Derivation

In the simple closed economy which we looked at, the IS curve is
represented by:

Y = α (Ā – br)

For an open economy, equilibrium is still where Y = E, but E is
now C + I + G + X – M
and

X = Xo
M = Mo + mY

Therefore at equilibrium: Y = E
Y = Co + Io + Go+ Xo – Mo –br + c1Y –c1tY +mY
Y – c1Y + c1tY- mY= Co + Io + Go + Xo – Mo - br

Y = α ‘(Ā – br)

The open economy multiplier is:
1/(1-c1+ c1t-m) = α’

This multiplier is smaller than the multiplier for a closed economy:
1/(1-c1+ c1t-m) < 1/(1-c1 + c1t)