Question

Why is the open economy autonomous expenditure multiplier smaller than the closed economy one?

Answer 1

In case of a closed economy, equilibrium level of income is given by

Y = C + cY + I + G

Or, Y − cY = C + I + G

Or, Y (1 − c) = C + I + G

Or, $Y=\frac{C+I+G}{1-c}$

Let, (C + I + G) = A₁

Or, $Y=\frac{A_1}{1-c}$
$\frac{∆Y}{∆A_1}=\frac{1}{1-c}$ (1)

In the case of an open economy, equilibrium level of income is given by

Y = C + cY + I + G + X − M − mY

Or, Y − cY + mY = C + I + G + X − M

Or, Y (1 − c + m) = C + I + G + X − M

Or, $Y=\frac{C+I+G+X-M}{1-c+m}$

Let autonomous expenditure (A₂) = C + I + G + X − M

Or, $Y=\frac{A_2}{1-c+m}$

$\frac{∆Y}{∆A_2}=\frac{1}{1-c+m}$ (1)

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.