Economics is about limited resources and unlimited wants, scarcity. And so is inequality: there are only so many things and some people have them and some don't. But sometimes the scarcity is artificial.
A good example of this would cable. A cable company buys intellectual property, television, and then sells access. It doesn't really cost the cable company anything to add additional subscribers, the reason they charge is to cover the initial cost of the intellectual property. It's what's called a non-rivalrous good.
Now, think of an economy where there are two different levels of income and half the people have a higher income than average, and half lower. So half the people here have more money to spend on television and half less. What the cable company decides to do here is offer two different services, basic cable and premium cable, which is all the basic channels plus some extra. There are all sorts of pricing schemes that content providers engage in, where they attempt to gauge how much customers are willing and able to spend and then charge them exactly that; but, for simplicity's sake, lets say what the different packages cost is proportional to amount the cable provider pays for the content. So the number of additional channels that come with each package is proportional to the total amount everybody (together) is paying for that package.
Assuming nominal spending remains constant, the number of cable channels people can watch on average will be directly proportional to the Gini Coefficient of the cable subscribers' spending on cable. Or, in other words, the more inequality there is, the fewer channels people get on average.
For example, if a cable company has ten million subscribers, and if half the customers have one hundred and twenty dollars to spend on cable, and half eighty, the cable company would take in 800 million in basic cable subscriptions and 200 million in additional premium subscriptions: 10 million basic subscribers each paying 80 dollars and 5 million subscribers each also paying for premium. If the cable company adds one channel for every 10 million dollars each service takes in, basic cable would come with eight channels, and premium cable with ten.
If everyone had a hundred dollars to spend on cable, there would be only one cable package and it would have ten channels. If instead, half the people had twenty dollars to spend on cable, and the other half none, there would also only be one package, and it would also have ten channels. But only half as many people would be able to watch it. No one would be better off: although half the people have twice as much money, inflation wipes out their gains. The real value of cable subscription halves, even though nominal spending remains constant.
The Gini coefficient of complete equality is zero, of half having all the income point five, of the first example, point one. At each point the number of cable channels equals ten times the inverse of the Gini coefficient.
If you fiddle around with this, add different levels of income, different levels of cable packages, this still holds.
There are all sorts of things in an economy that are non-rivalrous, and also all sorts of economies of scale. Up to a certain point, it does not cost as much to make an additional product as the previous ones. All this makes me think that a decrease in the Gini coefficient would cause an increase in real incomes, depending on the extent to which consumption is non-rivalrous.
This is all like when your roommates don't have money for a Netflix subscription.
