# Unemployment and Labor Force MacroEconomics

Suppose that the total population on the 1st of January 2001 was 40 million people, of which 30 million were above age 16. Suppose that among the latter, 12 million people were not working or actively looking for work, and 2 million were unemployed. 800,000 people are expected to turn 16 during 2001 and half of them are expected to keep studying and not to seek a job, while the other half is expected to seek a job and be ready to start working immediately. How many people have to find a job during 2001 for the unemployment rate to be 8 %.

• I got 12 million need to find a job, but I do not think that is correct. Oct 18 '15 at 23:10
• Could you show some of your work for us? Remember that the unemployment rate is just the number of people actively looking for jobs that don't have one divided by the number of people who have jobs plus those aforementioned job seekers. Oct 18 '15 at 23:29
• I found that the LF = 18.4 million and the number of unemployed and employed are 16 mill and 2.4 mill respectively I used this unemployment rate equation u = ut/LF, u was equal to .08 and ut was 2.4 million and I solved for a labor force when u was equal to 8% I then used LF = E + U and found the new value for employed with LF = to 30 mill and U equal to 2.4 million and then I minused the old E from the new E and found that was the amount of people that needed to find jobs. I dont know about that process though. Oct 18 '15 at 23:45

A short note: please try to show your math work in the original post, and maybe learn some basic Math TeX commands. It makes people much more willing to help with homework questions.

So first, we have our unemployment for the year 2000. Let $U_t, u_t, L_t$ denote the unemployment rate, number of unemployed, and number of laborers at time $t$, respectively.

$$U_t = \frac {u_t}{u_t + L_t}$$ $$U_{2000} = \frac {2,000,000}{2,000,000 + 16,000,000} = \frac{1}{9} \approx 0.111$$

So in the year 2001, 800,000 people turn 16, but half do not enter the labor force. So the question is how many people have to find a job for unemployment to fall below 8%.

$$U_{2001} = \frac{2,000,000 + (400,000 - n)}{2,000,000 + (400,000 - n) + 16,000,000 + n} = 0.08$$

where $n$ is the number of those who found jobs, and $400,000 - n$ is the net change in unemployment numbers. Solve for $n$.

$$\frac{2,400,000 - n}{18,400,000} = 0.08$$ $$\implies 1,472,000 = 2,400,000 - n \implies 928,000 = n$$

So what does this tell us? Even if all 400,000 new 16 year olds found jobs, that would not drive unemployment down to 8%. You need quite a few more people to find jobs.

• No problem. Good luck with your work, and keep in mind what I said. Oct 19 '15 at 3:23