Explain why G – T = (Sg – I) – (X – M). - Vidyadip

Question

Explain why G – T = (Sg – I) – (X – M).

✓

Answer

In a closed economy, savings and investment are at equilibrium level of income. However, In an open economy savings and investments differ.
Y = C + I + G + X - M
Y = C + I + G + NX [As NX = X - M]
Y= C - G = I + NX
S = I + NX
Saving in an economic include provate savings (S^p) and government saving(S^g):
So, S^p + S^g = I + NX
NX = S^p + S^g - I
NX = (Y - C - T) + (T - G) - I $\begin{bmatrix}\text{S}^{\text{p}}=\text{Y}-\text{C}-\text{T} \\\text{S}^{\text{g}}=\text{T}-\text{G}\ \ \ \ \ \ \ \ \end{bmatrix}$
NX = Y - C - T + T - G - I
NX = Y - C - G - I
G = Y - C - I - NX
G - T = Y - C - I - NX - T
G - T = Y - C - T - I - NX
G - T = (S^p - I) - NX
G - T = (S^g - I) - (X - M)[NX = X - M]

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