Households with the the highest 30 per cent of incomes will be better off by about 1 per cent of their pre-Budget incomes. In cash terms the top 10 per cent will be better off by an average of pounds 6.70 a week, compared with a pounds 2 average gain for all households and a loss of over 60 pence a week in the bottom 10 per cent.
Using the Microsimulation Unit's tax-benefit model, Polimod, the impact on the UK population as a whole - in all sorts of families - can be calculated.
The calculations take account of increases in allowances and thresholds over and above inflation, the cut in the standard rate, changes to excise duties and the projected abolition of one-parent benefit and the one parent premium in means-tested benefits. The calculation assumes these extra benefits are abolished outright, whereas what is proposed is their abolition only for new claimants.
The chart shows that on average the poorest 30 per cent of households lose from the Budget measures. Their incomes fall by relatively small cash amounts - about 50 pence a week on average - but this is as much as a proportion of pre-Budget incomes as the gains received by the rest of the population represent in proportional terms.
The income tax changes have their maximum cash effect for people with incomes at or above the higher rate threshold. The effect on each household unit depends on the number of such taxpayers in each household.
Households with several high earners stand to gain the most. Lone parents, least likely to be sharing their household with a high earner, stand to gain least or to lose substantial amounts of their benefit income.
The abolition of lone parent benefit is particularly damaging to lone parents who can support their family through employment. Only a lone parent with earnings approaching the average for all workers breaks even.
Losses of spending power is most heavily concentrated on poor households with children. On average households with children in the poorest tenth of the population will lose nearly 2.5 per cent of their income. The cut in benefits for lone parent families is not the only way this Budget delivers a surprise lowering of living standards. Increases in excise duties on tobacco products and road fuels tend to impact throughout the income distribution.
These increases in duty are justified on the basis that expenditure on both types of product should be discouraged. At high and middle income levels these tax increases are compensated for by income tax cuts.
However, in the bottom 10 per cent of households few people are income taxpayers - their incomes are too low. The increase in prices they will face is not offset in other ways. The poorest will bear the heaviest burden for policies that are designed to benefit us all.
The income tax package announced also has curious effects. Combining a cut in the basic rate with an increase in the main personal allowance and the width of the lower rate band by more than inflation has the effect of spreading the benefit of the tax cuts to all current income tax payers.
But the distribution is not equal. On average the bottom 10 per cent of households receive just 17p a week whereas the top 10 per cent receive pounds 7. The bottom half of households benefit by an average of 79p, contrasted with the gain in the top half of pounds 4.40.
Even in proportional terms households with higher incomes gain more. The rise in income of the bottom 10 per cent from these income tax cuts is just 0.2 per cent, compared with 1 per cent in the top 10 per cent. This is an inevitable result of making cuts in income tax.
Even the increase in tax-free allowances, the cut in income tax which best targets the low paid, only proportions 7 per cent of its benefit on the bottom 30 per cent of households. A Budget for the poor would need to find instruments other than income tax to have much effect. Cash benefits such as child benefit and one-parent benefit can be viewed as refundable tax credits, measures that compensate for the extra costs of children.
The author is director of the Microsimulation Unit, department of applied technology, Cambridge University