Monetary policy uses interest rates, the money supply and credit conditions to influence the economy, with quantitative easing (QE) as an additional tool. Its effectiveness varies with the type of problem and the state of the economy.
Controlling inflation. For demand-pull inflation, monetary policy is well suited: raising interest rates reduces consumption and investment, lowering AD and inflation, and an independent central bank gives the policy credibility that anchors inflation expectations. The quantity theory (MV = PT) supports controlling the money supply/credit to control inflation: if V and T are stable, restraining money growth restrains the price level. However, this assumes V and T are stable (Keynesians disagree — V varies, and with spare capacity more money raises output not prices), the money supply is hard to control (banks create credit), and monetary policy is useless against cost-push inflation, where tightening AD merely raises unemployment.
Stabilising the economy / QE. In a recession, cutting interest rates stimulates AD. But when rates hit the zero lower bound, conventional policy is exhausted, and QE is used: the central bank creates money to buy bonds, raising the money supply, lowering long-term rates, and (via cheaper borrowing, more lending and a wealth effect) boosting AD. Strengths: QE can support demand when normal policy fails, as after 2008. Weaknesses: its effects are uncertain — banks may not lend the extra reserves, confidence may be too low, and it mainly inflates asset prices, which can worsen inequality without much real-economy effect.
General limitations of monetary policy. It is a blunt instrument (affects the whole economy, can't be targeted), has time lags (12–24 months), and depends on confidence and the responsiveness of borrowing/spending. It cannot directly tackle structural problems, the balance of payments or inequality.
Judgement. Monetary policy, including QE, is effective for its core purpose — controlling demand-pull inflation and managing AD in normal conditions — and is the main tool of most central banks for inflation targeting, owing to its flexibility and credibility. But its effectiveness is conditional and partial: it is weak in a deep recession (zero bound, low confidence), useless against cost-push inflation, hard to fine-tune (uncertain money control and lags), and QE has uncertain effects and side effects on asset prices and inequality. The most defensible conclusion is that monetary policy is a valuable but limited tool, most effective for demand-pull inflation and AD management, and best combined with fiscal and supply-side policy — with QE as an emergency measure when conventional rates are exhausted, rather than a reliable everyday tool.