Suppose C = 100 + 0.75Y, $\triangle\text{I}=500,$ G = 750, taxes are 20% of income, X = 150, M = 100 + 0.2Y and classify whether it is budget deficit or surplus and trade deficit or surplus.
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C = 100 + 0.75Y, $\Delta\text{I}=500,$ G = 750 X = 150, M = 100 + 0.2Y Equilibdum Income$=\text{C + c(Y}-\text{T})+\text{I + G + X}-\text{M}-\text{mY}$
$\text{Y}=100+0.75\Big(\text{Y}-\frac{20}{100}\text{Y}\Big)\\+500+750+150-100-0.2\text{Y}$
$\text{Y}=100+0.75\times\frac{80\text{Y}}{100}\\+1400-100-0.2\text{Y}$
$\text{Y}=1400+0.6\text{Y}-0.2\text{Y}$
$\text{Y}=1400+0.4\text{Y}$
$\text{Y}-0.4\text{Y}=1400$
$0.6\text{Y}=1400$
$\text{Y}=\frac{1400}{0.6}$
$=\frac{700}{0.3}$
$=2333.3=\frac{7000}{3}$
Government tax $=\frac{20}{100}\times\frac{7000}{3}=\frac{1400}{3}=466.6$ Government expenditure > Government receipts It shows budget deficit$\text{NX = X}-\text{M}-\text{mY}$
$=150-100-\frac{2}{10}\times\frac{7000}{3}$
$=150-100-466.66$
$=-416.66$
Here, NX is negative. Thus, it implies trade deficit.
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