a. Private Saving: $6 trillion
b. Public Saving:

c. Government Purchases:

d. The government budget balance is 2 - G trillion, and as a result, the government budget is in surplus or deficit depending on the value of G.
Given:
- Y (GDP) = $15 trillion
- C (Consumption) = $7 trillion
- I (Investment) = $2 trillion
- TR (Transfer Payments) = $1 trillion
- T (Taxes) = $2 trillion
Calculations:
a. Private Saving:
Private Saving
is given by the formula:
![\[S_p = Y - C - T\]](https://img.qammunity.org/2024/formulas/business/high-school/gzir2reqo66k3ivtkbyy5z7w35loc0trgn.png)
![\[S_p = 15 - 7 - 2\]](https://img.qammunity.org/2024/formulas/business/high-school/4wkgs6l0sxqb0q001dbsg52yu6dp146ekp.png)
![\[S_p = 15 - 9\]](https://img.qammunity.org/2024/formulas/business/high-school/jgilxko3pte5f9bboq9wg0ooka4csr56tm.png)
![\[S_p = 6\]](https://img.qammunity.org/2024/formulas/business/high-school/icu7bpgxlyhst3qpipg3y2qo6dkxyd29dj.png)
b. Public Saving:
Public Saving
is given by the formula:
![\[S_g = T - TR - G\]](https://img.qammunity.org/2024/formulas/business/high-school/akflsiz5m39iikvd4qjj16xn9h5vqbc27g.png)
![\[S_g = 2 - 1 - G\]](https://img.qammunity.org/2024/formulas/business/high-school/m1r12x2n8l7zv9cuvdekoj4co59m5ez6op.png)
c. Government Purchases:
Government Purchases (G) can be calculated using the equation for the government budget balance:
![\[G = T - TR - S_g\]](https://img.qammunity.org/2024/formulas/business/high-school/shciwqu666f9vdoqy4ry6yjdlu1nsk3pmt.png)
![\[G = 2 - 1 - S_g\]](https://img.qammunity.org/2024/formulas/business/high-school/4ade6kew1o8csd6l6zn8uh0mvh1akxzaii.png)
d. Government Budget Balance and Status:
The government budget balance is the difference between government spending (G) and government revenue (T):
![\[Budget \ Balance = T - G\]](https://img.qammunity.org/2024/formulas/business/high-school/drtsd3f87eazj8rfr2ey8e2xgi3eqhn6q6.png)
![\[Budget \ Balance = 2 - G\]](https://img.qammunity.org/2024/formulas/business/high-school/996cyn1tgcskezfmoo4lb775o6tiny21lv.png)