The solution isn\'t really clear to me. Can someone show me how to work this pro
ID: 1201567 • Letter: T
Question
The solution isn't really clear to me. Can someone show me how to work this problem please?!
[14 points, CHALLENGE] Assume that in Babilonia no one is born or dies, but just spend their life either out of the labor force, or in the labor force and unemployed, or employed. Assume crucially that these percentages are unchanged, year after year. Every year 1% of those out of the labor force enter the labor force and 3.5% of those unemployed leave the labor force. Assume also that every year 24% of the unemployed find jobs, while 3% of those employed lose jobs, and become unemployed.
• What are the steady-state percentages of Babilonia residents out of the labor force, in the labor force and unemployed, and employed.
Hint: The flows into and out of the pool of people out of the labor force must balance and
the flow of people in and out of the pool of employed must balance. And, of course, all the percentages must add up to 100%. Now, set up three equations and three unknonws and solve.
• Make sure you show all your calculations. Solution:
Let x = fraction not participating, y = fraction in labor force and unemployed, z = fraction employed.
Then from the given information, we have three equations: x+y+z =100% & 3.5y =1x & 24y = 3z.
Solving, yields x=28%, y = 8%, and z= 64%.
Explanation / Answer
Indeed as you said question would be a confusing one for the beginner.
Let me simplify for you :
There are two cases :
either out of the labour force
in labour force employed or unemployed
we have been asked for steady state change of Babilonia residents out of the labor force, in the labor force and unemployed, and employed.
Here is the soultion you have given :
Let x = fraction not participating ( not in labour force), y = fraction in labor force and unemployed, z = fraction in labour force employed.
let write the information given in the question:
Every year 1% of those out of the labor force enter the labor force and 3.5% of those unemployed leave the labor force. Assume also that every year 24% of the unemployed find jobs, while 3% of those employed lose jobs, and become unemployed.
Then from the given information, we have three equations: x+y+z =100% & 3.5y =1x & 24y = 3z.
Solving, yields x=28%, y = 8%, and z= 64%
As per the condition we have to get total population to 100%
1% out of force have entered into labour and 3.5 % have left the labour
24 % un employed find jobs in the force who are in labour 3% of those employed lose job.
See , we have been asked to balance out the in and out
Now is the trickiest part comes into picture
1% is entering = 3.5 % leaving (agree ?)
3% lost job = 24 % got job ( agree ? )
from the assumptions we make
we can write 3.5y=1x
x=3.5y
24y=3z
z=24y/3
z = 8 y
now substitute x and z in the equation x+y+z = 100
we will get the value of y after solving
(3.5y+y+8y)=100
y(3.5+1+8)=100
y= 100/13.5
y=8 % approximately
substitute the smae in the x=3.5*7 = 25
Substitute in z we will get 8*8 right ? So, z=64
Totally we make 100 % so balance,,,
Hope this helped you ..
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Happy solving !