<p>You can google <a href="https://www.google.com/search?q=%22unemployment%22+ppf+frontier" rel="nofollow noreferrer">PPF unemployment</a> and <a href="https://www.google.com/search?q=%22retirement%22+ppf+frontier" rel="nofollow noreferrer">PPF retirement age</a>. One of the first entries, <code>homework.study.com</code> discusses both circumstances.</p>
<p>In any case, a <span class="math-container">$\color{blue}P$</span>roduction <span class="math-container">$\color{blue}P$</span>ossibility <span class="math-container">$\color{blue}F$</span>rontrier (<span class="math-container">$\color{blue}{PPF}$</span>) represents all possible combinations of output that can be produced by fully and efficiently utilizing all factors of production. See for example <a href="https://en.wikipedia.org/wiki/Production%E2%80%93possibility_frontier" rel="nofollow noreferrer">Wikipedia</a>. It is clear that an economy with unemployment is not fully utilizing its ressources (labour force). The Wikipedia article also offers a formula for a simple non linear frontier with two goods (linear would do as well).</p>
<p><span class="math-container">$$q2 = (q1 - 7/2)^{-1} + 7/2$$</span></p>
<p>where q2 and q1 are the quantities for each product. In the simplest case, there are only workers, and no technology or capital. In this case, you can just think of 7 being the number of workers (say millions).</p>
<p>Below, I use <a href="https://julialang.org/" rel="nofollow noreferrer">Julia</a> to plot this.</p>
<pre><code>ppf=[(unit -7/2)^-1 + 7/2 for unit in 0:0.1:(7/2)]
area = [0 for i in ppf]
plot(0:0.1:(7/2),ppf, label = &quot;PPF&quot;,fillrange = area, fillalpha = 0.35, c = 3)
title!(&quot;PPF Example Wikipeadia&quot;)
ylabel!(&quot;Quantity of second good Q2&quot;)
xlabel!(&quot;Quantity of first good Q1&quot;)
ylims!((0.0,5))
xlims!((0.0,5))
annotate!([1.25], [1], [&quot;possible region&quot;], :green)
annotate!([3.5], [3.5], [&quot;not possible region&quot;], :red)
annotate!([collect(0:0.1:(7/2))[length(ppf)-length(ppf[ppf .&lt; (1.5-7/2)^-1 + 7/2])-1]], [(1.5 -7/2)^-1 + 7/2].-0.11, (&quot;*&quot;, :blue, :left))
</code></pre>
<p><a href="https://i.sstatic.net/uNSvn.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/uNSvn.png" alt="enter image description here" /></a></p>
<p>This is more or less identical to the picture from Wikipedia but I added a blue dot representing the point where q1 = 1.5, which means q2 = 3. In this case, there is full employment and the economy is working at full capacity.</p>
<p>Adding a few lines similar to <a href="https://quant.stackexchange.com/a/69780/54838">this answer</a> makes the chart interactive. Unemployment means that only a subset of the entire labour force will be used as can be seen <a href="https://www.google.com/search?q=labour+force+employment+unemployment&amp;sxsrf=ALiCzsa7gTY2H2GiDGrB9Vv5UhVkcP4lhg:1669329545989&amp;source=lnms&amp;tbm=isch&amp;sa=X&amp;ved=2ahUKEwjn5-eU8cf7AhXUSfEDHfEPDdoQ_AUoAnoECAIQBA&amp;cshid=1669329562336205&amp;biw=1536&amp;bih=792&amp;dpr=1.25" rel="nofollow noreferrer">here</a>.</p>
<p><span class="math-container">$$ Labour \ Force = Employed + Unemployed$$</span></p>
<p>Hence, if you subtract unemployed from the labour force you end up with the number of employed people and a production that is not at full capacity.</p>
<p><a href="https://i.sstatic.net/Togy2.gif" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Togy2.gif" alt="enter image description here" /></a></p>
<p>Increasing the workforce moves the PPF outwards. People who retire, would <a href="https://www.econport.org/content/handbook/Unemployment/Define.html#:%7E:text=Labor%20Force%20Participation%20Rate&amp;text=In%20addition%2C%20students%2C%20retirees%2C,called%20labor%20force%20participation%20rate." rel="nofollow noreferrer">no longer be part</a> of the labour force, resulting in a downward shift in the PPF. Now at any given time, these people are not retired yet and it will not impact the PPF immediately. However, as soon as the first person would be retired under the old system, the PPF looks different.</p>
<p><a href="https://i.sstatic.net/FBVj5.gif" rel="nofollow noreferrer"><img src="https://i.sstatic.net/FBVj5.gif" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2022-11-24T06:47:53.590Z
2022-11-25T09:23:25.783Z
2022-11-25T09:23:25.783Z
AKdemy
<p>Which of the following will not shift a country's production possibility frontier (PPF) ? An increase in the age at which people retire or a fall in unemployment ?</p>
<p>To me, it is the increase in the age at which people retire that will not shift the country's PPF, this situation will represent a point in the bounded area (by the PPF, the axis and the origin), meaning that we can produce more but the PPF is not shifted, we still have the same technology and tools to produce. If a country can produce 100 cars and 50 tons of wheat, then if the people retire later, I do not see why the PPF could shift.</p>
<p>In the other hand, a fall in unemployment can imply more workers in development sectors of new technologies so it will shift it, we can produce more.</p>
<p>The correct answer was apparently fall in unemployment. This is very strange to me, according to me justification. I believe that if we make the assumptions that workers can only be employed in PPF sectors, then yes, a fall in unemployment will not shift the PPF. But that means that there are no people working in labs, in science, in developing new technologies etc. There are only people producing wheat and cars... Also, the question is not indicating by how much is the increase of age, so we can be very annoying, saying if I increase the age of retirement by 1 year or 1 day, it surely won't shift the PPF...</p>
<p>Also, mathematically speaking if fall in unemployment does not shift the PPF, then a rise in unemployment does not shift the PPF neither.
And an increase at the age at which people retire <span class="math-container">$\implies$</span> a rise in unemployment <span class="math-container">$\implies$</span> no shift of PPF. So for me an increase in the age at which people retire will not shift a country's PPF.</p>
<p>Who is right there ?</p>

