No, the result of increased wealth inequality, even if you maintained the same level of social mobility, will worsen not improve situation. The description of a rise in absolute mobility would be a misunderstanding of the issue.
If that is too theoretic, consider the analogy of a lottery where one group of children win automatically and an other group has say a 10% chance of winning during their life. Increasing the prize (i.e. a rise in inequity among classes) serves only to worsens the situation not only for the median and average members but the vast bulk of the lower class since those who don't rise (the vast majority) are now even worse off relatively.
Or indeed by your logic simply raising the salary of a CEO by a massive amount also raises the "absolute mobility" of all other employees
So unless mobility also raises by at least a corresponding amount, any worsening of inequality at birth will only worsen the situation by every meaningful standard. And even then it is probably a bad idea.
Or indeed by your logic simply raising the salary of a CEO by a massive amount also raises the "absolute mobility" of all other employees
Yes. If I had a 1% chance of being the CEO and having my income go from $100k to $1M, my expected payoff was $900k x 1% = $9k. If my income stays at $100k but the CEO income goes to $10M, and my odds of being the CEO stay at 1%, my expected payoff is $9.9M x 1% = 99k.
My situation has not been worsened and has a possibility of being improved.
You seem to think it somehow makes me worse off if my CEO makes more money. Can you explain? Note that I'm not a person prone to envy.
Or by that logic you could cut your pay from $100K to $1K and give your CEO $10M and be just as happy. There are plenty of people who live on $1K a year after all.
Although in the CEO's case, often no further harm is done, if half of a population has a massive increase in wealth while the other half does not then then poorer half must compete for limited resources with a group that will not only drive prices up but can now purchase assets as a form of rent seeking. So in fact, greater inequality acts as currency devaluation for the disadvantaged group.
The CEO example was not meant to cause unjustified envy but to show that according to your logic, instead of ever giving employees a raise you could simply give all raises to the CEO and tell employees that by cost benefit analysis the effect is the same, that they are better off.
To put it concretely, from now on, every time you ask for a raise just ask that your boss get that extra compensation instead. I think you will find the effect is not remotely the same.
Or from now on, ask for all of your pay check that exceeds poverty line for chances at a completely fair trillion dollar lottery.
Simple cost benefit multiplication is being erroneously applied in these cases (and often is)
if half of a population has a massive increase in wealth while the other half does not then then poorer half must compete for limited resources
You are not discussing an increase in wealth at all. You are discussing a situation of declining or fixed wealth and monetary inflation. They aren't the same thing.
I agree that we should try to avoid declines in wealth. Luckily wealth has only increased in the US and globally, for folks at the bottom and the top.
Everything I said is unchanged if you replace income with utility(income).
No it does not. If you received no utility for your work but instead a 1:1000,000 chance of a million incomes, you would starve to death. The math you are using does not describe reality and rational people, since about Galileo anyway, have known better than to insist on broken models.
There is a reason people are willing to buy $1 lottery tickets but not $1000 tickets. (hint: a certainty of misery or high chance of death is not compensated by a remote chance of enormous wealth of ever decreasing marginal utility)
You are simply misunderstanding the use cost benefit, I assume because it clashes with some ideological point.
But if you want to buy a one in a million chance for a trillion dollars, I have a bitcoin address you could send a million bucks too.
The math you are using does not describe reality and rational people, since about Galileo anyway, have known better than to insist on broken models.
First of all, it's a textbook exercise in topology to show that any rational decision process must have a utility function (at least for a countably infinite set of choices).
Let me repeat the statement for utility functions. Suppose I have a 1% chance of being CEO and increasing my utility to U(CEO pay) - U(my pay). Suppose this increases to U(10x CEO pay) - U(my pay).
It's simple arithmetic that 0.01 x U(10X CEO pay) + 0.99 x U(my pay) > 0.01 x U(CEO pay) + 0.99 x U(my pay).
Rearranging the arithmetic, this is merely the statement that U(10X CEO pay) > U(CEO pay) - i.e. I'll be happier as a CEO with 10M than with 1M. Do you disagree with this statement?
If that is too theoretic, consider the analogy of a lottery where one group of children win automatically and an other group has say a 10% chance of winning during their life. Increasing the prize (i.e. a rise in inequity among classes) serves only to worsens the situation not only for the median and average members but the vast bulk of the lower class since those who don't rise (the vast majority) are now even worse off relatively.
Or indeed by your logic simply raising the salary of a CEO by a massive amount also raises the "absolute mobility" of all other employees
So unless mobility also raises by at least a corresponding amount, any worsening of inequality at birth will only worsen the situation by every meaningful standard. And even then it is probably a bad idea.