Notation of a Cobb-Douglas function printed in 1989 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):

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

Two clues:


This is the usual specification.
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
$$
\frac{\partial Q_t}{\partial N_t} = \beta Q_t/N_t.
$$