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Inequality, a scourge of the XXI century

Social and economic inequality is a plague of the XXI Century. It is continuously widening, as the wealth of a relatively small group increases and, therefore, the rest of the world shares a shrinking fraction of resources. This situation has been predicted and denounced by economists and econophysicists. The latter ones have widely used models of market dynamics which consider that wealth distribution is the result of wealth exchanges among economic agents. A simple analogy relates the wealth in a society with the kinetic energy of the molecules in a gas, and the trade between agents to the energy exchange between the molecules during collisions. However, while in physical systems, thanks to the equipartition of energy, the gas eventually arrives at an equilibrium state, in many exchange models the economic system never equilibrates. Instead, it moves toward a "condensed" state, where one or a few agents concentrate all the wealth of the society and the rest of agents shares zero or a very small fraction of the total wealth. Here we discuss two ways of avoiding the "condensed" state. On one hand, we consider a regulatory policy that favors the poorest agent in the exchanges, thus increasing the probability that the wealth goes from the richest to the poorest agent. On the other hand, we study a tax system and its effects on wealth distribution. We compare the redistribution processes and conclude that complete control of the inequalities can be attained with simple regulations or interventions.