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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):Cobb-Douglas Function

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

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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 $$ \frac{\partial Q_t}{\partial N_t} = \beta Q_t/N_t. $$

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  • $\begingroup$ Ok, thank you. I thought it was bizarre but that maybe I was missing some special circumstance. $\endgroup$ – Jacob Dorsey Sep 12 '17 at 20:47

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