Consider the following model, characterized by an IS curve Yt = 2t - btrt, an inflation equation, Tt=Tt1+Kt and a modified interest rate rule that has the Fed respond to both inflation and output: rt = m(t Ft) + nyt 1. Derive the AD curve in this economy: an expression relating the amount of output consumers demand as a function of interest rates in the economy. 2. Draw the AD curve for an aggressive Fed (high n) and another one for a passive Fed (low n) in the same diagram. 3. Show how output and inflation respond over time to a negative demand shock at as a function of how aggressive the Fed is. Use both AD-AS diagrams (one for each Fed type) and also plot the time paths of output and inflation.