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Savings Identity or the Savings Investment Idenity
In economics, the assumption that the amount saved in an economy will be invested.
Expressed in equations, if Income is I, Consumption C and Savings S then
I=C+S
if Production is P, profit is p and Investment is i
I = P+p+i
If the market is in equilibrium, P+p=C
I=C+i
Since I=C+S subtract C from both sides
C+S=C+i
therefore
S=i
Smith notes assumed this in Wealth of Nations and it figures into the question of General Equilibrium and the General glut controversy. In the General Equilibrium model Savings must equal investment for the economy to clear.
Classical economics assumed that S=i at all times, and therefore the market is always in equilibrium.
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