Savings identity
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Savings identity or the savings investment identity is a concept in economics stating that the assumption that the amount saved (S) in an economy will be amount invested (I).
Private saving (S) is equal to disposable income (Yd) minus consumption (C):
S=Yd-C (1)
Where Yd=(Y-T) (1.A)
Combining (1) and (1.A) we can get Y=S+T+C (2)
In a close economy if the goods market is in equilibrium, the production function is equal to Demand, which is the sum of consumption, investment (I) and government expending (G).
Y = C+I+G (3)
Combining (2) and (3): S+T+C=C+I+G
hence,
S=I+G-T where (G-T) is public saving
Therefore,
Private Saving is equal to investment plus public saving. If the government have a balanced budget, saving is equal to investment.
Adam Smith notes 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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