A central bank that adopts a fixed exchange rate may sacrifice its autonomy in setting domestic monetary policy. It is sometimes argued that when this is the case, the central bank also gives up the ability to use monetary policy to combat the wage-price spiral. The argument goes like this: "Suppose workers demand higher wages and employers give in, but the employers then raise output prices to cover their higher costs.
Now the price level is higher and real balances are momentarily lower, so to prevent an interest rate rise that would appreciate the currency, the central bank must buy foreign exchange currencies and expand the money supply.
This action accommodates the initial wage demands with monetary growth, and the economy moves permanently to a higher level of wages and prices.
With a fixed exchange rate, there is thus no way of keeping wages and prices down."
What is wrong with this argument?