I'm not an expert statistician, but why can't you classify people's economic class based on the quantile their revenue falls in? You can assume a distribution based on the data (probably normally distributed) or go all non-parametric based on empirical quantiles.
I don't see how this cannot be easily understood with a number. Sure, you can never predict one observation, but the average in some quantile is quite standard modelling.
Are you calculating this quantile with respect to their neighbors' revenue? The rest of the city? County? State? Country? Or the entire world? You will get a different answer for each of them.
That's part of your modelling. If you're interested in the neighborhood's income distribution, then use the neighborhood's data. If you're interested in the world's distribution, then use world data.
This depends on how you want to look at the issue, but it comes down to a number yes.
Sure but that's true about any number, I can't think of any number which adds any value without some context. In statistics, your population is your context and all inference/conclusion depends on the population (local, city, world,etc). For social classes, I'd say the more local the more representative your number, which doesn't mean there isn't a number to represent the middle class.
I don't see how this cannot be easily understood with a number. Sure, you can never predict one observation, but the average in some quantile is quite standard modelling.