Instructions: Please show all work or points will be taken off. Good luck!1. (25 points – 5 points each part)a. On the Colbert Report, March 17, 2008, Stephen Colbert makes fun of the fact that the unemployment rate fell even though less people are working (feel free to Google it). Using the formula for the unemployment rate, show how this, the idea that the unemployment rate can fall even though less people are employed, is not as unusual as one may think. Be specific as to what happens, exactly, to the numerator and the denominator of the unemployment rate expression.We are now going to use real economic data to confirm that this phenomenon, the fact that the unemployment rate can fall along with the employed did occur just as Stephen Colbert said. Stephen was referring to the one month change in the unemployment rate between January and February 2008.b. Go to FRED and using the series UNRATE, confirm that the unemployment rate did fall between these two months (simply report the statistics from FRED)c. Using FRED again, search for NPPTTL (these are payrolls – the number of people working) and confirm that payrolls did decline between these two months.d. Finally, using FRED once again, search for UNEMPLOY (the number of people unemployed) and confirm that your reasoning in part a) above was correct.e. Suppose you are talking with someone, call her Mary, shortly after this particular report came out. Mary was trying to convince you that this report, showing that the unemployment fell between January and February 2008, clearly indicates that labor market conditions are getting better. Given that you know the facts, give Mary two specific reasons that suggest that labor market conditions are getting worse rather than better.2. (20 points total, 5 points each part) The table below shows the ‘hypothetical’ basket(s) of consumption goods for a ‘typical’ Penn State college student for 2012 and 2013.Answerthe following questions using the information in the table.2012 Basket for ‘typical PSU college student’2013 Basket for ‘typical PSU college student’ItemPriceQuantityItemPriceQuantityTextbooks$806Textbooks$906Rent$7001Rent$8001PSU sportingevents$156PSU sportingevents$203Dinners inState College$256Dinners inState College$258a. Calculate the rate of inflation between 2012 and 2013 assuming 2012 is the base year. Please show all work. Note, calculate the rate of inflation using price indexes.b. Now update the base year to 2013 and recalculate the rate of inflation between 2012 and 2013. Again, show all work! Calculate the rate of inflation using price indexes.c. Which rate of inflation accounts for the substitution bias? In your answer, identify and explain why, using relative prices, the substitution that this PSU college student rationally made.d. Calculate the ‘Chain Weighted’ rate of inflation (again, show all work).3. (10 points) Discuss the problems associated with using the unemployment rate as a gauge of labor market conditions. In your answer, make sure you mention how underemployment, discouraged workers, and working under the table play a role in terms distorting the signal that we would want the unemployment rate and changes in the unemployment rate to send in terms of labor market conditions.4. (5 points) Go to FRED and search for UNRATE (the unemployment rate) and NROUST (NAIRU) and using the most recent available data, compare the two. How much and in what direction would the actual unemployment rate have to change to get us to full employment = NAIRU? Note that NROUST is quarterly data so simply use the quarter that includes the month of the most recent UNRATE statistic.5. (25 points total) In this problem we are going to calculate real interest rates, both ex-post and ex-ante. The data you need for this problem are given in the links below:Nominal one year rates (i)Price index CPI (P)Expected InflationA couple of notes are in order:Expected inflation data is one year hence – so for example, expected inflation for the period from July 2010 to July 2011 is given in July 2010 and if you view the data, the expected inflation during this time is 2.7% = ?e.To calculate the actual rate of inflation, for example, during the July 2010 to July 2011 period you need to take the percent change in P = %? P. Using the CPI data, we have the price index equaling 217.6 in 7/2010 (beginning of August given the end of month data) and 225.4 in 7/2011 (end of July, 2011). Note, this is a 12 month period. The actual rate of inflation during this time is 3.58% = ?When using the one year nominal interest rate to calculate the all important real rate(s) of interest we need to be careful. For example, using the same one year time period (July 2010 – July 2011) we simply use the one year rate given as of July 2010. Think of buying the bond in July 2010, putting it in a safety deposit box (or under your mattress, a coffee can, etc.) and then cashing it in when it matures in July 2011 (you get your principal times whatever the nominal interest rate is). In viewing the data, the one year rate in July 2010 is 0.29%. So clearly (and by design of the Fed), both the ex-ante and ex-post real rate are negative during this period and differ because expected inflation was not equal to actual inflation.a. (10 points) Calculate the ex-ante and ex-post real rate of interest between June 2008 and June 2009 (note that June 2009 is the last month of the Great recession – the official recovery, began in July of 2009). Why are these real rates so different?Again, please show all work.b. (10 points) We know that most decisions are in part, based on expectations of the future. Suppose we have two people who are trying to decide whether to consume today (assume it is currently June 2008) or save for the future and consume one year later, in June 2009. One person, let’s call him Joe, is basing their decision on the exante real rate of interest like most of us do. The other person who has a crystal ball, we’ll call her Crystal, can see exactly what the actual rate of inflation is going to beand thus, has perfect foresight and bases their decision on the ex-post real rate. Given the difference in the ex-ante and ex-post real rates above, who would be more likely to save and who would be more likely to spend? Explain in detail and feel free to use the shopping cart example we used in lecture.We discussed the ‘evils’ of deflation.c. (5 points) Given your response in part b) above, is the behavior of either Joe or Crystal consistent with the ‘evils’ of deflation? Why or why not. Explain.6. (15 points total) Use the information in “Study shows costs of living for working families leveling off in Pa.” to answer the following questions:a. (5 points) Using Allegheny county as the base county, what is the price index in Centre county? In Chester county? Please show your work.b. (10 points) If you are currently making $75,000 per year in Centre county, how much would you need to make in Allegheny county to have the same real purchasing power as you have in Centre county? Answer the same question for Chester county (i.e., how much do you need to make in Chester county to have same purchasing power as you do with $75,000 in Centre county).7. (10 points) A friend of mine came to Penn State in the 1970s and told me that sticky buns at the College Diner cost $.75 (75 cents) in December of 1976. Using the CPI and assuming that the price of sticky buns rose in exact proportion to the CPI, what would the current price of sticky buns have now so that the ‘real price’ of sticky buns remains constant. Use the most recent available data for the CPI and please show work.
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