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Suppose the AD curve is relatively flat because the Fed wants a stable price level.

Which policy (monetary or fiscal) is ineffective?

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A flat AD-curve is not the result of the desire of a central bank to stabilize the price level, it is determined by the behaviour of the aggreggate economy (such as elasticities and taxes). Stabilizing the price level by using monetary or fiscal policy can be done by shifting the AD-curve (or influencing the slope of the curve, but that is a less standard option). In this context the effectiveness of monetary and fiscal policy depends on how easily policymakers can shift the AD-curve. If you have an equation for AD, this can be easily calculated as $\frac{\partial Y}{\partial X }$, $X$ being the variable in the AD-equation used to implement the policy.

The effectiveness of monetary or fiscal policy also depends on the slope of the AS-curve, possible shifts in the (short run) AS-curve in response to the policy (such as inflation expectations), and the objective of the policy: price stabilization or outputstabilization.

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