A tax-modified multiplier

To explore how taxation works as a fiscal policy tool, a modification can be made to the aggregate demand model and multiplier. To keep things simple, we will assume a tax rate for the whole economy, capturing the proportion of income raised from tax. The coefficient t can be defined as the rate of tax – i.e. the proportion of national income levied by tax. Hence the total revenue received by the government from tax (T) is

T = tY

With a national income (Y ) of £1200 billion, for example, and a tax rate of 1/3, the total tax revenue will be £400 billion.

The amount of income available for consumption (often referred to as disposable income) is now equal to income (Y ) minus taxation (tY ):

Y − tY = (1 − t )Y

It therefore follows that the tax-modified consumption function is

C = a + b(1 − t )Y

This tax-modified consumption function, shown in Figure 20, has a shallower slope than the consumption function shown in Figure 14. This new slope is represented by a new (tax-modified) marginal propensity to consume b(1 − t ).

Figure 20 Taxation and aggregate demand

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This diagram has Aggregate Demand on the vertical axis and Income on the horizontal axis.

A solid line slopes upwards from the origin at an angle of 44 degrees.

From a point a short way up the vertical axis, a horizontal line is drawn. This is labelled ‘I+G’.

From a point a little higher up the vertical axis, labelled ‘a’, a solid straight line slopes upwards diagonally to the right. This line is labelled ‘Consumption function’ and has the equation C=a+b(1-t)Y. It has quite a shallow slope.

Higher up the vertical axis, from a point labelled ‘a+I+G’, there is another upward sloping line, parallel to the consumption function. This line is labelled ‘Aggregate Demand schedule’ and has the equation AD= a+b(1-t)Y+I+G

Figure 20 Taxation and aggregate demand

We can now consider the effect of modelling tax on the structure of the multiplier, which was shown earlier in this section to take the form 1/(1 − b). It intuitively follows that instead of having a denominator 1 − b, the tax-modified multiplier has a denominator 1 − b(1 − t ). The marginal propensity to consume (b) is no longer the only determinant of the value of the multiplier. We now also need to take account of the leakage of tax, as shown in Figure 20, and the new multiplier is