<p>$$(\frac{r}{w} \frac{1-\alpha}{\alpha})*K$$
$$\equiv (\frac{r}{w} \frac{1-\alpha}{\alpha})[\frac{y}{a}(\frac{w}{r} \frac{\alpha}{1-\alpha})^{1-\alpha}]$$
$$\equiv (\frac{r}{w} \frac{1-\alpha}{\alpha})^{\alpha-1+1} \frac{y}{a}$$</p>

<p>$$\equiv (\frac{r}{w} \frac{1-\alpha}{\alpha})^{\alpha} \frac{y}{a}$$</p>

<p>Is that what you're looking for?  Just notice that between steps two and three, I inverted the part of K in parentheses and changed the exponent to account for the inversion. </p>

CC BY-SA 3.0
2016-12-10T18:44:34.737Z
2016-12-10T18:44:34.737Z
123
<p>I don't how to put maths in here so using an image:
<a href="https://i.sstatic.net/GRsOO.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/GRsOO.jpg" alt="enter image description here"></a></p>

<p><a href="https://i.sstatic.net/LKHnW.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/LKHnW.jpg" alt="enter image description here"></a></p>

CC BY-SA 3.0
2016-12-10T16:07:36.600Z
What solution are you trying to match?
123
CC BY-SA 3.0
2016-12-10T17:14:32.260Z
@123 I matched K but could not for L(look above)
Dashmone
<microeconomics><mathematical-economics><production-function>
conditional factor demand functions for capital and labor
Dashmone
# conditional factor demand functions for capital and labor

(Asked by: username_0 on 2016-12-10)

I don't how to put maths in here so using an image:
[![enter image description here](https://i.sstatic.net/GRsOO.jpg)](https://i.sstatic.net/GRsOO.jpg)

[![enter image description here](https://i.sstatic.net/LKHnW.jpg)](https://i.sstatic.net/LKHnW.jpg)

**Tags:** microeconomics, mathematical-economics, production-function

> **Comments:**
> **username_1**: What solution are you trying to match?  
> **username_0**: @username_1 I matched K but could not for L(look above)  

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## 1 answers

### Answer by username_1 on 2016-12-10. Score: 0 | Accepted answer

$$(\frac{r}{w} \frac{1-\alpha}{\alpha})\*K$$
$$\equiv (\frac{r}{w} \frac{1-\alpha}{\alpha})[\frac{y}{a}(\frac{w}{r} \frac{\alpha}{1-\alpha})^{1-\alpha}]$$
$$\equiv (\frac{r}{w} \frac{1-\alpha}{\alpha})^{\alpha-1+1} \frac{y}{a}$$

$$\equiv (\frac{r}{w} \frac{1-\alpha}{\alpha})^{\alpha} \frac{y}{a}$$

Is that what you're looking for? Just notice that between steps two and three, I inverted the part of K in parentheses and changed the exponent to account for the inversion.


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