Suppose C = 40 + 0.8Y D, T = 50, I = 60, G = 40, X = 90, M = 50 + 0.05Y.
- Find equilibrium income.
- Find the net export balance at equilibrium income.
- What happens to equilibrium income and the net export balance when the government purchases increase from 40 and 50?
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C = 40 + 0.8YD T = 50 I = 60 G = 40 X = 90 M = 50 + 0.05Y
$\text{Y}=\frac{\text{A}}{1-\text{c}+\text{m}}$ Where, A = C − CT + I + G + X − M
$=\frac{\text{C}-\text{cT}+\text{I}+\text{G}+\text{X}-\text{M}}{1-\text{c}+\text{m}}$
$=\frac{40-0.8\times50+60+40+90-50}{1-0.8+0.05}$
$=\frac{40-40+60+40+90-50}{1-0.75}$
$=\frac{140}{0.25}=\frac{140}{25}\times100$
$=560$
= 90 - 50 - (0.05 × 560)
= 40 - (28)
= 40 - 28 = 12
$=\frac{40-0.8\times50+60+50+90-50}{1-0.8+0.05}$
$=\frac{40-40+60+50+90-50}{1-0.8+0.05}$
$=\frac{150}{0.25}=\frac{150}{25}\times100=600$
Net export balance at equilibrium income NX = X - (M - mY) = 90 - 50 - (0.05 × 600) = 40 - (30) = 40 - 30 = 10
- Equilibrium level of income
$\text{Y}=\frac{\text{A}}{1-\text{c}+\text{m}}$ Where, A = C − CT + I + G + X − M
$=\frac{\text{C}-\text{cT}+\text{I}+\text{G}+\text{X}-\text{M}}{1-\text{c}+\text{m}}$
$=\frac{40-0.8\times50+60+40+90-50}{1-0.8+0.05}$
$=\frac{40-40+60+40+90-50}{1-0.75}$
$=\frac{140}{0.25}=\frac{140}{25}\times100$
$=560$
- Net exports at equilibrium income
= 90 - 50 - (0.05 × 560)
= 40 - (28)
= 40 - 28 = 12
- When G increase from 40 to 50,
$=\frac{40-0.8\times50+60+50+90-50}{1-0.8+0.05}$
$=\frac{40-40+60+50+90-50}{1-0.8+0.05}$
$=\frac{150}{0.25}=\frac{150}{25}\times100=600$
Net export balance at equilibrium income NX = X - (M - mY) = 90 - 50 - (0.05 × 600) = 40 - (30) = 40 - 30 = 10
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