<p>I think that the confusion is caused by the different meaning of "full employment" in both contexts.</p>

<p>In the Shapiro-Stiglitz model, full employment in the sense that $\bar{L}\rightarrow LN$ implies that the job finding rate $a\rightarrow \infty$, which means no frictional unemployment.</p>

<p>In the other definition, full employment is merely <em>defined</em> by any remaining unemployment being only frictional (or structural/voluntary, not important here). Situations of no full employment could exist, for example, due to minimum wages, according to this definition. This view considers the unemployment arising from workers being laid off and waiting some time to find a new job (frictional unemployment) as a technological necessity that cannot be avoided so as to further increase efficiency.</p>

<p>Last but not least, please note that your quote from Romer concerns the labor supply curve only, while the employment rate will be determined in equilibrium.</p>

CC BY-SA 3.0
2018-03-30T18:29:00.197Z
2018-04-01T11:47:03.813Z
2018-04-01T11:47:03.813Z
Murphy
<p>Under the <a href="https://en.wikipedia.org/wiki/Shapiro%E2%80%93Stiglitz_theory" rel="noreferrer">Shapiro-Stiglitz model</a> the <a href="https://en.wikipedia.org/wiki/Shapiro%E2%80%93Stiglitz_theory#No-shirking_condition" rel="noreferrer">No-Shirking Condition</a> is:</p>
<p><span class="math-container">$$w=\bar{e}+\left( \rho +\frac{\bar{L}}{\bar{L}-NL}b \right)\frac{\bar{e}}{q}$$</span></p>
<p>Where:</p>
<p><span class="math-container">$\bar{e}=$</span> exerted effort by employees</p>
<p><span class="math-container">$\rho=$</span> discount rate</p>
<p><span class="math-container">$\bar{L}=$</span> total number of workers</p>
<p><span class="math-container">$N\bar{L}=$</span> number of employed workers</p>
<p><span class="math-container">$b=$</span> job separation rate</p>
<p><span class="math-container">$q=$</span> shirking detection rate</p>
<p>(<em>From Romer's <a href="https://rads.stackoverflow.com/amzn/click/com/B003F8DCQS" rel="noreferrer" rel="nofollow noreferrer">Advanced Macroeconomics 3rd edition</a>, pg. 453</em>)</p>
<blockquote>
<p><em>[The no-shirking condition shows] the wage that firms must pay to induce workers to exert effort. When more workers are employed there are fewer unemployed workers and and more workers leaving their jobs; it is easier for unemployed workers to find employment. [...] <strong>At full employment, unemployed workers find work instantly, and so there is no cost to being fired and thus no wage can deter shirking</strong></em></p>
</blockquote>
<h1>My Question</h1>
<p>The definition of full employment is:</p>
<p>(Source from <a href="https://www.investopedia.com/terms/f/fullemployment.asp" rel="noreferrer">Investopeida</a>)</p>
<blockquote>
<p><em>Full employment is an economic situation in which all available labor resources are being used in the most efficient way possible. Full employment embodies the highest amount of skilled and unskilled labor that can be employed within an economy at any given time. <strong>Any remaining unemployment is considered to be frictional, structural or voluntary</strong></em></p>
</blockquote>
<p>Based on this definition is appears that even under full employment workers do not find work instantly under the Shapiro Stiglitz model. What exactly am I missing?</p>

CC BY-SA 3.0
2018-03-29T14:33:48.863Z
Just imagine this : full employment also including "jobs" from drugs-lord.
mootmoot
CC BY-SA 3.0
2018-03-29T15:37:21.737Z
@mootmoot what??
Bensstats
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2018-03-29T16:12:40.290Z
Will you take a job that against your own cultural value, or a job that pay less than your living cost, something that will risk your life. The list is endless.
mootmoot
<macroeconomics><labor-economics><unemployment>
The Shapiro-Stiglitz model. Why under full employment do unemployed workers find jobs instantly?
Bensstats
# The Shapiro-Stiglitz model. Why under full employment do unemployed workers find jobs instantly?

(Asked by: username_0 on 2018-03-29)

Under the [Shapiro-Stiglitz model](https://en.wikipedia.org/wiki/Shapiro%E2%80%93Stiglitz_theory) the [No-Shirking Condition](https://en.wikipedia.org/wiki/Shapiro%E2%80%93Stiglitz_theory#No-shirking_condition) is:

$$w=\bar{e}+\left( \rho +\frac{\bar{L}}{\bar{L}-NL}b \right)\frac{\bar{e}}{q}$$

Where:

$\bar{e}=$ exerted effort by employees

$\rho=$ discount rate

$\bar{L}=$ total number of workers

$N\bar{L}=$ number of employed workers

$b=$ job separation rate

$q=$ shirking detection rate

(*From Romer's [Advanced Macroeconomics 3rd edition](https://rads.stackoverflow.com/amzn/click/com/B003F8DCQS), pg. 453*)

> *[The no-shirking condition shows] the wage that firms must pay to induce workers to exert effort. When more workers are employed there are fewer unemployed workers and and more workers leaving their jobs; it is easier for unemployed workers to find employment. [...] **At full employment, unemployed workers find work instantly, and so there is no cost to being fired and thus no wage can deter shirking***

# My Question

The definition of full employment is:

(Source from [Investopeida](https://www.investopedia.com/terms/f/fullemployment.asp))

> *Full employment is an economic situation in which all available labor resources are being used in the most efficient way possible. Full employment embodies the highest amount of skilled and unskilled labor that can be employed within an economy at any given time. **Any remaining unemployment is considered to be frictional, structural or voluntary***

Based on this definition is appears that even under full employment workers do not find work instantly under the Shapiro Stiglitz model. What exactly am I missing?

**Tags:** macroeconomics, labor-economics, unemployment
> **Comments:**
> **username_1**: Just imagine this : full employment also including "jobs" from drugs-lord.  
> **username_0**: @mootmoot what??  
> **username_1**: Will you take a job that against your own cultural value, or a job that pay less than your living cost, something that will risk your life. The list is endless.  

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## 1 answers

### Answer by username_2 on 2018-03-30. Score: 2

I think that the confusion is caused by the different meaning of "full employment" in both contexts.

In the Shapiro-Stiglitz model, full employment in the sense that $\bar{L}\rightarrow LN$ implies that the job finding rate $a\rightarrow \infty$, which means no frictional unemployment.

In the other definition, full employment is merely *defined* by any remaining unemployment being only frictional (or structural/voluntary, not important here). Situations of no full employment could exist, for example, due to minimum wages, according to this definition. This view considers the unemployment arising from workers being laid off and waiting some time to find a new job (frictional unemployment) as a technological necessity that cannot be avoided so as to further increase efficiency.

Last but not least, please note that your quote from Romer concerns the labor supply curve only, while the employment rate will be determined in equilibrium.


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