True or False?
The statement is true. When the exchange rate is allowed to float the small country's equilibrium is determined by the intersection of the LM curve and the world interest rate line. The IS curve adjusts automatically through changes in the nominal and real exchange rates to pass through the intersection of LM with the real interest rate line. Any change in the world real interest rate will cause a movement along the LM curve and a change in the small country's output and income in the short run. Insulation from-big country shocks therefore does not occur. Shocks to the small country's IS curve---that is, real shocks in the small country---are automatically neutralized by endogenous changes in the nominal and real exchange rate, so insulation does occur in this case.
The crucial things to keep in mind here is that the LM curve in the small country is positively sloped, so any shift in the world real interest rate line must cause output to change when equilibrium occurs at the intersection of the LM curve and the real interest rate line. You should well understand by now that a flexible exchange rate implies that the equilibrium level of output (and prices) is determined where LM intersects with the world real interest rate. And you should be well aware that real shocks---such as, for example, fiscal policy, in a small open economy do not affect output, employment, and prices when the exchange rate is flexible.