<p>It can be both. The number of working hours are of course easier to interpret. You can also make the assumption that every employee works some fixed number of hours, say 8 per day (or 220 per month, or 38 a week, etc). In this case if you denote by $n$ the number of workers and $L$ the number of hours worked you have of course
$$
n \cdot 8 = L
$$
and then
$$
A \cdot K^{1-\alpha} \cdot L^{\alpha} = A \cdot K^{1-\alpha}  \cdot ( n \cdot 8 ) ^{\alpha} = 8^{\alpha} \cdot A \cdot K^{1-\alpha}  \cdot n ^{\alpha} = \left(8^{\alpha} \cdot A\right) \cdot K^{1-\alpha}  \cdot n ^{\alpha}.
$$
So you can choose $L$ to represent either quantity as long as you take it into consideration when choosing/calibrating $A$. <br> (Provided that some conditions like $n \cdot 8 = L$ hold or are a reasonable approximation of reality.)</p>

CC BY-SA 3.0
2015-07-21T11:47:39.310Z
2015-07-21T11:47:39.310Z
Giskard
<p>Cobb-Douglas is $Y = AK^{1-\alpha}L^{\alpha}$.
What exactly is $L$ in Cobb-Douglas? Is $L$ the number of workers available in a single year? Working hours?</p>

<macroeconomics><production-function>
What exactly is L in a Cobb-Douglas production function?
qrs
# What exactly is L in a Cobb-Douglas production function?

(Asked by: username_0 on 2015-07-21)

Cobb-Douglas is $Y = AK^{1-\alpha}L^{\alpha}$.
What exactly is $L$ in Cobb-Douglas? Is $L$ the number of workers available in a single year? Working hours?

**Tags:** macroeconomics, production-function


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## 1 answers

### Answer by username_1 on 2015-07-21. Score: 6

It can be both. The number of working hours are of course easier to interpret. You can also make the assumption that every employee works some fixed number of hours, say 8 per day (or 220 per month, or 38 a week, etc). In this case if you denote by $n$ the number of workers and $L$ the number of hours worked you have of course
$$
n \cdot 8 = L
$$
and then
$$
A \cdot K^{1-\alpha} \cdot L^{\alpha} = A \cdot K^{1-\alpha} \cdot ( n \cdot 8 ) ^{\alpha} = 8^{\alpha} \cdot A \cdot K^{1-\alpha} \cdot n ^{\alpha} = \left(8^{\alpha} \cdot A\right) \cdot K^{1-\alpha} \cdot n ^{\alpha}.
$$
So you can choose $L$ to represent either quantity as long as you take it into consideration when choosing/calibrating $A$.   
 (Provided that some conditions like $n \cdot 8 = L$ hold or are a reasonable approximation of reality.)


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