<p>Max <a href="https://i.sstatic.net/29prg.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/29prg.png" alt="enter image description here"></a></p>

<p>Then you have: Max <a href="https://i.sstatic.net/fAMWo.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/fAMWo.png" alt="200*L^(0.5) - 10*L - 16000"></a></p>

<p>Which gives you: <a href="https://i.sstatic.net/8TZ8L.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/8TZ8L.png" alt="enter image description here"></a></p>

<p>So L = 100, and you have a loss of 15000</p>

CC BY-SA 4.0
2019-05-21T04:42:21.050Z
He is right. The problem with your calculations is that you want to use MPl/MPk= w/v whenever you are finding both K and L (typically considered the Long run solution) Here since you already have K fixed (often considered the short run problem), you want to equate the value of the marginal productivity of labor to the wage: P*MPl=w. This is exactly his third equation. Notice how in the problem before taking derivatives he plugged in the value of K
Regio
CC BY-SA 4.0
2019-05-21T11:28:51.600Z
Sorry, in the first equation it's 16*K.
Guilherme Cruz
CC BY-SA 4.0
2019-05-21T00:38:48.107Z
2019-05-21T00:49:30.583Z
2019-05-21T00:49:30.583Z
Guilherme Cruz
<p>​Hi, I don't get how the answer of d is deduced in this question because I don't think I made any mistakes in my calculation and have also used all the information given. After knowing L is 800, I found out the did 200*Q which gives me 5656 and I worked out the profit to be negative but it is not -15000. What did I do wrong in my calculation?
<a href="https://i.sstatic.net/lpWuF.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/lpWuF.png" alt="enter image description here"></a>
Thanks</p>

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

<microeconomics><production-function><profit-maximization><marginal><cost-functions>
Production function involving profit maximisation
onetwothree
# Production function involving profit maximisation

(Asked by: username_0 on 2019-05-20)

​Hi, I don't get how the answer of d is deduced in this question because I don't think I made any mistakes in my calculation and have also used all the information given. After knowing L is 800, I found out the did 200\*Q which gives me 5656 and I worked out the profit to be negative but it is not -15000. What did I do wrong in my calculation?
[![enter image description here](https://i.sstatic.net/lpWuF.png)](https://i.sstatic.net/lpWuF.png)
Thanks

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

**Tags:** microeconomics, production-function, profit-maximization, marginal, cost-functions

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## 1 answers

### Answer by username_1 on 2019-05-21. Score: 1 | Accepted answer

Max [![enter image description here](https://i.sstatic.net/29prg.png)](https://i.sstatic.net/29prg.png)

Then you have: Max [![200*L^(0.5) - 10*L - 16000](https://i.sstatic.net/fAMWo.png)](https://i.sstatic.net/fAMWo.png)

Which gives you: [![enter image description here](https://i.sstatic.net/8TZ8L.png)](https://i.sstatic.net/8TZ8L.png)

So L = 100, and you have a loss of 15000

> **Comments:**
> **username_2**: He is right. The problem with your calculations is that you want to use MPl/MPk= w/v whenever you are finding both K and L (typically considered the Long run solution) Here since you already have K fixed (often considered the short run problem), you want to equate the value of the marginal productivity of labor to the wage: P*MPl=w. This is exactly his third equation. Notice how in the problem before taking derivatives he plugged in the value of K  
> **username_1**: Sorry, in the first equation it's 16*K.  

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