Budget surplus
Given a certain level of taxes (T) with the assumed level of government spending (G), there is a budget surplus.
Subtracting this same level of taxes (T) and the assumed level of consumption (C) from the GDP, there is positive private saving.
The sum of budget surplus and positive private saving must then be equal to investment.
If government spending expands while taxes stay the same, a budget deficit results.
Private saving is not affected by the larger government spending because taxes and consumption stay the same as before.
But total saving is reduced by the amount of budget deficit.
Because net saving has been reduced, investment must be reduced to match the lower saving.
Thus, the government budget deficit in effect has crowded out investment.