Q. How A Central Bank Fixes the Exchange Rate?
Answer: The Central bank should always be willing to trade currencies at the fixed exchange rate with the private actors in the foreign exchange market to hold exchange rate constant. Presume central bank fixes exchange rate at E0. Foreign exchange market is in balance when interest parity condition holds - when R the domestic interest rate equals R* the foreign interest rate plus (Ee - E)/E, the expected rate of depreciation of the domestic currency against foreign currency.
E0 is today's balance exchange rate only if:
R = R*
To embrace the domestic interest at R* the central bank's foreign exchange intervention should adjust the money supply so that R* equates aggregate real domestic money demand and the real money supply.
MS/P = L(R*,Y)
When central bank interfere to hold exchange rate fixed it should automatically adjust the domestic money supply thus that money market equilibrium is maintained with R = R*.