y. We assume that everybody has the same utility function.
One of the most common phenomena in economics is the presence of diminishing returns. The marginal utility is decreasing. We assume that this holds true for the utility gained by the consumers in the economy, ie that U(y) is concave.
Now the total utility gained in the economy is

U = SUM(k=1, n)(U(y_k)).

Application of the Jensen inequality gives that

U ≤ n*U(SUM(k=1)(y_k/n)) = n*U(Y/n)

Equality holds iff r₁ = r₂ = ... = r_n, which shows that total utility in the economy is maximised when income is equally distributed.


A few remarks:
Economics tends to be rather much about providing abstract theories to justify neo-liberal economic policies. When right-wing politicians propose economic policies to distribute wealth from the poor to the rich they are backed up by "hard", "scientific" "fact". When someone claims that it might be right to have more equal distribution of wealth they can easily be dismissed as woolly, normative statements.
This model is quite simple. I have devised it myself. Probably someone else has already thought about it, but I never heard about it when I studied economics. Instead we were taught lots of model justifying minimal state interference in the economy.
Marx claimed that philosophers should not just explain the world, but change it. Well, the explanations of the economists tend to be crap, but in this era of independent central banks they sure have a lot of power to influence society.

1: It assumes that utility is directly related to financial wellbeing. This is ridiculous. Having an equal standard of living can give the (former) poor more leisure time in which to be happy -- but it can also give them more liesure time in which to be depressed. Conversely, if I give you a present, my net resources are less, but presumably my utility is higher, because I've given you a present. There's no logical reason to posit a causal relation between "Having standard of living X" and "Being happy."

Furthermore, to say that utility is based on the disparity in the levels of wealth is to base an economic system on jealousy and schadenfreude. That doesn't sound like good policy to me.

2: It assumes that everyone can and will make the most of their allocated capital. This is a magical world free from junkies and alcoholics, free from stupidity and full of amazing economic and tactical geniuses. In real life, we have to address the fact that some people are money sink-holes, and everyone wastes something, but always in varying degrees. The absolute worst way to minimise the effects of a money sink-hole on the rest of society at large is to take money away from other people and start throwing it at the sink-hole in question. Qlippothic wastefulness best dealt with by economic isolation, letting them only destroy what they can get their hands on. In other words, waste not, want not.

3: It assumes that the utility of individual X has priority over the freedom of individual Y. Let's say "X" is poor and "Y" is rich. Now, let's also assume (falsely, I think) that improving X's standard of living will also improve his persona utility ("happiness"). In order to allocate Y's money to X, we are de facto imposing restrictions on Y to which X is not subject.

On a related tangent, I hardly think that stripping Y of his freedom in order to give X some material satisfaction is going to maximise net utility in society. The same silly argument could be made in favour of slavery.

4: It assumes there's only a limited amount of wealth to go around, and that the main social problem lies in the rich-poor gap. It characterises "right-wing" policies as having the intention to "distribute wealth from the poor to the rich." That's odd, I've never heard of a policy that proposed the distribution of wealth from the poor at all.

I've said it before and I'll say it again: The rich-poor gap is not the problem. There is nothing wrong with the rich getting richer. Good for them. And it's impossible for the poor to get any poorer, because, being poor, they have nothing left to lose. The problem is when an increasing segment of the lower or middle class get pushed further down the economic scale toward poverty.

Anyone can create wealth at no one else's expense, maintaining a baseline and increasing the net wealth of society. Consider this: If I make a robot that can do the work of 100 workers, I've effectively increased my productive power by 9,900%. If I apply this productive power, I've increased my wealth exponentially. Where did this wealth come from? Merely from my own work. Now let's say that I had an investor, a patron who gave me money to live while I was building this robot. But that was under the sole condition that I give him 20% of the wealth I create. Now, my investor was already rich; that's why he can afford to take this risk by throwing money at me for this crazy project. That doesn't matter. I'm still going to be rich, and my investor is going to have even more money to invest in future projects that effectively create wealth out of nothing. Who loses? Nobody. Who wins? Both parties involved. This is the idea of capitalism.

But in case you doubt that wealth can be created out of nothing, let's take a look at a different example. Instead of a robot, let's say I create a sculpture. It does no "work" per se, except insofar as it does what all art does. Now let's say that I invested 160 hours (roughly full-time work for a month) on a budget of $500, the materials cost $300. That's $800. Now let's say I sell the sculpture for $8,000. Where did the extra $7,200 come from? Superficially, it seems that I bilked it out of the sucker who bought my sculpture. But the dollar sign exists only in the trade; the work of art itself is potential value that is, in this case, realised to a value of $7,200. The person who spent this money didn't lose that much wealth, however, because he still has the sculpture, which he could later sell, possibly even for more, and from which, in any event, he presumably derives some satisfaction. The wealth itself was created out of nothing, on the basis of inspiration -- "made out" of the inspiration in a strictly figurative sense.

