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The central bank is independant from the political power. We have to distinguish the monetary policy (central bank) from the fiscal policy (government). If the central bank increases the money supply (how much money there is in the economy), it's not going to lower interest rates as they are already near zero, and thus it's not going to increase investments, and thus it's not going to increase GDP. That's the liquidity trap. Britain spending money is something different, it's about the fiscal policy. It might help the country exit the liquidity trap, but it's not what the liquidity trap is fundamentally about.