45 Wl 5G @ { EC12Problem Set4 Q Problem Set 4 Macroeconomic Theory EC12 Tufts University Spring 2024 Prof. Fusillo Please answer all questions. The due date is April 7" at midnight. 1) Assume a technological advance leads to lower production costs. Show the effect of such an event on national income, unemployment, inflation, and interest rates with the help of an AD-AS diagram. Assume completely flexible wages. How would your analysis differ (if at all) if wages were rigid? 2) Suppose the supply of money in your economy has been growing at 6% per year while real output grows at the same rate. If velocity is constant and the growth rate of money rises to 10% per year, what would be the impact of such a change on: a) the annual rate of inflation (Use the quantity Equation) b) the real interest rate c) the nominal interest rate d) investment (ignore both taxes and uncertainty) e) real GDP 3) Suppose the Phillips curve can be written as 1, = mf + 0.2 5u a) Derive the natural rate of unemployment for this economy. b) Suppose now that expectations are set via the expression { = &m,_,where & is a coefficient governing the response of expected inflation in the current period to actual inflation in the previous period. If = 0, what does this say about how expectations are formed? Are the rational or adaptive? What about if > 0? c) Assume that = 0 and that the government of this country wants to reduce unemployment to 3.0% forever. What would the effect of this policy be on inflation in any given future year? Can this hold intuitively? d) Now suppose that the government insists on holding to the 3% unemployment rate policy. For the first three periods, agents' inflation expectations continue to be uninfluenced by past inflation. Starting in period 4, however, agents begin to wise up and change their expectations for inflation according to 7, = . What is the rate of inflation in periods 4-6? Does this make more, or less sense than the outcome in part (c)? 4) Suppose that on average it takes you 10 weeks to find a job once you enter the labor market and that on average, jobs last for a total of 400 weeks. a) What s the rate of job finding per month? b) What s the rate of job separation? c) What s the natural rate of unemployment for this economy? d) Now suppose the initial unemployment rate is 8.0 percent and the unemployment rate evolves monthly according to Uy = Uy + S_; fU,_, where is the rate of job separation, f is the rate of job finding and e is the share of employed workers. How long before the economy converges (to three digits) to the natural rate? (A spreadsheet wil be useful here) e) How would your answer be impacted if the government raised unemployment benefits as in the case of the 2008-09 \"Great Recession\"? D (! D &'08 (o= (ol T To Do Notifications Inbox