Using the tax system to deliver a living wage

In a previous post, I proposed a formula for calculating income tax that would provide for a  negative income tax. I did so because I believe a negative income tax system would be simpler, fairer, more humane, technically more feasible , and cheaper to develop than the current Universal Credit project being rolled out by Her Majesty’s government. A negative income tax would be administered by HMRC and have at its core the following formula for calculating income tax:

T(n) = m∑Y(n) – c∑H(n) – ∑T(n-1)


m is the single marginal tax rate;

c is the hourly value of the tax shield

∑Y(n) is the cumulative market income received by the end of period n

∑H(n) is the cumulative hours worked by the end of period n

∑T(n-1) is the cumulative income tax paid by the start of period n.


The proposed tax system has a single marginal tax rate. The choice of this rate is a political as well as a technical decision (i.e., achieving the desired behavioural effects) An individual’s hourly tax-free pay is given by the grossed-up tax shield (c / m).

In this post, I want to show how a negative income tax system can deliver what many describe as a “living wage”. The figure of £10 / hour has been mooted as a living wage. I shall hence assume this figure for the living wage  in my illustration.


In this post, I will incorporate the UK’s national minimum wage (NMW), currently £6.50 per hour, into the model.

I will also use a marginal tax rate of 40%, a tax rate which is both comparable to and competitive with existing UK income tax rates (20%, 40%, and 45%). Hence m has been set to 40% or 0.4 in my illustrations.

I will assume a working week of 35 hours and an individual’s weekly hours will be capped at this level.

I will also show how the model can be used to generate a basic income. I will briefly set out my views on whether a basic income should be conditional or unconditional.

Calculating the tax shield

In this section, I will show how negative income tax can transform the minimum wage of £6.50 / hour into a living wage of £10.00 / hour.  To achieve this, the value of the tax shield (c) must be calculated with reference to the minimum wage and to the living wage of £10.00. The value of the tax shield (c) must be set so that the hourly negative tax payment makes up the difference of £3.50 

Ignoring the summations in the above f ormula (they are not necessary here), we have

T = m x (£6.50) – c = – £3.50

T= 0.4 x £6.50 – c = – £3.50

c = £6.10

The tax formula that transforms the hourly national minimum wage of £6.50 to an hourly living wage of £10 will thus be

T(n) = 0.4 x ∑Y(n) – £6.10 x ∑H(n) – ∑T(n-1)

or on a week 1 basis, the hourly tax charge will be:

T = 0.4 x £6.50 – £6.10

= – £3.50 (negative,  as required)


Lenny earns the adult minimum wage. He works 35 hours per week. His pay slip will show:

Market income (35 hours x £6.50/hour)                                       £227.50

Negative income tax  (35 hours x £3.50)                                     £122.50

Take home pay (35 hours x £10 hour)                                         £350.00


Lenny now receives £10 per hour.


The hourly post-tax income of someone whose market income is £10 would be transformed to £12.10.

T= 0.4 x (£10.00) – £6.10 = – £2.10 (negative)

Hence that individual would take home £10 – (- £2.10) = £12.10 for every hour worked at or below the 35 hour weekly cap on hours. So although the “differentials” between market incomes have narrowed the higher paid worker still receives more per hour than the minimum wage worker.

Tax free allowance

The break-even hourly income with an hourly tax shield of £6.10 and a marginal tax rate of 40% is £15.25. This means a worker with an hourly income of £15.25 will neither pay income tax nor receive a tax payment. This is equivalent to an annual tax free allowance of £27,755 (compared to the current allowance of £10,000 p.a.). Individuals with a a market income of above £15.25 per hour or £27,755 per annum would pay income tax of 40% on the excess.

Basic income

The parameters used in the formula produce an amount 0f £6.10 per hour for those who have no market income. This could be taken to be a basic income payable to anyone whose market income is zero.

T = 0.4 x £0.00 / hour – £6.10 / hour

= – £6.10 per hour (negative)

The issue is whether this fortunate by-product of negative income tax should be conditional or unconditional.

Unconditional basic income

An unconditional basic income would credit every citizen with 35 hours. The basic income would thus be received by every citizen of working age.  The basic income would amount to £213.50 (35 hours x £6.10 per hour).

Hourly income with unconditional basic income and living wage of £10/hour

Hourly income with unconditional basic income and living wage of £10/hour

Conditional basic income

A conditional basic income would credit some groups with 35 hours a week but not others. For example, the disabled, the infirm, and those with caring responsibilities could be credited.  This would automatically trigger a payment at HMRC of £213.50 to individuals falling in these groups. The unemployed would be credited with hours only to the extent of their hourly contributions to society via voluntary work and / or participation in counter hysteresis activities (such as internships, work placements, or work programmes).

