A negative shock in aggregate demand will likely result in a permanently lower equilibrium inflation rate, unless the central bank responds by lowering interest rates.
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True.
When aggregate demand falls, the AD curve shifts leftward, lowering both price level and real GDP. In absence of intervention, in long run, lower price level decreases cost of inputs and firms incraese output, increasing aggregate supply. As a result, new short run aggregate supply curve intersects new AD curve at a further lower price level, increasing output.
But if central bank lowers interest rate when AD falls, it boosts consumption and investment, increasing aggregate demand. The AD curve shifts rightward, restoring higher output at a higher price level, therefore inflation rises compared to a no-intervention policy.
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