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Economics Max profit question

  1. Jan 23, 2007 #1
    I Think I am right on a, but not quite sure on B. I put this in the calc section, because I think B needs to be solved as a dirivitive.
    Thank you

    Given a firms profit curve of:
    Profit= -3 + 15Q - 1.25Q^2
    a) Calculate the output that would maximize the firms's profit.

    15-1.25Q^2=0
    15=1.25
    15/1.25 = 12
    Output = 12


    b)Calculate the maximum profit:
    -3 + 15Q-1.25Q^2
    -3 +15 (12) - 1.25 (24)=
    57-30=27
     
  2. jcsd
  3. Jan 23, 2007 #2

    Hootenanny

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    Hi ditchqueen and welcome to the forums.

    On question (a) you have the right idea, but you haven't differentiated correctly, check the final term. As for (b) you have answered this correctly, except you have used the incorrect values from question (a). Also note that [itex]12^2\neq24[/itex].
     
  4. Jan 24, 2007 #3
    Lost

    I think I am lost on the differentiated part. I can't believe I had 12^2 as 24!! I know better then that sorry :)
    Ok I think I did it!! Is the dir 0?
     
    Last edited: Jan 24, 2007
  5. Jan 24, 2007 #4

    HallsofIvy

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    Actually, it is A that requires the derivative

    The derivative of -3+ 15Q- 1.25Q2 is 15- 2(1.25)Q= 15- 2.5Q

    15- 2.5Q= 0 so 2.5Q= 15. Q= 15(2/5)= 6

    Q= 6, not 24.
     
  6. Jan 24, 2007 #5
    Thank you! I have some questions though
    -3+ 15Q- 1.25Q2 is 15- 2(1.25)Q= 15- 2.5Q
    What happened to the -3? also , is it 2(1.25) because the Q was squared?
    Thank you
     
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