What does Locke's system say about ever-widening income inequality?
The only people who whine about this imaginary problem are people like you.
There is no guarantee that we all earn the same amount of money. There is no guarantee we are all born with the same abilities, intellect, work ethic, luck, misfortune, health, etc...
You are basing your entire standing here on the theory of "equality of outcome"..
There is no such thing. Even in a society where there is total government control of all income and redistribution, there are haves and have nots.
Equality of outcome is a dream thought up by those wishing for the existence of a socialist utopia.
Here we are guaranteed equal treatment under the law. There is no guarantee to equal economic standing. That is impossible unless all people are genetically engineered to be identical and if they are raised under identical conditions where there is 100% environmental control and people have no right to choose.
You're the only one using the phrase "equality of outcome."
For thirty years between roughly 1947 to 1977 government provided a reasonable approximation of equality under the law as far as economics was concerned for most Americans. During those decades when the economy grew almost everyone came out ahead, including the rich.
Robert Reich:
"The pay of workers in the bottom fifth grew 116 percent over these years — faster than the pay of those in the top fifth (which rose 99 percent), and in the top 5 percent (86 percent).
"Productivity also grew quickly. Labor productivity — average output per hour worked — doubled. So did median incomes. Expressed in 2007 dollars, the typical family’s income rose from about $25,000 to $55,000. The basic bargain was cinched.
"The middle class had the means to buy, and their buying created new jobs. As the economy grew,
the national debt shrank as a percentage of it."
During the last ten years only the USSR has lost more jobs in a single decade than the US.
In the same time period the richest 1% have doubled their share of returns to wealth.
The two events are related; they are not imaginary.
One does not happen without the other.
The Truth About the American Economy