Savings and income are equal at equilibrium level in an economy while in an open economy savings and investments are different.
Y = C + I + G + X – M
NX = NX = X – M
Y = C + I + G + NX
Y – C – G = I + NX (eq.1)
Y – C – G can be regarded as national savings (S) or the net national income which is obtained after all consumption and government spending.
Therefore, it can be written that
Y – C – G = S
Or, S = I + NX
S = Private Savings (Sp) + Government Savings (Sg)
Now
S = Sp + Sg
Sp + Sg = I + NX (as S = I + NX)
NX = Sp + Sg – I (eq.2)
We know,
Sp = Y – C – T
Sg = T – G
Putting the values in eq.2 we get
NX = Y – C – T + T – G – I
NX = Y – C – G – I
G = Y – C – I – NX
Now subtracting T from both sides
G – T = Y – C – I – NX – T
G – T = Y – C – T – I – NX
G – T = (Sp– I) – NX
Where, NX = X – M
G – T = (SP– I) – (X – M)