How can savings equal investment?
Saving (S) is equal to your disposable income (YD) minus consumption (C)
S=YD-C so what you don’t consume you save. Where does Your Disposable income come from?
It’s YD=Y-T, total income minus taxes. Perhaps it would have been better to say that savings is equal to income minus taxes minus consumption.
S = Y-T-C
Where would be be without the state? Public saving is equal to taxes (net of transfers) minus government spending, (T-G).
When G>T, government runs a deficit, when G<T, we have a surplus.
Production in a closed equilibrium system is equal to demand, which is the sum of consumption, government expenditure, and investment. (we’re leaving out imports exports for now)
Y = C+I+G
Take taxes from both sides, move consumption to the RHS:
Y-T-C = I + G-T
Now slot in your savings identity, you have
S = I + G-T.
I = S+(T-G),
This says that equilibrium in the goods market requires that investment is equal to saving–the sum of private and public saving.
Imagine an economy with 1 person in it. This one person has essentially the same investment and saving decision. The macroeconomy is one thing, though composed of millions of parts. So, in a closed system in equilibrium I=S.
Hat tip to Stephen Kinsella who helped me join the dots (as in did all the actual work!)