Assume that the job separation rate s is 001 1 per month and

Assume that the job separation rate s is 0.01 (1%) per month and that the job
finding rate f is 0.2 (20%) per month.

Assume that the labor force today (period t = 0) is 100 million.

(a) What is the steady state unemployment rate for this economy?

(b) Given that L = 100 million, what is the steady state number of employed
E and unemployed U today in period t = 0?

(c) Assume U.S. immigration policy changed tomorrow (period t = 1) such
that we allowed more people to enter the country and L increased to 110
million from its inital value of 100 million. Assume that these new entrants
would be unemployed first and then find jobs at the job finding rate f .That
is, at time t = 1, the number of unemployed is U1 =U+10 million, and
the number of employed equals E1 = E. Create a table (maybe in Excel)
that shows how Et , Ut , and Ut=L evolve over time, given s = 0:01 and
f = 0:2, starting at t = 1 and ending when the unemployment rate reaches
its steady stateU=L rounded to the nearest thousandth (tenth of a percent).

(d) In the table from the previous scenario, how many periods does it take for
the unemployment rate to reach its steady state level rounded to the nearest
thousandth (tenth of a percent)?

Solution

a) Job separation rate (s) = 0.01
Job finding rate (f) = 0.2
The steady state unemployment rate is (u) = s / (s+f) = 0.01/(0.01+0.2) = 0.0476 or 4.7 percent
b) The labor force is 100 million, this means 100 × 0.0476 = 4.76 million people are unemployed in steady state. The rest, 100 4.76 = 95.24 million people are employed. The steady state flow into unemployment each month is s(1 u) = 0.01(1 0.0476) = 0.009524 of 100 million, so 0.9524 million people lose jobs each month. This is matched by a steady state flow out of unemployment each quarter of fu = 0.2 * 0.0476 = 0.009524 of 100 million, so 0.9524 million people find jobs each quarter. Two points for each of these.

c) At t =1 ,
Employed = 95.24 million
Unemployed = 4.76 +10 =14.76 million
d) Unemployment rate to reach steady state = 14.76/4.7 = 3.14 = 3 period approx