Explain why $G – T = (Sg – I) – (X – M).$
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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, $S^p + S^g = I + NX$
$NX = S^p + S^g - I$
$NX = (Y - C - T) + (T - G) - I$ $\begin{bmatrix}\text{S}^{\text{p}}=\text{Y}-\text{C}-\text{T} \\\text{S}^{\text{g}}=\text{T}-\text{G}\ \ \ \ \ \ \ \ \end{bmatrix}$
$NX = Y - C - T + T - G - I$
$NX = Y - C - G - I$
$G = Y - C - I - NX$
$G - T = Y - C - I - NX - T$
$G - T = Y - C - T - I - NX$
$G - T = (S^p - I) - NX$
$G - T = (S^g - I) - (X - M)[NX = X - M]$
$Y = C + I + G + X - M$
$Y = C + I + G + NX [As NX = X - M]$
$Y= C - G = I + NX$
$S = I + NX$
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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