Answer
Consumption is 6 trillion dollars
Government purchases are 1.3 trillion dollars
National saving is 0.7 trillion dollars
Investment is 0.7 trillion dollars
Work Step by Step
All numbers are in trillions of dollars
GDP is 8
Taxes are 1.5
Private saving is 0.5
Public saving is 0.2
GDP = Y
$Y = C + I + G + NX$
Under a closed economy, there are no net exports
$Y = C + I + G + NX$
$Y = C + I + G$
National saving is the same as investment
$S=I$
$Y = C + I + G$
$Y = C + S + G$
$Y - C - G = C + S + G - C - G$
$Y - C - G = S$
$Y - C - G + T - T = S$
$(Y - T - C) + (T - G) = S$
$Y - T - C$ is private saving
$T + G$ is public saving
Private saving
$Y - T - C = .5$
$8 - 1.5 - C = .5$
$6.5 - C = .5$
$C = 6$
Public saving
$1.5 - G$
National saving (and investment)
$Y - T - C + T + G$
$Y - C + G$
$8 - C + G$
$Y = C + I + G$
$Y - I - G = C + I + G - I - G$
$Y - I - G = C$
public saving = taxes - government spending
$0.2 = 1.5 - G$
$G= 1.3$
$Y - I - G = C$
$8 - I - 1.3 = 6$
$6.7 - I = 6$
$6.7 = I + 6$
$.7 = I$
$S = I$
$S = .7$