CC BY-SA 4.0
2022-11-24T06:49:55.403Z
Unemployment is underutilization of resources, thus a point inside the curve (below).

The maximum capacity moves if more people are in the workforce. A PPF is not simply production.its the entire possibility of an economy (simplified in a simple curve model). I suggest you don't need to waste 50 reputation on a bounty for this. If you Google PPF unemployment you will get nice answers.
AKdemy
CC BY-SA 4.0
2022-11-24T08:14:34.693Z
@AKdemy what about an increase at the age at which people retire ? Does it shift the PPF or not ?
Kilkik
CC BY-SA 4.0
2022-11-24T16:12:11.040Z
If you entire economy has a maximum workforce of 100, would adding 10 retired people back into the workforce increase your productive capacity or not?
AKdemy
CC BY-SA 4.0
2022-11-24T17:10:56.730Z
@AKdemy Thanks for answering. Is this really the right question ? Its not about adding retired people but rather keeping same workforce longer
Kilkik
CC BY-SA 4.0
2022-11-24T22:02:26.663Z
Don't overcomplicate things. What would happen if you have 100 but 10 retire? Either way, changing the workforce will shift the PPF. Unemployment is simply underutilization. Maybe just plot a simply PPF and try it out yourself.
AKdemy
<microeconomics><production-function>
Effects of retirement and unemployment on PPF
Kilkik
# Effects of retirement and unemployment on PPF

(Asked by: username_0 on 2022-11-21)

Which of the following will not shift a country's production possibility frontier (PPF) ? An increase in the age at which people retire or a fall in unemployment ?

To me, it is the increase in the age at which people retire that will not shift the country's PPF, this situation will represent a point in the bounded area (by the PPF, the axis and the origin), meaning that we can produce more but the PPF is not shifted, we still have the same technology and tools to produce. If a country can produce 100 cars and 50 tons of wheat, then if the people retire later, I do not see why the PPF could shift.

In the other hand, a fall in unemployment can imply more workers in development sectors of new technologies so it will shift it, we can produce more.

