Mathematical models for sustainable wealth redistribution

[摘要] ENGLISH ABSTRACT: Economic inequality has increased in most large free-market economies during the last century and it has been suggested that this phenomenon is an inherent feature of free-market activities.It seems self-evident, however, that a continual rise in economic inequality is unsustainable. Infact, severe economic inequality has historically been associated with negative effects such as pooreconomic growth, severe financial recessions or even violent revolutions. Wealth redistribution is present in every form of government, although the extent thereof varies, and existing theoretical justifications of redistributive actions usually rely heavily on utility theory.Most economic postulates related to inequality are empirically inspired and defended, but becauseof the vast variety of possible economic contexts in which they may prevail, many of these claims are disputed. One example is the so-called Robin Hood paradox, which asserts that the extent of wealth redistribution is less in more unequal societies, where it is needed most, than inmore economically equal societies. Another is the Kuznets curve, which predicts that the extent of inequality in a developing economy will follow an inverted `u' curve as a result of development over time.The implications of increasing relative inequality over time as an inherent feature of wealth growth are investigated in the presence of wealth redistribution. Very simple mathematical model abstractions are employed to shed light on the possible evolution over time of wealthdistribution in the context of very basic assumptions, since such behaviour may perhaps thenalso be inferred in more complicated settings.Assuming increasing per capita wealth growth-rate functions is one way of capturing increasingrelative inequality over time, the very simplest case being linearly increasing per capita wealth growth-rate functions, which are considered in this thesis. Two examples of redistribution dynamicsare investigated. One example mimics diffusion-like effects of trickle-down redistribution,while the other represents a conservative, linear-tax transfer scheme.It is established analytically within the context of the aforementioned mathematical models thatincreases in economic inequality can always be limited by means of sufficient redistribution. It isalso demonstrated that the Robin Hood paradox may follow from very simple assumptions. It isfurthermore illustrated that fluctuating behaviour in the evolution over time of wealth inequality can even manifest itself in the absence of time-dependent processes, and hence that explanationsof such trends which merely assume time-dependent underlying processes might be of dubiousvalue. Examples of analytical formulations of theoretical justifications for redistributive actions,independent of utility theory, are finally also provided.

[发布机构] Stellenbosch University