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​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 Thanks

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Max enter image description here

Then you have: Max 200*L^(0.5) - 10*L - 16000

Which gives you: enter image description here

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

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    $\begingroup$ 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 $\endgroup$
    – Regio
    May 21 '19 at 4:42
  • $\begingroup$ Thanks a lot! This is helpful. $\endgroup$
    – onetwothree
    May 21 '19 at 9:25
  • $\begingroup$ Sorry, in the first equation it's 16*K. $\endgroup$
    – Guilherme Cruz
    May 21 '19 at 11:28

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