# Problem Set _ 9 Unemployment Steady States and Un-Steady States.pdf by tongxiamy

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```									        Econ 30233                            Intermediate Macroeconomics                      John Lovett

Problem Set # 9

Overview: In this problem set you will use the model described in chapter 6 of Mankiw’s
Macroeconomics to determine the unemployment rate under various conditions.

Instructions
0. All of your work should be done a separate sheet(s) of paper, not this handout. Base your
answers on the model presented in chapter 6 of Mankiw’s Macroeconomics. Assume that all
values are monthly values (ex. s = monthly separation rate) unless otherwise noted. Assume
the labor force is 200 million in all scenarios.

1. The Natural Rate: Assume s = 0.04. Assume that f = .20. This are the economy’s long-run
job separation and job finding rates. i.e. They are the “natural values” for the economy.
a. Algebraically, solve for the economy’s steady state unemployment rate (URate). Next solve
for the # unemloyed (U), and the # employed (E).
b. Construct a chart like that shown below and fill it in the second (blank) row.     This is to
demonstrate that you have truly solved for a steady state.
Job      Job
U           E            L    URate     finders losers per
per mo.    mo.
state values. Then shift 1 million →
people from the employed to the
unemployed.

state values. Then shift 1 million →
people from the unemployed to
the employed.
c. Let’s tweak things a bit. Start from the steady state. Then shift 1 million people from the
employed to the unemployed. Assume s and f have not changed. Fill in this row on your
chart.
• Is the labor market in a steady state after this change?
• If not, is the labor market heading back towards the steady state? Explain how you
know this.

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Econ 30233                                    Intermediate Macroeconomics                                   John Lovett

d. In the words of Will Smith, “let’s get tweaky”.1 Start from the steady state. Then shift 1
million people from the employed to the unemployed. Assume s and f have not changed.
Fill in this row on your chart.
• Is the labor market in a steady state after this change?
• If not, is the labor market heading back towards the steady state? Explain how you
know this.

2. Recession!: Yowza! In July 2005, a recession rocks the land. Job separation rates increase
and job finding rates decrease. Assume that s = 0.08. Assume that f = .10. However, it may
take a while for the economy to reach a new steady state.
a. Insert the natural steady state values you solved for in problem 1a and 1b. This is where the
economy starts from.
b. Now assume that jobs are lost and found at the new rates. Show the condition of labor
markets one month later (July 2005).
The number leaving jobs from June to July is equal to s×EJune.
The number getting new jobs from June to July is equal to f×UJune.
The change in the # unemployed = ∆U = existing jobs lost – new jobs found.
The change in the number employed = ∆E = new jobs found – existing jobs lost.
New jobs Existing
U             E             L            URate
found jobs lost

June 2005: Insert the natural rate
→
steady state values here (from 1a & 1b).

July 2005: Values 1 month later               →

August 2005: Values 2 months later              →
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The new (recession) steady state.              →

c. Calculate the values after 2 months of recession, i.e for August 2005. Fill in this row.
d. Calculate the new steady state if these values of s and f hold indefinitely. Fill in this row.

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7 out of 8 economists surveyed think that saying this quote makes them sound really cool. 7 out of 8 students
surveyed believe that: 1) no it doesn’t, and 2) Will Smith actually said something else.
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Econ 30233                           Intermediate Macroeconomics                         John Lovett

3. Recovery!: Thank goodness! In July 2007, the economy begins to recover. Job separation
rates decrease and job finding rates increase. Both return to their natural levels, Assume that s =
0.04. Assume that f = .20. However, it may take a while for the economy to reach a new
a. Insert the natural steady state values you solved for in problem 1. This is where the
economy starts from.
b. Now assume that jobs are lost and found at the new rates. Show the condition of labor
markets one month later (July 2007).
The number leaving jobs from June to July is equal to s×EJune.
The number getting new jobs from June to July is equal to f×UJune.
The change in the # unemployed = ∆U = existing jobs lost – new jobs found.
The change in the number employed = ∆E = new jobs found – existing jobs lost.
New jobs Existing
U          E           L            URate
found jobs lost

June 2007: Insert the recession steady
→
state values here (from 2d).

July 2007: Values 1 month later       →

August 2007: Values 2 months later     →
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The new (natural rate) steady state.
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Same as in 1a and 1b.

c. Calculate the values after 2 months of recovery, i.e for August 2007. Fill in this row.

d. Calculate the new steady state if these values of s and f hold indefinitely. Hint. This should
look a lot like 1a and 1b. Fill in this row.

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