# Explain how and why each of the other variables in this condition influences .

ECONOMICS 305: INTERMEDIATE MACROECONOMICSPROBLEM SET 4Please read Chapters 7, 8, and 9 before attempting this assignment, as well as the lectureslides.Question 1: The Labor MarketSuppose that the product and labor market are characterized by the following threeequations: = = (1 + ) = (1 ? + )a) Explain and interpret each of these equations in turn, and carefully define each ofthe variables and parameters in each equation.b) Why and how is the first equation related to the second equation?c) Combine the second and third equations to derive a short-run labor marketequilibrium condition, expressed as an equation that determines the price .Explain how and why each of the other variables in this condition influences .d) Use the first equation, and the algebra we saw in class that relates the level of outputand employment to the unemployment rate, to re-express the short-run labormarket equilibrium condition that you derived in c) as a relationship between and .e) Now derive the medium-run labor market equilibrium condition and solve for thenatural rate of unemployment in this equilibrium. What is the key assumption whichcharacterizes medium-run equilibrium but not short-run equilibrium? Depictmedium run equilibrium in a graph.f) Derive and/or show graphically the response of the natural rate of unemploymentto an increase in m. Derive and/or show graphically the response of the natural rateof unemployment to an increase in z. Explain carefully why increases in m and zaffect the natural unemployment rate as they do. Question 2: Labor Market DataStudy the data at this link: http://www.bls.gov/web/empsit/cpsee_e01.pdf. For the “Total”numbers in the first few rows of the table, show exactly how the following numbers arecalculated, by doing your own computation and showing your workings for each quarterfrom 2013:4 to 2016:4;a) The participation rateb) The employment-population (employment rate) ratioc) The unemployment rated) Those not in the labor forceSummarize the differences in participation rate across the following groups and offer abrief explanation for the differences:a) Men vs. womenb) Men 16 years and older vs. men 20 years and olderc) Both sexes 16 to 19 years vs. totalQuestion 3: The Phillips CurveSuppose that a country’s Modified Phillips Curve is given by = + 0.1 ? 2a) Define each variable in the Phillips Curve relationship. Briefly describe therelationship that it represents. [Hint: relate the Phillips Curve back to the type ofshort-run labor market equilibrium condition that you discussed in Question 1.]b) Solve for the numerical value of the natural rate of unemployment in this country.Show all of your workings, and briefly explain them.Assume = ?1 and suppose that ? is initially equal to 0. In addition, assume that therate of unemployment is initially equal to its natural rate. In year t, policy authoritiesdecide to bring the unemployment rate down to 3% and hold it there forever. c) Determine the rate of inflation in years t, t+1, and t+5. Do you think that theinflation expectations mechanism assumed (i.e. ? = 0) is reasonable? Why or whynot?Suppose that in year t+5, ? increases from 0 to 1. Suppose that the government is stilldetermined to keep the unemployment rate at 3% forever.d) Why might ? increase from 0 to 1? [Hint: recall our discussion of inflation dynamicsin the pre-1960 era and after 1960.]e) What will the inflation rate be in years t+5, t+6, and t+7? Do you think the inflationexpectations mechanism assumed here (i.e. ? = 1) is reasonable? Why or why not?Question 4: IS-LM-PCUse the IS-LM-PC Model of Chapter 9 to answer this question. Assume that the economyinitially begins in medium run equilibrium.a) In any medium run equilibrium, what are the values of the unemployment rate, theemployment level, the output level, and the expected inflation rate? Depict thismedium run equilibrium in an IS-LM-PC diagram – and consider this equilibrium toobtain at date t.b) Suppose there is an increase in consumer confidence in period t+1. How does the IScurve shift? What does the resulting short-run equilibrium look like in an IS-LM-PCdiagram? How do the values of the unemployment rate, the employment level, theoutput level, and the expected inflation rate change relative to their initial mediumrun values? What are the economic mechanisms that lead to these changes?c) Suppose that expected inflation rate at t+2 equals the actual inflation rate at t+1. Inother words, suppose that expected inflation just equals last period’s inflation rate, +2= +1 .If the central bank leaves the policy real interest rate unchanged at t+2, how doesactual inflation at date t+2 compare to inflation at t+1? What would this equilibriumlook like in an IS-LM-PC diagram? Given expected inflation, what must the centralbank do to the nominal policy rate to maintain a constant real interest rate?Continue to period t+3 assuming the same expectations mechanism for inflation,and compare actual inflation in t+3 to actual inflation in t+2.d) Suppose that in t+4, the central bank decides to change the real policy rate in such away to return the economy to the medium-run equilibrium output level and to theinitial inflation rate. What must the central bank do to achieve these two goals?Show the path of central real rate policy, of equilibrium output, and inflation vs. expected inflation as the economy moves towards medium run equilibrium in adiagram and explain your diagram carefully. e) Suppose now that expected inflation is constant and, at t+2, it is given by +2= ?.Re-do parts c) and d) under this alternative assumption and compare your results.

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