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

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 = A₁/(1 -C) ……………………………… (i)
Or, ΔY/ΔA₁ = 1/(1 - C)
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= A₂ /1-c+m
ΔY/(ΔA₂) = 1/(1 - C + 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.