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

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

<p><strong>EDIT:</strong>
I wrote the formula wrong... its <span class="math-container">$\frac{\dot{Y}}{Y} = \frac{\dot{A}}{A} + \frac{F_{K}' K \dot{K}}{F K} + \frac{F_{L}' L \dot{L}}{F L}$</span></p>

CC BY-SA 4.0
2019-09-03T13:58:16.850Z
This seems straightforward: have you tried differentiating w.r.t. $t$ and then dividing by $Y$?
Giskard
CC BY-SA 4.0
2019-09-03T15:16:58.137Z
Yes but I cannot get the K and L in the denominator in the two fractions...
EternalStruggle
CC BY-SA 4.0
2019-09-03T15:39:47.513Z
In response to the edit: you can just simplify by $K$ and $L$.
Giskard
CC BY-SA 4.0
2019-09-03T15:42:29.467Z
Yes I realised that... such a dumb mistake :-)
EternalStruggle
CC BY-SA 4.0
2019-09-03T15:45:32.613Z
I'm voting to close this question as it was solved in the comments.
Giskard
<macroeconomics><production-function><aggregate-production>
Log differentiation of aggregate production function
EternalStruggle
# Log differentiation of aggregate production function

(Asked by: username_0 on 2019-09-03)

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

**Tags:** macroeconomics, production-function, aggregate-production

> **Comments:**
> **username_1**: This seems straightforward: have you tried differentiating w.r.t. $t$ and then dividing by $Y$?  
> **username_0**: Yes but I cannot get the K and L in the denominator in the two fractions...  
> **username_1**: In response to the edit: you can just simplify by $K$ and $L$.  
> **username_0**: Yes I realised that... such a dumb mistake :-)  
> **username_1**: I'm voting to close this question as it was solved in the comments.  

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## 0 answers

