Question

An open economy with a government sector is in equilibrium. Assume the following:  Marginal propensity to save = 0.4

Marginal propensity to tax = 0.2

Marginal propensity to import = 0.2

Showing your method of working, calculate by how much the equilibrium level of national income would fall, if injections in the economy are reduced by $60m.

Answer 1

N.I(Y)=C+I-M

I)We first calculate after tax income:

Marginal propensity to tax = 0.2

Therefore,tax amount is 0.2Y and after tax income is Y-0.2Y=0.8Y

II)We then calculate consumption:

Marginal propensity to save = 0.4 therefore the marginal propensity to consume becomes 1-0.4=0.6

Therefore consumption C=0.6$\times$ 0.8Y=0.48Y

III)We then calculate Imports;

=after tax income $\times$ Marginal propensity to import

=0.8Y$\times$ 02

= 0.16Y

N.I(Y)=C+I-M

Inputting the values obtained above:

Y=0.48Y+$\$60$-0.16Y

0.68Y=$\$60$

Y=$\$$ 88.24

Therefore if government injections reduced by $\$60m$ ,N.I equilibrium would reduce by:

$\frac{\$88.25-\$60}{\$88.25}\times 100=32\%$