Hourly income with a conditional basic income and a living wage of £10/hour

Hourly income with a conditional basic income and a living wage of £10/hour

Conditional or unconditional basic income?

My main concern is that every UK citizen should have access to honest and adequate income. For disadvantaged groups, income accessability, particularly with increased benefit conditionality, can often be an issue.

Provided plentiful opportunities for voluntary work and / or opportunities to engage in counter hysteresis activities are made available to physically and mentally capable individuals without a market income then basic income should be conditional along the lines described above. A reasonably generous income of £213.50 per week would accrue to such individuals if their engagement in these activities was for 35 hours a week. Lesser contributions would be rewarded proportionately.

Summary of the model

Basic income = £6.10 /hour. May be conditional or unconditional. Could replace unemployment benefit.

Minimum wage (statutory)  = £6.50 / hour.

Living wage (assumed) = £10.00 /hour.

Break-even wage = £15.25 /hour.

Marginal tax rate = 40%

Maximum hours of credit = 35

Some final points

The withdrawal rate for someone transiting from unemployment to minimum wage work is about 43% (0.4 x £6.50 / £6.10). This is substantially better than the proposed withdrawal rate of 65% planned for Universal Credit.

However, the withdrawal rate rises as the starting hourly wage rate rises. At a starting rate of £15.25 per hour the withdrawal rate is 100%. It is unlikely that such a high withdrawal rate would be a disincentive to accept work at this wage rate.

It seems likely that a negative income tax designed with the parameters outlined in this post would lead to a lower overall income tax take for the government. Some of this might  be due to a lower marginal tax rate of 40% for top earners compared to their current 45% and because the tax free allowance is more generous than the current £10,000 annual allowance. For this reason, it may be better to use income tax as a means of correcting the inequalities that arise from distortions in the labour market (eg directors effectively setting their own pay) rather than as a means of raising revenue.

Capping the corporation tax deductibility of market incomes to £27,779 per employee (the annual tax free allowance) may also help to mitigate reductions in the income tax take.

The redistribution of income arising from this variant of a negative income tax system is likely to have a stimulative effect on the economy. Poorer workers with a high propensity to consume relative to richer workers should increase demand and hence economic activity.



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  3. Great site. Just discovered it.
    Can I presume that your version of Income Tax replaces the deeply regressive National Insurance?
    If so, then corporations could be expected to pay the same kind of total that they now do in Employers NI. This “Employers Income Tax” could be set by a curve to be progressive at both ends i.e. higher tax rates for very high and very low pay.
    The lower end tax rates could effectively manipulated to set minimum and living wages

    • Thanks Bob

      My thoughts on National Insurance are not very well developed.

      For what it’s worth, my thinking at the moment is that employee’s NI should remain (ie not amalgamated with income tax), but should be a weekly flat contribution to a state pension scheme.

      Employer’s NI is a bit more problematic as it currently serves as a tax on jobs, something I am sure you agree is undesirable. Ideally, it should not exist but the revenue implications of abolishing it are rather severe. Perhaps, the employer’s contribution should be a flat rate contribution to the employee’s state pension scheme too. Making it a flat sum, as distinct from a percentage, should reduce employers’ cost of employing people, whilst simultaneously deferring employee wages into old age.

      • Employer’s NI is paid by the employee, someone has to work to generate that revenue after all. Wages are depressed by it (particularly in the high-skill sectors). It should really be rolled in to a single “labour tax” along with payroll income and employees NI. As an intermediate step I think that directing it in to an employees pension (state, or later private) wouldn’t be a bad idea though.

      • Yes, Mike. The incidence of employer’s NI is thought to fall on employees – it depresses their current wage.

        But if it’s deferred into the future as a state pension, then this is surely better than merging NI with income tax?. NI should remain as insurance (for old age), so that the beneficiary will be the same person on whom the incidence has fallen.

        Those without market income but who receive payment under NIT could have the “employer” NI contribution credited to them by the state so that they accrue pension rights alongside those who receive a market income. The claw back rate is the marginal income tax rate (40% in the example I have used). So NIT payments will be recovered quite quick;y for many workers when they enter paid employment.

  4. Possibly. Business taxes are significant factor in state revenue and I don’t think that Income tax can be addressed in a vacuum. The same goes for all other forms of taxation…

    Do you know of any (necessarily simplified) models which allow you to play with various tax rates?

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