3 Inequality and Tax Progressivity
This section summarises the various distributions discussed in the previous section and presents the resulting inequality and tax progressivity measures.
3.1 Thirteen Distributions
The various distributions discussed in the previous section can be summarised in Table 4. This shows thirteen distributions although, as discussed above, these could easily be extended by treating indirect taxes separately, both using adult equivalent scales and the explicit sharing or allocation rule.[19]
The number of households is H; the number of individuals in household i is ni; the adult equivalent size of household iis mi; and the number of individuals with positive market income is NW. The number of individuals is 
and the number of adult equivalents is 
.
The numerical example was constructed so that the four hypothetical households have the same total market income of 100. After the application of a progressive tax and transfer system, the four household disposable incomes are:
Hence many people would argue that a comparison of the inequality of distributions 1 and 2 from Table 4 would serve little value; tax and transfer systems are designed to allow for differences in the demographic structure of households. Hence a simple comparison of this kind, which ignores differences in household composition, would be meaningless (in this example it would suggest that the tax structure is inequality increasing). However, as discussed in Section 2, not everyone would agree with this judgement.
| No. | Welfare metric | Unit | Sharing | No of Units |
|---|---|---|---|---|
| 1 | Total market HH income | Household | N/A | H |
| 2 | Total disposable HH income | Household | N/A | H |
| 3 | Total market HH inc per adult equiv | Household | N/A | H |
| 4 | Total disp HH inc per adult equiv | Household | N/A | H |
| 5 | Total market HH inc per adult equiv | Individual | Equal | N |
| 6 | Total disp HH inc per adult equiv | Individual | Equal | N |
| 7 | Total market HH inc per adult equiv | Equiv indiv | Equal | NE |
| 8 | Total disp HH inc per adult equiv | Equiv indiv | Equal | NE |
| 9 | Individual market income | Individual | No | NW |
| 10 | Indiv disposable income | Individual | No | NW |
| 11 | Individual market income | Individual | Yes | N |
| 12 | Individual disposable income | Individual | Yes | N |
| 13 | Individual final income | Individual | Yes | N |
Notes
- [19]Hence there could be three distributions (for three income units) of income per adult equivalent after direct taxes and transfers and the deduction of indirect taxes, plus a distribution of individual post tax and transfers income after sharing and the deduction of indirect taxes.
