Steady-state unemployment in the labor market is fU = sE . In District 12, at th
ID: 1133476 • Letter: S
Question
Steady-state unemployment in the labor market is fU = sE. In District 12, at the beginning of July, there are 30 people, 27 of them are employed, and 3 of them are unemployed and actively looking for work. The following events occur in July and August:
July 30: Sandy retires from Mellark's bakery
August 12: Terry, who was unemployed, got a job
August 21: Pat, who had a job, got laid off and started looking for work
Show your work while answering these questions:
(6 points) What are the values of L, E, and U at the beginning of August?
(10 points) What are the values of L, E, U, s, and f at the end of August? (s and f to 3 decimal places)
(3 points) What is the unemployment rate in District 12 at the end of August? (whole percent)
(3 points) What other changes in the labor force would have to occur in August to bring the labor market in District 12 to steady state?
(3 points) What effect did Sandy's retirement have on the unemployment rate in July? Explain.
Explanation / Answer
Solution:
f*U = s*E, where, f is the rate of job finding, s is the rate of job seperation, U is the number of unemployed people and E is the number of employed people.
In the beginning of July, E = 27, U = 3 and L = 27 + 3 = 30
1) At the beginning of August, only one transition has taken place i.e, Sandy has retired. Note that once retired, a person isn't actively looking for job as well. So, Sandy is no longer a part of the labor force as well. Thus, L = 30 - 1 = 29
So, now E = 27 - number of people who are no more employed = 27 - 1 = 26
There has been clearly no change in the number of unemployed people, so U = 3
2) By the end of August, additional transitions that have taken place are:
Unemployed person Terry got a job, so a transition from no job to job (movement from unemployment to employment). Since, f is the fraction of those among unemployed who found a job, and as here, only 1 person among 3 unemployed persons has found a job. So, f = 1/3 = 0.333
Pat got laid off, though he is still looking for work actively. So, since he got laid off, he is no more part of employed people, but since he is still actively looking for a job, he's part of the labor force. s is the fraction of those who have separated from the jobs among employed persons. Since, Sandy has also retired, total job separations = 2 (Pat and Sandy). So, s = 2/27 = 0.074
By the end of August, then
Number of employed, E = 27 - 2 + 1 = 26 (job seperation of Pat and Sandy, addition of Terry)
Number of Unemployed, U = 3 - 1 + 1 = 3 (Terry moved out of unemployment, but Pat moved in unemployment section)
Labor force, L= E + U = 26 + 3 = 29 (or simply 30 - 1 = 29, as calculated in part 1), for retirement of Sandy)
3) Unemployment rate, u = U/L. So, at the end of August, in District 12, u = 3/29 = 0.103
4) Now, f*U = (1/3)*3 = 1
And, s*E = (2/27)*26 = 1.926
Clearly, f*U isn't equal to s*E, so District 12 hasn't yet reached the steady state level. So, changes in labor force could be Decrease in s or E or increase in f or U, that is lower fraction of number of persons separating from job, or lower number of people employed, or higher fraction of number of people who found job or more unemployed number.
5) Sandy' retirement decreased the labor supply from 1, giving new labor supply = 30 - 1 = 29. Unemployed number of people is still the same (due to argument mentioned above that post-retirement, person won't search for a job and so will no more be a part of either employed, or labor force)
So, in July, unemployment rate = 3/29 = 0.103