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Why must aggregate demand be equal to aggregate supply at the equilibrium level of income and output? Explain with the help of a diagram.

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According to Keynes , the equilibrium is reached only when aggregate demand (AD) equals aggregate supply (AS) because at this level , there is no tendency for income and output to change.
image
In the diagram equilibrium is at K where AD intersects `45^(@)` line. At this point , AD= AS
When AD is more than AS (say, at point R) , then the planned inventory would fall below the desired level. To bring back the inventory at the desired level, the producers expand the output. More output means more income. Rise in output means rise in AS and rise in income means rise in AD. Both continue to rise till they reach K, where AD=AS.
When AD is less than AS (say, at point S) then planned inventory rises above the desired level. To lear the unwanted increase in inventory, firms plan to reduce the output till AD becomes equal to AS.
So equilibrium takes place only at point K, when AD=AS.

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