Profit Maximization

Discussion in 'Chit-Chat' started by Eurasian =--(O), Nov 22, 2005.

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  1. Eurasian =--(O)

    Eurasian =--(O) Regular Member

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    Hey.. I have an econ assignment due tommorow and was wondering if anyone could figure out this question b/c as of now its beyond me.

    A firm has a production function y=4L^1/4 x k^1/4. This implies Marginal Price of L = L^1/4 x K^-3/4 and Marginal Price of K = L^1/4 x K^-3/4. The price of its output is 1000. The wage rate is 10 and the price of capital is 2. What is the profit maximizing output? (Hint: find the profit maximizing inputs first.)

    My assumptions L=Labor=10 K=capital=2
    Marginal Price L / Marginal Price K = prices1 / prices 2

    Ya i dont really get this question at all.

    lol i know im already asking a lot but if u figure it out can u post the work too? I'll owe u!
     
    #1 Eurasian =--(O), Nov 22, 2005
    Last edited: Nov 22, 2005
  2. taneepak

    taneepak Regular Member

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    Shouldn't you be doing this assignment yourself? :confused:
     
    #2 taneepak, Nov 22, 2005
  3. Pete LSD

    Pete LSD Regular Member

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    Darn, it's been more than eight years since I touched on quantitative economics :D . I need to dig up my old textbooks.

    This looks like a micro-economic question.
     
    #3 Pete LSD, Nov 22, 2005
  4. Loh

    Loh Regular Member

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    He is trying to but can't figure out yet. Therefore he needs help from some friendly BF'ers who might be able to assist. ;)

    Sorry I can't be of any help.
     
    #4 Loh, Nov 22, 2005
  5. Eurasian =--(O)

    Eurasian =--(O) Regular Member

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    University is hard! :crying:
     
    #5 Eurasian =--(O), Nov 22, 2005
  6. Loh

    Loh Regular Member

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    I can't even understand those signs you posted. So it is real hard or did you make it harder for me? Hope they are what you intended, those equations.
     
    #6 Loh, Nov 22, 2005
  7. Eurasian =--(O)

    Eurasian =--(O) Regular Member

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    ^ means to the power of if that helps

    x means to multiply both
     
    #7 Eurasian =--(O), Nov 22, 2005
  8. Pete LSD

    Pete LSD Regular Member

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    minimize W1Z1 + W2Z2

    by choice of Z1 and Z2

    subject to the constraint Y = F(Z1,Z2)
     
    #8 Pete LSD, Nov 22, 2005
  9. Eurasian =--(O)

    Eurasian =--(O) Regular Member

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    ya i really dont know how to do that... no one i've talked to has been able to figure it out... like 5 people :D
     
    #9 Eurasian =--(O), Nov 22, 2005
  10. Eurasian =--(O)

    Eurasian =--(O) Regular Member

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    I tried to figure out MR=MC and MRC=MRP... i duno if im on the right track
     
    #10 Eurasian =--(O), Nov 22, 2005
  11. Pete LSD

    Pete LSD Regular Member

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    Marginal Rate of Technical Substitution


    MRTS(Z*1,Z*2) = W1/W2
    MP1 / MP2 = W1 / W2

    Lagrange Transformation (? I am not sure. It's been a long long time . . . )

    L(Z1, Z2, lambda) = W1Z1 + W2Z2 + lambda [Y - F(Z1, Z2)]


     
    #11 Pete LSD, Nov 22, 2005
  12. Pete LSD

    Pete LSD Regular Member

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    W1 - Lambda*f1(z*1,z*2) = 0
    W2 - Lambda*f2(z*1,z*2) = 0
    Y - F(z*1,z*2) = 0
     
    #12 Pete LSD, Nov 22, 2005
  13. Eurasian =--(O)

    Eurasian =--(O) Regular Member

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    so MP1/MP2 =W1/W2 = (L^-3/4 x K^1/4) / (L^1/4 x K^-3/4) ? then what solve for..? i dont see when to factor the wage and capital prices into the process... sorry for the noob questions, truth is i'm having a lot of trouble with school lately. Dunno why, just my developmental processes im hoping
     
    #13 Eurasian =--(O), Nov 22, 2005
  14. Eurasian =--(O)

    Eurasian =--(O) Regular Member

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    we haven't used lambda at all
     
    #14 Eurasian =--(O), Nov 22, 2005
  15. Pete LSD

    Pete LSD Regular Member

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    Combining the first two conditions to eliminate lambda* yields:

    F1(Z*1, Z*2) / F2(Z*1,Z*2) = W1 / W2

    MRTS(Z*1, Z*2) = W1 / W2
     
    #15 Pete LSD, Nov 22, 2005
  16. Eurasian =--(O)

    Eurasian =--(O) Regular Member

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    is MP1/MP2 =W1/W2 = (L^-3/4 x K^1/4) / (L^1/4 x K^-3/4) a correct step?
     
    #16 Eurasian =--(O), Nov 22, 2005
  17. Pete LSD

    Pete LSD Regular Member

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    My memory is very sketchy. I think the math whizz should have their inputs here. Hmmm, Chi Ho and Kwun :) . Euroasian needs HELP!!!

    Smashingbird, aren't you majoring in economics? Please help out a fellow econo student. Economics can be the most torturous subject :) .
     
    #17 Pete LSD, Nov 22, 2005
    Last edited: Nov 22, 2005
  18. Eurasian =--(O)

    Eurasian =--(O) Regular Member

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    Well thanks for your effort Pete!! :)
     
    #18 Eurasian =--(O), Nov 22, 2005
  19. Pete LSD

    Pete LSD Regular Member

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    My pleasure but sorry I couldn't offer more insights. I find the TA's usually saves the day in a university setting. The professors aren't that helpful most of the time. They are more into research than teaching.

     
    #19 Pete LSD, Nov 22, 2005
  20. Pete LSD

    Pete LSD Regular Member

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    Hey 604badder,

    Your math is very good. Please help out Euroasian :D .
     
    #20 Pete LSD, Nov 22, 2005
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