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Check out this graph:

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

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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