The AD curve is the aggregate demand

AD curve demonstrates not only the equilibrium combinations of P and Y - it also demonstrates the aggregated demand as a function of P when both markets are in equilibrium. This follows from equilibrium condition in the goods market that requires aggregate demand to be equal to GDP. When we change P, AD curve will tell us the response of Y and thus also the response of Y_D. You may hence use the AD curve to find the aggregate demand for different prices under the condition that both markets are in equilibrium. 

Primarily, this may seem like a contradiction. We claimed that only endogenous variables that affect aggregate demand where Y andR. Particularly we stated that P doesn't affect Y_D as long as we kept R and Y fixed.

• If we start in equilibrium and change P however keep R and Y constant, Y_Dwon't change though we will no longer be in equilibrium in money market.
• If we require both markets to be in equilibrium, R and Y should change when P changes.
• Specifically, R should fall and Y should increase when P decreases if both markets are to be in equilibrium.
• As Y_Drelies positively on Y and negatively on R, Y_D will then increase.
• So Y_D increases when P falls when both markets remain in equilibrium and there is no contradiction.