True or False?
The statement is true. The key-currency country sets the level of its LM curve by choosing its money supply. The world interest rate will be determined by the intersection of this LM with the key-currency country's IS curve. The peripheral country will be out of asset equilibrium whenever the resulting world real interest rate line does not pass through the intersection of its IS and LM curves. To maintain the exchange rate parity, it will thus be forced to adjust its money supply until its LM curve crosses its IS curve at the world interest rate line. Any attempt to expand its money supply will result in an equivalent loss of foreign exchange reserves.
Even if the key-currency country were much smaller than the aggregate of all peripheral countries the result will be the same. As long as the key-currency country holds its money supply constant at some chosen level its equilibrium will be determined entirely by the intersection of its LM curve with its IS curve. Nothing that happens in the peripheral countries can change that intersection as long as the key-currency country does not care about the situation in the peripheral countries and manage its money supply with respect to conditions beyond its borders.
We are assuming that peripheral countries hold their foreign exchange reserves in key-currency country interest-bearing assets. Were they to hold these reserves in key-currency cash, increases in the stock of peripheral country foreign exchange reserves would, by taking key-currency out of circulation, reduce the key-currency country's money supply. A huge peripheral country attempting to expand its money supply, and losing reserves as a result, would thus reduce the money supply of the much smaller key-currency country and thereby raise the world interest rate and reduce output and employment both abroad and at home. Its expansionary monetary policy would thus have the opposite effect to that intended.