The Shapiro-Stiglitz model. Why under full employment do unemployed workers find jobs instantly?

Under the Shapiro-Stiglitz model the 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, 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)

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?

• Just imagine this : full employment also including "jobs" from drugs-lord. – mootmoot Mar 29 '18 at 14:33
• @mootmoot what?? – FreakconFrank Mar 29 '18 at 15:37
• 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 Mar 29 '18 at 16:12
• One is an unrealistic, simplifying assumption used in a model. The other is an attempt to define full unemployment in the real world. I don't think there is any reason to expect the two to coincide. In particular, I don't think Shapiro/Stiglitz/Romer actually believe that there are any circumstances under which workers will generally be able to find work "instantly" (whatever "instantly" that means). – Kenny LJ Apr 1 '18 at 1:36

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.