Question:

I have a demand function of Q=100-2p. Marginal Cost is 0. How do I find the price to charge?

by Guest56475  |  earlier

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I have a demand function of Q=100-2p. Marginal Cost is 0. How do I find the price to charge?

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  1. MC=MR. We need to find out what MR is.

    TR=p x q. (As the answer above me stated, MR is the derivative of TR in terms of Q, so we need to solve this in terms of q.

    p x 100 - 2p = 100p - 2p²

    MR = dTR/dQ

    = 100 - 4p

    4p=100

    p=25

    Price that should be charged is 25.


  2. MR=MC

    TR=p*Q

    But we first need to get this in terms of Q, because marginal revenue is the derivative of TR in terms of Q.

    2p=100-Q

    p=50-Q/2

    p*Q=50Q-Q^2/2

    MR=dTR/dQ

         =50-Q

    MC=0

    50-Q=0

    Q=50

    50=100-2p

    2p=50

    p=25

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