1. manage the exchange rate to keep it constant in the face of big-country monetary shocks.
2. contract the domestic money supply when the big country experiences a negative monetary shock.
3. expand the domestic money supply when the domestic currency devalues as a result of a monetary shock in the big country.
4. do all of the above.
Choose the correct option.
Option 2 is the correct one. When the big country experiences a negative monetary shock its LM curve will shift to the left and the world real interest rate will rise. If the exchange rate is flexible small-country equilibrium will be at the intersection of its LM curve and the real interest rate line. Since the LM curve is positively sloped, output will increase. To prevent output from rising, the small country's central bank has to contract the money supply, shifting LM to the left. The currency will have to depreciate in real and nominal terms to shift the IS curve to the right to cross the interest rate line at the original level of output. The small country's money supply will be contracting, not expanding, as the domestic currency devalues.
In the long-run, of course, when LM* and the world real interest rate return to their initial pre-shock levels the authorities in the small country have to expand the money supply to its initial level to shift LM back to its original position---otherwise the domestic price level would have to fall.