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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 $\frac{\dot{Y}}{Y} = \frac{\dot{A}}{A} + \frac{F_{K}' K \dot{K}}{F K} + \frac{F_{L}' L \dot{L}}{F L}$

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

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  • $\begingroup$ 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
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    $\begingroup$ I'm voting to close this question as it was solved in the comments. $\endgroup$ – Giskard Sep 3 at 15:45