Here is an economic model suggesting that an equal distribution of income maximises the utility gained by people in an economy.

We assume that in an economy consisting of n individuals i1, i2, ..., in there is a finite total income Y to be distributed. This is distributed so that the individual ik receives income yk.
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(yk)).

Application of the Jensen inequality gives that

U ≤ n*U(SUM(k=1)(yk/n)) = n*U(Y/n)

Equality holds iff r1 = r2 = ... = rn, 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.

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.

The road to hell is paved with good intentions.

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.

Another way of stating krimson's writeup is simply: "Taxing $10K from a person whose income is $100K produces more revenue and less unhappiness than taxing $5K from someone whose income is $15K."

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.

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