What do you think should be the statistical distribution we see in any competitive endeavor?
You two are marching down a path that calls for a really solid understanding of the science aspect of economics and a good understanding of statistics and math in general. Put another way, this is the level of understanding that I've often on USMB written about folks, seemingly by my read of their remarks, not having which in turn leads them to think they can argue for or against the summarizations, conclusions and predictions economists make (sometimes even at a far more basic level than this, which is admittedly (after the first link below) not "basic" at all) about what will or won't happen in response to "this or that" policy action.
I think you and the other member may find the following resources helpful and informative. The first four (first level) links provide the background content one needs to understand the principles connected with the matter of income inequality. The linked content after that are lay audience based discussions of the history of income inequality.
As you can see from the information above, one can legitimately extrapolate economics principles to all manners of competitive situations where scarcity, choice and individual or group performance yields greater and lesser reward as a result of performance. As goes the application of that idea to the matter of income distribution among groups, I don't know that there is a precise or even right answer to the question you asked, @JimBowie for the answer to that question in particular depends on the value society places on the various productive activities that people perform.
In my observation, modern society has long assigned higher value to intellectual labor than to physical labor. I don't see that changing. Now what's essential to understand is that in this Information Age in which we find ourselves, the U.S. has, as I've stated many times, shifted from an economy where physical production, tangible things and processing/building and selling them, was that in which the U.S. had a competitive advantage to one wherein information -- processing it, applying it to solve problems and create new things that machines (things made possible by thought leadership not "build it" leadership) build things -- is the area in which the U.S. find its comparative advantage.
Why is that so critical to recognize and accept? Well, one need only look at what types of workers have seen their wages grow, and grow quite well, to know why. It's the wages of "knowledge workers" that have more than adequately grown over the past score of years. Ever wonder why movies about the future always depict a society comprised of people who basically don't "get dirty" doing their work? The transition from physical to intellectual labor is one that's long been understood as the natural progression in the presence of ever more capable technology.
Sure some physical laborers, notably in "white collar" fields, have managed to keep pace, but make no mistake, their days are numbered, although perhaps not as much as nor as soon to pass as have those of the rote labor factory worker. What so-called white collar laborer am I speaking of? Surgeons. The only reason they remain very well paid is because robotics and automation hasn't reached the point whereby the surgeon's job can be performed as depicted in science fiction movies and novels. But make no mistake, that day will come, sooner for less intricate types of surgery than for for others, but come it will. In time, all human labor will be more akin to the envisioning and execution an artist performs than that which accountants and surgeons perform.
Sidebar:
For the "peanut gallery," I'm not suggesting that surgery will occur absent human participation. I'm saying the human participation needed to perform it will be far less than it is now, which is exactly what we observe with the production of goods in factories. Surgeon salaries may, however, remain high simply because they "do their thing" on humans and human life/health will (hopefully) always have a high value.)
End of sidebar.
So in trying to answer the question you asked, I can't say what should be the statistical distribution of wealth. I can see that the inequality we observe now will ameliorate as more and more "regular folks" act to become part of the new economy, but for now, it may well be that the distribution we observe is exactly as it should be given the point we are at in the economic transition, people's natural (albeit irrational) resistance to change, and so on. I know it doesn't feel ethically "right," but from an economic progression standpoint, it may yet be precisely what is expected.
Given that as my response, I think there are other questions, the answers to which one must ponder (carefully, which is to say not in binary thinking mode that is the preferred approach of most folks):
- What is the world going to do with all these people that occupy it? Is all that "grey matter" going to be put to good use somehow? If so how? I don't have a definitive answer to that, only suppositions, but I do know that if we don't plan for that eventuality, it'll be calamity when the time arrives. Perhaps moving humanity to "the next level" whereby we conquer space flight and colonize new worlds, in turn giving folks and society a reason to have the physical labor capacity it does?
- Will the problems alluded to in the prior bullet be solved peacefully or will it take war on such a scale that it literally culls the human species? Again, I don't know. I merely can see that there are two basic ways "things" can go. Both will "get the job done," but one is clearly more gruesome than the other, and that the less gruesome approach will require the masses to "get on board with program" rather than fighting it and pining for what won't, barring great disaster, be again.