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 = (C+ I +G)/(1-c)`

Let, (C + I + G) = A₁

_{`Or, Y=A_1/(1-c)`}

`(DeltaY)/(DeltaA_1) = 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 = (C+I+G+X-M)/(1 - c + m)`

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

` Or, Y=(A_2)/(1-c+m)`

`(DeltaY)/(DeltaA_2) = 1/(1-c+m)   .........(2)`

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.