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.