Suppose we have an aggregate production function $Y = A F(K, L)$. I'm following some slides which then states that we if log differentiate we get the following: $\frac{\dot{Y}}{Y} = \frac{\dot{A}}{A} + \frac{F_{K}' \dot{K}}{F K} + \frac{F_{L}' \dot{L}}{F L}$. Where the dot notation $\dot{Y}$ is the differential of Y wrt. t. I've tried to using eulers theorem about homogen functions so that we can write $Y = F_{k}'K + F_{L}'L$, but I can't see where I would get the $\frac{\dot{K}}{K}$ terms.

Can anyone guide me? Please ask for more information if i'm not clear enough, thanks!

EDIT: I wrote the formula wrong... its $\frac{\dot{Y}}{Y} = \frac{\dot{A}}{A} + \frac{F_{K}' K \dot{K}}{F K} + \frac{F_{L}' L \dot{L}}{F L}$


closed as off-topic by Giskard, Herr K., E. Sommer, jmbejara, Adam Bailey Sep 8 at 21:14

  • This question does not appear to be about economics, within the scope defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ This seems straightforward: have you tried differentiating w.r.t. $t$ and then dividing by $Y$? $\endgroup$ – Giskard Sep 3 at 13:58
  • $\begingroup$ Yes but I cannot get the K and L in the denominator in the two fractions... $\endgroup$ – EternalStruggle Sep 3 at 15:16
  • $\begingroup$ In response to the edit: you can just simplify by $K$ and $L$. $\endgroup$ – Giskard Sep 3 at 15:39
  • $\begingroup$ Yes I realised that... such a dumb mistake :-) $\endgroup$ – EternalStruggle Sep 3 at 15:42
  • 5
    $\begingroup$ I'm voting to close this question as it was solved in the comments. $\endgroup$ – Giskard Sep 3 at 15:45