Another way to look at this position of equilibrium is the following: since income must be either consumed or saved, Y is identical to C + S. In equilibrium, Y = C + I. Substituting for Y in the equation, we learn that in equilibrium:
C + S = C + I
and subtracting C from both sides leaves us with another equilibrium condition:
S = I
This is illustrated in the figure below:
Saving is sometimes described as a leakage out of the spending stream (funds that are saved are not spent by the household). But saving funds investment; the funds that consumers (for example) deposit in banks are lent by banks. So the funds come back into the economy as an injection called investment. In equilibrium, the leakage is equal to the investment.
For this reason, the saving/investment approach to equilibrium is also called the leakages/injections approach.
Adjustment to Equilibrium
As long as planned aggregate expenditures are not equal to aggregate output, there is a tendency for the economy to change. When output is less than planned aggregate expenditures, output increases until the two are equal. If aggregate output is more than planned aggregate expenditures, output declines until the two are equal. When they are equal, however, there is no tendency for the economy to change. Therefore, the condition where planned aggregate expenditure equals aggregate output is the equilibrium output for the economy.
REALITY CHECK: Suppose consumers spend more than firms had expected. Inventories are unexpectedly drawn down, and firms react by producing more, which leads to an increase in Y. Similarly, if consumers spend less, inventories build up, firms cut back, and Y decreases. The only way Y can be in equilibrium (not changing) is if there is no unexpected change in inventories.