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Exercises · Q9

Q.Suppose marginal propensity to consume is 0.75 and there is a 20 per cent proportional income tax. Find the change in equilibrium income for the following

(a) Government purchases increase by 20
(b) Transfers decrease by 20.
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With MPC c=0.75c = 0.75 and a proportional income tax t=0.20t = 0.20, the effective MPC out of national income is c(1−t)=0.60c(1-t) = 0.60. A rise of 2020 in government purchases raises equilibrium income by 5050; a fall of 2020 in transfers lowers it by 37.537.5.

Why a proportional tax shrinks the multiplier

A proportional income tax collects a fraction tt of every rupee earned, so households keep only (1−t)(1-t) as disposable income and consume cc of that. The effective marginal propensity to consume out of national income becomes c(1−t)c(1-t), and each round of spending leaks faster — to both saving and taxes.

The two multipliers

Government-expenditure multiplier=11−c(1−t)\text{Government-expenditure multiplier} = \frac{1}{1 - c(1-t)}

Transfer multiplier=c1−c(1−t)\text{Transfer multiplier} = \frac{c}{1 - c(1-t)}

The transfer multiplier carries an extra factor cc because a transfer must first be consumed (only cc of it) before it enters the income stream, whereas government purchases enter in full.

With c=0.75c = 0.75 and t=0.20t = 0.20:

c(1−t)=0.75×0.80=0.60,1−c(1−t)=0.40.c(1-t) = 0.75 \times 0.80 = 0.60, \qquad 1 - c(1-t) = 0.40. …

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