And in case you want to argue that the workers replaced by the robot are harmed, you're assuming that I'm taking something away from them that they're somehow entitled to. Not so. There's nothing standing in their way of doing the same thing I did. Give the workers some startup capital to pursue education and become robot builders and maintainers themselves. There is always a demand for labour of some sort; the workers who have been laid off in favour of robot-work must get new training and find a new trade, and while this is a hassle, it is not a harm.

The implementation of new technology does not reduce the funds of the workers. It eliminates their income; there is a huge difference. The workers own all the funds they have at any given time; but do they own future, counterfactual funds that are currently under the ostensive control of the investor? I think that's silly. Until the investor pays them, the money is not theirs.

Nobody has a "right" not to be made obsolete. They have freedom not to become obsolete. Education! And before you challenge that education costs money and time, remember that labour is always in demand, and it's often in an employer's interests (or potential employer's interests) for his employee to acquire new skills, and therefore many employers will fund some education for their employees. But this is very different from having it be the investor's obligation to keep throwing money down the proverbial drain because the workers won't get an education.

5: It involves an absurd degree of enforcement. Let's say X and Y are friends in this "wonderful" economic system. Now, let's say X gives Y a present. But uh-oh! X isn't allowed to do that; or more to the point, the state must then take away Y's present and give it back to X. X has attempted to change the balance of equal distribution by reducing his wealth and augmenting Y's. To maintain a strictly equal distribution, gifts would have to be outlawed!

Arguments of the type presented above are not revolutionary; they've been around for hundreds of years. The Levellers, for example, were an English sect that sought to apply this model and "level" all social classes. But except on the small, communal scale, which is a private enterprise, equal distribution becomes impossible and quite undesirable, actually hindering the advancement of the standard of living. If you and a group of like-minded individuals want to implement this model, capitalism permits that; but capitalism and its benefits would be quite impossible to start up in a state-enforced equal distribution paradigm.

You can't create a system in which no one will be oppressed. This is because systems do not run themselves; they are run by people, each with his own agenda, and people will always figure out ways to bend systems to oppress people. The debate is whether or not this kind of power should be concentrated in the state (as an equal distribution paradigm would demand), or decentralised and diffused throughout the populace (as capitalism suggests). I think democracy and freedom are better served by a free market, even if taxes are skimmed off the top.

Noder's Note (April 2, 2003): Coming back to this now, I realized I left out one important point, relating to the law of the market and to Mises's Socialist calculation problem.

6: Trying to make everyone equally wealthy ends up making everyone equally wretched in poverty. If economic inequality was part of a process by which the worst poverty was alleviated or even eliminated, wouldn't inequality be preferable to equality? If the very nature of the act of trying to control the economy destroyed it, but the very nature of the processes of market exchanges tended to improve the material standard of living of everyone participating, wouldn't the inequality be worth it? Of course, these might seem like contentious claims; but economics is a strange science. If you want explanations of the law of the market and of the socialist calculation problem, follow those links.

Note: The content of this writeup has become redundant by the nuking of TheLady's writeup which used to be right above mine. The rest of my writeup is preserved below:

TheLady: If a machine is invented that can do the work of 100 workers, what should be done for the sake of the poor workers? Ban its use? Lynch the inventor?

Perhaps society would be better off before the invention of the loom, which drove thousands of cloth weavers out of business as it allowed one person to do the job of many. How about the printing press? Before that was invented, books could only be copied by hand, a painstakingly long process. Goodness knows how many book copying monks were told that their services were no longer necessary ...

Yup. That's capitalism for you. If you don't like it, I suggest that you start learning how to weave.

TheLady again - Technological change tends to be stepwise rather than gradual. There will always be sudden changes in the workforce. The workers can either adapt, find new work elsewhere or they can be retrenched. It is that simple.

The other thing is that capital risked for development of the same robot did not come out of the workers who have yet to be retrenched. Someone with money (not necessarily even someone from the same company) risked his/her money in order to develop the new machine. That the workers become redundant is coincidental.

It is the way of things. It happens all the time in nature but when it happens to humans, all sorts of whining usually eventuates even though it there usually are all sorts of warning signs long before the eventual deadline.

The important point here is someone risked money in development. All too many projects die and the ones that survive tend to do well because they have proven that they can survive in the marketplace. People lose money on failed projects.

As I see it, the best economy is one where interference from the government is limited to ensuring that nobody breaks the law. Trying to fiddle with interest rates, taxation policies and the currency markets is like trying to wash your car with a lever controlling the release of water from the Hoover dam as your tap.

