Abstract
This document explores the relationship between mathematics and wealth inequality, discussing how mathematical tools can both exacerbate and mitigate economic disparities. It delves into the concept of the Lorenz curve, Thomas Piketty's inequality, and the role of mathematics in understanding and addressing wealth inequality.
Extract
[...] Indeed, mathematics are not only an ally of the rich, they can be useful to the most modest in identifying inequalities, which can push public authorities to act. And to start this second part, I will show that a simple inequality between two values can serve as an alert tool. Indeed, economist Thomas Piketty, has shown in his book Capital in the 21st Century, what happens when the capital return rate, which we will note is higher than the economy's growth rate, noted as , inequalities tend to worsen. [...]
[...] This is a mathematical mechanism that allows France to redistribute wealth and therefore reduce inequalities. By recalculating the Lorenz curve after tax, we observe that the curve approaches the equality line, which means that thanks to this function, mathematics not only measures inequalities, but also corrects them concretely. Mathematically, this corresponds to exponential growth, which can be written as: For example, it is common for economists to use differential equations to obtain Imagine a capital who evolves over time. The interest rate is always per year. [...]
[...] By plotting it over its domain, corresponding to of the wealth and of the country's wealth, we realize that it is very largely below the line of perfect equality. We can also study this function in more detail by calculating its derivative and then its second derivative. Its second derivative is approximately 1.85x-0.95, and is therefore positive over its entire domain of definition. We deduce that the function L is convex, which means that as we move further into the population, the rich capture a large part of the total income. Conclusion : In conclusion, we can say that mathematics plays a double role in our society. [...]
[...] In this sense, we can therefore affirm that mathematics are indeed an invisible ally of the rich, since it is a matter of mechanisms that we do not visualize in a concrete way. But on the other hand, they also offer simple and powerful tools to understand these inequalities, serve as an indicator to reduce inequalities through models such as Thomas Piketty's inequality or the Lorenz curve. We can even go further by asking how mathematics could, beyond identifying inequalities, serve to limit them or even correct them as much as possible. [...]
[...] The rate is the same, but the initial wealth makes all the difference, which makes math an invisible ally of the rich, strongly exacerbating inequalities. Furthermore, probabilities also favor the rich. To show this, we will model a new situation with different possible investments. We will consider a binomial law of n identical and independent Bernoulli trials. This binomial law follows the parameters the success of achieving an investment equal to 0.6 according to INSEE, and the number of investments attempted. [...]
