In a closed economy, savings and investments are equal at equilibrium level of income.
However, in an open economy savings and investments differ.
Y = C + I + G + X – M
Or, Y = C + I + G + NX [As NX = X - M]
Or, Y - C - G = I + NX .....(1)
Now, the component on the LHS can be regarded as national savings. That is, net national income which is left after consumption and government spending.
Or, = I + NX
National Savings ( ) in an economy include private savings ( SP) and government savings ( Sg).
So, SP + Sg = I + NX
Or, NX = SP + Sg – I
Or, NX = (Y - C - T) + (T - G) - I [SP = Y - C - T, Sg = T G]
Or, NX = Y - C - T +T - G – I
Or, NX = Y - C - G – I
Or, G = Y - C - I – NX
Or, G - T = Y - C - I - NX - T [Subtracting T from both sides]
Or, G - T = Y - C - T - I – NX
Or, G - T = ( SP - I) – NX
Or, G - T = ( SP - I) - (X - M) [NX = X - M]
Note: There is a misprint in the question as the equation mention Sg instead of Sp.
