2  Net and gross incomes

Tax and transfer systems are typically specified in terms of a set of gross income thresholds and associated marginal tax, or benefit withdrawal (sometimes called ‘taper’), rates applying above the thresholds. Such rates and thresholds generally refer to a particular type of individual or household, depending on its composition. For this reason a popular way of illustrating the nature of the system is to use a diagram with gross income, from all non-benefit sources, on the horizontal axis and net income on the vertical axis, as in Figure 1.

Figure 1 – Net and gross income

This type of diagram has the advantage that it displays the tax thresholds and rates clearly and applies to all those in the specified demographic group. Along the line, net and gross incomes are equal. Figure 1 also shows a simple proportional income tax applied to all income at the rate . The vertical distance between the tax schedule and the line, at any gross income level, shows the amount of tax paid, and the vertical height of the schedule shows net income, The slope of the line therefore measures the proportion of each $ retained after tax, that is .

2.1  A basic income – flat tax

Figure 2 – A basic income - flat tax

Figure 2 combines the proportional income tax with an unconditional transfer payment equal to B. Hence the relationship between gross and net income is shifted up by an amount, B, at all points. This is the simplest possible tax and transfer system imaginable; it is referred to as a basic income - flat tax, or BI/FT, scheme. This system, despite its simplicity, nevertheless gives rise to many complexities. It has been referred to by several other names, including negative income tax (NIT), social dividend, and linear tax scheme.

The figure shows immediately the ‘break-even’ income level, where net and gross income are equal; all those below receive a net gain. The BI/FT need not necessarily be administered as an unconditional benefit combined with a proportional tax. It may involve an integrated system in which those below pay no tax and receive the vertical distance between the tax schedule and the line, while those above the break-even point only pay tax, determined as a fixed proportion of income measured in excess of so that tax is

This comparison shows that the measurement of ‘total expenditure’ and ‘total taxation’ in a tax/transfer system is rather arbitrary; gross expenditure may be very high (in this case it is where is the number of people), while total expenditure less total taxation may be negligible. Nevertheless, critics of the BI/FT scheme argue that it requires a high value of relative to existing income tax rates (though not benefit withdrawal rates). There are two policy instruments, and but they cannot be chosen independently because of the existence of a government budget constraint; for example, given the choice of is determined by the budget constraint. In a ‘pure transfer’ system, where all tax revenue is redistributed in transfer payments, the tax rate is simply or the ratio of the social dividend to arithmetic mean income. Hence the break-even point is the arithmetic mean,

A generous BI/FT scheme therefore appears to require a relatively high marginal tax rate, but it should be remembered that the average tax rate (ATR) is less than the marginal tax rate (MTR) for all individuals, and is negative for all those below The marginal and average rate schedules are shown in Figure 3.

Figure 3 – Marginal and average tax rates

This demonstrates that considerable redistribution can be achieved with a tax system having a constant, rather than increasing, marginal rate structure. A progressive tax structure requires only an increasing average tax rate at all income levels. Indeed, in the limit such a system can achieve complete equality if and . Indeed, with a positively skewed gross income distribution, this would be brought about by a system of majority voting over taxation, since all those (the majority) with unambiguously favour while all those with favour Of course, this type of argument has implicitly made the clearly false assumption that gross incomes are unaffected by the tax structure. When allowance is made for labour supply incentives, there are strong limits to redistribution (even the amount desired by a policy-maker with a high degree of inequality aversion) and majority voting is considerably complicated.[2] This raises the ‘trade-off’ between ‘equity and efficiency’ that cannot be avoided when labour supply effects exist.

Figure 4 – A tax-free threshold

Many income tax structures have a tax-free area, and Figure 4 shows an income tax structure of this kind, where taxation above the threshold, is equal to . The tax schedule thus follows the 45 degree line from the origin until A, and is then AB. However, if AB is extended to the left, it hits the vertical axis at a net income of This demonstrates that, for taxpayers (for whom ), the tax-free threshold system is equivalent to a BI/FT scheme. An increase in the threshold takes a few individuals out of the tax ‘net’ but provides an increase in the effective basic income for all taxpayers. This result is quite general. Any multi-rate income tax structure, even in the absence of a tax-free area, looks, for those above the first tax rate, like a single rate structure with a tax-free threshold (which can be expressed as a function of the earlier rates and thresholds).

2.2  Means-tested benefits

Typically, tax and transfer systems have a degree of means-testing whereby benefits are withdrawn as individuals obtain higher gross incomes. A typical system is shown in Figure 5, where the tax schedule ABCD has a range AB where there is a benefit taper, or withdrawal rate, and a further range CD where the marginal income tax rate is increased. However, the highest marginal effective tax rate is faced by the lowest income recipients, as is evident from the lower gradient of the section AB of the tax schedule. The loss of a degree of freedom in policy choices as a result of the government’s budget constraint has already been mentioned. In the means-tested system of Figure 5, a further degree of freedom is lost because of the need to avoid a discontinuity, particularly at the point B. Such a discontinuity would produce a sudden drop in net income, or large increase, for a small increase in gross income. The means-testing thresholds and rates must be set alongside those of the income tax system, to avoid discontinuities. However, in practice, because various benefits are planned independently and thresholds are often adjusted independently of others, they often exist.

Figure 5 – A typical multi-rate system

A means-tested system is said to achieve high ‘target efficiency’, compared with the BI/FT, where the main - indeed, only - aim of a transfers system is thought to be the avoidance of poverty. However, it raises the problem of adverse labour supply incentives.

The use of a diagram showing the relationship between net and gross income implied by a tax and transfer system is convenient from the point of view of design, such as avoiding discontinuities, and can relate to many individuals, as well as making the thresholds and rates transparent. However, it has serious limitations as a device for examining labour supply incentive effects of taxes. With this in mind, it is necessary to turn to individual budget constraints.