It is possible for a country to have a fixed exchange rate and an independent monetary policy. However, it is only possible if the country does not also allow for the free flow of capital in and out of the country. If the country allows capital to enter and leave, it will not be able to engage in expansionary monetary policy while still having a fixed exchange rate.
Let us say that a country is in a recession. In order to solve this problem, it will want to lower its interest rates. When it does this, it will increase its money supply and will thereby stimulate its economy. However, when it lowers its interest rates, it will become less attractive as a destination for investors’ money. People will want to take their money and invest it in other countries where they are likely to get higher returns on their investments. This will mean that money will leave the country.
This is where the problem sets in. If money leaves the country, the exchange rate will have to drop. People are selling the country’s currency as they rid themselves of assets from that country. This increases the supply of the country’s currency and drops the demand for it. Together, these factors cause the value of the currency to drop.
If the country wants a fixed exchange rate, it cannot let this happen. It will have to buy up its currency to reduce supply and maintain demand. If a great deal of money leaves the country, the government will have to spend a great deal of money buying up its currency. It may well run out of foreign currency to use to buy back its own currency.
Because of this, it will be impossible for the government to maintain an independent monetary policy while also maintaining a fixed exchange rate. The only way it can do this is by preventing capital from entering and leaving the country. However, this is a bad thing to do because it limits the country’s ability to expand its economy.