The simple rationale behind a progressive tax system.

The more you earn, the more you get taxed. This notion seems natural to most of us. The question is, how do you determine the magnitudes?

This is the relationship between the Economic concept of marginal utility and progressive taxes

In brief, as people gain more wealth, their marginal utility for money decreases.

For example, an additional $50,000 for someone with a net worth of 10 million does not result in a large increase of positive marginal utility whereas $50,000 for someone with a net worth of 300,000 results in a rather large amount of positive marginal utility. This matches our intuition.

Here is a graph illustrating this, “happiness” is the concept behind the term utility in economics. Keep in mind the Y-axis “Happiness” here is representing Total Utility, not Total Marginal Utility.

Here is what the graph of Total Marginal Utility on the Y-Axis and money on the X-axis would look most like. For people with a math background, marginal utility is the first derivative of utility. If you want to know the difference between Marginal Utility and Utility I have an answer to this on another Quora question.

(We can use the mathematical properties of concavity in the first graph and convexity in the second graph to justify the following statements but it is also reasonable to just think about human psychology with regards to money and get to the same answer.) The math here is our tool to quantify and formulate these qualitative thoughts.

The logic here is that as money increases your purchasing power and standard of living also increases, however, the rate of increase starts to fade off at a certain level of wealth. At some magnitude, additional money does not make a significant impact on your standard of living.

Engage in a thought experiment and ask yourself what else are you looking to buy after about 10 million? Does the happiness you receive from additional income have the same weight it did when your net worth was below 1 million?

This is one assumption of multiple causal reasons that justify our progressive tax rates. A higher tax rate on a wealthy person won’t affect their marginal utility by much, there are quantifiable measurements and calculations that can be done on this given appropriate data to further support the notion. Therefore since their marginal utility is not affected significantly we can tax the rich at a higher rate but we can’t tax the lower net worth individuals at those tax rates since it will result in a drastic decrease of their marginal utility.