THE LORENZ ORDER AND THE EFFECTS OF TAXATION POLICIES

To any finite population of n individuals with associated incomes x ₁…, x _n we can associate a Lorenz curve. By associating this population with a random variable X representing the income of a randomly chosen individual of the population, the concept of a Lorenz curve and the associated partial order (the Lorenz Order) based on nested Lorenz curves is readily extended to be defined in the class of all non-negative integrable random variables. In this context well known results on inequality attenuating and inequality rank preserving taxation policies are found to admit simple more general proofs. Some results on the effects of random taxation are also reviewed. The effects of applying different taxation policies within subpopulations lead one to consider questions regarding inequality attenuation results in mixture settings. It is observed that, more generally, inequality comparisons can be unambiguously made between any non-negative variables even if measured in dissimilar units.