Abstract
In this paper, an elementary mathematical model describing the introduction of a universal basic income in a closed market society is constructed. The model is formulated in terms of a system of nonlinear ordinary differential equations, each of which gives account of how the number of individuals in a certain income class changes in time. Societies ruled by different fiscal systems (with no taxes, with taxation and redistribution, with a welfare system) are considered and the effect of the presence of a basic income in the various cases is analysed by means of numerical simulations. The main findings are that basic income effectively acts as a tool of poverty alleviation: indeed, in its presence the portion of individuals in the poorest classes and economic inequality diminish. Of course, the issue of a universal basic income in the real world is more complex and involves a variety of aspects. The goal here is simply to show how mathematical models can help in forecasting scenarios resulting from one or the other policy.
Highlights
A lively debate on the appropriateness of introducing some form of universal basic income (UBI) has been ongoing in several countries for a long time
A toy model is proposed which provides a stylised description of the introduction of a universal basic income in a closed society
The model is expressed in terms of differential equations, whose dynamics is explored by means of numerical simulations
Summary
A lively debate on the appropriateness of introducing some form of universal basic income (UBI) has been ongoing in several countries for a long time (for concepts, methodologies, practice and much more see for example the recent papers [1,2,3] and books [4,5]which in turn provide several further references). A lively debate on the appropriateness of introducing some form of universal basic income (UBI) has been ongoing in several countries for a long time The goal is to illustrate, through a technical approach, how numerical simulations of mathematical models can help predict long-term effects of different policies, in particular related to UBI. This can help to explore different possible scenarios emerging in correspondence of different political programs. A serious and attentive contribution (not to be found here) cannot ignore and should definitely take into account several related socio-economic facets and elements
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