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Deriving the Aggregate Demand Curve

Check out this graph:
aggregate demand curve
For a given nominal money stock, a price level decrease increases the real money stock. This shifts the LM curve outward, and the interest rate goes down and income increases. Therefore, along the AD curve, a price level decrease )holding the nominal money stock constant) is consistent with an income increase, and the AD curve slopes downward.

Mathematical Derivation of AD Curve

aggregate demand curve

This equation is the AD curve. It summarizes the IS-LM relation, relating Y and P for given levels of A and M. Since P is in the denomination AD curve slopes downward.
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