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National Income Identity in a Closed Economy without Government

In a simplified economic model of a closed economy without a government, the national income identity is expressed as YC+I+IIY \equiv C + I + II. Here, Y is national income, C is consumption, I is planned fixed investment, and II is inventory investment. This relationship is an identity—meaning it is true by definition at all times—because total output (Y) by its construction includes both planned expenditures (C and I) and any unplanned changes in business inventories (II). This holds true even when the economy is not in equilibrium.

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