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

(i) Government purchases increase by 20

(ii) Transfers decrease by 20

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Solution

(i) $Δ Y = \frac{1}{1 - c (1 - t)} \times Δ G$

$= \frac{1}{1 - 0.75 (1 - 0.2)} \times 20$

$= \frac{1}{1 - 0.75 \times 0.8} \times 20$

$= \frac{20}{1 - 0.60}$

$= \frac{20}{0.4}$

= 50

(ii) $Δ Y = \frac{c}{1 - c} Δ T$

$= \frac{0.75}{1 - 0.75} \times 20$

$= \frac{0.75}{0.25} \times 20 = 60$

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Suppose marginal propensity to consume is 0.75 and there is a 20% proportional income tax. Find the change in equilibrium income for the following: (i) Government purchases increase by 20 (ii) Transfers decrease by 20

(i) ΔY=11−c(1−t)×ΔG =11−0.75(1−0.2)×20 =11−0.75×0.8×20 =201−0.60 =200.4 = 50 (ii) ΔY=c1−cΔT =0.751−0.75×20 =0.750.25×20=60

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

(i) Government purchases increase by 20

(ii) Transfers decrease by 20

(i) $Δ Y = \frac{1}{1 - c (1 - t)} \times Δ G$

$= \frac{1}{1 - 0.75 (1 - 0.2)} \times 20$

$= \frac{1}{1 - 0.75 \times 0.8} \times 20$

$= \frac{20}{1 - 0.60}$

$= \frac{20}{0.4}$

= 50

(ii) $Δ Y = \frac{c}{1 - c} Δ T$

$= \frac{0.75}{1 - 0.75} \times 20$

$= \frac{0.75}{0.25} \times 20 = 60$