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.

You may also be interested in this post relating to the aggregate demand curve and how it is consistent with the quantity theory of money.

To derive the AD either from IS/LM or QT of Money (equation of exchange) requires an assumption of an exogenous money supply (i.e. a fixed nominal stock of money). Most people now accept that is not so.

Just about all economists reject the quantity theory and even Hicks himself rejected IS/LM.

Is AD a valid concept?