Question 4: Quantifying the AS/AD dynamics (8 points) In the AS-AD model, Central Banks face a trade-off between inflation and output gap following costpush shocks. We now quantitatively assess the extent of this trade-off. Consider the standard AS-AD model derived in class. 1. Compute the response on impact of short-run output and inflation to a positive cost-push shock as a function of the parameters of the model? Do you expect the unemployment rate to increase or decrease in response to the shock? 2. How does the inflation and output response change if the Fed becomes more aggressive in fighting inflation? Prove your answer mathematically and provide an intuition graphically. Let's simulate the response of output and inflation over time. For this part you can use any software to help you with calculation and plotting. If you are using a software, export the graphs and solutions on a pdf file. For this part consider the following parameters: =2%,v=0.5,m=0.5,b=0.5. Assume the economy starts at potential (in t=0,0= and Y~0=0 ). 3. In period one (t=1), the economy is hit by a cost-push shock, o1=2%, lasting one period. Compute the values of short-run output and inflation rate for the first 10 periods after the shock. (Hint: solve the AS-AD system of two equations in two unknowns, t,Y~t, for t going from 1 to 10.) Graphically illustrate the dynamics of the economy. How does your answer change if m=0.1 ? Explain the intuition. Focus on the response of inflation and output on impact and the persistence of the effects over time. 4. In period one (t=1), the economy is hit by a demand shock, a=2%, lasting two periods. 4 Compute the value of short-run output and inflation rate for the first 10 periods after the shock. Graphically illustrate the dynamics of the economy. How does your answer change if the demand shock lasts four periods? Explain the intuition. Focus on the response of inflation and output on impact and the persistence of the effects over time