How Retirement Changes Affect Unemployment Rates

[s3a]

Homework Statement

If increasing retirements by 'baby-boomers' reduce the annual growth rate of the labour force from 3 percent to 2 percent while employment continues to grow by 2.5 percent, then:

A) The unemployment rate will remain unchanged.
B) The unemployment rate will decrease by about 0.5%. [CORRECT ANSWER]
C) The unemployment rate will decrease by about 4.5%.
D) The unemployment rate will increase by about 0.5%.
E) The unemployment rate will increase by about 4.5%.

Homework Equations

i. Employment Rate = (Number of Employed / Total population that's the minimum age for holding a job)
ii. Unemployment Rate = (Number of Unemployed / Labour Force) * 100
iii. Labor Force = Number of Employed + Number of Unemployed

The Attempt at a Solution

I've been trying, for several days, to understand why what I am doing works.

Basically, mechanically, I get that one can do as follows.:
Labor Force = Number of Employed + Number of Unemployed
+2% = +2.5% + Number of Unemployed
2% = 2.5% + Number of Unemployed
2% - 2.5% = Number of Unemployed
Number of Unemployed = 2% - 2.5%
Number of Unemployed = -0.5% (which gives B as the correct answer)

What confuses me is that the employment rate and unemployment rate have different denominators, where the employment rate and unemployment rate can change for reasons other than the number of people employed or number of people unemployed changing.

For example, what if something changes with the total population that's the minimum age for holding a job or with the labour force (in other words, the denominators of the employment and unemployment rates)? Then, the rates would change, but the number of people employment or unemployed wouldn't, so why does the Labor Force = Number of Employed + Number of Unemployed work?

How can I justify that the Labor Force = Number of Employed + Number of Unemployed works with rates of change rather than the raw numbers for people in the labour force, people employed and people unemployed? Put differently, why does it work in solving the problem I posted on this thread?

If something is unclear, tell me, and I will attempt to clarify it.

 

[mfb]

The employment rate is not used at all. Just the total employment ("Number of Employed") is used. And apparently its growth is measured relative to the total labor force (this is not clear from the problem statement, just from the answer) which looks a bit odd.

Maybe they do mean employment rate, and absolute 2.5% (e.g. "before 90% had a job, now we generated new jobs equivalent to 2.5% of the total labor force). Otherwise the answer does not fit.

 

[s3a]

So, basically, the question is using the word "rate" in the mathematical sense (as in the rate at which the number of employed people increases) instead of the macroeconomic-term sense (as in the formulas with no summation in my first post)?

I ask because if I use the formula (unemployment rate) = (number of people unemployed) / (total labour force) as follows, I get something other than -0.5%.:
(unemployment rate) = (-0.5%) / (+2%) * 100%
(unemployment rate) = -25%

Is it just me or is the word "rate" generally a misnomer in employment "rate" and unemployment "rate"? Would a better word for these macroeconomic terms be "ratio"?

 

[s3a]

Actually, to be pedantic, this website ( http://en.wiktionary.org/wiki/rate#Noun ) says that a rate is "the proportional relationship between one amount, value etc. and another", so I guess "rate" is not a misnomer.

But, what about what I said above that which suggests the word "rate" it's a misnomer?

 

[dragoneyes001]

employment continuing to grow at 2.5% is a rate of growth.
removing the baby boomers into retirement to slow the increase in the labor force from 3 to 2 percent would make the "highlighted" answer correct.

the number of people who can work is being altered making a stable/constant increase in jobs have a positive effect on unemployment numbers. the reverse could be that a new increase in births 15 odd years ago could flood the labor force making a 2.5 % increase in jobs be an increase in unemployed.When compared to the labor force.