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    Hello
    I was wondering if anyone could help me out if this question. I've completed it on how I thought it should be but was wondering if someone could go through it to make sure I am doing it correctly.

    The demand curve for a monopolist's product is given by the equation

    Q=12-0.5P

    Find the marginal revenue Function MR(Q) for this monopolist and at what level of sales does the monopolist maximise revenue.

    Q=12-0.5P

    0.5P=12-Q

    P=12/0.5 - Q/0.5

    P=24-2Q

    TR=PQ

    P=24-2Q
    Q=24Q-2Q^2

    MR= (dTR/dQ)

    =24-2Q
    Q=24-2
    Q=12

    Monopolist maximise revenue

    Do i then just put Q=12 into the formula?

    So,

    22=12-0.5P

    22-12=-0.5P
    10=-0.5P
    10/0.5=P
    20=P

    Is this correct?

    Thank you
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    (Original post by anon2332)
    Hello
    I was wondering if anyone could help me out if this question. I've completed it on how I thought it should be but was wondering if someone could go through it to make sure I am doing it correctly.

    The demand curve for a monopolist's product is given by the equation

    Q=12-0.5P

    Find the marginal revenue Function MR(Q) for this monopolist and at what level of sales does the monopolist maximise revenue.

    Q=12-0.5P

    0.5P=12-Q

    P=12/0.5 - Q/0.5

    P=24-2Q

    TR=PQ

    P=24-2Q
    Q=24Q-2Q^2

    MR= (dTR/dQ)

    =24-2Q
    Q=24-2
    Q=12

    Monopolist maximise revenue

    Do i then just put Q=12 into the formula?

    So,

    22=12-0.5P

    22-12=-0.5P
    10=-0.5P
    10/0.5=P
    20=P

    Is this correct?

    Thank you
    For marginal revenue you differentiated slightly wrong:

    R = 24Q - 2Q^2

    dR/dQ = 24 - 4Q so I think your values for revenue maximising Q and P are a bit off ...i.e I think Q = 6,

    other than that its the right method
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    (Original post by dreadnaut)
    R = 24Q - 2Q^2

    dR/dQ = 24 - 4Q so I think your values for revenue maximising Q and P are a bit off ...i.e I think Q = 6,
    YES this :yep:
    so
    Q=6
    &
    P=12


    (Original post by anon2332)
    Q=12
    Monopolist maximise revenue
    Do i then just put Q=12 into the formula?

    So,
    22=12-0.5P<<<

    22-12=-0.5P
    10=-0.5P
    10/0.5=P
    20=P
    Little mistake in your own working putting
    22=12-0.5P
    instead of the Q=12 value you got
    12=12-0.5P

    BUT the Q=6 anyway so just redo it with that.

    6=12-0.5P
    0.5P=12-6
    0.5P=6
    P=12
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    Thanks for the replies.

    So is this it?

    Q=12-0.5P

    Find the marginal revenue Function MR(Q) for this monopolist and at what level of sales does the monopolist maximise revenue.

    Q=12-0.5P

    0.5P=12-Q

    P=12/0.5 - Q/0.5

    P=24-2Q

    TR=PQ

    P=24-2Q
    Q=24Q-2Q^2

    MR= (dTR/dQ)

    =24Q-2Q^2
    Q=24-4Q
    Q=6

    So,

    6=12-0.5P
    0.5P=12-6
    0.5P=6
    P=12

    Marginal function (Q) = 24-4Q

    The level of sales which the monopolist maximises revenue is Q=6

    I alos have to sketch the marginal revue function, shall id this on the same diagram as Q=12-0.5P?

    Is this correct?

    Thank you
    xx
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    (Original post by anon2332)
    Thanks for the replies.

    So is this it?

    Q=12-0.5P

    Find the marginal revenue Function MR(Q) for this monopolist and at what level of sales does the monopolist maximise revenue.

    Q=12-0.5P

    0.5P=12-Q

    P=12/0.5 - Q/0.5

    P=24-2Q

    TR=PQ

    P=24-2Q
    Q=24Q-2Q^2

    MR= (dTR/dQ)

    =24Q-2Q^2
    Q=24-4Q
    Q=6

    So,

    6=12-0.5P
    0.5P=12-6
    0.5P=6
    P=12

    Marginal function (Q) = 24-4Q

    The level of sales which the monopolist maximises revenue is Q=6

    I alos have to sketch the marginal revue function, shall id this on the same diagram as Q=12-0.5P?

    Is this correct?

    Thank you
    xx
    Looks fine to me.

    It's up to you where you sketch it, you could do on the same diagram, I doubt it matters much.
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    (Original post by anon2332)
    P=24-2Q

    TR=PQ

    P=24-2Q
    Q=24Q-2Q^2

    MR= (dTR/dQ)

    =24Q-2Q^2
    Q=24-4Q

    Q=6

    So,

    6=12-0.5P
    0.5P=12-6
    0.5P=6
    P=12

    Marginal function (Q) = 24-4Q

    The level of sales which the monopolist maximises revenue is Q=6

    I alos have to sketch the marginal revue function, shall id this on the same diagram as Q=12-0.5P?

    Is this correct?

    Thank you
    xx

    This should be
    TR=24Q-2Q^2
    not Q=24Q-2Q^2

    This should be
    0=24Q-2Q^2
    0=24-4Q
    since you have differentiated

    It would probably not lose you marks in the exam but it might confuse you if you have to go back so please be careful with your working! :yep:


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    please let this be uni stuff and not A2 eco.
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    (Original post by TylerDurden)
    please let this be uni stuff and not A2 eco.
    It's first year uni stuff, maybe second year depending on the course, but don't worry it's not hard! You could probably do it now if taught.
 
 
 
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