Income Equality

Income equality is one measure that can be used to indicate the equality of a society. I have analysed the 2011 income distribution and show how a UBI (Universal Basic Income) can create greater income equality. The details of the UBI and its benefits are detailed in other places. Quite a lot of discussion has occurred regarding the benefits and pro's and con's of it as well.

2011 Income Distribution

In the graph below the red line would be what the income distribution would be, when 50% of the income earning population received 50% of the income, 10% received 10% etc. In other words, if the income was evenly distributed among the population.

The blue line represents the actual NZ distribution of income in 2011.

The stepper the blue curve and the less area under the curve the more uneven the distribution of income. The closer it moves to the red line or the greater the area under the curve the more even the distribution of income. The steeper the curve the more income is earned by less of the population and less even the income distribution. By measuring the area under the blue line and subtracting it from the area under the red line you get a measure of inequality. (The area shaded in red). An index if you like.

% of Population earning less than the income band per annum.

% of Population Approx Income Band
 20% $11k
 40% $19k
 60% $34k
 80% $54k 

2011 Income Distribution

UBI Income Distribution

Applying a UBI of $9080 and a flat tax rate of 33% the curve looks like this. This has been selected based on analysis done by Perce Harpham in the attached documents. Alternatives schemes can be selected and various options are possible. The attached spreadsheet enables the experimenting with different numbers. 

UBI Income Distribution

Other Scenarios and Comparisons

The table below offers a comparison of other scenarios. The closer the Equality Index % is to 100% the more even the income distribution. 
The 2007 scenario shows historically what the equality index was.
The 25K scenario is what would happen if the first $25K of income was tax free. 
The UBI scenario gives people a UBI of $9,080 tax free and sets the tax rate at 33%. 
The Flat scenario is what would happen if all income was charged at 33%.
Note the change in government tax income and the equality % change between the different scenarios.

The 25K and  UBI scenarios alter the government funding so would need to recover that by other means assuming no loss of government service. 
For the UBI an asset tax is proposed to fund it and savings would result from the simplified system and less bureaucracy in the administration and management of benefits.

Equality Index Income ($m) Tax ($m) Tax take change from 2011 ($m) UBI Cost ($m) Government Income Change from 2011
2007 52.37% 106,085.50 25,192.10 1,039.60 1,039.60
2011 53.00% 121,153.40 24,152.50 0.00 0.00
25K 57.21% 107,525.15 13,628.25 (10,524.25) (10,524.25)
UBI 64.69% 112,441.12 39,980.62 15,828.12 31,268.34 (15,440.22)
Flat 53.00% 81,172.78 39,980.62 15,828.12 15,828.12

From the graph below it can be seen that the 25K tax free scenario reduces inequality a little and benefits middle to high income earners more than low income earners. The UBI has a much more significant effect spreading the benefits more evenly among the population.

Scenario Distributions

For more details on the UBI scheme as proposed by Perce Harpham refer to the attached documents.


Phillip Lee,
Jan 19, 2014, 2:34 PM
Phillip Lee,
Jan 19, 2014, 1:50 PM
Phillip Lee,
Jan 19, 2014, 1:50 PM