Seven Propositions on the Income Redistribution Effects of the UBI-FIT Model

This study presents and proves seven propositions on the income redistribution effects of the UBI-FIT (Universal Basic Income-Flat Income Tax) model. The seven propositions are as follows. Proposition 1: The t% UBI-FIT model, where there is no tax exemption point and basic income is distributed equally to all, reduces the Gini coefficient exactly t% regardless of the income distribution. Proposition 2: Even if there is a tax exemption, the t% UBI-FIT model, where basic income is equally distributed to all members, if the pre-tax income of all members of the society is above the tax exemption point, reduces the Gini coefficient precisely t% as above. However, part of the income redistribution effect in Proposition 1 that arises from the ‘after-tax stage’ to the ‘after-tax-and-transfer stage’ is merely transferred in Proposition 2 from the ‘pre-policy stage’ to the ‘after-tax stage’ by identical amount. In both cases, the final income distribution is the same. Proposition 3: In the t% UBI-FIT model, where there is no tax exemption point and basic income is distributed equally to all, if the value of t increases, the net benefit amount increases in proportion to t, but the percentage of net beneficiary group remains constant. Proposition 4: Under the t% UBI-FIT model, where there is no tax exemption point and basic income is distributed equally to all, in a positively-skewed unimodal distribution, the rate of net beneficiaries is higher than that of net contributors; in negatively-skewed unimodal distributions, the proportion of net contributors is higher than that of net beneficiaries; in the symmetrical unimodal distribution, the percentage of the net beneficiaries is identical to that of net contributors. Specifically, where α is the proportion of people located between median income and average income in the negatively-skewed unimodal distribution, the rate of net contributors is (50+α)%; where β is the proportion of people between median income and average income in the positively-skewed unimodal distribution, the percentage of net beneficiaries is (50+β)%. Proposition 5: Rank reversal does not occur under the t% UBI-FIT model, where t is less than 100 and basic income is equally distributed to all. Likewise, if the t values are all less than 100 and the basic income is distributed equally to all, then no rank reversal occurs at the UBI-PIT (Universal Basic Income-Progressive Income Tax) model or the UBI-RIT (Universal Basic Income-Regressive Income Tax) model. Proposition 6: If a tax exemption is established and the pre-tax income of some members of the society is less than the tax exemption point, the t% UBI-FIT model, where basic income is distributed equally to all, reduces the Gini coefficient to less than t% when compared to the pre-policy stage, regardless of the income distribution. Proposition 7: In the t% UBI-FIT model, where a tax exemption point is set and basic income is equally distributed to all, and if some members of the society earn less than the tax exemption point, the higher the tax exemption point, the less the Gini coefficient reduction rate, compared to the before tax and transfer regardless of the income distribution. Finally, some policy implications that can be drawn through the seven propositions are discussed.