It would be more accurate to say that they pick the money supply necessary to make interest rates be what they want. When the Fed announces a cut in interest rates, this is normally equivalent to increasing the rate of money supply growth. Aggregate Demand Policy With Keynesian AS, AD shifts can affect output as well as the price level. Compensate for fluctuations that exist due to menu costs and money illusion. Compensate for problems created by other government policies, such as minimum wage.
Some effects happen quickly, others take more time to unfold.
When events happen, it takes time for the government to find out what happened. Once the government finds out what has happened, it takes time to decide what, if anything, to do differently. Once the Fed decides to do something differently, this decision affects some aspects of the economy quickly, others more slowly. Due to lags, policies may in principle be helpful, but in practice still unworkable. You may wind up responding to problems that will have solved themselves by the time your policies take effect.