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Here's an explanation via Mustard Street of a progressive tax system using a simple forumula: Ten buddies drinking beer.

The Tax System - Explained With Beer

Suppose that every day, ten men go out for beer and the bill for all ten comes to $100. If they paid their bill the way we pay our taxes, it would go something like this:

The first four men (the poorest) would pay nothing.
The fifth would pay $1.
The sixth would pay $3.
The seventh would pay $7.
The eighth would pay $12.
The ninth would pay $18.
The tenth man (the richest) would pay $59.

So, that's what they decided to do.

The ten men drank in the bar every day and seemed quite happy with the arrangement, until one day, the owner threw them a curve. "Since you are all such good customers," he said, "I'm going to reduce the cost of your daily beer by $20." Drinks for the ten now cost just $80.

Read the whole thing.