# Production function involving profit maximisation

​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? Thanks ## 1 Answer

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

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