# Explain and interpret each of these equations in turn, and carefully define each of the variables and parameters in each equation.

ECONOMICS 305: INTERMEDIATE MACROECONOMICS

PROBLEM SET 4

Please read Chapters 7, 8, and 9 before attempting this assignment, as well as the lecture

slides.

Question 1: The Labor Market

Suppose that the product and labor market are characterized by the following three

equations: = = (1 + ) = (1 ? + )

a) Explain and interpret each of these equations in turn, and carefully define each of

the 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 market

equilibrium 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 output

and employment to the unemployment rate, to re-express the short-run labor

market 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 the

natural rate of unemployment in this equilibrium. What is the key assumption which

characterizes medium-run equilibrium but not short-run equilibrium? Depict

medium run equilibrium in a graph.

f) Derive and/or show graphically the response of the natural rate of unemployment

to an increase in m. Derive and/or show graphically the response of the natural rate

of unemployment to an increase in z. Explain carefully why increases in m and z

affect the natural unemployment rate as they do. Question 2: Labor Market Data

Study 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 are

calculated, by doing your own computation and showing your workings for each quarter

from 2013:4 to 2016:4;

a) The participation rate

b) The employment-population (employment rate) ratio

c) The unemployment rate

d) Those not in the labor force

Summarize the differences in participation rate across the following groups and offer a

brief explanation for the differences:

a) Men vs. women

b) Men 16 years and older vs. men 20 years and older

c) Both sexes 16 to 19 years vs. total

Question 3: The Phillips Curve

Suppose that a country’s Modified Phillips Curve is given by = + 0.1 ? 2

a) Define each variable in the Phillips Curve relationship. Briefly describe the

relationship that it represents. [Hint: relate the Phillips Curve back to the type of

short-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 the

rate of unemployment is initially equal to its natural rate. In year t, policy authorities

decide 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 the

inflation expectations mechanism assumed (i.e. ? = 0) is reasonable? Why or why

not?

Suppose that in year t+5, ? increases from 0 to 1. Suppose that the government is still

determined to keep the unemployment rate at 3% forever.

d) Why might ? increase from 0 to 1? [Hint: recall our discussion of inflation dynamics

in 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 inflation

expectations mechanism assumed here (i.e. ? = 1) is reasonable? Why or why not?

Question 4: IS-LM-PC

Use the IS-LM-PC Model of Chapter 9 to answer this question. Assume that the economy

initially begins in medium run equilibrium.

a) In any medium run equilibrium, what are the values of the unemployment rate, the

employment level, the output level, and the expected inflation rate? Depict this

medium run equilibrium in an IS-LM-PC diagram – and consider this equilibrium to

obtain at date t.

b) Suppose there is an increase in consumer confidence in period t+1. How does the IS

curve shift? What does the resulting short-run equilibrium look like in an IS-LM-PC

diagram? How do the values of the unemployment rate, the employment level, the

output level, and the expected inflation rate change relative to their initial medium

run 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. In

other 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 does

actual inflation at date t+2 compare to inflation at t+1? What would this equilibrium

look like in an IS-LM-PC diagram? Given expected inflation, what must the central

bank 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 a

way to return the economy to the medium-run equilibrium output level and to the

initial 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 a

diagram 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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