# 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 $$Q_t = A_t*(K_t^\alpha N^\beta_t T_t^\rho).$$
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 $$\frac{\partial Q_t}{\partial N_t} = \beta Q_t/N_t.$$