Using equations for public and private saving, show that saving must equal investment in a closed economy. Begin with the expression for total saving in the economy

Question

What will be an ideal response?

Answer 1

Start with the expression of total saving in the economy. This is the sum of private saving and public saving:
S = Sprivate + Spublic (1 )
where private saving is:
Sprivate = Y + TR - C - T. (2 )
This states that private saving is what is left over from household income after consumption expenditures (C) and taxes (T) are subtracted and transfers (TR) are added.
Public saving is:
Spublic = T - G- TR. (3 )
Public saving is what is left over after government spending (G) and transfer payments (TR) are subtracted from taxes (T).
Combining (2 ) and (3 ) into (1 ) we get
S = Y + TR - C - T + T - G- TR. Note that taxes and transfers cancel each other out leaving:
S = Y - C - G. (4 )
Because we know that income (Y) is exactly equal to production or
Y = C + I + G in a closed economy, we can substitute the right hand side of this expression into
(4), and we get S = C + I + G - C - G. The consumption values cancel as does the level of government spending, leaving S = I.