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Savings identity : ウィキペディア英語版
Savings identity
The savings identity or the savings-investment identity is a concept in national income accounting stating that the amount saved in an economy will be the amount invested in new physical machinery, new inventories, and alike. More specifically, in an open economy (an economy with foreign trade and capital flows), private saving plus governmental saving (the government budget surplus or the negative of the deficit) plus foreign investment domestically (capital inflows from abroad) must equal private physical investment. In other words, investment must be financed by some combination of private domestic savings, government savings (surplus), and foreign savings (foreign capital inflows).
Note that this is an "identity", meaning it is true by definition. This identity only holds true because investment here is defined as including inventory accumulation. Thus, should consumers decide to save more, and spend less, the fall in demand would lead to an increase in business inventories. The change in inventories brings savings and investment into balance without any intention by business to increase investment.〔 And also the identity holds true because savings are defined to include private savings and "public savings" (actually public saving is positive when there is budget surplus, that is, public debt reduction).
Note, that as such, this does not imply that an increase in savings must lead directly to an increase in investment. Indeed, business may respond to increased inventories by decreasing both output and intended investment. Likewise, this reduction in output by business will reduce incomes, forcing an unintended reduction in savings. Even if the end result of this process is ultimately a lower level of investment, it will nonetheless remain true at any given point in time that the savings-investment identity holds.〔
== Algebraic statement ==
In a closed economy with government, we have
Y = C + I + G \to I = Y - C - G
meaning that whatever of aggregate output (Y) is neither consumed by the private (C) nor the government (G) must be what is invested (I). But it is also true that
Y = C + S + T \to S = Y - T - C
meaning that savings must be disposable income (Y-T) minus consumption. Combining both expressions (by solving for Y - C on one side and equating) gives
I + G = S + T \to I = \underbrace_____{\text{capital inflow}}

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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