Explain why G – T = (S^{p} – I) – (X – M).

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)

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