<p>Seems to be the second one, so $$ Q_t = A_t*(K_t^\alpha N^\beta_t T_t^\rho). $$</p>

<p>Two clues:</p>

<ol>
<li><p>This is the usual specification.</p></li>
<li><p>On the top of page 14 it is written that
$$
w_t = \beta Q_t/N_t.
$$ 
Given a competitive labor market you have
$$
w_t = \frac{\partial Q_t}{\partial N_t}.
$$ 
If you assume the production function above then you indeed have
$$
\frac{\partial Q_t}{\partial N_t} = \beta Q_t/N_t.
$$ </p></li>
</ol>

CC BY-SA 3.0
2017-09-12T20:47:29.763Z
Ok, thank you. I thought it was bizarre but that maybe I was missing some special circumstance.
Jacob Dorsey
CC BY-SA 3.0
2017-09-12T20:42:47.237Z
2017-09-12T20:42:47.237Z
Giskard
<p>I am trying to understand a paper written back in 1989 about long run population growth. It seems like the PDF is a scanned image of the paper.</p>

<p>The notation for the function is on page 11 of the pdf (<a href="http://faculty.econ.ucdavis.edu/faculty/gclark/papers/clark_evolution.pdf" rel="nofollow noreferrer">here</a>):<a href="https://i.sstatic.net/YQChZ.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/YQChZ.png" alt="Cobb-Douglas Function"></a></p>

<p>Is it:</p>

<p>$$ Q_t = A_t*(K_t^\alpha N^t_\beta T_t^\rho) $$ </p>

<p>or</p>

<p>$$ Q_t = A_t*(K_t^\alpha N^\beta_t T_t^\rho) $$ </p>

<p>Im not sure its a typo or not because it shows up the same way later in the paper on page 14.</p>

<p>*Edit:  I also have no idea what $\hat c$ is in the paper:</p>

<p>I don't see where it is defined.  Only where consumption is compared to it.</p>

<p><a href="https://i.sstatic.net/8SKgb.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/8SKgb.png" alt="enter image description here"></a></p>

<production-function><cobb-douglas>
Notation of a Cobb-Douglas function printed in 1989
Jacob Dorsey
# Notation of a Cobb-Douglas function printed in 1989

(Asked by: username_0 on 2017-09-12)

I am trying to understand a paper written back in 1989 about long run population growth. It seems like the PDF is a scanned image of the paper.

The notation for the function is on page 11 of the pdf ([here](http://faculty.econ.ucdavis.edu/faculty/gclark/papers/clark_evolution.pdf)):[![Cobb-Douglas Function](https://i.sstatic.net/YQChZ.png)](https://i.sstatic.net/YQChZ.png)

Is it:

$$ Q\_t = A\_t\*(K\_t^\alpha N^t\_\beta T\_t^\rho) $$

or

$$ Q\_t = A\_t\*(K\_t^\alpha N^\beta\_t T\_t^\rho) $$

Im not sure its a typo or not because it shows up the same way later in the paper on page 14.

\*Edit: I also have no idea what $\hat c$ is in the paper:

I don't see where it is defined. Only where consumption is compared to it.

[![enter image description here](https://i.sstatic.net/8SKgb.png)](https://i.sstatic.net/8SKgb.png)

**Tags:** production-function, cobb-douglas

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## 1 answers

### Answer by username_1 on 2017-09-12. Score: 5 | Accepted answer

Seems to be the second one, so $$ Q\_t = A\_t\*(K\_t^\alpha N^\beta\_t T\_t^\rho). $$

Two clues:

1. This is the usual specification.
2. On the top of page 14 it is written that
   $$
   w\_t = \beta Q\_t/N\_t.
   $$
   Given a competitive labor market you have
   $$
   w\_t = \frac{\partial Q\_t}{\partial N\_t}.
   $$
   If you assume the production function above then you indeed have
   $$
   \frac{\partial Q\_t}{\partial N\_t} = \beta Q\_t/N\_t.
   $$

> **Comments:**
> **username_0**: Ok, thank you. I thought it was bizarre but that maybe I was missing some special circumstance.  

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