True or False?
The statement is true. By the word endogenous we mean determined entirely be other variables in the model. The level of the IS curve is indeed endogenous. Under less-than-full-employment conditions, the nominal and real exchange rates will always adjust to ensure that the IS curve crosses the ZZ line at the same point as the LM curve crosses it. Under continuous full-employment conditions, the nominal but not the real exchange rate will adjust to maintain the real exchange rate at its full-employment level when the domestic price level rises and falls as a consequence of monetary shocks, thereby maintaining the IS curve at the position where it crosses through the intersection of the LM curve, the ZZ line and the vertical full-employment YF line. Changes in the domestic demand and supply of money will cause the domestic price level to change so as to ensure that the LM curve crosses through the intersection of the ZZ and YF lines. The nominal exchange rate will then adjust in the same proportion as the domestic price level to maintain the real exchange rate at a level consistent with the IS curve passing through that intersection.
To be sure, exogenous shocks will occur to variables determining the level of the IS curve---for example, to desired imports and exports. But these shocks will be exactly matched by offsetting adjustments of the real exchange rate to maintain the IS curve unchanged.