Describe when and why central banks buy either their own currency or the currency of another nation in an effort to control exchange rates?

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Hayley Clarke answered
In macroeconomic terms, exchange rates are determined by demand and supply. A managed float system is what the name for such involvement is, the purpose of which is to prevent sudden large swings in the value of a nation’s currency.

$1.5 trillion worth of currencies changes hands every day in the world market, making it difficult for any one agency to force significant changes in exchange rates. The country’s central bank might seek to hold off further increases in currency rises in order to prevent a major reduction in net exports. An announcement that further increases in its exchange rate are unacceptable  followed by sales of that country’s currency by the central bank, in order to bring its exchange rate down, can sometimes convince other participants in the currency market that the exchange rate will not rise further.

That change in expectations could reduce demand for and increase supply of the currency, thus achieving the goal of holding the exchange rate down. In a fixed exchange rate in which the exchange rate between two currencies is set by government policy, the exchange rate between two currencies is set by government policy, a modern-day version of the gold standard, where commodity was king.

With each currency’s value fixed in terms of the commodity, currencies are fixed relative to one another. In 1944 a new mechanism through which international trade could be financed after the war was made. The Bretton Woods Agreement of 1944 called for each currency’s value to be fixed relative to other currencies. The mechanism for maintaining these rates was to be intervention by central banks in the currency market.

When a central bank sells an asset, the checks that come into it reduce the money supply and bank reserves; when it purchases assets, it adds reserves to the system and increases the money supply. Fixed exchange rate systems offer the advantage of predictable currency values, but countries participating in them must maintain domestic economic conditions that will keep equilibrium currency values close to the fixed rates. When exchange rates are fixed, but fiscal and monetary policies are not coordinated, equilibrium exchange rates can move away from their fixed levels.

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