Question

2. Suppose GDP of a closed economy is $10 billion, consumption is $7 billion, private saving is $1 billion and public saving is $0.2 billion. Calculate taxes, government purchases, national saving and investment.

Answer 1

The AE is $\dpi{80} AE = C + I + G$ , and the equilibrium output is where $\dpi{80} Y = AE$ or $\dpi{80} Y = C + I + G$ . Further, we have $\dpi{80} Y - C - G = I$ , and applying the saving equal investment equation, we have $\dpi{80} S = Y - C - G = I$ . Also, the national saving is $\dpi{80} S = Y - C - G$ , and we have $\dpi{80} S = (Y - T - C) + (T - G)$ or $\dpi{80} S = S_{Private} + S_{Public}$ , ie the private saving is Y-T-C while public saving is T-G, summing up for the national saving.

We have $\dpi{80} Y = 10$ billion dollar, $\dpi{80} C = 7$ billion dollar, $\dpi{80} Y - T - C = 1$ billion dollar and $\dpi{80} T - G = 0.2$ billion dollar.

The national saving would be $\dpi{80} S = 1 + 0.2$ or $\dpi{80} S = 1.2$ billion dollar, and for the equality of saving and investment, we have $\dpi{80} I = 1.2$ billion dollar.

For $\dpi{80} Y = C + I + G$ , we have $\dpi{80} 10 = 7 + 1.2 + G$ or $\dpi{80} G = 10 - 8.2$ or $\dpi{80} G = 1.8$ billion dollar. Since $\dpi{80} T - G = 0.2$ , we have $\dpi{80} T = 0.2 + G$ or $\dpi{80} T = 0.2 + 1.8$ or $\dpi{80} T = 2$ billion dollar. Note that we can obtain it from the analogous equation $\dpi{80} S = Y - C - G$ .

Hence, the taxes is 2 billion dollar, government purchases is 1.8 billion dollar, national saving is 1.2 billion dollar and investment is 1.2 billion dollar.