They involve tax rates horrendously high or the minimum incomes so low that ihe UMI is not a viable means of eliminating poverty.

The notion of a universal minimum income has had a long gestation. Some say it originated with a proposal for a ‘social dividend’ by Lady Rhys Williams as far back as 1942 but you can find precursors even to that. The American origin is Milton Friedman’s ‘negative income tax’. When Minster of Finance, Roger Douglas promised a Guaranteed Minimum Family Income but he never implemented it.

Today the notion is usually described as a Universal Minimum Income (UMI), in which the government provides everyone with a basic income which it funds by taxing market income. It is a popular idea and seems eminently sensible so why has it not been implemented?

Many advocates put the UMI forward without doing the sums. Those who do, find that the required tax rates are horrendous or the minimum income is so low that it is not a viable means of eliminating poverty. Among the latter are New Zealanders Douglas, Gareth Morgan and Keith Rankin.

What the notion falls foul of is a simple mathematical theorem. Like all economic analysis it requires some simplification but once you have got it, then the tradeoff is obvious because the simplifications do not affect the logic of the outcome.

Let me explain how it works. Suppose you set the minimum income that all New Zealanders should get as X% of the average income.

(An important aside, this is not the same as the average wage, because each wage supports, on average, other people such as children and non-earning household members. The last time I did the calculation, the average private disposable income (including investment income) was about 60 percent of the average wage before tax.)

When I have asked people, they usually suggest a minimum income of about 60% of the average income. That is X = 60%. Bingo! You have just set the average income tax rate at 60%. It is as simple as that. The average tax rate is the same ratio of the minimum income as a proportion of average income. Relax the simplifications (like the state providing public services such as education and health care) and you still get the same broad result: a high minimum income requires, on average, a high tax rate.

That explains why those on the benefits face horrendous marginal tax rates, sometimes over 100 percent. By increasing theirs we can lower tax rates on everyone else – including the rich.

I have known this result for a long time (it is obvious once you have done the mathematics) and try as I might, I cannot find a way around the logic. For instance, you could raise the tax rate on the rich to, say, 80 percent and lower the rate on the rest – but not by that much. The poor would still find about half of every dollar they earned would be taken from them.

Now to the crunch. I said there were assumptions in the mathematics. One is that there is no behavioural responses to the change in tax rates, that faced with higher tax rates, people do not work less and do not take other measures to reduce their tax burden (including moving offshore). Yeah right. At this point the modelling gets messy, but the clear result is that if people faced by high tax rates cut back their effort (and their savings), tax rates would have to be even higher for a given UMI. Ooops. (Beneficiaries currently facing ultra-high rates might work more but their additional work would not compensate for everyone else cutting back.)

Others have argued that we simply need to drop the minimum to say 25 percent of average incomes (the rate Friedman mentioned) which would reduce the average tax rate to 25 percent, close to its current one. Most advocates of the UMI would not support that because it would not eliminate poverty.

I have thought of but one way out of the dilemma. Suppose we split the community into two groups based on whether they should work (in the earning workforce) or not. (This is a thought experiment, you understand; it might be an administrative and political nightmare.) Those who should work would get nothing but they get a job and its after-tax income, those that cannot work get a guaranteed minimum income as in the UMI scheme. If the second group was only 40% of the population, then the required average tax rate for a 60 percent minimum income would be only 24 percent (i.e 60 *40%).

There are two conceptual difficulties. The first is that earners and non-earners (including children) live together in the same house so the non-earners may not have a guaranteed UMI. The second is some of the earners will be on occasions unemployed. Bother, bother, bother.

So I ended up thinking about how to improve the current system, which kind of (clumsily) works a bit like this two group option. To me the priority is giving additional support to children and those that care for them.

The government talks about doing this in its next budget, but it seems to be very muddled. I guess I’ll be coming back to the issue of the child poverty – before and after the budget.