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consumption increased by c times the increase in income. AD = Y With proportional taxes, AD consumption will rise by less, (c AD' = C + c(1 – t')Y – ct = c (1 – t)) times the increase + I + G E' in income. For changes in G, the multiplier AD = C + c(1 – t)Y + I + G will now be given by E ∆Y = ∆G + c (1 – t)∆Y (5.19) 1 ∆G ∆Y = 1– c(1– t) (5.20) Y Y' Y The income increases from Y * Fig. 5.5 to Y′ as shown in Fig. 5.4. The decrease in taxes works in Effects of a Reduction in the Proportional Tax Rate effect like an increase in propensity to consume as shown in Fig. 5.5. The AD curve shifts up to AD′. At the initial level of income, aggregate demand for goods exceeds output because the tax reduction causes increased consumption. The new higher level of income is Y′. EXAMPLE 5.2 In Example 5.1, if we take a tax rate of 0.25, we find consumption will now rise by 0.60 (c (1 – t) = 0.8 × 0.75) for every unit increase in income instead of the earlier 0.80. Thus, consumption will increase by less than before. The 1 1 1 government expenditure multiplier will be 1– c(1– t) = 1– 0.6 = 0.4 = 2.5 which is smaller than that obtained with lump-sum taxes. If government expenditure rises by 100, output will rise by the multiplier times the rise in government expenditure, that is, by 2.5 × 100 = 250. This is smaller than the increase in output with lump-sum taxes. 77 n G The proportional income tax, thus, acts as an automatic stabiliser – a t e e nr shock absorber because it makes disposable income, and thus consumer c em spending, less sensitive to fluctuations in GDP. When GDP rises, disposable n nt m u income also rises but by less than the rise in GDP because a part of it is y g siphoned off as taxes. This helps limit the upward fluctuation in t consumption spending. During a recession when GDP falls, disposable income falls less sharply, and consumption does not drop as much as it otherwise would have fallen had the tax liability been fixed. This reduces the fall in aggregate demand and stabilises the economy. We note that these fiscal policy instruments can be varied to offset the effects of undesirable shifts in investment demand. That is, if investment falls from I to I , government spending can be raised from G to G so that 0 1 0 1 autonomous expenditure (C + I + 0 = C0+ I + G1) an1 equilibrium income remain the same. This deliberate action to stabilise the economy is often referred to as discretionary fiscal policy to distinguish it from the inherent automatic stabilising properties of the fiscal system. As discussed earlier, proportional taxes help to stabilise the economy against upward and downward movements. Welfare transfers also help to stabilise income. Reprint 2026-27