I am trying to understand the interaction between the IS-LM model and AD.
First - if we look at the IS curve: If the government lowers interest rates; this will make borrowing cheaper and thus, investment will increase, resulting in a right shift in the IS curve to IS curve(2). MD>MS which leads to a movement (up and right) along the LM curve to the new intersection of the IS(2) curve.
Now at this new point, this correponds with a higher level of output but at a higher level of interest, not a lower level?
In the IS/LM Model, interest rate fluctuations result in movement along the curves, and not shifts of curves. A shift in the IS curve to the right might come from an increase in the budget deficit. In this case, the interest rate has to increase in order to keep the equilibrium on the money market (if you wanted to keep the interest rate stable, the central bank would need to use an expansionary monetary policy in order to offset the shift of Md).