In a closed economy the savings and investments are equal at equilibrium level of income whereas in an open economy the savings and investments differ.

Y = C + I + G + X – M

NX = NX = X - M

Or,Y = C + I + G + NX

Or,Y - C - G = I + NX .....(1)

Y - C - G can be regarded as national savings (S) or the net national income after all consumption and government spending.

So, we can write -

Y - C - G = S

Or, S = I + NX

S = Private Savings (S^p) + Government Savings (S^g)

Therefore,

S = S^p + S^g

Or, S^p + S^g = I + NX

Or, NX = S^p + S^g - I

S^p = Y - C - T

S^g = T - G

So, NX = Y - C - T + T - G - I

Or, NX = Y - C - G – I

Or, G = Y - C - I – NX

Subtracting T from both sides

Or, G - T = Y - C - I - NX - T

Or, G - T = Y - C - T - I – NX

Or, G - T = (S^p- I) – NX

Where, NX = X - M

G - T = (S^P- I) - (X - M)