The basics of economics were described earlier. This page describes many aspects related to inequality.
In common parlance, inequality is usually associated with unfairness, usually stated as, "Rich people are taking more than their fair share, leaving me poor." That kind of inequality is a rather complicated issue, involving ethics, social values, governance, corruption, etc., and is not directly addressed here.
Instead, this page just considers inequality in its simplest sense, of people being unequal. As usual, these scenarios are best understood in relation to the default state of Subsistence, where each person lives on ten fish a day.
The 100 people catch, on average, 10 fish per person per day. But 50 people catch 12 fish a day, because they are lucky, or more skilled, or work more. The other 50 people catch only 8 fish a day, because they are unlucky, or less skilled, or work less. So 50 people feast and live in comfort, while the other 50 are hungry and live in discomfort.
How does this situation compare to Subsistence, where each person gets 10 fish per day? Given the choice, if they do not know if they will be among the lucky 50 or the unlucky 50, most people will prefer equality, as the possible advantage of getting 2 extra fish a day is out-weighed by the possible disadvantage of getting 2 fewer fish a day (see Rawls' Veil of Ignorance). Other factors being equal, most people would prefer to avoid that uncertainty.
The 100 people catch fish as described in Variability: 50 people catch 12 fish a day, while the remaining 50 people catch 8 fish a day, because of luck, skill or amount of work. But each of the first 50 voluntarily gives 2 fish a day to each of the second 50, for whatever reason; and each of the second 50 people are happy to receive an extra 2 fish a day. Ultimately, each person gets to eat 10 fish a day.
How does this situation compare to Variability, where no fish are donated? All 100 people prefer this situaton to Variability: the first 50 people prefer this situation, as they choose to give 2 fish a day; and the second 50 people also prefer this situation, as they choose to accept 2 fish a day.
So both Subsistence and Charity are better than Variability. Is Charity better than Subsistence? Some people enjoy giving charity, if they have more than they need. Some people might be happy receiving charity, if they need it, but presumably they would prefer not to need it at all. On balance, probably most people would choose the state of Subsistence over the state of Charity (again see Rawls' Veil of Ignorance).
There are many possible variations of Charity. E.g., consider the situation half-way between Variability and Charity: each of the 50 people that catch 12 fish a day donate just 1 fish to each of the 50 people that catch 8 fish a day. So the first group gets 11 fish a day, while the second group gets 9 fish a day.
Supporting a family is a variety of Charity. In the simplest case, one person, maybe a child, does not catch any fish. Some person, maybe the parent, catches 20 fish a day, and gives 10 fish a day to the child. So both get 10 fish a day. Such inequality within a family is normally not regarded as something to be avoided.
10 people figure out a way to catch 13 fish per day by swimming more quietly. They show the technique to the other 90 people, but the others are unable to do it. So 10 people get 13 fish a day, while the other 90 continue to get 10 fish a day.
Is this situation better than Subsistence? There is now inequality among the population. Maybe the 90 are envious of the 10, even though the 90 are no worse off than before.
Given the choice, would the 90 allow the 10 to catch more? Would the 90 prefer that all 100 be the same? Or would the 90 be happy to let 10 others do better, while the 90 continue to catch the same? These are questions outside the realm of economics.
For safety reasons, all 100 people must fish in the same lagoon. They discuss whether to fish in a new lagoon, that has more fish, but murkier water. In that lagoon, 60 people can catch 12 fish a day, two more than usual. But the murkiness of the water affects the other 40 people more, for some reason, so they can catch only 9 fish a day, one fewer than usual.
Should the group of 100 people prefer the new lagoon? The majority of the group benefits. Averaged over the group, each person catches nearly 11 fish each day.
The fortunate 60 can give the unfortunate 40 one fish each, so that the 40 are no worse than before. Even after doing so, the 60 still have over 11 fish a day, better than at their old lagoon. This arrangement seems pretty fair. But how would it be enforced? What if some of the 60 refuse to participate?
Can democracy help? Maybe enough of the 100 would vote for the equitable arrangement that leave the 40 no worse off. Or maybe all 60 would vote to switch to the new lagoon, with no recompense to the 40.
What if the situation is more extreme? Suppose that, in the new lagoon, 95 people can catch 20 fish a day, while the remaining 5 people catch 9 fish a day. Should those 5 people let their minor loss obstruct the large gain of the 95? If the matter is subject to a vote, many of the 95 may feel that the 5 people should just learn to deal better with the murky water.
The group of 100 people organizes a lottery. Each person voluntarily contributes one fish that day. The lucky winner, chosen randomly, gets 100 extra fish that day, enough to feast for ten days.
This certainly constitutes inequality. But is it unfair? Would the other 99 regard the winner with envy or anger? They would presumably be mollified by the knowledge that they all had the same chance of having been the lottery winner. Thus, a lottery winner, who got rich by sheer luck, is typically regarded positively, while a fisher who catches more fish through skill or hard work is often regarded with envy and resentment.