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    Hey

    Im really stuck on this question and i need some guidance, could someone please point me in the right direction?

    The toal cost function of a firm is given by

    TC = 400 + 37.5Q + 0.75Q^2 + 0.005Q^3

    The firm is able to sell any volume of output at a price of £25 per unit. How much output should the firm produce so as to maximise profits? Be sure you check you have found a maximum.


    TC = 400 + 37.5Q + 0.75Q^2 + 0.005Q^3

    = 37.5 + 1.5Q + 0.015Q^2

    = -1.5 + 0.030Q

    Q = 1.5/0.030

    Q = 50

    Thanks
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    All you did was prove that the TC function was convex by finding a postitive second derivative.

    What you should include is MR = MC, and another equation too, can you find the other equation?

    otherwise you'll be short on equations and too many unkowns.
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    So like this?

    TC = 400 + 37.5Q + 0.75Q^2 + 0.005Q^3

    = 37.5 + 1.5Q + 0.015Q^2

    = -1.5 + 0.030Q

    25 = -1.5 + 0.030Q

    25 + 1.5 = 0.030Q

    26.5 = 0.030Q

    26.5/0.030 = Q

    833.33 = Q
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    (Original post by stem01)
    So like this?

    TC = 400 + 37.5Q + 0.75Q^2 + 0.005Q^3

    MC= 37.5 + 1.5Q + 0.015Q^2

    = -1.5 + 0.030Q
    Not sure why you differentiated the marginal cost. Since profit maximisation is at MR = MC, you only to differentiate TC once to get MC.

    And you know that MR = 50Q, since the firm's demand curve is P=25Q. Thus TR = 25Q^2 and MR = 50Q. From there on it's a simple equation.
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    Hello

    Im lost on what i do next. I know:

    TR = 25Q^2
    MR = 50Q
    P = 25

    Do i just have to put 50Q back into the the formula to get my final answer?

    TC = 400 + 37.5(50) + 0.75(50)^2 + 0.005(50)^3


    Thanks
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    (Original post by stem01)
    Hello

    Im lost on what i do next. I know:

    TR = 25Q^2
    MR = 50Q
    P = 25

    Do i just have to put 50Q back into the the formula to get my final answer?

    TC = 400 + 37.5(50) + 0.75(50)^2 + 0.005(50)^3


    Thanks
    Prof max is at the point where MR = MC

    MR = 50Q
    MC = 37.5 + 1.5Q + 0.015Q^2

    Thus:

    50Q = 37.5 + 1.5Q + 0.015Q^2

    Now solve for Q, that's the profit maximising quantity.
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    so i would divide 50 where Q is in the formula to get 37.5?
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    (Original post by stem01)
    so i would divide 50 where Q is in the formula to get 37.5?
    It's a quadratic equation.
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    (Original post by stem01)
    The firm is able to sell any volume of output at a price of £25 per unit. How much output should the firm produce so as to maximise profits? Be sure you check you have found a maximum.[/B]
    I see that and I'm thinking TR=25Q, MR=25=P
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    (Original post by Chrrye)
    I see that and I'm thinking TR=25Q, MR=25=P
    Gosh, you're right. Christ, don't know what I was thinking, had the correct graph visualised in my head, but chucked an extra Q in there for some reason.

    Sorry for that OP, simplifies your working a tad (it's still a quadratic, however).
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    (Original post by chidona)
    Gosh, you're right. Christ, don't know what I was thinking, had the correct graph visualised in my head, but chucked an extra Q in there for some reason.

    Sorry for that OP, simplifies your working a tad (it's still a quadratic, however).
    Simpler than that. The cost is going up at 37.5Q + some

    Theres only going to be one outcome to this...
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    (Original post by Chrrye)
    Simpler than that. The cost is going up at 37.5Q + some

    Theres only going to be one outcome to this...
    Apologies if I'm misinterpreting you, but...

    TC = 400 + 37.5Q + 0.75Q^2 + 0.005Q^3

    MC = 37.5 + 1.5Q + 0.015Q^2

    TR = 25Q

    MR = 25

    Prof. max is when MR = MC

    25 = 37.5 + 1.5Q + 0.015Q^2

    0.015Q^2 + 1.5Q + 12.5 = 0

    Surely? I get the same equation by going through the method of working out the profit function. Even though it's yielding me two negative results, which is always heartening (knew I should have done some practice sooner).
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    (Original post by chidona)
    Apologies if I'm misinterpreting you, but...

    TC = 400 + 37.5Q + 0.75Q^2 + 0.005Q^3

    MC = 37.5 + 1.5Q + 0.015Q^2

    TR = 25Q

    MR = 25

    Prof. max is when MR = MC

    25 = 37.5 + 1.5Q + 0.015Q^2

    0.015Q^2 + 1.5Q + 12.5 = 0

    Surely? I get the same equation by going through the method of working out the profit function. Even though it's yielding me two negative results, which is always heartening (knew I should have done some practice sooner).
    Yar, as in profit is maximised at negative Q value

    Theyr not going to produce anything as MC >MR for positive Q values
    therefore OUTPUT=Q=0 / would not enter

    That would be the answer to the question but I'm not sure why theyd ask it. Seems a bit pointless.
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    (Original post by Chrrye)
    Yar, as in profit is maximised at negative Q value

    Theyr not going to produce anything as MC >MR for positive Q values
    therefore OUTPUT=Q=0 / would not enter

    That would be the answer to the question but I'm not sure why theyd ask it. Seems a bit pointless.
    Ah, yes, same wavelength now. I'd be peeved if they asked that to me in an exam, really would =/
 
 
 
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