There is one grand fallacy in the model proposed here: it assumes too much. Cletus has done a good job of outlining most of these, but he missed one very important one:

We assume that everybody has the same utility function.

For this to be true, it would require that all people are able to perform every single known type of job, all at equal levels of ability. This is quite clearly false; different jobs require different levels and amounts of training, and in addition to this some people can simply perform a given job better than others can, for reasons that can't really be explained (but are often attributed to innate talent or simply blind luck). Perhaps the two most extreme examples of this are the fields of medicine and law. Both require years of training beyond even college, and there are very good reasons for this. I would not want a lawyer performing my heart surgery any more than I would want a doctor arguing the Microsoft case.

It should be pointed out here that if wealth were distributed equally to the current per capita income of the US (slightly over $30,000) no one would be able to afford medical school or law school, and thus there would be no doctors or lawyers. Since income is meant to be distributed equally, there would be no chance for loans under this system (as they would upsst the artificial "balance" of wealth). Whatever you may think of lawyers, clearly this scenario would be disastrous.

Another note: resources, even wealth, are finite. It is assumed that equal redistribution of wealth would raise the standards of living of the majority, but this is not true. The median income in the US (the point at which 50% of the people earn a greater amount and 50% earn less) is actually much higher than the mean, which is often called per capita income. So in the end, more people will suffer under this system than will gain from it. I doubt this is what anyone wants.

And one final thing: many here speak of "the gap between rich and poor" as if the current distribution of wealth were actually that clear. The fact is, it isn't. Our economy is not a pyramid with the rich on the top and the poor on the bottom; in the end it is more like a diamond. There are a very few extremely wealthy people at the top, and there are some poor at the bottom, but by far the most people are somewhere in the middle (and in fact, in the current economy the widest point of the diamond is somewhat above its vertical center). In other words, the distribution of wealth is not equal at this point, but it does follow normal distribution ("normal" being used in the statistical sense).

In the end, while this may not be perfect or ideal, it may well be the best we can hope for given the non-ideal world in which we live. It sounds callous, I know, but you cannot end the suffering of the few without causing the many to suffer. Given this, the best we can offer is equal opportunity to succeed, while acknowledging that this does not necessarily guarantee equal results.

History is filled with well-meaning, bright young men who decided that they could make things work. History is also filled with the horrible and frighteningly swift collapses of these societies.

It can be seen time and time again that the societies and countries which allow the greatest amount of freedom (especially economically) are the same societies and countries which grow and thrive and survive.

Bright young men think they can make things work. They think that people can be forced into a certain mold that works better.

Older, 'disillusioned' men know that they can't make things work. They know that people tend to break the mold they're placed in, even if it was 'for their own good'.

Brilliant men, men like Thomas Jefferson, realize that you can't make things work, but you can create a system that allows things to work. This system is called Democracy. This system is called Capitalism. In all it's alleged unfairness, all it's supposed bloody-mindedness, it is a hundred times better than any other way of living together. For all it's flaws, it's the best we have.

I'm not saying you don't mean well. But just having good intentions doesn't count for much when the stakes are this high and the scope is so broad. Learn from history, lest we repeat those mistakes. Monarchy, tribalism, Communism, socialism of all flavors, anarchy, Empirism, they've all failed. Democracy works. Capitalism thrives. It's the best we've got.

But that's neither here nor there. I would prefer to reply to Cletus the Foetus' writeup. Although I agree in general with him, there are some specific statments that I quite disagree with. Specifically:

In point 1: "The fulfillment of envy is *not* utility!"

Actually, it is. We are defining utility for the sake of this discussion to be happiness and well-being. Envy is something that produces unhappiness. So to remove that unhappiness is to increase utility. Of course, that action may have other effects that create unhappiness in other ways, but on the face of it, your statement is incorrect.

In point 2: "some people are money sink-holes"

Specifically, you mention alcoholics and other drug addicts. How is an alcoholic a money sinkhole? She goes to work, earns money, and spends it, just like anyone else. If capitalism produces that which people want, and people want alcohol, it will produce alcohol. You can't claim that capitalism leaves people free to make their own decision but that people must make certain decisions for the good of capitalism.

In point 3: "The same silly argument could be made in favour of slavery."

Perhaps. The problem with slavery is that freedom makes people happy, so that enslaving certain people would have to put other people in a state of unending bliss in order to balance things out, utility-wise. Combined with the difficulties in maintaining a state of slavery, as well the dehumanizing aspects of the matter, it means that a system of slavery will never produce an increase in utility.

This is not to say that freedom trumps utility as a value. If it made people happier on balance to have a slave class, then having a slave class would be the right thing to do. To be unfree and happy is better than being free and unhappy. You cannot say that it is impossible to be unfree and happy, since you have above suggested that a lack of leisure time can keep the poor from being depressed.