The correct answer was apparently fall in unemployment. This is very strange to me, according to me justification. I believe that if we make the assumptions that workers can only be employed in PPF sectors, then yes, a fall in unemployment will not shift the PPF. But that means that there are no people working in labs, in science, in developing new technologies etc. There are only people producing wheat and cars... Also, the question is not indicating by how much is the increase of age, so we can be very annoying, saying if I increase the age of retirement by 1 year or 1 day, it surely won't shift the PPF...

Also, mathematically speaking if fall in unemployment does not shift the PPF, then a rise in unemployment does not shift the PPF neither.
And an increase at the age at which people retire $\implies$ a rise in unemployment $\implies$ no shift of PPF. So for me an increase in the age at which people retire will not shift a country's PPF.

Who is right there ?

**Tags:** microeconomics, production-function
> **Comments:**
> **username_1**: Unemployment is underutilization of resources, thus a point inside the curve (below).  The maximum capacity moves if more people are in the workforce. A PPF is not simply production.its the entire possibility of an economy (simplified in a simple curve model). I suggest you don't need to waste 50 reputation on a bounty for this. If you Google PPF unemployment you will get nice answers.  
> **username_0**: @AKdemy what about an increase at the age at which people retire ? Does it shift the PPF or not ?  
> **username_1**: If you entire economy has a maximum workforce of 100, would adding 10 retired people back into the workforce increase your productive capacity or not?  
> **username_0**: @AKdemy Thanks for answering. Is this really the right question ? Its not about adding retired people but rather keeping same workforce longer  
> **username_1**: Don't overcomplicate things. What would happen if you have 100 but 10 retire? Either way, changing the workforce will shift the PPF. Unemployment is simply underutilization. Maybe just plot a simply PPF and try it out yourself.  

---

## 1 answers

### Answer by username_1 on 2022-11-24. Score: 1 | Accepted answer

You can google PPF unemployment and PPF retirement age. One of the first entries, homework.study.com discusses both circumstances.
In any case, a $\color{blue}P$roduction $\color{blue}P$ossibility $\color{blue}F$rontrier ($\color{blue}{PPF}$) represents all possible combinations of output that can be produced by fully and efficiently utilizing all factors of production. See for example Wikipedia. It is clear that an economy with unemployment is not fully utilizing its ressources (labour force). The Wikipedia article also offers a formula for a simple non linear frontier with two goods (linear would do as well).
$$q2 = (q1 - 7/2)^{-1} + 7/2$$
where q2 and q1 are the quantities for each product. In the simplest case, there are only workers, and no technology or capital. In this case, you can just think of 7 being the number of workers (say millions).
Below, I use Julia to plot this.
ppf=[(unit -7/2)^-1 + 7/2 for unit in 0:0.1:(7/2)]
area = [0 for i in ppf]
plot(0:0.1:(7/2),ppf, label = "PPF",fillrange = area, fillalpha = 0.35, c = 3)
title!("PPF Example Wikipeadia")
ylabel!("Quantity of second good Q2")
xlabel!("Quantity of first good Q1")
ylims!((0.0,5))
xlims!((0.0,5))
annotate!([1.25], [1], ["possible region"], :green)
annotate!([3.5], [3.5], ["not possible region"], :red)
annotate!([collect(0:0.1:(7/2))[length(ppf)-length(ppf[ppf .< (1.5-7/2)^-1 + 7/2])-1]], [(1.5 -7/2)^-1 + 7/2].-0.11, ("*", :blue, :left))


This is more or less identical to the picture from Wikipedia but I added a blue dot representing the point where q1 = 1.5, which means q2 = 3. In this case, there is full employment and the economy is working at full capacity.
Adding a few lines similar to this answer makes the chart interactive. Unemployment means that only a subset of the entire labour force will be used as can be seen here.
$$ Labour \ Force = Employed + Unemployed$$
Hence, if you subtract unemployed from the labour force you end up with the number of employed people and a production that is not at full capacity.

Increasing the workforce moves the PPF outwards. People who retire, would no longer be part of the labour force, resulting in a downward shift in the PPF. Now at any given time, these people are not retired yet and it will not impact the PPF immediately. However, as soon as the first person would be retired under the old system, the PPF looks different.


---

