Why is the open economy autonomous expenditure multiplier smaller than the closed economy one?
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In case of a closed economy, equilibrium level of income is given by: $Y = C + cY + I + G Y - cY = C + I + G Y (1 - c) = C + I + G\text{Y}=\frac{\text{C}+\text{I}+\text{G}}{1-\text{c}}$
Let, $(\text{C}+\text{I}+\text{G})=\text{A}_1 Y =\frac{\text{A}_1}{1-\text{c}} …………………… (i)\frac{\Delta\text{Y}}{\Delta\text{A}_1}=\frac{1}{1-\text{c}}$
In the case of an open economy, equilibrium level of income is given by: $Y = C + cY + I + G + X - M – mY Y - cY + mY = C + I + G + X –M Y (1 - c + m) $$= C + I + G + X – M Y = (C + I + G + X - M) / 1 - c + m$
Let autonomous expenditure $(\text{A}_2) = C + I + G + X – M Y$$= A_2 / 1 - c + m\Delta\text{Y}/\Delta(\text{A}_2)=1/1-\text{c}+\text{m} ………………………….. (ii)$
Comparing equations $(1)$ and $(2)$ and the denominators of the two multipliers,
we can conclude that multiplier in an open economy is smaller
than that in a closed economy, as the denominator in an open economy is greater than denominator in a closed economy.
Let, $(\text{C}+\text{I}+\text{G})=\text{A}_1 Y =\frac{\text{A}_1}{1-\text{c}} …………………… (i)\frac{\Delta\text{Y}}{\Delta\text{A}_1}=\frac{1}{1-\text{c}}$
In the case of an open economy, equilibrium level of income is given by: $Y = C + cY + I + G + X - M – mY Y - cY + mY = C + I + G + X –M Y (1 - c + m) $$= C + I + G + X – M Y = (C + I + G + X - M) / 1 - c + m$
Let autonomous expenditure $(\text{A}_2) = C + I + G + X – M Y$$= A_2 / 1 - c + m\Delta\text{Y}/\Delta(\text{A}_2)=1/1-\text{c}+\text{m} ………………………….. (ii)$
Comparing equations $(1)$ and $(2)$ and the denominators of the two multipliers,
we can conclude that multiplier in an open economy is smaller
than that in a closed economy, as the denominator in an open economy is greater than denominator in a closed economy.
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